{"input": "Solve 3x - 5/3 = 0", "output": "3x - 5/3 = 0\n3x = 5/3\nx = 5/3 / 3\nx = 5/9"} {"input": "Solve quickly: x^2 + 4/5x - 12/5 = 0", "output": "x^2 + 4/5x - 12/5 = 0\n(x - 6/5)(x - -2) = 0\nx - 6/5 = 0 or x - -2 = 0\nx = 6/5\nx = -2"} {"input": "Compute the solution of x^2 + 1/4x - 9/2 = 0", "output": "x^2 + 1/4x - 9/2 = 0\n(x - -9/4)(x - 2) = 0\nx - -9/4 = 0 or x - 2 = 0\nx = -9/4\nx = 2"} {"input": "Find x and y such that\n5x + 2y = 41/3\n3x + 10y = -5", "output": "5x + 2y = 41/3\n3x + 10y = -5\n\nUsing elimination\n3*(5x + 2y = 41/3)\n5*(3x + 10y = -5)\n15x + 6y = 41\n15x + 50y = -25\nSubtract equations\n-44y = 66\ny = 66/-44\ny = -3/2\n\nSubstitute y\n5x + 2(-3/2) = 41/3\n5x = 50/3\nx = 50/3/5\nx = 10/3"} {"input": "Determine x in x^3 - 241/70x^2 + 113/35x - 24/35 = 0", "output": "x^3 - 241/70x^2 + 113/35x - 24/35 = 0\n(x - 2)(x - 8/7)(x - 3/10) = 0\nx - 2 = 0\nx - 8/7 = 0\nx - 3/10 = 0\nx = 2\nx = 8/7\nx = 3/10"} {"input": "Solve x^2 + 97/6x + 247/6 = 0", "output": "x^2 + 97/6x + 247/6 = 0\n(x - -19/6)(x - -13) = 0\nx - -19/6 = 0 or x - -13 = 0\nx = -19/6\nx = -13"} {"input": "Find x in x^3 - 277/40x^2 + 91/16x + 1881/80 = 0", "output": "x^3 - 277/40x^2 + 91/16x + 1881/80 = 0\n(x - -11/8)(x - 19/5)(x - 9/2) = 0\nx - -11/8 = 0\nx - 19/5 = 0\nx - 9/2 = 0\nx = -11/8\nx = 19/5\nx = 9/2"} {"input": "Determine x in x^2 + 50/63x - 32/7 = 0", "output": "x^2 + 50/63x - 32/7 = 0\n(x - -18/7)(x - 16/9) = 0\nx - -18/7 = 0 or x - 16/9 = 0\nx = -18/7\nx = 16/9"} {"input": "Find x and y such that\n6x + 9y = -18\n8x + 4y = -40/3", "output": "6x + 9y = -18\n8x + 4y = -40/3\n\nUsing elimination\n8*(6x + 9y = -18)\n6*(8x + 4y = -40/3)\n48x + 72y = -144\n48x + 24y = -80\nSubtract equations\n48y = -64\ny = -64/48\ny = -4/3\n\nSubstitute y\n6x + 9(-4/3) = -18\n6x = -6\nx = -6/6\nx = -1"} {"input": "Find the solution to x^3 - 7/12x^2 - 77/3x + 221/4 = 0", "output": "x^3 - 7/12x^2 - 77/3x + 221/4 = 0\n(x - 13/4)(x - 3)(x - -17/3) = 0\nx - 13/4 = 0\nx - 3 = 0\nx - -17/3 = 0\nx = 13/4\nx = 3\nx = -17/3"} {"input": "Compute the solution of 2x + 17/3 = 0", "output": "2x + 17/3 = 0\n2x = -17/3\nx = -17/3 / 2\nx = -17/6"} {"input": "Compute the solution of x^2 - 47/20x - 11/10 = 0", "output": "x^2 - 47/20x - 11/10 = 0\n(x - -2/5)(x - 11/4) = 0\nx - -2/5 = 0 or x - 11/4 = 0\nx = -2/5\nx = 11/4"} {"input": "Solve x^3 - 9x^2 + 74/9x + 544/9 = 0", "output": "x^3 - 9x^2 + 74/9x + 544/9 = 0\n(x - -2)(x - 17/3)(x - 16/3) = 0\nx - -2 = 0\nx - 17/3 = 0\nx - 16/3 = 0\nx = -2\nx = 17/3\nx = 16/3"} {"input": "Solve the equations:\n7x + 3y = 38\n3x + 8y = 93/2", "output": "7x + 3y = 38\n3x + 8y = 93/2\n\nUsing elimination\n3*(7x + 3y = 38)\n7*(3x + 8y = 93/2)\n21x + 9y = 114\n21x + 56y = 651/2\nSubtract equations\n-47y = -423/2\ny = -423/2/-47\ny = 9/2\n\nSubstitute y\n7x + 3(9/2) = 38\n7x = 49/2\nx = 49/2/7\nx = 7/2"} {"input": "Solve quickly: x^2 + 13/5x - 6/5 = 0", "output": "x^2 + 13/5x - 6/5 = 0\n(x - -3)(x - 2/5) = 0\nx - -3 = 0 or x - 2/5 = 0\nx = -3\nx = 2/5"} {"input": "Solve the system:\n6x + 9y = 21/2\n1x + 4y = 1/2", "output": "6x + 9y = 21/2\n1x + 4y = 1/2\n\nUsing elimination\n1*(6x + 9y = 21/2)\n6*(1x + 4y = 1/2)\n6x + 9y = 21/2\n6x + 24y = 3\nSubtract equations\n-15y = 15/2\ny = 15/2/-15\ny = -1/2\n\nSubstitute y\n6x + 9(-1/2) = 21/2\n6x = 15\nx = 15/6\nx = 5/2"} {"input": "Solve the equation x^3 + 15/4x^2 + 13/8x = 0", "output": "x^3 + 15/4x^2 + 13/8x = 0\n(x - -13/4)(x - -1/2)(x - 0) = 0\nx - -13/4 = 0\nx - -1/2 = 0\nx - 0 = 0\nx = -13/4\nx = -1/2\nx = 0"} {"input": "Find the solution to 6x + 24/5 = 0", "output": "6x + 24/5 = 0\n6x = -24/5\nx = -24/5 / 6\nx = -4/5"} {"input": "Solve the equations:\n5x + 8y = -161/5\n10x + 2y = -84/5", "output": "5x + 8y = -161/5\n10x + 2y = -84/5\n\nUsing elimination\n10*(5x + 8y = -161/5)\n5*(10x + 2y = -84/5)\n50x + 80y = -322\n50x + 10y = -84\nSubtract equations\n70y = -238\ny = -238/70\ny = -17/5\n\nSubstitute y\n5x + 8(-17/5) = -161/5\n5x = -5\nx = -5/5\nx = -1"} {"input": "Find x for 5x + 65/8 = 0", "output": "5x + 65/8 = 0\n5x = -65/8\nx = -65/8 / 5\nx = -13/8"} {"input": "Find x in 2x + 2/3 = 0", "output": "2x + 2/3 = 0\n2x = -2/3\nx = -2/3 / 2\nx = -1/3"} {"input": "Solve the equation x^3 - 557/28x^2 - 195/28x + 675/7 = 0", "output": "x^3 - 557/28x^2 - 195/28x + 675/7 = 0\n(x - -9/4)(x - 15/7)(x - 20) = 0\nx - -9/4 = 0\nx - 15/7 = 0\nx - 20 = 0\nx = -9/4\nx = 15/7\nx = 20"} {"input": "Solve the system:\n6x + 10y = -97/7\n3x + 1y = 31/14", "output": "6x + 10y = -97/7\n3x + 1y = 31/14\n\nUsing elimination\n3*(6x + 10y = -97/7)\n6*(3x + 1y = 31/14)\n18x + 30y = -291/7\n18x + 6y = 93/7\nSubtract equations\n24y = -384/7\ny = -384/7/24\ny = -16/7\n\nSubstitute y\n6x + 10(-16/7) = -97/7\n6x = 9\nx = 9/6\nx = 3/2"} {"input": "Find the solution to 9x + 36/5 = 0", "output": "9x + 36/5 = 0\n9x = -36/5\nx = -36/5 / 9\nx = -4/5"} {"input": "Find x for x^2 + 81/4x + 95/4 = 0", "output": "x^2 + 81/4x + 95/4 = 0\n(x - -5/4)(x - -19) = 0\nx - -5/4 = 0 or x - -19 = 0\nx = -5/4\nx = -19"} {"input": "Compute the solution of x^3 - 1/15x^2 - 1321/300x + 91/25 = 0", "output": "x^3 - 1/15x^2 - 1321/300x + 91/25 = 0\n(x - 13/10)(x - 7/6)(x - -12/5) = 0\nx - 13/10 = 0\nx - 7/6 = 0\nx - -12/5 = 0\nx = 13/10\nx = 7/6\nx = -12/5"} {"input": "Solve the equations:\n7x + 2y = 35\n5x + 10y = 25", "output": "7x + 2y = 35\n5x + 10y = 25\n\nUsing elimination\n5*(7x + 2y = 35)\n7*(5x + 10y = 25)\n35x + 10y = 175\n35x + 70y = 175\nSubtract equations\n-60y = 0\ny = 0/-60\ny = 0\n\nSubstitute y\n7x + 2(0) = 35\n7x = 35\nx = 35/7\nx = 5"} {"input": "Solve simultaneously:\n7x + 4y = -119/30\n2x + 5y = -23/6", "output": "7x + 4y = -119/30\n2x + 5y = -23/6\n\nUsing elimination\n2*(7x + 4y = -119/30)\n7*(2x + 5y = -23/6)\n14x + 8y = -119/15\n14x + 35y = -161/6\nSubtract equations\n-27y = 189/10\ny = 189/10/-27\ny = -7/10\n\nSubstitute y\n7x + 4(-7/10) = -119/30\n7x = -7/6\nx = -7/6/7\nx = -1/6"} {"input": "Find x and y such that\n6x + 8y = -179/20\n6x + 1y = -193/20", "output": "6x + 8y = -179/20\n6x + 1y = -193/20\n\nUsing elimination\n6*(6x + 8y = -179/20)\n6*(6x + 1y = -193/20)\n36x + 48y = -537/10\n36x + 6y = -579/10\nSubtract equations\n42y = 21/5\ny = 21/5/42\ny = 1/10\n\nSubstitute y\n6x + 8(1/10) = -179/20\n6x = -39/4\nx = -39/4/6\nx = -13/8"} {"input": "Solve x^3 - 139/72x^2 - 19/18x = 0", "output": "x^3 - 139/72x^2 - 19/18x = 0\n(x - 0)(x - -4/9)(x - 19/8) = 0\nx - 0 = 0\nx - -4/9 = 0\nx - 19/8 = 0\nx = 0\nx = -4/9\nx = 19/8"} {"input": "Solve the equation x^2 - 7x - 30 = 0", "output": "x^2 - 7x - 30 = 0\n(x - -3)(x - 10) = 0\nx - -3 = 0 or x - 10 = 0\nx = -3\nx = 10"} {"input": "Solve quickly: 1x + 15 = 0", "output": "1x + 15 = 0\n1x = -15\nx = -15 / 1\nx = -15"} {"input": "Determine x in x^3 + 305/56x^2 - 291/28x + 27/8 = 0", "output": "x^3 + 305/56x^2 - 291/28x + 27/8 = 0\n(x - 9/8)(x - 3/7)(x - -7) = 0\nx - 9/8 = 0\nx - 3/7 = 0\nx - -7 = 0\nx = 9/8\nx = 3/7\nx = -7"} {"input": "Solve quickly: 3x - 42 = 0", "output": "3x - 42 = 0\n3x = 42\nx = 42 / 3\nx = 14"} {"input": "Find x in 8x + 32 = 0", "output": "8x + 32 = 0\n8x = -32\nx = -32 / 8\nx = -4"} {"input": "Find x for 2x - 36 = 0", "output": "2x - 36 = 0\n2x = 36\nx = 36 / 2\nx = 18"} {"input": "Solve the system:\n3x + 6y = -3\n6x + 5y = -13", "output": "3x + 6y = -3\n6x + 5y = -13\n\nUsing elimination\n6*(3x + 6y = -3)\n3*(6x + 5y = -13)\n18x + 36y = -18\n18x + 15y = -39\nSubtract equations\n21y = 21\ny = 21/21\ny = 1\n\nSubstitute y\n3x + 6(1) = -3\n3x = -9\nx = -9/3\nx = -3"} {"input": "Solve x^3 - 41/14x^2 - 34/7x + 10 = 0", "output": "x^3 - 41/14x^2 - 34/7x + 10 = 0\n(x - 7/2)(x - 10/7)(x - -2) = 0\nx - 7/2 = 0\nx - 10/7 = 0\nx - -2 = 0\nx = 7/2\nx = 10/7\nx = -2"} {"input": "Find x and y such that\n1x + 7y = 23/4\n5x + 6y = 7", "output": "1x + 7y = 23/4\n5x + 6y = 7\n\nUsing elimination\n5*(1x + 7y = 23/4)\n1*(5x + 6y = 7)\n5x + 35y = 115/4\n5x + 6y = 7\nSubtract equations\n29y = 87/4\ny = 87/4/29\ny = 3/4\n\nSubstitute y\n1x + 7(3/4) = 23/4\n1x = 1/2\nx = 1/2/1\nx = 1/2"} {"input": "Solve the equation x^2 + 31/7x + 12/7 = 0", "output": "x^2 + 31/7x + 12/7 = 0\n(x - -3/7)(x - -4) = 0\nx - -3/7 = 0 or x - -4 = 0\nx = -3/7\nx = -4"} {"input": "Compute the solution of x^2 + 133/45x - 68/45 = 0", "output": "x^2 + 133/45x - 68/45 = 0\n(x - 4/9)(x - -17/5) = 0\nx - 4/9 = 0 or x - -17/5 = 0\nx = 4/9\nx = -17/5"} {"input": "Find x and y such that\n9x + 4y = 117\n2x + 4y = 26", "output": "9x + 4y = 117\n2x + 4y = 26\n\nUsing elimination\n2*(9x + 4y = 117)\n9*(2x + 4y = 26)\n18x + 8y = 234\n18x + 36y = 234\nSubtract equations\n-28y = 0\ny = 0/-28\ny = 0\n\nSubstitute y\n9x + 4(0) = 117\n9x = 117\nx = 117/9\nx = 13"} {"input": "Find x for x^3 - 83/30x^2 - 35/12x + 209/40 = 0", "output": "x^3 - 83/30x^2 - 35/12x + 209/40 = 0\n(x - 11/10)(x - 19/6)(x - -3/2) = 0\nx - 11/10 = 0\nx - 19/6 = 0\nx - -3/2 = 0\nx = 11/10\nx = 19/6\nx = -3/2"} {"input": "Find the solution to x^2 - 4 = 0", "output": "x^2 - 4 = 0\n(x - -2)(x - 2) = 0\nx - -2 = 0 or x - 2 = 0\nx = -2\nx = 2"} {"input": "Find x for 3x + 21/2 = 0", "output": "3x + 21/2 = 0\n3x = -21/2\nx = -21/2 / 3\nx = -7/2"} {"input": "Solve quickly: 5x + 5/2 = 0", "output": "5x + 5/2 = 0\n5x = -5/2\nx = -5/2 / 5\nx = -1/2"} {"input": "Find x and y such that\n1x + 3y = 24/5\n9x + 9y = 297/5", "output": "1x + 3y = 24/5\n9x + 9y = 297/5\n\nUsing elimination\n9*(1x + 3y = 24/5)\n1*(9x + 9y = 297/5)\n9x + 27y = 216/5\n9x + 9y = 297/5\nSubtract equations\n18y = -81/5\ny = -81/5/18\ny = -9/10\n\nSubstitute y\n1x + 3(-9/10) = 24/5\n1x = 15/2\nx = 15/2/1\nx = 15/2"} {"input": "Solve simultaneously:\n1x + 9y = 453/20\n2x + 9y = 219/10", "output": "1x + 9y = 453/20\n2x + 9y = 219/10\n\nUsing elimination\n2*(1x + 9y = 453/20)\n1*(2x + 9y = 219/10)\n2x + 18y = 453/10\n2x + 9y = 219/10\nSubtract equations\n9y = 117/5\ny = 117/5/9\ny = 13/5\n\nSubstitute y\n1x + 9(13/5) = 453/20\n1x = -3/4\nx = -3/4/1\nx = -3/4"} {"input": "Determine x in 1x + 3/7 = 0", "output": "1x + 3/7 = 0\n1x = -3/7\nx = -3/7 / 1\nx = -3/7"} {"input": "Solve the equations:\n4x + 10y = -206/3\n1x + 5y = -94/3", "output": "4x + 10y = -206/3\n1x + 5y = -94/3\n\nUsing elimination\n1*(4x + 10y = -206/3)\n4*(1x + 5y = -94/3)\n4x + 10y = -206/3\n4x + 20y = -376/3\nSubtract equations\n-10y = 170/3\ny = 170/3/-10\ny = -17/3\n\nSubstitute y\n4x + 10(-17/3) = -206/3\n4x = -12\nx = -12/4\nx = -3"} {"input": "Compute the solution of x^3 - 16/7x^2 - 95/7x = 0", "output": "x^3 - 16/7x^2 - 95/7x = 0\n(x - 5)(x - -19/7)(x - 0) = 0\nx - 5 = 0\nx - -19/7 = 0\nx - 0 = 0\nx = 5\nx = -19/7\nx = 0"} {"input": "Compute the solution of 6x + 48 = 0", "output": "6x + 48 = 0\n6x = -48\nx = -48 / 6\nx = -8"} {"input": "Find x in x^3 - 17x^2 + 134/25x + 4256/25 = 0", "output": "x^3 - 17x^2 + 134/25x + 4256/25 = 0\n(x - 19/5)(x - 16)(x - -14/5) = 0\nx - 19/5 = 0\nx - 16 = 0\nx - -14/5 = 0\nx = 19/5\nx = 16\nx = -14/5"} {"input": "Find the solution to 10x - 50/3 = 0", "output": "10x - 50/3 = 0\n10x = 50/3\nx = 50/3 / 10\nx = 5/3"} {"input": "Find x for 1x - 8/3 = 0", "output": "1x - 8/3 = 0\n1x = 8/3\nx = 8/3 / 1\nx = 8/3"} {"input": "Determine x in x^3 + 179/30x^2 + 57/5x + 104/15 = 0", "output": "x^3 + 179/30x^2 + 57/5x + 104/15 = 0\n(x - -2)(x - -8/3)(x - -13/10) = 0\nx - -2 = 0\nx - -8/3 = 0\nx - -13/10 = 0\nx = -2\nx = -8/3\nx = -13/10"} {"input": "Solve 10x + 130/9 = 0", "output": "10x + 130/9 = 0\n10x = -130/9\nx = -130/9 / 10\nx = -13/9"} {"input": "Solve x^2 - 14/9x + 13/81 = 0", "output": "x^2 - 14/9x + 13/81 = 0\n(x - 13/9)(x - 1/9) = 0\nx - 13/9 = 0 or x - 1/9 = 0\nx = 13/9\nx = 1/9"} {"input": "Solve 7x + 2 = 0", "output": "7x + 2 = 0\n7x = -2\nx = -2 / 7\nx = -2/7"} {"input": "Find the solution to x^3 + 149/40x^2 + 201/200x - 54/25 = 0", "output": "x^3 + 149/40x^2 + 201/200x - 54/25 = 0\n(x - 3/5)(x - -16/5)(x - -9/8) = 0\nx - 3/5 = 0\nx - -16/5 = 0\nx - -9/8 = 0\nx = 3/5\nx = -16/5\nx = -9/8"} {"input": "What value of x satisfies 5x - 90 = 0", "output": "5x - 90 = 0\n5x = 90\nx = 90 / 5\nx = 18"} {"input": "What value of x satisfies x^3 - 16/3x^2 + 13/9x + 10/9 = 0", "output": "x^3 - 16/3x^2 + 13/9x + 10/9 = 0\n(x - -1/3)(x - 5)(x - 2/3) = 0\nx - -1/3 = 0\nx - 5 = 0\nx - 2/3 = 0\nx = -1/3\nx = 5\nx = 2/3"} {"input": "Solve the system:\n7x + 1y = -51/8\n7x + 2y = -53/8", "output": "7x + 1y = -51/8\n7x + 2y = -53/8\n\nUsing elimination\n7*(7x + 1y = -51/8)\n7*(7x + 2y = -53/8)\n49x + 7y = -357/8\n49x + 14y = -371/8\nSubtract equations\n-7y = 7/4\ny = 7/4/-7\ny = -1/4\n\nSubstitute y\n7x + 1(-1/4) = -51/8\n7x = -49/8\nx = -49/8/7\nx = -7/8"} {"input": "Solve x^2 - 9/2x + 5 = 0", "output": "x^2 - 9/2x + 5 = 0\n(x - 5/2)(x - 2) = 0\nx - 5/2 = 0 or x - 2 = 0\nx = 5/2\nx = 2"} {"input": "Find x and y such that\n1x + 7y = -173/4\n8x + 2y = -22", "output": "1x + 7y = -173/4\n8x + 2y = -22\n\nUsing elimination\n8*(1x + 7y = -173/4)\n1*(8x + 2y = -22)\n8x + 56y = -346\n8x + 2y = -22\nSubtract equations\n54y = -324\ny = -324/54\ny = -6\n\nSubstitute y\n1x + 7(-6) = -173/4\n1x = -5/4\nx = -5/4/1\nx = -5/4"} {"input": "Solve quickly: x^2 + 5/2x - 6 = 0", "output": "x^2 + 5/2x - 6 = 0\n(x - 3/2)(x - -4) = 0\nx - 3/2 = 0 or x - -4 = 0\nx = 3/2\nx = -4"} {"input": "Find x in x^3 + 269/126x^2 + 101/189x + 13/378 = 0", "output": "x^3 + 269/126x^2 + 101/189x + 13/378 = 0\n(x - -1/9)(x - -1/6)(x - -13/7) = 0\nx - -1/9 = 0\nx - -1/6 = 0\nx - -13/7 = 0\nx = -1/9\nx = -1/6\nx = -13/7"} {"input": "Compute the solution of 2x - 3/4 = 0", "output": "2x - 3/4 = 0\n2x = 3/4\nx = 3/4 / 2\nx = 3/8"} {"input": "What value of x satisfies x^2 + 31/2x + 21 = 0", "output": "x^2 + 31/2x + 21 = 0\n(x - -3/2)(x - -14) = 0\nx - -3/2 = 0 or x - -14 = 0\nx = -3/2\nx = -14"} {"input": "Compute the solution of x^2 + 15/2x + 9 = 0", "output": "x^2 + 15/2x + 9 = 0\n(x - -3/2)(x - -6) = 0\nx - -3/2 = 0 or x - -6 = 0\nx = -3/2\nx = -6"} {"input": "What value of x satisfies x^3 - 21/4x - 5/2 = 0", "output": "x^3 - 21/4x - 5/2 = 0\n(x - 5/2)(x - -1/2)(x - -2) = 0\nx - 5/2 = 0\nx - -1/2 = 0\nx - -2 = 0\nx = 5/2\nx = -1/2\nx = -2"} {"input": "Find x for x^3 - 81/35x^2 - 871/175x + 153/35 = 0", "output": "x^3 - 81/35x^2 - 871/175x + 153/35 = 0\n(x - -9/5)(x - 17/5)(x - 5/7) = 0\nx - -9/5 = 0\nx - 17/5 = 0\nx - 5/7 = 0\nx = -9/5\nx = 17/5\nx = 5/7"} {"input": "Determine x in 9x + 8 = 0", "output": "9x + 8 = 0\n9x = -8\nx = -8 / 9\nx = -8/9"} {"input": "Solve simultaneously:\n5x + 2y = 9/2\n6x + 3y = 15/4", "output": "5x + 2y = 9/2\n6x + 3y = 15/4\n\nUsing elimination\n6*(5x + 2y = 9/2)\n5*(6x + 3y = 15/4)\n30x + 12y = 27\n30x + 15y = 75/4\nSubtract equations\n-3y = 33/4\ny = 33/4/-3\ny = -11/4\n\nSubstitute y\n5x + 2(-11/4) = 9/2\n5x = 10\nx = 10/5\nx = 2"} {"input": "Solve simultaneously:\n5x + 4y = 87/2\n8x + 6y = 277/4", "output": "5x + 4y = 87/2\n8x + 6y = 277/4\n\nUsing elimination\n8*(5x + 4y = 87/2)\n5*(8x + 6y = 277/4)\n40x + 32y = 348\n40x + 30y = 1385/4\nSubtract equations\n2y = 7/4\ny = 7/4/2\ny = 7/8\n\nSubstitute y\n5x + 4(7/8) = 87/2\n5x = 40\nx = 40/5\nx = 8"} {"input": "Find the solution to x^3 - 361/70x^2 + 181/35x + 4 = 0", "output": "x^3 - 361/70x^2 + 181/35x + 4 = 0\n(x - 14/5)(x - -1/2)(x - 20/7) = 0\nx - 14/5 = 0\nx - -1/2 = 0\nx - 20/7 = 0\nx = 14/5\nx = -1/2\nx = 20/7"} {"input": "Find x and y such that\n6x + 10y = -56/3\n4x + 10y = -148/9", "output": "6x + 10y = -56/3\n4x + 10y = -148/9\n\nUsing elimination\n4*(6x + 10y = -56/3)\n6*(4x + 10y = -148/9)\n24x + 40y = -224/3\n24x + 60y = -296/3\nSubtract equations\n-20y = 24\ny = 24/-20\ny = -6/5\n\nSubstitute y\n6x + 10(-6/5) = -56/3\n6x = -20/3\nx = -20/3/6\nx = -10/9"} {"input": "Determine x in x^3 + 38/3x^2 - 485/3x - 300 = 0", "output": "x^3 + 38/3x^2 - 485/3x - 300 = 0\n(x - 9)(x - -20)(x - -5/3) = 0\nx - 9 = 0\nx - -20 = 0\nx - -5/3 = 0\nx = 9\nx = -20\nx = -5/3"} {"input": "Find x for x^2 + 11/6x - 13/18 = 0", "output": "x^2 + 11/6x - 13/18 = 0\n(x - 1/3)(x - -13/6) = 0\nx - 1/3 = 0 or x - -13/6 = 0\nx = 1/3\nx = -13/6"} {"input": "Find x and y such that\n6x + 9y = 48\n9x + 4y = 53", "output": "6x + 9y = 48\n9x + 4y = 53\n\nUsing elimination\n9*(6x + 9y = 48)\n6*(9x + 4y = 53)\n54x + 81y = 432\n54x + 24y = 318\nSubtract equations\n57y = 114\ny = 114/57\ny = 2\n\nSubstitute y\n6x + 9(2) = 48\n6x = 30\nx = 30/6\nx = 5"} {"input": "Determine x in 8x + 80/3 = 0", "output": "8x + 80/3 = 0\n8x = -80/3\nx = -80/3 / 8\nx = -10/3"} {"input": "Solve simultaneously:\n7x + 3y = -235/6\n7x + 10y = -733/18", "output": "7x + 3y = -235/6\n7x + 10y = -733/18\n\nUsing elimination\n7*(7x + 3y = -235/6)\n7*(7x + 10y = -733/18)\n49x + 21y = -1645/6\n49x + 70y = -5131/18\nSubtract equations\n-49y = 98/9\ny = 98/9/-49\ny = -2/9\n\nSubstitute y\n7x + 3(-2/9) = -235/6\n7x = -77/2\nx = -77/2/7\nx = -11/2"} {"input": "Solve x^3 + 1/3x^2 - 301/81x - 247/81 = 0", "output": "x^3 + 1/3x^2 - 301/81x - 247/81 = 0\n(x - -1)(x - -13/9)(x - 19/9) = 0\nx - -1 = 0\nx - -13/9 = 0\nx - 19/9 = 0\nx = -1\nx = -13/9\nx = 19/9"} {"input": "Determine x in x^3 - 136/35x^2 + 689/175x - 16/25 = 0", "output": "x^3 - 136/35x^2 + 689/175x - 16/25 = 0\n(x - 7/5)(x - 16/7)(x - 1/5) = 0\nx - 7/5 = 0\nx - 16/7 = 0\nx - 1/5 = 0\nx = 7/5\nx = 16/7\nx = 1/5"} {"input": "Find the solution to x^2 + 80/63x - 16/21 = 0", "output": "x^2 + 80/63x - 16/21 = 0\n(x - 4/9)(x - -12/7) = 0\nx - 4/9 = 0 or x - -12/7 = 0\nx = 4/9\nx = -12/7"} {"input": "Compute the solution of x^2 - 127/7x + 240/7 = 0", "output": "x^2 - 127/7x + 240/7 = 0\n(x - 16)(x - 15/7) = 0\nx - 16 = 0 or x - 15/7 = 0\nx = 16\nx = 15/7"} {"input": "Compute the solution of x^3 + 1/14x^2 - 793/175x - 187/50 = 0", "output": "x^3 + 1/14x^2 - 793/175x - 187/50 = 0\n(x - -7/5)(x - 17/7)(x - -11/10) = 0\nx - -7/5 = 0\nx - 17/7 = 0\nx - -11/10 = 0\nx = -7/5\nx = 17/7\nx = -11/10"} {"input": "Solve quickly: 5x + 35/2 = 0", "output": "5x + 35/2 = 0\n5x = -35/2\nx = -35/2 / 5\nx = -7/2"} {"input": "What value of x satisfies x^3 + 515/168x^2 - 19/21x - 30/7 = 0", "output": "x^3 + 515/168x^2 - 19/21x - 30/7 = 0\n(x - -20/7)(x - -4/3)(x - 9/8) = 0\nx - -20/7 = 0\nx - -4/3 = 0\nx - 9/8 = 0\nx = -20/7\nx = -4/3\nx = 9/8"} {"input": "Find x for 3x - 3 = 0", "output": "3x - 3 = 0\n3x = 3\nx = 3 / 3\nx = 1"} {"input": "Solve simultaneously:\n6x + 10y = -78/35\n7x + 3y = -351/35", "output": "6x + 10y = -78/35\n7x + 3y = -351/35\n\nUsing elimination\n7*(6x + 10y = -78/35)\n6*(7x + 3y = -351/35)\n42x + 70y = -78/5\n42x + 18y = -2106/35\nSubtract equations\n52y = 312/7\ny = 312/7/52\ny = 6/7\n\nSubstitute y\n6x + 10(6/7) = -78/35\n6x = -54/5\nx = -54/5/6\nx = -9/5"} {"input": "Compute the solution of x^3 + 10x^2 + 433/49x - 72/49 = 0", "output": "x^3 + 10x^2 + 433/49x - 72/49 = 0\n(x - 1/7)(x - -8/7)(x - -9) = 0\nx - 1/7 = 0\nx - -8/7 = 0\nx - -9 = 0\nx = 1/7\nx = -8/7\nx = -9"} {"input": "Find x and y such that\n1x + 5y = -53/4\n9x + 4y = -909/20", "output": "1x + 5y = -53/4\n9x + 4y = -909/20\n\nUsing elimination\n9*(1x + 5y = -53/4)\n1*(9x + 4y = -909/20)\n9x + 45y = -477/4\n9x + 4y = -909/20\nSubtract equations\n41y = -369/5\ny = -369/5/41\ny = -9/5\n\nSubstitute y\n1x + 5(-9/5) = -53/4\n1x = -17/4\nx = -17/4/1\nx = -17/4"} {"input": "What value of x satisfies x^3 - 55/4x^2 + 397/8x - 85/2 = 0", "output": "x^3 - 55/4x^2 + 397/8x - 85/2 = 0\n(x - 17/2)(x - 4)(x - 5/4) = 0\nx - 17/2 = 0\nx - 4 = 0\nx - 5/4 = 0\nx = 17/2\nx = 4\nx = 5/4"} {"input": "Find x for x^2 + 19/5x + 84/25 = 0", "output": "x^2 + 19/5x + 84/25 = 0\n(x - -7/5)(x - -12/5) = 0\nx - -7/5 = 0 or x - -12/5 = 0\nx = -7/5\nx = -12/5"} {"input": "Solve the equations:\n10x + 7y = 109/14\n1x + 2y = 10/7", "output": "10x + 7y = 109/14\n1x + 2y = 10/7\n\nUsing elimination\n1*(10x + 7y = 109/14)\n10*(1x + 2y = 10/7)\n10x + 7y = 109/14\n10x + 20y = 100/7\nSubtract equations\n-13y = -13/2\ny = -13/2/-13\ny = 1/2\n\nSubstitute y\n10x + 7(1/2) = 109/14\n10x = 30/7\nx = 30/7/10\nx = 3/7"} {"input": "Determine x in x^3 + 4/5x^2 - 1/25x - 4/125 = 0", "output": "x^3 + 4/5x^2 - 1/25x - 4/125 = 0\n(x - -4/5)(x - 1/5)(x - -1/5) = 0\nx - -4/5 = 0\nx - 1/5 = 0\nx - -1/5 = 0\nx = -4/5\nx = 1/5\nx = -1/5"} {"input": "Solve simultaneously:\n10x + 1y = 83/4\n1x + 4y = 64/5", "output": "10x + 1y = 83/4\n1x + 4y = 64/5\n\nUsing elimination\n1*(10x + 1y = 83/4)\n10*(1x + 4y = 64/5)\n10x + 1y = 83/4\n10x + 40y = 128\nSubtract equations\n-39y = -429/4\ny = -429/4/-39\ny = 11/4\n\nSubstitute y\n10x + 1(11/4) = 83/4\n10x = 18\nx = 18/10\nx = 9/5"} {"input": "Find the solution to x^3 + 117/35x^2 - 72/5x + 324/35 = 0", "output": "x^3 + 117/35x^2 - 72/5x + 324/35 = 0\n(x - 6/7)(x - -6)(x - 9/5) = 0\nx - 6/7 = 0\nx - -6 = 0\nx - 9/5 = 0\nx = 6/7\nx = -6\nx = 9/5"} {"input": "Solve x^3 - 239/30x^2 + 103/5x - 171/10 = 0", "output": "x^3 - 239/30x^2 + 103/5x - 171/10 = 0\n(x - 3)(x - 19/6)(x - 9/5) = 0\nx - 3 = 0\nx - 19/6 = 0\nx - 9/5 = 0\nx = 3\nx = 19/6\nx = 9/5"} {"input": "Solve the system:\n2x + 8y = -12\n9x + 3y = 147/4", "output": "2x + 8y = -12\n9x + 3y = 147/4\n\nUsing elimination\n9*(2x + 8y = -12)\n2*(9x + 3y = 147/4)\n18x + 72y = -108\n18x + 6y = 147/2\nSubtract equations\n66y = -363/2\ny = -363/2/66\ny = -11/4\n\nSubstitute y\n2x + 8(-11/4) = -12\n2x = 10\nx = 10/2\nx = 5"} {"input": "Find the solution to x^3 + 201/20x^2 + 67/2x + 741/20 = 0", "output": "x^3 + 201/20x^2 + 67/2x + 741/20 = 0\n(x - -3)(x - -13/4)(x - -19/5) = 0\nx - -3 = 0\nx - -13/4 = 0\nx - -19/5 = 0\nx = -3\nx = -13/4\nx = -19/5"} {"input": "Solve x^2 - 77/18x + 49/18 = 0", "output": "x^2 - 77/18x + 49/18 = 0\n(x - 7/2)(x - 7/9) = 0\nx - 7/2 = 0 or x - 7/9 = 0\nx = 7/2\nx = 7/9"} {"input": "Solve the system:\n3x + 3y = -687/40\n6x + 7y = -1459/40", "output": "3x + 3y = -687/40\n6x + 7y = -1459/40\n\nUsing elimination\n6*(3x + 3y = -687/40)\n3*(6x + 7y = -1459/40)\n18x + 18y = -2061/20\n18x + 21y = -4377/40\nSubtract equations\n-3y = 51/8\ny = 51/8/-3\ny = -17/8\n\nSubstitute y\n3x + 3(-17/8) = -687/40\n3x = -54/5\nx = -54/5/3\nx = -18/5"} {"input": "Find x in x^2 + 75/8x + 133/8 = 0", "output": "x^2 + 75/8x + 133/8 = 0\n(x - -7)(x - -19/8) = 0\nx - -7 = 0 or x - -19/8 = 0\nx = -7\nx = -19/8"} {"input": "Find x for x^2 - 59/3x - 20/3 = 0", "output": "x^2 - 59/3x - 20/3 = 0\n(x - 20)(x - -1/3) = 0\nx - 20 = 0 or x - -1/3 = 0\nx = 20\nx = -1/3"} {"input": "Solve quickly: x^3 + 50/9x^2 + 137/27x - 70/9 = 0", "output": "x^3 + 50/9x^2 + 137/27x - 70/9 = 0\n(x - 7/9)(x - -3)(x - -10/3) = 0\nx - 7/9 = 0\nx - -3 = 0\nx - -10/3 = 0\nx = 7/9\nx = -3\nx = -10/3"} {"input": "Compute the solution of x^2 - 17x + 30 = 0", "output": "x^2 - 17x + 30 = 0\n(x - 2)(x - 15) = 0\nx - 2 = 0 or x - 15 = 0\nx = 2\nx = 15"} {"input": "Compute the solution of x^3 - 509/210x^2 + 149/210x + 19/35 = 0", "output": "x^3 - 509/210x^2 + 149/210x + 19/35 = 0\n(x - -1/3)(x - 19/10)(x - 6/7) = 0\nx - -1/3 = 0\nx - 19/10 = 0\nx - 6/7 = 0\nx = -1/3\nx = 19/10\nx = 6/7"} {"input": "Solve simultaneously:\n4x + 7y = 64/3\n9x + 1y = -11", "output": "4x + 7y = 64/3\n9x + 1y = -11\n\nUsing elimination\n9*(4x + 7y = 64/3)\n4*(9x + 1y = -11)\n36x + 63y = 192\n36x + 4y = -44\nSubtract equations\n59y = 236\ny = 236/59\ny = 4\n\nSubstitute y\n4x + 7(4) = 64/3\n4x = -20/3\nx = -20/3/4\nx = -5/3"} {"input": "Determine x in 2x - 22/3 = 0", "output": "2x - 22/3 = 0\n2x = 22/3\nx = 22/3 / 2\nx = 11/3"} {"input": "Find x in 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "Find the solution to 4x + 8/3 = 0", "output": "4x + 8/3 = 0\n4x = -8/3\nx = -8/3 / 4\nx = -2/3"} {"input": "Solve the equation 8x - 60 = 0", "output": "8x - 60 = 0\n8x = 60\nx = 60 / 8\nx = 15/2"} {"input": "Solve the system:\n8x + 6y = 31\n4x + 6y = 11", "output": "8x + 6y = 31\n4x + 6y = 11\n\nUsing elimination\n4*(8x + 6y = 31)\n8*(4x + 6y = 11)\n32x + 24y = 124\n32x + 48y = 88\nSubtract equations\n-24y = 36\ny = 36/-24\ny = -3/2\n\nSubstitute y\n8x + 6(-3/2) = 31\n8x = 40\nx = 40/8\nx = 5"} {"input": "Find the solution to 9x + 144/7 = 0", "output": "9x + 144/7 = 0\n9x = -144/7\nx = -144/7 / 9\nx = -16/7"} {"input": "Solve simultaneously:\n10x + 2y = 21\n1x + 3y = 7/6", "output": "10x + 2y = 21\n1x + 3y = 7/6\n\nUsing elimination\n1*(10x + 2y = 21)\n10*(1x + 3y = 7/6)\n10x + 2y = 21\n10x + 30y = 35/3\nSubtract equations\n-28y = 28/3\ny = 28/3/-28\ny = -1/3\n\nSubstitute y\n10x + 2(-1/3) = 21\n10x = 65/3\nx = 65/3/10\nx = 13/6"} {"input": "Find the solution to x^3 - 11/2x^2 + 41/6x + 35/27 = 0", "output": "x^3 - 11/2x^2 + 41/6x + 35/27 = 0\n(x - 10/3)(x - 7/3)(x - -1/6) = 0\nx - 10/3 = 0\nx - 7/3 = 0\nx - -1/6 = 0\nx = 10/3\nx = 7/3\nx = -1/6"} {"input": "Compute the solution of x^2 - 55/12x + 13/12 = 0", "output": "x^2 - 55/12x + 13/12 = 0\n(x - 1/4)(x - 13/3) = 0\nx - 1/4 = 0 or x - 13/3 = 0\nx = 1/4\nx = 13/3"} {"input": "Find x for x^2 - 6x = 0", "output": "x^2 - 6x = 0\n(x - 6)(x - 0) = 0\nx - 6 = 0 or x - 0 = 0\nx = 6\nx = 0"} {"input": "Solve quickly: x^2 - 29/40x - 9/20 = 0", "output": "x^2 - 29/40x - 9/20 = 0\n(x - -2/5)(x - 9/8) = 0\nx - -2/5 = 0 or x - 9/8 = 0\nx = -2/5\nx = 9/8"} {"input": "Solve the equation 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "What value of x satisfies x^2 + 56/15x + 49/15 = 0", "output": "x^2 + 56/15x + 49/15 = 0\n(x - -7/3)(x - -7/5) = 0\nx - -7/3 = 0 or x - -7/5 = 0\nx = -7/3\nx = -7/5"} {"input": "Compute the solution of x^2 + 10x - 171 = 0", "output": "x^2 + 10x - 171 = 0\n(x - -19)(x - 9) = 0\nx - -19 = 0 or x - 9 = 0\nx = -19\nx = 9"} {"input": "Find x in 4x - 64/3 = 0", "output": "4x - 64/3 = 0\n4x = 64/3\nx = 64/3 / 4\nx = 16/3"} {"input": "Solve quickly: x^2 - 7/9x - 20/27 = 0", "output": "x^2 - 7/9x - 20/27 = 0\n(x - 4/3)(x - -5/9) = 0\nx - 4/3 = 0 or x - -5/9 = 0\nx = 4/3\nx = -5/9"} {"input": "Find x and y such that\n2x + 4y = 468/7\n6x + 2y = 214/7", "output": "2x + 4y = 468/7\n6x + 2y = 214/7\n\nUsing elimination\n6*(2x + 4y = 468/7)\n2*(6x + 2y = 214/7)\n12x + 24y = 2808/7\n12x + 4y = 428/7\nSubtract equations\n20y = 340\ny = 340/20\ny = 17\n\nSubstitute y\n2x + 4(17) = 468/7\n2x = -8/7\nx = -8/7/2\nx = -4/7"} {"input": "Determine x in x^3 - 34/5x^2 + 15x - 54/5 = 0", "output": "x^3 - 34/5x^2 + 15x - 54/5 = 0\n(x - 9/5)(x - 2)(x - 3) = 0\nx - 9/5 = 0\nx - 2 = 0\nx - 3 = 0\nx = 9/5\nx = 2\nx = 3"} {"input": "Solve x^3 - 1/6x^2 - 26/3x + 10 = 0", "output": "x^3 - 1/6x^2 - 26/3x + 10 = 0\n(x - 3/2)(x - 2)(x - -10/3) = 0\nx - 3/2 = 0\nx - 2 = 0\nx - -10/3 = 0\nx = 3/2\nx = 2\nx = -10/3"} {"input": "Solve simultaneously:\n10x + 8y = 431/12\n2x + 2y = 107/12", "output": "10x + 8y = 431/12\n2x + 2y = 107/12\n\nUsing elimination\n2*(10x + 8y = 431/12)\n10*(2x + 2y = 107/12)\n20x + 16y = 431/6\n20x + 20y = 535/6\nSubtract equations\n-4y = -52/3\ny = -52/3/-4\ny = 13/3\n\nSubstitute y\n10x + 8(13/3) = 431/12\n10x = 5/4\nx = 5/4/10\nx = 1/8"} {"input": "Solve simultaneously:\n8x + 5y = -60\n8x + 7y = -68", "output": "8x + 5y = -60\n8x + 7y = -68\n\nUsing elimination\n8*(8x + 5y = -60)\n8*(8x + 7y = -68)\n64x + 40y = -480\n64x + 56y = -544\nSubtract equations\n-16y = 64\ny = 64/-16\ny = -4\n\nSubstitute y\n8x + 5(-4) = -60\n8x = -40\nx = -40/8\nx = -5"} {"input": "What value of x satisfies 9x + 27/5 = 0", "output": "9x + 27/5 = 0\n9x = -27/5\nx = -27/5 / 9\nx = -3/5"} {"input": "Solve quickly: x^2 + 32/3x + 64/3 = 0", "output": "x^2 + 32/3x + 64/3 = 0\n(x - -8/3)(x - -8) = 0\nx - -8/3 = 0 or x - -8 = 0\nx = -8/3\nx = -8"} {"input": "Solve 6x + 51/5 = 0", "output": "6x + 51/5 = 0\n6x = -51/5\nx = -51/5 / 6\nx = -17/10"} {"input": "Find x for x^3 - 25/3x^2 - 8x + 132 = 0", "output": "x^3 - 25/3x^2 - 8x + 132 = 0\n(x - -11/3)(x - 6)(x - 6) = 0\nx - -11/3 = 0\nx - 6 = 0\nx - 6 = 0\nx = -11/3\nx = 6\nx = 6"} {"input": "Compute the solution of x^2 + 153/35x + 76/35 = 0", "output": "x^2 + 153/35x + 76/35 = 0\n(x - -4/7)(x - -19/5) = 0\nx - -4/7 = 0 or x - -19/5 = 0\nx = -4/7\nx = -19/5"} {"input": "Find x in x^3 - 34/3x^2 + 112/3x - 32 = 0", "output": "x^3 - 34/3x^2 + 112/3x - 32 = 0\n(x - 4/3)(x - 4)(x - 6) = 0\nx - 4/3 = 0\nx - 4 = 0\nx - 6 = 0\nx = 4/3\nx = 4\nx = 6"} {"input": "Solve quickly: 9x + 63/4 = 0", "output": "9x + 63/4 = 0\n9x = -63/4\nx = -63/4 / 9\nx = -7/4"} {"input": "Determine x in x^3 - 3x^2 + 95/64x + 33/32 = 0", "output": "x^3 - 3x^2 + 95/64x + 33/32 = 0\n(x - -3/8)(x - 2)(x - 11/8) = 0\nx - -3/8 = 0\nx - 2 = 0\nx - 11/8 = 0\nx = -3/8\nx = 2\nx = 11/8"} {"input": "Find x for x^2 + 5x - 14 = 0", "output": "x^2 + 5x - 14 = 0\n(x - 2)(x - -7) = 0\nx - 2 = 0 or x - -7 = 0\nx = 2\nx = -7"} {"input": "Solve x^2 - 47/3x - 68/3 = 0", "output": "x^2 - 47/3x - 68/3 = 0\n(x - 17)(x - -4/3) = 0\nx - 17 = 0 or x - -4/3 = 0\nx = 17\nx = -4/3"} {"input": "What value of x satisfies 2x + 4 = 0", "output": "2x + 4 = 0\n2x = -4\nx = -4 / 2\nx = -2"} {"input": "Solve quickly: x^3 + 115/3x^2 + 1174/3x + 456 = 0", "output": "x^3 + 115/3x^2 + 1174/3x + 456 = 0\n(x - -19)(x - -4/3)(x - -18) = 0\nx - -19 = 0\nx - -4/3 = 0\nx - -18 = 0\nx = -19\nx = -4/3\nx = -18"} {"input": "Compute the solution of x^3 - 163/90x^2 - 116/27x + 119/30 = 0", "output": "x^3 - 163/90x^2 - 116/27x + 119/30 = 0\n(x - 17/6)(x - -9/5)(x - 7/9) = 0\nx - 17/6 = 0\nx - -9/5 = 0\nx - 7/9 = 0\nx = 17/6\nx = -9/5\nx = 7/9"} {"input": "Find x for x^3 + 5/9x^2 - 356/81x - 320/81 = 0", "output": "x^3 + 5/9x^2 - 356/81x - 320/81 = 0\n(x - 20/9)(x - -1)(x - -16/9) = 0\nx - 20/9 = 0\nx - -1 = 0\nx - -16/9 = 0\nx = 20/9\nx = -1\nx = -16/9"} {"input": "Find the solution to x^2 - 43/5x - 14 = 0", "output": "x^2 - 43/5x - 14 = 0\n(x - -7/5)(x - 10) = 0\nx - -7/5 = 0 or x - 10 = 0\nx = -7/5\nx = 10"} {"input": "Determine x in x^2 + 38/3x - 361/3 = 0", "output": "x^2 + 38/3x - 361/3 = 0\n(x - -19)(x - 19/3) = 0\nx - -19 = 0 or x - 19/3 = 0\nx = -19\nx = 19/3"} {"input": "Determine x in 5x - 15 = 0", "output": "5x - 15 = 0\n5x = 15\nx = 15 / 5\nx = 3"} {"input": "Solve 9x + 45 = 0", "output": "9x + 45 = 0\n9x = -45\nx = -45 / 9\nx = -5"} {"input": "Determine x in x^2 - 35/2x + 75/2 = 0", "output": "x^2 - 35/2x + 75/2 = 0\n(x - 15)(x - 5/2) = 0\nx - 15 = 0 or x - 5/2 = 0\nx = 15\nx = 5/2"} {"input": "Solve simultaneously:\n8x + 1y = 82/5\n6x + 3y = 84/5", "output": "8x + 1y = 82/5\n6x + 3y = 84/5\n\nUsing elimination\n6*(8x + 1y = 82/5)\n8*(6x + 3y = 84/5)\n48x + 6y = 492/5\n48x + 24y = 672/5\nSubtract equations\n-18y = -36\ny = -36/-18\ny = 2\n\nSubstitute y\n8x + 1(2) = 82/5\n8x = 72/5\nx = 72/5/8\nx = 9/5"} {"input": "Find x and y such that\n8x + 9y = -53\n10x + 2y = -587/9", "output": "8x + 9y = -53\n10x + 2y = -587/9\n\nUsing elimination\n10*(8x + 9y = -53)\n8*(10x + 2y = -587/9)\n80x + 90y = -530\n80x + 16y = -4696/9\nSubtract equations\n74y = -74/9\ny = -74/9/74\ny = -1/9\n\nSubstitute y\n8x + 9(-1/9) = -53\n8x = -52\nx = -52/8\nx = -13/2"} {"input": "Solve simultaneously:\n1x + 1y = -8\n6x + 4y = -50", "output": "1x + 1y = -8\n6x + 4y = -50\n\nUsing elimination\n6*(1x + 1y = -8)\n1*(6x + 4y = -50)\n6x + 6y = -48\n6x + 4y = -50\nSubtract equations\n2y = 2\ny = 2/2\ny = 1\n\nSubstitute y\n1x + 1(1) = -8\n1x = -9\nx = -9/1\nx = -9"} {"input": "Find x for x^2 - 41/12x + 11/6 = 0", "output": "x^2 - 41/12x + 11/6 = 0\n(x - 2/3)(x - 11/4) = 0\nx - 2/3 = 0 or x - 11/4 = 0\nx = 2/3\nx = 11/4"} {"input": "Find x and y such that\n2x + 5y = 46/7\n8x + 2y = -592/35", "output": "2x + 5y = 46/7\n8x + 2y = -592/35\n\nUsing elimination\n8*(2x + 5y = 46/7)\n2*(8x + 2y = -592/35)\n16x + 40y = 368/7\n16x + 4y = -1184/35\nSubtract equations\n36y = 432/5\ny = 432/5/36\ny = 12/5\n\nSubstitute y\n2x + 5(12/5) = 46/7\n2x = -38/7\nx = -38/7/2\nx = -19/7"} {"input": "Solve x^3 - 49/10x^2 - 45x + 612/5 = 0", "output": "x^3 - 49/10x^2 - 45x + 612/5 = 0\n(x - 17/2)(x - 12/5)(x - -6) = 0\nx - 17/2 = 0\nx - 12/5 = 0\nx - -6 = 0\nx = 17/2\nx = 12/5\nx = -6"} {"input": "Find x for x^2 + 11/3x + 2 = 0", "output": "x^2 + 11/3x + 2 = 0\n(x - -2/3)(x - -3) = 0\nx - -2/3 = 0 or x - -3 = 0\nx = -2/3\nx = -3"} {"input": "Compute the solution of 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Solve 4x - 5 = 0", "output": "4x - 5 = 0\n4x = 5\nx = 5 / 4\nx = 5/4"} {"input": "What value of x satisfies 1x - 15/4 = 0", "output": "1x - 15/4 = 0\n1x = 15/4\nx = 15/4 / 1\nx = 15/4"} {"input": "What value of x satisfies 9x + 27/7 = 0", "output": "9x + 27/7 = 0\n9x = -27/7\nx = -27/7 / 9\nx = -3/7"} {"input": "Solve quickly: x^2 + 29/6x + 5 = 0", "output": "x^2 + 29/6x + 5 = 0\n(x - -10/3)(x - -3/2) = 0\nx - -10/3 = 0 or x - -3/2 = 0\nx = -10/3\nx = -3/2"} {"input": "Find the solution to 7x + 35/2 = 0", "output": "7x + 35/2 = 0\n7x = -35/2\nx = -35/2 / 7\nx = -5/2"} {"input": "Find x in 5x - 7 = 0", "output": "5x - 7 = 0\n5x = 7\nx = 7 / 5\nx = 7/5"} {"input": "Solve the equations:\n2x + 10y = -76/3\n5x + 9y = -662/15", "output": "2x + 10y = -76/3\n5x + 9y = -662/15\n\nUsing elimination\n5*(2x + 10y = -76/3)\n2*(5x + 9y = -662/15)\n10x + 50y = -380/3\n10x + 18y = -1324/15\nSubtract equations\n32y = -192/5\ny = -192/5/32\ny = -6/5\n\nSubstitute y\n2x + 10(-6/5) = -76/3\n2x = -40/3\nx = -40/3/2\nx = -20/3"} {"input": "What value of x satisfies 5x - 20/3 = 0", "output": "5x - 20/3 = 0\n5x = 20/3\nx = 20/3 / 5\nx = 4/3"} {"input": "Compute the solution of 9x - 36 = 0", "output": "9x - 36 = 0\n9x = 36\nx = 36 / 9\nx = 4"} {"input": "Determine x in x^3 - 131/21x^2 - 1789/21x - 247/7 = 0", "output": "x^3 - 131/21x^2 - 1789/21x - 247/7 = 0\n(x - -3/7)(x - -19/3)(x - 13) = 0\nx - -3/7 = 0\nx - -19/3 = 0\nx - 13 = 0\nx = -3/7\nx = -19/3\nx = 13"} {"input": "Find x and y such that\n8x + 6y = 22/3\n8x + 2y = 10/3", "output": "8x + 6y = 22/3\n8x + 2y = 10/3\n\nUsing elimination\n8*(8x + 6y = 22/3)\n8*(8x + 2y = 10/3)\n64x + 48y = 176/3\n64x + 16y = 80/3\nSubtract equations\n32y = 32\ny = 32/32\ny = 1\n\nSubstitute y\n8x + 6(1) = 22/3\n8x = 4/3\nx = 4/3/8\nx = 1/6"} {"input": "Find x and y such that\n10x + 4y = -371/9\n3x + 8y = -413/18", "output": "10x + 4y = -371/9\n3x + 8y = -413/18\n\nUsing elimination\n3*(10x + 4y = -371/9)\n10*(3x + 8y = -413/18)\n30x + 12y = -371/3\n30x + 80y = -2065/9\nSubtract equations\n-68y = 952/9\ny = 952/9/-68\ny = -14/9\n\nSubstitute y\n10x + 4(-14/9) = -371/9\n10x = -35\nx = -35/10\nx = -7/2"} {"input": "Find the solution to x^2 + 93/4x + 323/4 = 0", "output": "x^2 + 93/4x + 323/4 = 0\n(x - -17/4)(x - -19) = 0\nx - -17/4 = 0 or x - -19 = 0\nx = -17/4\nx = -19"} {"input": "Find x and y such that\n7x + 3y = -167/8\n6x + 2y = -77/4", "output": "7x + 3y = -167/8\n6x + 2y = -77/4\n\nUsing elimination\n6*(7x + 3y = -167/8)\n7*(6x + 2y = -77/4)\n42x + 18y = -501/4\n42x + 14y = -539/4\nSubtract equations\n4y = 19/2\ny = 19/2/4\ny = 19/8\n\nSubstitute y\n7x + 3(19/8) = -167/8\n7x = -28\nx = -28/7\nx = -4"} {"input": "Solve the system:\n1x + 6y = -3\n5x + 3y = 12", "output": "1x + 6y = -3\n5x + 3y = 12\n\nUsing elimination\n5*(1x + 6y = -3)\n1*(5x + 3y = 12)\n5x + 30y = -15\n5x + 3y = 12\nSubtract equations\n27y = -27\ny = -27/27\ny = -1\n\nSubstitute y\n1x + 6(-1) = -3\n1x = 3\nx = 3/1\nx = 3"} {"input": "Find x in x^3 - 17/3x^2 + 607/64x - 95/24 = 0", "output": "x^3 - 17/3x^2 + 607/64x - 95/24 = 0\n(x - 19/8)(x - 5/8)(x - 8/3) = 0\nx - 19/8 = 0\nx - 5/8 = 0\nx - 8/3 = 0\nx = 19/8\nx = 5/8\nx = 8/3"} {"input": "Find the solution to x^2 - 95/6x + 361/6 = 0", "output": "x^2 - 95/6x + 361/6 = 0\n(x - 19/2)(x - 19/3) = 0\nx - 19/2 = 0 or x - 19/3 = 0\nx = 19/2\nx = 19/3"} {"input": "Solve 2x + 20/7 = 0", "output": "2x + 20/7 = 0\n2x = -20/7\nx = -20/7 / 2\nx = -10/7"} {"input": "Solve the equations:\n3x + 6y = 57/5\n7x + 10y = 113/5", "output": "3x + 6y = 57/5\n7x + 10y = 113/5\n\nUsing elimination\n7*(3x + 6y = 57/5)\n3*(7x + 10y = 113/5)\n21x + 42y = 399/5\n21x + 30y = 339/5\nSubtract equations\n12y = 12\ny = 12/12\ny = 1\n\nSubstitute y\n3x + 6(1) = 57/5\n3x = 27/5\nx = 27/5/3\nx = 9/5"} {"input": "What value of x satisfies x^2 + 3x - 45/16 = 0", "output": "x^2 + 3x - 45/16 = 0\n(x - -15/4)(x - 3/4) = 0\nx - -15/4 = 0 or x - 3/4 = 0\nx = -15/4\nx = 3/4"} {"input": "Determine x in x^3 - 179/10x^2 + 227/5x - 57/2 = 0", "output": "x^3 - 179/10x^2 + 227/5x - 57/2 = 0\n(x - 15)(x - 19/10)(x - 1) = 0\nx - 15 = 0\nx - 19/10 = 0\nx - 1 = 0\nx = 15\nx = 19/10\nx = 1"} {"input": "Find x in 9x - 63/8 = 0", "output": "9x - 63/8 = 0\n9x = 63/8\nx = 63/8 / 9\nx = 7/8"} {"input": "Find x in x^2 - 8/3x + 5/3 = 0", "output": "x^2 - 8/3x + 5/3 = 0\n(x - 5/3)(x - 1) = 0\nx - 5/3 = 0 or x - 1 = 0\nx = 5/3\nx = 1"} {"input": "Solve the system:\n6x + 10y = -131/2\n4x + 9y = -53", "output": "6x + 10y = -131/2\n4x + 9y = -53\n\nUsing elimination\n4*(6x + 10y = -131/2)\n6*(4x + 9y = -53)\n24x + 40y = -262\n24x + 54y = -318\nSubtract equations\n-14y = 56\ny = 56/-14\ny = -4\n\nSubstitute y\n6x + 10(-4) = -131/2\n6x = -51/2\nx = -51/2/6\nx = -17/4"} {"input": "Compute the solution of x^3 - 1x^2 - 37/16x + 5/8 = 0", "output": "x^3 - 1x^2 - 37/16x + 5/8 = 0\n(x - 1/4)(x - -5/4)(x - 2) = 0\nx - 1/4 = 0\nx - -5/4 = 0\nx - 2 = 0\nx = 1/4\nx = -5/4\nx = 2"} {"input": "Compute the solution of 5x - 100/7 = 0", "output": "5x - 100/7 = 0\n5x = 100/7\nx = 100/7 / 5\nx = 20/7"} {"input": "Find the solution to 6x + 18/7 = 0", "output": "6x + 18/7 = 0\n6x = -18/7\nx = -18/7 / 6\nx = -3/7"} {"input": "Find x in x^2 + 13x + 42 = 0", "output": "x^2 + 13x + 42 = 0\n(x - -6)(x - -7) = 0\nx - -6 = 0 or x - -7 = 0\nx = -6\nx = -7"} {"input": "Find x for x^3 - 24/5x^2 + 84/25x - 16/25 = 0", "output": "x^3 - 24/5x^2 + 84/25x - 16/25 = 0\n(x - 4)(x - 2/5)(x - 2/5) = 0\nx - 4 = 0\nx - 2/5 = 0\nx - 2/5 = 0\nx = 4\nx = 2/5\nx = 2/5"} {"input": "Solve quickly: x^2 + 127/63x + 44/63 = 0", "output": "x^2 + 127/63x + 44/63 = 0\n(x - -11/7)(x - -4/9) = 0\nx - -11/7 = 0 or x - -4/9 = 0\nx = -11/7\nx = -4/9"} {"input": "Determine x in x^2 + 74/21x - 16/3 = 0", "output": "x^2 + 74/21x - 16/3 = 0\n(x - -14/3)(x - 8/7) = 0\nx - -14/3 = 0 or x - 8/7 = 0\nx = -14/3\nx = 8/7"} {"input": "Determine x in x^3 + 851/168x^2 + 157/21x + 10/3 = 0", "output": "x^3 + 851/168x^2 + 157/21x + 10/3 = 0\n(x - -7/8)(x - -20/7)(x - -4/3) = 0\nx - -7/8 = 0\nx - -20/7 = 0\nx - -4/3 = 0\nx = -7/8\nx = -20/7\nx = -4/3"} {"input": "Solve the equations:\n9x + 10y = -227/7\n10x + 9y = -401/14", "output": "9x + 10y = -227/7\n10x + 9y = -401/14\n\nUsing elimination\n10*(9x + 10y = -227/7)\n9*(10x + 9y = -401/14)\n90x + 100y = -2270/7\n90x + 81y = -3609/14\nSubtract equations\n19y = -133/2\ny = -133/2/19\ny = -7/2\n\nSubstitute y\n9x + 10(-7/2) = -227/7\n9x = 18/7\nx = 18/7/9\nx = 2/7"} {"input": "Compute the solution of x^2 + 149/90x + 11/18 = 0", "output": "x^2 + 149/90x + 11/18 = 0\n(x - -11/10)(x - -5/9) = 0\nx - -11/10 = 0 or x - -5/9 = 0\nx = -11/10\nx = -5/9"} {"input": "Find x for 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "What value of x satisfies 7x + 7/3 = 0", "output": "7x + 7/3 = 0\n7x = -7/3\nx = -7/3 / 7\nx = -1/3"} {"input": "Solve the equations:\n9x + 9y = -351/10\n1x + 2y = -19/5", "output": "9x + 9y = -351/10\n1x + 2y = -19/5\n\nUsing elimination\n1*(9x + 9y = -351/10)\n9*(1x + 2y = -19/5)\n9x + 9y = -351/10\n9x + 18y = -171/5\nSubtract equations\n-9y = -9/10\ny = -9/10/-9\ny = 1/10\n\nSubstitute y\n9x + 9(1/10) = -351/10\n9x = -36\nx = -36/9\nx = -4"} {"input": "Solve simultaneously:\n1x + 8y = 255/8\n6x + 3y = 0", "output": "1x + 8y = 255/8\n6x + 3y = 0\n\nUsing elimination\n6*(1x + 8y = 255/8)\n1*(6x + 3y = 0)\n6x + 48y = 765/4\n6x + 3y = 0\nSubtract equations\n45y = 765/4\ny = 765/4/45\ny = 17/4\n\nSubstitute y\n1x + 8(17/4) = 255/8\n1x = -17/8\nx = -17/8/1\nx = -17/8"} {"input": "Solve quickly: 8x + 8 = 0", "output": "8x + 8 = 0\n8x = -8\nx = -8 / 8\nx = -1"} {"input": "Find x in x^2 + 37/10x + 7/10 = 0", "output": "x^2 + 37/10x + 7/10 = 0\n(x - -1/5)(x - -7/2) = 0\nx - -1/5 = 0 or x - -7/2 = 0\nx = -1/5\nx = -7/2"} {"input": "Find x for 4x - 20/9 = 0", "output": "4x - 20/9 = 0\n4x = 20/9\nx = 20/9 / 4\nx = 5/9"} {"input": "Determine x in x^2 + 5/7x - 12/7 = 0", "output": "x^2 + 5/7x - 12/7 = 0\n(x - 1)(x - -12/7) = 0\nx - 1 = 0 or x - -12/7 = 0\nx = 1\nx = -12/7"} {"input": "Solve the system:\n8x + 2y = 30\n1x + 5y = 37", "output": "8x + 2y = 30\n1x + 5y = 37\n\nUsing elimination\n1*(8x + 2y = 30)\n8*(1x + 5y = 37)\n8x + 2y = 30\n8x + 40y = 296\nSubtract equations\n-38y = -266\ny = -266/-38\ny = 7\n\nSubstitute y\n8x + 2(7) = 30\n8x = 16\nx = 16/8\nx = 2"} {"input": "Solve the equation x^3 - 79/10x^2 - 104/5x - 2 = 0", "output": "x^3 - 79/10x^2 - 104/5x - 2 = 0\n(x - -1/10)(x - -2)(x - 10) = 0\nx - -1/10 = 0\nx - -2 = 0\nx - 10 = 0\nx = -1/10\nx = -2\nx = 10"} {"input": "Solve quickly: x^2 + 27/10x + 17/10 = 0", "output": "x^2 + 27/10x + 17/10 = 0\n(x - -17/10)(x - -1) = 0\nx - -17/10 = 0 or x - -1 = 0\nx = -17/10\nx = -1"} {"input": "Solve quickly: x^3 - 4x^2 - 3/4x + 45/4 = 0", "output": "x^3 - 4x^2 - 3/4x + 45/4 = 0\n(x - -3/2)(x - 5/2)(x - 3) = 0\nx - -3/2 = 0\nx - 5/2 = 0\nx - 3 = 0\nx = -3/2\nx = 5/2\nx = 3"} {"input": "Solve simultaneously:\n3x + 3y = -11/10\n1x + 5y = 5/6", "output": "3x + 3y = -11/10\n1x + 5y = 5/6\n\nUsing elimination\n1*(3x + 3y = -11/10)\n3*(1x + 5y = 5/6)\n3x + 3y = -11/10\n3x + 15y = 5/2\nSubtract equations\n-12y = -18/5\ny = -18/5/-12\ny = 3/10\n\nSubstitute y\n3x + 3(3/10) = -11/10\n3x = -2\nx = -2/3\nx = -2/3"} {"input": "Determine x in x^2 + 64/7x + 15 = 0", "output": "x^2 + 64/7x + 15 = 0\n(x - -15/7)(x - -7) = 0\nx - -15/7 = 0 or x - -7 = 0\nx = -15/7\nx = -7"} {"input": "Compute the solution of x^3 + 493/90x^2 + 581/90x + 98/45 = 0", "output": "x^3 + 493/90x^2 + 581/90x + 98/45 = 0\n(x - -7/10)(x - -4)(x - -7/9) = 0\nx - -7/10 = 0\nx - -4 = 0\nx - -7/9 = 0\nx = -7/10\nx = -4\nx = -7/9"} {"input": "Compute the solution of x^3 - 8x^2 - 121x - 112 = 0", "output": "x^3 - 8x^2 - 121x - 112 = 0\n(x - -7)(x - 16)(x - -1) = 0\nx - -7 = 0\nx - 16 = 0\nx - -1 = 0\nx = -7\nx = 16\nx = -1"} {"input": "Find x in x^3 - 253/12x^2 + 441/4x - 931/6 = 0", "output": "x^3 - 253/12x^2 + 441/4x - 931/6 = 0\n(x - 19/4)(x - 14)(x - 7/3) = 0\nx - 19/4 = 0\nx - 14 = 0\nx - 7/3 = 0\nx = 19/4\nx = 14\nx = 7/3"} {"input": "Find x and y such that\n9x + 10y = 243/4\n8x + 3y = 55/2", "output": "9x + 10y = 243/4\n8x + 3y = 55/2\n\nUsing elimination\n8*(9x + 10y = 243/4)\n9*(8x + 3y = 55/2)\n72x + 80y = 486\n72x + 27y = 495/2\nSubtract equations\n53y = 477/2\ny = 477/2/53\ny = 9/2\n\nSubstitute y\n9x + 10(9/2) = 243/4\n9x = 63/4\nx = 63/4/9\nx = 7/4"} {"input": "Find x for x^2 + 17/15x - 22/3 = 0", "output": "x^2 + 17/15x - 22/3 = 0\n(x - 11/5)(x - -10/3) = 0\nx - 11/5 = 0 or x - -10/3 = 0\nx = 11/5\nx = -10/3"} {"input": "Solve the equation x^3 + 67/9x^2 - 24x + 140/9 = 0", "output": "x^3 + 67/9x^2 - 24x + 140/9 = 0\n(x - 14/9)(x - 1)(x - -10) = 0\nx - 14/9 = 0\nx - 1 = 0\nx - -10 = 0\nx = 14/9\nx = 1\nx = -10"} {"input": "Find x for x^3 + 52/35x^2 - 569/175x + 6/5 = 0", "output": "x^3 + 52/35x^2 - 569/175x + 6/5 = 0\n(x - 5/7)(x - 3/5)(x - -14/5) = 0\nx - 5/7 = 0\nx - 3/5 = 0\nx - -14/5 = 0\nx = 5/7\nx = 3/5\nx = -14/5"} {"input": "Find the solution to x^3 - 33/10x^2 - 43/10x + 63/5 = 0", "output": "x^3 - 33/10x^2 - 43/10x + 63/5 = 0\n(x - -2)(x - 9/5)(x - 7/2) = 0\nx - -2 = 0\nx - 9/5 = 0\nx - 7/2 = 0\nx = -2\nx = 9/5\nx = 7/2"} {"input": "Solve the equations:\n7x + 8y = -169/18\n2x + 6y = -13/3", "output": "7x + 8y = -169/18\n2x + 6y = -13/3\n\nUsing elimination\n2*(7x + 8y = -169/18)\n7*(2x + 6y = -13/3)\n14x + 16y = -169/9\n14x + 42y = -91/3\nSubtract equations\n-26y = 104/9\ny = 104/9/-26\ny = -4/9\n\nSubstitute y\n7x + 8(-4/9) = -169/18\n7x = -35/6\nx = -35/6/7\nx = -5/6"} {"input": "Find x for x^2 - 23/3x + 20/3 = 0", "output": "x^2 - 23/3x + 20/3 = 0\n(x - 1)(x - 20/3) = 0\nx - 1 = 0 or x - 20/3 = 0\nx = 1\nx = 20/3"} {"input": "Determine x in x^3 - 35/12x^2 - 31/8x + 33/8 = 0", "output": "x^3 - 35/12x^2 - 31/8x + 33/8 = 0\n(x - -3/2)(x - 11/3)(x - 3/4) = 0\nx - -3/2 = 0\nx - 11/3 = 0\nx - 3/4 = 0\nx = -3/2\nx = 11/3\nx = 3/4"} {"input": "Solve simultaneously:\n8x + 3y = -321/56\n4x + 2y = -75/28", "output": "8x + 3y = -321/56\n4x + 2y = -75/28\n\nUsing elimination\n4*(8x + 3y = -321/56)\n8*(4x + 2y = -75/28)\n32x + 12y = -321/14\n32x + 16y = -150/7\nSubtract equations\n-4y = -3/2\ny = -3/2/-4\ny = 3/8\n\nSubstitute y\n8x + 3(3/8) = -321/56\n8x = -48/7\nx = -48/7/8\nx = -6/7"} {"input": "Determine x in 6x - 32 = 0", "output": "6x - 32 = 0\n6x = 32\nx = 32 / 6\nx = 16/3"} {"input": "Find the solution to x^2 - 41/45x - 38/15 = 0", "output": "x^2 - 41/45x - 38/15 = 0\n(x - 19/9)(x - -6/5) = 0\nx - 19/9 = 0 or x - -6/5 = 0\nx = 19/9\nx = -6/5"} {"input": "Solve the equations:\n8x + 6y = 652/9\n7x + 7y = 728/9", "output": "8x + 6y = 652/9\n7x + 7y = 728/9\n\nUsing elimination\n7*(8x + 6y = 652/9)\n8*(7x + 7y = 728/9)\n56x + 42y = 4564/9\n56x + 56y = 5824/9\nSubtract equations\n-14y = -140\ny = -140/-14\ny = 10\n\nSubstitute y\n8x + 6(10) = 652/9\n8x = 112/9\nx = 112/9/8\nx = 14/9"} {"input": "Compute the solution of x^3 - 49/36x^2 - 49/12x + 95/18 = 0", "output": "x^3 - 49/36x^2 - 49/12x + 95/18 = 0\n(x - -2)(x - 5/4)(x - 19/9) = 0\nx - -2 = 0\nx - 5/4 = 0\nx - 19/9 = 0\nx = -2\nx = 5/4\nx = 19/9"} {"input": "Find x for 5x - 80 = 0", "output": "5x - 80 = 0\n5x = 80\nx = 80 / 5\nx = 16"} {"input": "Solve the system:\n9x + 7y = 1528/9\n1x + 4y = 202/9", "output": "9x + 7y = 1528/9\n1x + 4y = 202/9\n\nUsing elimination\n1*(9x + 7y = 1528/9)\n9*(1x + 4y = 202/9)\n9x + 7y = 1528/9\n9x + 36y = 202\nSubtract equations\n-29y = -290/9\ny = -290/9/-29\ny = 10/9\n\nSubstitute y\n9x + 7(10/9) = 1528/9\n9x = 162\nx = 162/9\nx = 18"} {"input": "Find x in 10x - 26 = 0", "output": "10x - 26 = 0\n10x = 26\nx = 26 / 10\nx = 13/5"} {"input": "Determine x in x^2 + 79/18x - 1/2 = 0", "output": "x^2 + 79/18x - 1/2 = 0\n(x - 1/9)(x - -9/2) = 0\nx - 1/9 = 0 or x - -9/2 = 0\nx = 1/9\nx = -9/2"} {"input": "Find x in x^3 + 7/4x^2 - 9x = 0", "output": "x^3 + 7/4x^2 - 9x = 0\n(x - -4)(x - 9/4)(x - 0) = 0\nx - -4 = 0\nx - 9/4 = 0\nx - 0 = 0\nx = -4\nx = 9/4\nx = 0"} {"input": "Find the solution to x^2 - 159/70x + 34/35 = 0", "output": "x^2 - 159/70x + 34/35 = 0\n(x - 17/10)(x - 4/7) = 0\nx - 17/10 = 0 or x - 4/7 = 0\nx = 17/10\nx = 4/7"} {"input": "Determine x in x^2 + 17/5x - 8 = 0", "output": "x^2 + 17/5x - 8 = 0\n(x - -5)(x - 8/5) = 0\nx - -5 = 0 or x - 8/5 = 0\nx = -5\nx = 8/5"} {"input": "Solve the system:\n8x + 10y = 84\n10x + 2y = 84", "output": "8x + 10y = 84\n10x + 2y = 84\n\nUsing elimination\n10*(8x + 10y = 84)\n8*(10x + 2y = 84)\n80x + 100y = 840\n80x + 16y = 672\nSubtract equations\n84y = 168\ny = 168/84\ny = 2\n\nSubstitute y\n8x + 10(2) = 84\n8x = 64\nx = 64/8\nx = 8"} {"input": "Find x for 8x + 120/7 = 0", "output": "8x + 120/7 = 0\n8x = -120/7\nx = -120/7 / 8\nx = -15/7"} {"input": "Determine x in 10x - 75/2 = 0", "output": "10x - 75/2 = 0\n10x = 75/2\nx = 75/2 / 10\nx = 15/4"} {"input": "Find x for 7x - 7/2 = 0", "output": "7x - 7/2 = 0\n7x = 7/2\nx = 7/2 / 7\nx = 1/2"} {"input": "Find x in 4x + 56/3 = 0", "output": "4x + 56/3 = 0\n4x = -56/3\nx = -56/3 / 4\nx = -14/3"} {"input": "Solve quickly: x^3 - 14/5x^2 - 1001/20x + 338/5 = 0", "output": "x^3 - 14/5x^2 - 1001/20x + 338/5 = 0\n(x - 8)(x - -13/2)(x - 13/10) = 0\nx - 8 = 0\nx - -13/2 = 0\nx - 13/10 = 0\nx = 8\nx = -13/2\nx = 13/10"} {"input": "Solve quickly: x^2 + 12/7x - 27/7 = 0", "output": "x^2 + 12/7x - 27/7 = 0\n(x - 9/7)(x - -3) = 0\nx - 9/7 = 0 or x - -3 = 0\nx = 9/7\nx = -3"} {"input": "Solve the equation 5x + 95/4 = 0", "output": "5x + 95/4 = 0\n5x = -95/4\nx = -95/4 / 5\nx = -19/4"} {"input": "Find x and y such that\n9x + 2y = 182/5\n9x + 3y = 183/5", "output": "9x + 2y = 182/5\n9x + 3y = 183/5\n\nUsing elimination\n9*(9x + 2y = 182/5)\n9*(9x + 3y = 183/5)\n81x + 18y = 1638/5\n81x + 27y = 1647/5\nSubtract equations\n-9y = -9/5\ny = -9/5/-9\ny = 1/5\n\nSubstitute y\n9x + 2(1/5) = 182/5\n9x = 36\nx = 36/9\nx = 4"} {"input": "Find x in x^2 + 39/7x + 20/7 = 0", "output": "x^2 + 39/7x + 20/7 = 0\n(x - -4/7)(x - -5) = 0\nx - -4/7 = 0 or x - -5 = 0\nx = -4/7\nx = -5"} {"input": "What value of x satisfies x^2 + 2/5x - 24/25 = 0", "output": "x^2 + 2/5x - 24/25 = 0\n(x - 4/5)(x - -6/5) = 0\nx - 4/5 = 0 or x - -6/5 = 0\nx = 4/5\nx = -6/5"} {"input": "Solve the equations:\n8x + 9y = 76/15\n6x + 10y = 9", "output": "8x + 9y = 76/15\n6x + 10y = 9\n\nUsing elimination\n6*(8x + 9y = 76/15)\n8*(6x + 10y = 9)\n48x + 54y = 152/5\n48x + 80y = 72\nSubtract equations\n-26y = -208/5\ny = -208/5/-26\ny = 8/5\n\nSubstitute y\n8x + 9(8/5) = 76/15\n8x = -28/3\nx = -28/3/8\nx = -7/6"} {"input": "Solve the equation x^3 - 8/9x^2 - 19/3x = 0", "output": "x^3 - 8/9x^2 - 19/3x = 0\n(x - -19/9)(x - 3)(x - 0) = 0\nx - -19/9 = 0\nx - 3 = 0\nx - 0 = 0\nx = -19/9\nx = 3\nx = 0"} {"input": "Solve simultaneously:\n3x + 3y = -279/14\n10x + 1y = -330/7", "output": "3x + 3y = -279/14\n10x + 1y = -330/7\n\nUsing elimination\n10*(3x + 3y = -279/14)\n3*(10x + 1y = -330/7)\n30x + 30y = -1395/7\n30x + 3y = -990/7\nSubtract equations\n27y = -405/7\ny = -405/7/27\ny = -15/7\n\nSubstitute y\n3x + 3(-15/7) = -279/14\n3x = -27/2\nx = -27/2/3\nx = -9/2"} {"input": "Solve quickly: x^3 - 139/28x^2 - 89/28x + 15 = 0", "output": "x^3 - 139/28x^2 - 89/28x + 15 = 0\n(x - -7/4)(x - 5)(x - 12/7) = 0\nx - -7/4 = 0\nx - 5 = 0\nx - 12/7 = 0\nx = -7/4\nx = 5\nx = 12/7"} {"input": "Solve the equation x^3 + 4/5x^2 - 147/25x + 54/25 = 0", "output": "x^3 + 4/5x^2 - 147/25x + 54/25 = 0\n(x - -3)(x - 2/5)(x - 9/5) = 0\nx - -3 = 0\nx - 2/5 = 0\nx - 9/5 = 0\nx = -3\nx = 2/5\nx = 9/5"} {"input": "Find x and y such that\n5x + 2y = 49/18\n4x + 9y = -22/5", "output": "5x + 2y = 49/18\n4x + 9y = -22/5\n\nUsing elimination\n4*(5x + 2y = 49/18)\n5*(4x + 9y = -22/5)\n20x + 8y = 98/9\n20x + 45y = -22\nSubtract equations\n-37y = 296/9\ny = 296/9/-37\ny = -8/9\n\nSubstitute y\n5x + 2(-8/9) = 49/18\n5x = 9/2\nx = 9/2/5\nx = 9/10"} {"input": "What value of x satisfies x^2 - 14/3x + 8/3 = 0", "output": "x^2 - 14/3x + 8/3 = 0\n(x - 4)(x - 2/3) = 0\nx - 4 = 0 or x - 2/3 = 0\nx = 4\nx = 2/3"} {"input": "Solve quickly: x^3 - 76/21x^2 + 76/21x - 16/21 = 0", "output": "x^3 - 76/21x^2 + 76/21x - 16/21 = 0\n(x - 2)(x - 4/3)(x - 2/7) = 0\nx - 2 = 0\nx - 4/3 = 0\nx - 2/7 = 0\nx = 2\nx = 4/3\nx = 2/7"} {"input": "Compute the solution of x^2 - 14/9x + 16/27 = 0", "output": "x^2 - 14/9x + 16/27 = 0\n(x - 8/9)(x - 2/3) = 0\nx - 8/9 = 0 or x - 2/3 = 0\nx = 8/9\nx = 2/3"} {"input": "Compute the solution of x^3 - 365/36x^2 + 431/72x + 19/24 = 0", "output": "x^3 - 365/36x^2 + 431/72x + 19/24 = 0\n(x - 19/2)(x - -1/9)(x - 3/4) = 0\nx - 19/2 = 0\nx - -1/9 = 0\nx - 3/4 = 0\nx = 19/2\nx = -1/9\nx = 3/4"} {"input": "What value of x satisfies x^3 + 20/9x^2 - 37/3x + 70/9 = 0", "output": "x^3 + 20/9x^2 - 37/3x + 70/9 = 0\n(x - -5)(x - 2)(x - 7/9) = 0\nx - -5 = 0\nx - 2 = 0\nx - 7/9 = 0\nx = -5\nx = 2\nx = 7/9"} {"input": "Find x for 10x + 25 = 0", "output": "10x + 25 = 0\n10x = -25\nx = -25 / 10\nx = -5/2"} {"input": "Solve the equations:\n9x + 6y = 339/20\n9x + 3y = 327/20", "output": "9x + 6y = 339/20\n9x + 3y = 327/20\n\nUsing elimination\n9*(9x + 6y = 339/20)\n9*(9x + 3y = 327/20)\n81x + 54y = 3051/20\n81x + 27y = 2943/20\nSubtract equations\n27y = 27/5\ny = 27/5/27\ny = 1/5\n\nSubstitute y\n9x + 6(1/5) = 339/20\n9x = 63/4\nx = 63/4/9\nx = 7/4"} {"input": "Find x for x^3 - 51/7x^2 + 108/7x - 64/7 = 0", "output": "x^3 - 51/7x^2 + 108/7x - 64/7 = 0\n(x - 4)(x - 1)(x - 16/7) = 0\nx - 4 = 0\nx - 1 = 0\nx - 16/7 = 0\nx = 4\nx = 1\nx = 16/7"} {"input": "Solve quickly: 2x + 2 = 0", "output": "2x + 2 = 0\n2x = -2\nx = -2 / 2\nx = -1"} {"input": "Solve the equation x^2 + 247/30x + 361/30 = 0", "output": "x^2 + 247/30x + 361/30 = 0\n(x - -19/3)(x - -19/10) = 0\nx - -19/3 = 0 or x - -19/10 = 0\nx = -19/3\nx = -19/10"} {"input": "Solve x^2 + 44/45x - 64/45 = 0", "output": "x^2 + 44/45x - 64/45 = 0\n(x - -16/9)(x - 4/5) = 0\nx - -16/9 = 0 or x - 4/5 = 0\nx = -16/9\nx = 4/5"} {"input": "Solve the equations:\n5x + 10y = -245/4\n6x + 8y = -66", "output": "5x + 10y = -245/4\n6x + 8y = -66\n\nUsing elimination\n6*(5x + 10y = -245/4)\n5*(6x + 8y = -66)\n30x + 60y = -735/2\n30x + 40y = -330\nSubtract equations\n20y = -75/2\ny = -75/2/20\ny = -15/8\n\nSubstitute y\n5x + 10(-15/8) = -245/4\n5x = -85/2\nx = -85/2/5\nx = -17/2"} {"input": "Find x and y such that\n8x + 2y = -82/5\n3x + 8y = -96/5", "output": "8x + 2y = -82/5\n3x + 8y = -96/5\n\nUsing elimination\n3*(8x + 2y = -82/5)\n8*(3x + 8y = -96/5)\n24x + 6y = -246/5\n24x + 64y = -768/5\nSubtract equations\n-58y = 522/5\ny = 522/5/-58\ny = -9/5\n\nSubstitute y\n8x + 2(-9/5) = -82/5\n8x = -64/5\nx = -64/5/8\nx = -8/5"} {"input": "Find x for 5x - 25/6 = 0", "output": "5x - 25/6 = 0\n5x = 25/6\nx = 25/6 / 5\nx = 5/6"} {"input": "Find the solution to 1x + 5 = 0", "output": "1x + 5 = 0\n1x = -5\nx = -5 / 1\nx = -5"} {"input": "Solve x^2 + 53/6x + 55/3 = 0", "output": "x^2 + 53/6x + 55/3 = 0\n(x - -11/2)(x - -10/3) = 0\nx - -11/2 = 0 or x - -10/3 = 0\nx = -11/2\nx = -10/3"} {"input": "Find x for 6x + 8/3 = 0", "output": "6x + 8/3 = 0\n6x = -8/3\nx = -8/3 / 6\nx = -4/9"} {"input": "What value of x satisfies 2x + 36/7 = 0", "output": "2x + 36/7 = 0\n2x = -36/7\nx = -36/7 / 2\nx = -18/7"} {"input": "Find x and y such that\n9x + 5y = 138/7\n5x + 7y = 102/7", "output": "9x + 5y = 138/7\n5x + 7y = 102/7\n\nUsing elimination\n5*(9x + 5y = 138/7)\n9*(5x + 7y = 102/7)\n45x + 25y = 690/7\n45x + 63y = 918/7\nSubtract equations\n-38y = -228/7\ny = -228/7/-38\ny = 6/7\n\nSubstitute y\n9x + 5(6/7) = 138/7\n9x = 108/7\nx = 108/7/9\nx = 12/7"} {"input": "Find x for 1x + 8/5 = 0", "output": "1x + 8/5 = 0\n1x = -8/5\nx = -8/5 / 1\nx = -8/5"} {"input": "Solve the system:\n3x + 1y = 5/4\n6x + 4y = -1", "output": "3x + 1y = 5/4\n6x + 4y = -1\n\nUsing elimination\n6*(3x + 1y = 5/4)\n3*(6x + 4y = -1)\n18x + 6y = 15/2\n18x + 12y = -3\nSubtract equations\n-6y = 21/2\ny = 21/2/-6\ny = -7/4\n\nSubstitute y\n3x + 1(-7/4) = 5/4\n3x = 3\nx = 3/3\nx = 1"} {"input": "Solve the system:\n10x + 5y = -27\n7x + 1y = -77/5", "output": "10x + 5y = -27\n7x + 1y = -77/5\n\nUsing elimination\n7*(10x + 5y = -27)\n10*(7x + 1y = -77/5)\n70x + 35y = -189\n70x + 10y = -154\nSubtract equations\n25y = -35\ny = -35/25\ny = -7/5\n\nSubstitute y\n10x + 5(-7/5) = -27\n10x = -20\nx = -20/10\nx = -2"} {"input": "Determine x in 1x - 5 = 0", "output": "1x - 5 = 0\n1x = 5\nx = 5 / 1\nx = 5"} {"input": "Solve quickly: x^2 - 11/2x - 38 = 0", "output": "x^2 - 11/2x - 38 = 0\n(x - -4)(x - 19/2) = 0\nx - -4 = 0 or x - 19/2 = 0\nx = -4\nx = 19/2"} {"input": "Find x for x^3 + 341/90x^2 + 34/9x + 16/15 = 0", "output": "x^3 + 341/90x^2 + 34/9x + 16/15 = 0\n(x - -8/9)(x - -12/5)(x - -1/2) = 0\nx - -8/9 = 0\nx - -12/5 = 0\nx - -1/2 = 0\nx = -8/9\nx = -12/5\nx = -1/2"} {"input": "Solve the equation x^3 + 93/70x^2 - 313/70x - 153/35 = 0", "output": "x^3 + 93/70x^2 - 313/70x - 153/35 = 0\n(x - -9/10)(x - 2)(x - -17/7) = 0\nx - -9/10 = 0\nx - 2 = 0\nx - -17/7 = 0\nx = -9/10\nx = 2\nx = -17/7"} {"input": "Solve the equations:\n9x + 10y = -1493/24\n1x + 9y = -455/8", "output": "9x + 10y = -1493/24\n1x + 9y = -455/8\n\nUsing elimination\n1*(9x + 10y = -1493/24)\n9*(1x + 9y = -455/8)\n9x + 10y = -1493/24\n9x + 81y = -4095/8\nSubtract equations\n-71y = 1349/3\ny = 1349/3/-71\ny = -19/3\n\nSubstitute y\n9x + 10(-19/3) = -1493/24\n9x = 9/8\nx = 9/8/9\nx = 1/8"} {"input": "Find x in x^3 - 1/5x^2 - 13/20x - 3/20 = 0", "output": "x^3 - 1/5x^2 - 13/20x - 3/20 = 0\n(x - -3/10)(x - -1/2)(x - 1) = 0\nx - -3/10 = 0\nx - -1/2 = 0\nx - 1 = 0\nx = -3/10\nx = -1/2\nx = 1"} {"input": "Determine x in x^3 - 9/8x^2 - 695/32x + 1425/32 = 0", "output": "x^3 - 9/8x^2 - 695/32x + 1425/32 = 0\n(x - -5)(x - 15/4)(x - 19/8) = 0\nx - -5 = 0\nx - 15/4 = 0\nx - 19/8 = 0\nx = -5\nx = 15/4\nx = 19/8"} {"input": "Determine x in x^2 - 19/4x + 15/4 = 0", "output": "x^2 - 19/4x + 15/4 = 0\n(x - 1)(x - 15/4) = 0\nx - 1 = 0 or x - 15/4 = 0\nx = 1\nx = 15/4"} {"input": "Solve quickly: x^2 - 11/2x - 38 = 0", "output": "x^2 - 11/2x - 38 = 0\n(x - -4)(x - 19/2) = 0\nx - -4 = 0 or x - 19/2 = 0\nx = -4\nx = 19/2"} {"input": "Solve quickly: x^2 + 7/10x - 6/5 = 0", "output": "x^2 + 7/10x - 6/5 = 0\n(x - 4/5)(x - -3/2) = 0\nx - 4/5 = 0 or x - -3/2 = 0\nx = 4/5\nx = -3/2"} {"input": "Find the solution to x^2 + 14/3x - 17/3 = 0", "output": "x^2 + 14/3x - 17/3 = 0\n(x - -17/3)(x - 1) = 0\nx - -17/3 = 0 or x - 1 = 0\nx = -17/3\nx = 1"} {"input": "Solve the equations:\n8x + 10y = 13\n4x + 6y = 19/2", "output": "8x + 10y = 13\n4x + 6y = 19/2\n\nUsing elimination\n4*(8x + 10y = 13)\n8*(4x + 6y = 19/2)\n32x + 40y = 52\n32x + 48y = 76\nSubtract equations\n-8y = -24\ny = -24/-8\ny = 3\n\nSubstitute y\n8x + 10(3) = 13\n8x = -17\nx = -17/8\nx = -17/8"} {"input": "Find x for x^2 + 4x - 12 = 0", "output": "x^2 + 4x - 12 = 0\n(x - -6)(x - 2) = 0\nx - -6 = 0 or x - 2 = 0\nx = -6\nx = 2"} {"input": "Determine x in x^2 + 21x + 20 = 0", "output": "x^2 + 21x + 20 = 0\n(x - -1)(x - -20) = 0\nx - -1 = 0 or x - -20 = 0\nx = -1\nx = -20"} {"input": "Find x for x^3 + 8/3x^2 = 0", "output": "x^3 + 8/3x^2 = 0\n(x - 0)(x - -8/3)(x - 0) = 0\nx - 0 = 0\nx - -8/3 = 0\nx - 0 = 0\nx = 0\nx = -8/3\nx = 0"} {"input": "Solve the equation x^2 - 18x + 17 = 0", "output": "x^2 - 18x + 17 = 0\n(x - 17)(x - 1) = 0\nx - 17 = 0 or x - 1 = 0\nx = 17\nx = 1"} {"input": "Find x in x^3 + 37/15x^2 + 2x + 8/15 = 0", "output": "x^3 + 37/15x^2 + 2x + 8/15 = 0\n(x - -1)(x - -2/3)(x - -4/5) = 0\nx - -1 = 0\nx - -2/3 = 0\nx - -4/5 = 0\nx = -1\nx = -2/3\nx = -4/5"} {"input": "Find the solution to x^2 - 73/30x + 11/10 = 0", "output": "x^2 - 73/30x + 11/10 = 0\n(x - 3/5)(x - 11/6) = 0\nx - 3/5 = 0 or x - 11/6 = 0\nx = 3/5\nx = 11/6"} {"input": "Determine x in x^2 - 86/9x - 143/9 = 0", "output": "x^2 - 86/9x - 143/9 = 0\n(x - -13/9)(x - 11) = 0\nx - -13/9 = 0 or x - 11 = 0\nx = -13/9\nx = 11"} {"input": "Solve the equations:\n5x + 7y = -689/30\n6x + 9y = -281/10", "output": "5x + 7y = -689/30\n6x + 9y = -281/10\n\nUsing elimination\n6*(5x + 7y = -689/30)\n5*(6x + 9y = -281/10)\n30x + 42y = -689/5\n30x + 45y = -281/2\nSubtract equations\n-3y = 27/10\ny = 27/10/-3\ny = -9/10\n\nSubstitute y\n5x + 7(-9/10) = -689/30\n5x = -50/3\nx = -50/3/5\nx = -10/3"} {"input": "Solve x^2 + 9/4x - 9/4 = 0", "output": "x^2 + 9/4x - 9/4 = 0\n(x - -3)(x - 3/4) = 0\nx - -3 = 0 or x - 3/4 = 0\nx = -3\nx = 3/4"} {"input": "Solve quickly: x^2 - 41/3x - 14/3 = 0", "output": "x^2 - 41/3x - 14/3 = 0\n(x - -1/3)(x - 14) = 0\nx - -1/3 = 0 or x - 14 = 0\nx = -1/3\nx = 14"} {"input": "Solve the system:\n9x + 4y = -476/15\n2x + 3y = -81/5", "output": "9x + 4y = -476/15\n2x + 3y = -81/5\n\nUsing elimination\n2*(9x + 4y = -476/15)\n9*(2x + 3y = -81/5)\n18x + 8y = -952/15\n18x + 27y = -729/5\nSubtract equations\n-19y = 247/3\ny = 247/3/-19\ny = -13/3\n\nSubstitute y\n9x + 4(-13/3) = -476/15\n9x = -72/5\nx = -72/5/9\nx = -8/5"} {"input": "Solve simultaneously:\n7x + 4y = 593/10\n6x + 7y = 222/5", "output": "7x + 4y = 593/10\n6x + 7y = 222/5\n\nUsing elimination\n6*(7x + 4y = 593/10)\n7*(6x + 7y = 222/5)\n42x + 24y = 1779/5\n42x + 49y = 1554/5\nSubtract equations\n-25y = 45\ny = 45/-25\ny = -9/5\n\nSubstitute y\n7x + 4(-9/5) = 593/10\n7x = 133/2\nx = 133/2/7\nx = 19/2"} {"input": "Find the solution to 7x - 21/2 = 0", "output": "7x - 21/2 = 0\n7x = 21/2\nx = 21/2 / 7\nx = 3/2"} {"input": "Solve x^2 - 59/18x - 7/9 = 0", "output": "x^2 - 59/18x - 7/9 = 0\n(x - -2/9)(x - 7/2) = 0\nx - -2/9 = 0 or x - 7/2 = 0\nx = -2/9\nx = 7/2"} {"input": "Compute the solution of x^3 - 8x^2 - 309/4x - 189/2 = 0", "output": "x^3 - 8x^2 - 309/4x - 189/2 = 0\n(x - -3/2)(x - -9/2)(x - 14) = 0\nx - -3/2 = 0\nx - -9/2 = 0\nx - 14 = 0\nx = -3/2\nx = -9/2\nx = 14"} {"input": "Solve the equation x^3 - 373/36x^2 + 233/12x - 38/9 = 0", "output": "x^3 - 373/36x^2 + 233/12x - 38/9 = 0\n(x - 8)(x - 19/9)(x - 1/4) = 0\nx - 8 = 0\nx - 19/9 = 0\nx - 1/4 = 0\nx = 8\nx = 19/9\nx = 1/4"} {"input": "Find x in x^2 + 67/6x + 76/3 = 0", "output": "x^2 + 67/6x + 76/3 = 0\n(x - -8)(x - -19/6) = 0\nx - -8 = 0 or x - -19/6 = 0\nx = -8\nx = -19/6"} {"input": "Solve the equation 1x - 20/3 = 0", "output": "1x - 20/3 = 0\n1x = 20/3\nx = 20/3 / 1\nx = 20/3"} {"input": "Determine x in x^3 + 4x^2 + 9/4x - 9/4 = 0", "output": "x^3 + 4x^2 + 9/4x - 9/4 = 0\n(x - -3/2)(x - -3)(x - 1/2) = 0\nx - -3/2 = 0\nx - -3 = 0\nx - 1/2 = 0\nx = -3/2\nx = -3\nx = 1/2"} {"input": "Find x and y such that\n5x + 9y = 73\n7x + 8y = 281/5", "output": "5x + 9y = 73\n7x + 8y = 281/5\n\nUsing elimination\n7*(5x + 9y = 73)\n5*(7x + 8y = 281/5)\n35x + 63y = 511\n35x + 40y = 281\nSubtract equations\n23y = 230\ny = 230/23\ny = 10\n\nSubstitute y\n5x + 9(10) = 73\n5x = -17\nx = -17/5\nx = -17/5"} {"input": "Solve the equations:\n6x + 10y = 125/2\n10x + 8y = 76", "output": "6x + 10y = 125/2\n10x + 8y = 76\n\nUsing elimination\n10*(6x + 10y = 125/2)\n6*(10x + 8y = 76)\n60x + 100y = 625\n60x + 48y = 456\nSubtract equations\n52y = 169\ny = 169/52\ny = 13/4\n\nSubstitute y\n6x + 10(13/4) = 125/2\n6x = 30\nx = 30/6\nx = 5"} {"input": "Find the solution to x^2 + 20/9x + 4/9 = 0", "output": "x^2 + 20/9x + 4/9 = 0\n(x - -2/9)(x - -2) = 0\nx - -2/9 = 0 or x - -2 = 0\nx = -2/9\nx = -2"} {"input": "Solve x^2 + 2/9x = 0", "output": "x^2 + 2/9x = 0\n(x - -2/9)(x - 0) = 0\nx - -2/9 = 0 or x - 0 = 0\nx = -2/9\nx = 0"} {"input": "Solve 8x - 120/7 = 0", "output": "8x - 120/7 = 0\n8x = 120/7\nx = 120/7 / 8\nx = 15/7"} {"input": "Solve quickly: x^2 - 27/20x - 81/10 = 0", "output": "x^2 - 27/20x - 81/10 = 0\n(x - -9/4)(x - 18/5) = 0\nx - -9/4 = 0 or x - 18/5 = 0\nx = -9/4\nx = 18/5"} {"input": "Solve x^3 + 4x^2 + 21/4x + 9/4 = 0", "output": "x^3 + 4x^2 + 21/4x + 9/4 = 0\n(x - -1)(x - -3/2)(x - -3/2) = 0\nx - -1 = 0\nx - -3/2 = 0\nx - -3/2 = 0\nx = -1\nx = -3/2\nx = -3/2"} {"input": "Solve quickly: 6x + 57/2 = 0", "output": "6x + 57/2 = 0\n6x = -57/2\nx = -57/2 / 6\nx = -19/4"} {"input": "Find x and y such that\n6x + 6y = -36\n2x + 1y = -15", "output": "6x + 6y = -36\n2x + 1y = -15\n\nUsing elimination\n2*(6x + 6y = -36)\n6*(2x + 1y = -15)\n12x + 12y = -72\n12x + 6y = -90\nSubtract equations\n6y = 18\ny = 18/6\ny = 3\n\nSubstitute y\n6x + 6(3) = -36\n6x = -54\nx = -54/6\nx = -9"} {"input": "Find x and y such that\n3x + 7y = 4\n5x + 7y = 2", "output": "3x + 7y = 4\n5x + 7y = 2\n\nUsing elimination\n5*(3x + 7y = 4)\n3*(5x + 7y = 2)\n15x + 35y = 20\n15x + 21y = 6\nSubtract equations\n14y = 14\ny = 14/14\ny = 1\n\nSubstitute y\n3x + 7(1) = 4\n3x = -3\nx = -3/3\nx = -1"} {"input": "Solve quickly: x^3 + 73/36x^2 - 1/2x = 0", "output": "x^3 + 73/36x^2 - 1/2x = 0\n(x - 0)(x - -9/4)(x - 2/9) = 0\nx - 0 = 0\nx - -9/4 = 0\nx - 2/9 = 0\nx = 0\nx = -9/4\nx = 2/9"} {"input": "Compute the solution of x^2 - 8/3x + 140/81 = 0", "output": "x^2 - 8/3x + 140/81 = 0\n(x - 10/9)(x - 14/9) = 0\nx - 10/9 = 0 or x - 14/9 = 0\nx = 10/9\nx = 14/9"} {"input": "Find x in x^2 + 9x + 18 = 0", "output": "x^2 + 9x + 18 = 0\n(x - -6)(x - -3) = 0\nx - -6 = 0 or x - -3 = 0\nx = -6\nx = -3"} {"input": "Find the solution to x^2 - 25/18x - 152/27 = 0", "output": "x^2 - 25/18x - 152/27 = 0\n(x - -16/9)(x - 19/6) = 0\nx - -16/9 = 0 or x - 19/6 = 0\nx = -16/9\nx = 19/6"} {"input": "Compute the solution of x^2 + 7/9x - 136/27 = 0", "output": "x^2 + 7/9x - 136/27 = 0\n(x - -8/3)(x - 17/9) = 0\nx - -8/3 = 0 or x - 17/9 = 0\nx = -8/3\nx = 17/9"} {"input": "Compute the solution of x^3 + 33/4x^2 - 185/2x + 525/4 = 0", "output": "x^3 + 33/4x^2 - 185/2x + 525/4 = 0\n(x - 5)(x - -15)(x - 7/4) = 0\nx - 5 = 0\nx - -15 = 0\nx - 7/4 = 0\nx = 5\nx = -15\nx = 7/4"} {"input": "Find the solution to x^3 - 9x = 0", "output": "x^3 - 9x = 0\n(x - 0)(x - -3)(x - 3) = 0\nx - 0 = 0\nx - -3 = 0\nx - 3 = 0\nx = 0\nx = -3\nx = 3"} {"input": "Find x for x^2 + 83/24x + 17/6 = 0", "output": "x^2 + 83/24x + 17/6 = 0\n(x - -4/3)(x - -17/8) = 0\nx - -4/3 = 0 or x - -17/8 = 0\nx = -4/3\nx = -17/8"} {"input": "What value of x satisfies 1x + 11/4 = 0", "output": "1x + 11/4 = 0\n1x = -11/4\nx = -11/4 / 1\nx = -11/4"} {"input": "Find x in 2x - 11/4 = 0", "output": "2x - 11/4 = 0\n2x = 11/4\nx = 11/4 / 2\nx = 11/8"} {"input": "Solve the equation x^3 + 58/35x^2 - 313/35x + 12/7 = 0", "output": "x^3 + 58/35x^2 - 313/35x + 12/7 = 0\n(x - 15/7)(x - -4)(x - 1/5) = 0\nx - 15/7 = 0\nx - -4 = 0\nx - 1/5 = 0\nx = 15/7\nx = -4\nx = 1/5"} {"input": "Solve the equations:\n2x + 6y = 68/5\n8x + 7y = 136/5", "output": "2x + 6y = 68/5\n8x + 7y = 136/5\n\nUsing elimination\n8*(2x + 6y = 68/5)\n2*(8x + 7y = 136/5)\n16x + 48y = 544/5\n16x + 14y = 272/5\nSubtract equations\n34y = 272/5\ny = 272/5/34\ny = 8/5\n\nSubstitute y\n2x + 6(8/5) = 68/5\n2x = 4\nx = 4/2\nx = 2"} {"input": "Solve the equation 2x + 40/7 = 0", "output": "2x + 40/7 = 0\n2x = -40/7\nx = -40/7 / 2\nx = -20/7"} {"input": "Compute the solution of x^3 - 5/4x^2 - 63/8x - 45/8 = 0", "output": "x^3 - 5/4x^2 - 63/8x - 45/8 = 0\n(x - 15/4)(x - -1)(x - -3/2) = 0\nx - 15/4 = 0\nx - -1 = 0\nx - -3/2 = 0\nx = 15/4\nx = -1\nx = -3/2"} {"input": "Solve 1x + 3 = 0", "output": "1x + 3 = 0\n1x = -3\nx = -3 / 1\nx = -3"} {"input": "Solve the equations:\n9x + 5y = 96/5\n6x + 2y = 48/5", "output": "9x + 5y = 96/5\n6x + 2y = 48/5\n\nUsing elimination\n6*(9x + 5y = 96/5)\n9*(6x + 2y = 48/5)\n54x + 30y = 576/5\n54x + 18y = 432/5\nSubtract equations\n12y = 144/5\ny = 144/5/12\ny = 12/5\n\nSubstitute y\n9x + 5(12/5) = 96/5\n9x = 36/5\nx = 36/5/9\nx = 4/5"} {"input": "Solve the system:\n4x + 1y = -174/5\n9x + 2y = -393/5", "output": "4x + 1y = -174/5\n9x + 2y = -393/5\n\nUsing elimination\n9*(4x + 1y = -174/5)\n4*(9x + 2y = -393/5)\n36x + 9y = -1566/5\n36x + 8y = -1572/5\nSubtract equations\n1y = 6/5\ny = 6/5/1\ny = 6/5\n\nSubstitute y\n4x + 1(6/5) = -174/5\n4x = -36\nx = -36/4\nx = -9"} {"input": "Determine x in x^3 - 23/9x^2 + 76/81x = 0", "output": "x^3 - 23/9x^2 + 76/81x = 0\n(x - 19/9)(x - 4/9)(x - 0) = 0\nx - 19/9 = 0\nx - 4/9 = 0\nx - 0 = 0\nx = 19/9\nx = 4/9\nx = 0"} {"input": "What value of x satisfies 3x + 9/4 = 0", "output": "3x + 9/4 = 0\n3x = -9/4\nx = -9/4 / 3\nx = -3/4"} {"input": "Solve the equations:\n2x + 4y = 29/5\n2x + 2y = 19/5", "output": "2x + 4y = 29/5\n2x + 2y = 19/5\n\nUsing elimination\n2*(2x + 4y = 29/5)\n2*(2x + 2y = 19/5)\n4x + 8y = 58/5\n4x + 4y = 38/5\nSubtract equations\n4y = 4\ny = 4/4\ny = 1\n\nSubstitute y\n2x + 4(1) = 29/5\n2x = 9/5\nx = 9/5/2\nx = 9/10"} {"input": "Solve quickly: x^2 - 151/8x + 63/4 = 0", "output": "x^2 - 151/8x + 63/4 = 0\n(x - 7/8)(x - 18) = 0\nx - 7/8 = 0 or x - 18 = 0\nx = 7/8\nx = 18"} {"input": "Solve the equation 9x + 13 = 0", "output": "9x + 13 = 0\n9x = -13\nx = -13 / 9\nx = -13/9"} {"input": "Solve quickly: x^3 - 47/10x^2 - 71/80x + 91/5 = 0", "output": "x^3 - 47/10x^2 - 71/80x + 91/5 = 0\n(x - 13/4)(x - -7/4)(x - 16/5) = 0\nx - 13/4 = 0\nx - -7/4 = 0\nx - 16/5 = 0\nx = 13/4\nx = -7/4\nx = 16/5"} {"input": "Solve the equation x^2 - 129/40x + 13/5 = 0", "output": "x^2 - 129/40x + 13/5 = 0\n(x - 13/8)(x - 8/5) = 0\nx - 13/8 = 0 or x - 8/5 = 0\nx = 13/8\nx = 8/5"} {"input": "Find the solution to x^2 - 17/4x + 1 = 0", "output": "x^2 - 17/4x + 1 = 0\n(x - 4)(x - 1/4) = 0\nx - 4 = 0 or x - 1/4 = 0\nx = 4\nx = 1/4"} {"input": "Solve quickly: x^3 - 7/5x^2 + 53/100x - 1/25 = 0", "output": "x^3 - 7/5x^2 + 53/100x - 1/25 = 0\n(x - 1/10)(x - 1/2)(x - 4/5) = 0\nx - 1/10 = 0\nx - 1/2 = 0\nx - 4/5 = 0\nx = 1/10\nx = 1/2\nx = 4/5"} {"input": "Find the solution to 2x - 9 = 0", "output": "2x - 9 = 0\n2x = 9\nx = 9 / 2\nx = 9/2"} {"input": "Solve the equation x^2 - 29/18x - 19/18 = 0", "output": "x^2 - 29/18x - 19/18 = 0\n(x - 19/9)(x - -1/2) = 0\nx - 19/9 = 0 or x - -1/2 = 0\nx = 19/9\nx = -1/2"} {"input": "Determine x in x^2 - 10/9x - 56/81 = 0", "output": "x^2 - 10/9x - 56/81 = 0\n(x - -4/9)(x - 14/9) = 0\nx - -4/9 = 0 or x - 14/9 = 0\nx = -4/9\nx = 14/9"} {"input": "Solve the system:\n3x + 10y = -1121/30\n3x + 9y = -171/5", "output": "3x + 10y = -1121/30\n3x + 9y = -171/5\n\nUsing elimination\n3*(3x + 10y = -1121/30)\n3*(3x + 9y = -171/5)\n9x + 30y = -1121/10\n9x + 27y = -513/5\nSubtract equations\n3y = -19/2\ny = -19/2/3\ny = -19/6\n\nSubstitute y\n3x + 10(-19/6) = -1121/30\n3x = -57/10\nx = -57/10/3\nx = -19/10"} {"input": "What value of x satisfies x^3 - 4/9x^2 - 85/36x + 7/6 = 0", "output": "x^3 - 4/9x^2 - 85/36x + 7/6 = 0\n(x - 3/2)(x - -14/9)(x - 1/2) = 0\nx - 3/2 = 0\nx - -14/9 = 0\nx - 1/2 = 0\nx = 3/2\nx = -14/9\nx = 1/2"} {"input": "Solve 3x + 12 = 0", "output": "3x + 12 = 0\n3x = -12\nx = -12 / 3\nx = -4"} {"input": "Determine x in x^3 + 76/15x^2 + 32/5x = 0", "output": "x^3 + 76/15x^2 + 32/5x = 0\n(x - -12/5)(x - 0)(x - -8/3) = 0\nx - -12/5 = 0\nx - 0 = 0\nx - -8/3 = 0\nx = -12/5\nx = 0\nx = -8/3"} {"input": "Solve the system:\n7x + 7y = 28\n6x + 1y = 53/2", "output": "7x + 7y = 28\n6x + 1y = 53/2\n\nUsing elimination\n6*(7x + 7y = 28)\n7*(6x + 1y = 53/2)\n42x + 42y = 168\n42x + 7y = 371/2\nSubtract equations\n35y = -35/2\ny = -35/2/35\ny = -1/2\n\nSubstitute y\n7x + 7(-1/2) = 28\n7x = 63/2\nx = 63/2/7\nx = 9/2"} {"input": "Find x for x^2 + 15/2x - 77/2 = 0", "output": "x^2 + 15/2x - 77/2 = 0\n(x - -11)(x - 7/2) = 0\nx - -11 = 0 or x - 7/2 = 0\nx = -11\nx = 7/2"} {"input": "Solve x^3 - 73/5x^2 + 242/5x - 24 = 0", "output": "x^3 - 73/5x^2 + 242/5x - 24 = 0\n(x - 10)(x - 3/5)(x - 4) = 0\nx - 10 = 0\nx - 3/5 = 0\nx - 4 = 0\nx = 10\nx = 3/5\nx = 4"} {"input": "Find the solution to x^3 - 47/10x^2 + 1/10x + 18/5 = 0", "output": "x^3 - 47/10x^2 + 1/10x + 18/5 = 0\n(x - 1)(x - -4/5)(x - 9/2) = 0\nx - 1 = 0\nx - -4/5 = 0\nx - 9/2 = 0\nx = 1\nx = -4/5\nx = 9/2"} {"input": "Solve the equations:\n8x + 10y = 8\n6x + 5y = 11", "output": "8x + 10y = 8\n6x + 5y = 11\n\nUsing elimination\n6*(8x + 10y = 8)\n8*(6x + 5y = 11)\n48x + 60y = 48\n48x + 40y = 88\nSubtract equations\n20y = -40\ny = -40/20\ny = -2\n\nSubstitute y\n8x + 10(-2) = 8\n8x = 28\nx = 28/8\nx = 7/2"} {"input": "Solve the equations:\n7x + 9y = -99/8\n2x + 7y = 47/8", "output": "7x + 9y = -99/8\n2x + 7y = 47/8\n\nUsing elimination\n2*(7x + 9y = -99/8)\n7*(2x + 7y = 47/8)\n14x + 18y = -99/4\n14x + 49y = 329/8\nSubtract equations\n-31y = -527/8\ny = -527/8/-31\ny = 17/8\n\nSubstitute y\n7x + 9(17/8) = -99/8\n7x = -63/2\nx = -63/2/7\nx = -9/2"} {"input": "Find x for x^3 + 55/6x^2 - 9x - 20/3 = 0", "output": "x^3 + 55/6x^2 - 9x - 20/3 = 0\n(x - -1/2)(x - -10)(x - 4/3) = 0\nx - -1/2 = 0\nx - -10 = 0\nx - 4/3 = 0\nx = -1/2\nx = -10\nx = 4/3"} {"input": "Find x in 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "Find x for x^2 - 20/7x = 0", "output": "x^2 - 20/7x = 0\n(x - 0)(x - 20/7) = 0\nx - 0 = 0 or x - 20/7 = 0\nx = 0\nx = 20/7"} {"input": "Find x for 1x + 13/4 = 0", "output": "1x + 13/4 = 0\n1x = -13/4\nx = -13/4 / 1\nx = -13/4"} {"input": "Solve the system:\n6x + 1y = 19/6\n1x + 1y = 47/18", "output": "6x + 1y = 19/6\n1x + 1y = 47/18\n\nUsing elimination\n1*(6x + 1y = 19/6)\n6*(1x + 1y = 47/18)\n6x + 1y = 19/6\n6x + 6y = 47/3\nSubtract equations\n-5y = -25/2\ny = -25/2/-5\ny = 5/2\n\nSubstitute y\n6x + 1(5/2) = 19/6\n6x = 2/3\nx = 2/3/6\nx = 1/9"} {"input": "Find x for 4x + 8 = 0", "output": "4x + 8 = 0\n4x = -8\nx = -8 / 4\nx = -2"} {"input": "Compute the solution of 9x - 6 = 0", "output": "9x - 6 = 0\n9x = 6\nx = 6 / 9\nx = 2/3"} {"input": "What value of x satisfies x^2 - 9/28x - 81/14 = 0", "output": "x^2 - 9/28x - 81/14 = 0\n(x - -9/4)(x - 18/7) = 0\nx - -9/4 = 0 or x - 18/7 = 0\nx = -9/4\nx = 18/7"} {"input": "Solve quickly: x^3 - 568/35x^2 + 1559/35x - 234/7 = 0", "output": "x^3 - 568/35x^2 + 1559/35x - 234/7 = 0\n(x - 13)(x - 10/7)(x - 9/5) = 0\nx - 13 = 0\nx - 10/7 = 0\nx - 9/5 = 0\nx = 13\nx = 10/7\nx = 9/5"} {"input": "Find x for x^2 + 13/30x - 11/15 = 0", "output": "x^2 + 13/30x - 11/15 = 0\n(x - 2/3)(x - -11/10) = 0\nx - 2/3 = 0 or x - -11/10 = 0\nx = 2/3\nx = -11/10"} {"input": "Find the solution to x^3 - 323/30x^2 + 121/12x + 741/40 = 0", "output": "x^3 - 323/30x^2 + 121/12x + 741/40 = 0\n(x - 19/2)(x - 13/6)(x - -9/10) = 0\nx - 19/2 = 0\nx - 13/6 = 0\nx - -9/10 = 0\nx = 19/2\nx = 13/6\nx = -9/10"} {"input": "Solve quickly: x^2 - 166/45x + 17/5 = 0", "output": "x^2 - 166/45x + 17/5 = 0\n(x - 9/5)(x - 17/9) = 0\nx - 9/5 = 0 or x - 17/9 = 0\nx = 9/5\nx = 17/9"} {"input": "Solve the equation x^3 + 85/28x^2 + 7/4x - 9/14 = 0", "output": "x^3 + 85/28x^2 + 7/4x - 9/14 = 0\n(x - -2)(x - 1/4)(x - -9/7) = 0\nx - -2 = 0\nx - 1/4 = 0\nx - -9/7 = 0\nx = -2\nx = 1/4\nx = -9/7"} {"input": "Solve quickly: x^3 + 8/3x^2 - 5/9x - 28/9 = 0", "output": "x^3 + 8/3x^2 - 5/9x - 28/9 = 0\n(x - 1)(x - -7/3)(x - -4/3) = 0\nx - 1 = 0\nx - -7/3 = 0\nx - -4/3 = 0\nx = 1\nx = -7/3\nx = -4/3"} {"input": "Find x and y such that\n7x + 1y = 53/3\n4x + 3y = 74/3", "output": "7x + 1y = 53/3\n4x + 3y = 74/3\n\nUsing elimination\n4*(7x + 1y = 53/3)\n7*(4x + 3y = 74/3)\n28x + 4y = 212/3\n28x + 21y = 518/3\nSubtract equations\n-17y = -102\ny = -102/-17\ny = 6\n\nSubstitute y\n7x + 1(6) = 53/3\n7x = 35/3\nx = 35/3/7\nx = 5/3"} {"input": "Find x in x^2 + 269/63x + 38/9 = 0", "output": "x^2 + 269/63x + 38/9 = 0\n(x - -14/9)(x - -19/7) = 0\nx - -14/9 = 0 or x - -19/7 = 0\nx = -14/9\nx = -19/7"} {"input": "What value of x satisfies x^3 - 25/12x^2 - 191/36x + 10 = 0", "output": "x^3 - 25/12x^2 - 191/36x + 10 = 0\n(x - -9/4)(x - 8/3)(x - 5/3) = 0\nx - -9/4 = 0\nx - 8/3 = 0\nx - 5/3 = 0\nx = -9/4\nx = 8/3\nx = 5/3"} {"input": "What value of x satisfies 7x - 7/2 = 0", "output": "7x - 7/2 = 0\n7x = 7/2\nx = 7/2 / 7\nx = 1/2"} {"input": "Find x in x^2 - 24/35x - 27/35 = 0", "output": "x^2 - 24/35x - 27/35 = 0\n(x - -3/5)(x - 9/7) = 0\nx - -3/5 = 0 or x - 9/7 = 0\nx = -3/5\nx = 9/7"} {"input": "Solve quickly: x^2 - 4x = 0", "output": "x^2 - 4x = 0\n(x - 0)(x - 4) = 0\nx - 0 = 0 or x - 4 = 0\nx = 0\nx = 4"} {"input": "Solve quickly: 5x - 10 = 0", "output": "5x - 10 = 0\n5x = 10\nx = 10 / 5\nx = 2"} {"input": "Determine x in x^2 + 10x + 9 = 0", "output": "x^2 + 10x + 9 = 0\n(x - -9)(x - -1) = 0\nx - -9 = 0 or x - -1 = 0\nx = -9\nx = -1"} {"input": "Find x for 7x - 91/10 = 0", "output": "7x - 91/10 = 0\n7x = 91/10\nx = 91/10 / 7\nx = 13/10"} {"input": "Find x in x^3 + 44/45x^2 - 359/135x - 76/135 = 0", "output": "x^3 + 44/45x^2 - 359/135x - 76/135 = 0\n(x - -1/5)(x - 4/3)(x - -19/9) = 0\nx - -1/5 = 0\nx - 4/3 = 0\nx - -19/9 = 0\nx = -1/5\nx = 4/3\nx = -19/9"} {"input": "Determine x in x^3 - 94/35x^2 + 481/245x - 8/35 = 0", "output": "x^3 - 94/35x^2 + 481/245x - 8/35 = 0\n(x - 8/7)(x - 1/7)(x - 7/5) = 0\nx - 8/7 = 0\nx - 1/7 = 0\nx - 7/5 = 0\nx = 8/7\nx = 1/7\nx = 7/5"} {"input": "Solve quickly: 6x - 15/4 = 0", "output": "6x - 15/4 = 0\n6x = 15/4\nx = 15/4 / 6\nx = 5/8"} {"input": "Find x in x^2 + 1/8x - 17/4 = 0", "output": "x^2 + 1/8x - 17/4 = 0\n(x - 2)(x - -17/8) = 0\nx - 2 = 0 or x - -17/8 = 0\nx = 2\nx = -17/8"} {"input": "Compute the solution of x^3 - 7/2x^2 - 7x + 20 = 0", "output": "x^3 - 7/2x^2 - 7x + 20 = 0\n(x - 4)(x - -5/2)(x - 2) = 0\nx - 4 = 0\nx - -5/2 = 0\nx - 2 = 0\nx = 4\nx = -5/2\nx = 2"} {"input": "Solve x^3 - 337/40x^2 + 89/4x - 91/5 = 0", "output": "x^3 - 337/40x^2 + 89/4x - 91/5 = 0\n(x - 4)(x - 13/8)(x - 14/5) = 0\nx - 4 = 0\nx - 13/8 = 0\nx - 14/5 = 0\nx = 4\nx = 13/8\nx = 14/5"} {"input": "Find x for x^3 - 59/8x^2 + 7/32x + 539/32 = 0", "output": "x^3 - 59/8x^2 + 7/32x + 539/32 = 0\n(x - 7)(x - 7/4)(x - -11/8) = 0\nx - 7 = 0\nx - 7/4 = 0\nx - -11/8 = 0\nx = 7\nx = 7/4\nx = -11/8"} {"input": "Determine x in 6x + 38/3 = 0", "output": "6x + 38/3 = 0\n6x = -38/3\nx = -38/3 / 6\nx = -19/9"} {"input": "Find x for 8x + 80/3 = 0", "output": "8x + 80/3 = 0\n8x = -80/3\nx = -80/3 / 8\nx = -10/3"} {"input": "Find x for x^2 - 71/10x + 44/5 = 0", "output": "x^2 - 71/10x + 44/5 = 0\n(x - 8/5)(x - 11/2) = 0\nx - 8/5 = 0 or x - 11/2 = 0\nx = 8/5\nx = 11/2"} {"input": "Find x for x^2 - 41/10x + 91/25 = 0", "output": "x^2 - 41/10x + 91/25 = 0\n(x - 14/5)(x - 13/10) = 0\nx - 14/5 = 0 or x - 13/10 = 0\nx = 14/5\nx = 13/10"} {"input": "Find x and y such that\n6x + 8y = 32\n3x + 8y = -22", "output": "6x + 8y = 32\n3x + 8y = -22\n\nUsing elimination\n3*(6x + 8y = 32)\n6*(3x + 8y = -22)\n18x + 24y = 96\n18x + 48y = -132\nSubtract equations\n-24y = 228\ny = 228/-24\ny = -19/2\n\nSubstitute y\n6x + 8(-19/2) = 32\n6x = 108\nx = 108/6\nx = 18"} {"input": "Determine x in x^3 + 22x^2 + 57x = 0", "output": "x^3 + 22x^2 + 57x = 0\n(x - 0)(x - -19)(x - -3) = 0\nx - 0 = 0\nx - -19 = 0\nx - -3 = 0\nx = 0\nx = -19\nx = -3"} {"input": "What value of x satisfies x^3 + 11/2x^2 + 39/16x - 171/32 = 0", "output": "x^3 + 11/2x^2 + 39/16x - 171/32 = 0\n(x - -19/4)(x - 3/4)(x - -3/2) = 0\nx - -19/4 = 0\nx - 3/4 = 0\nx - -3/2 = 0\nx = -19/4\nx = 3/4\nx = -3/2"} {"input": "Solve simultaneously:\n6x + 1y = 209/21\n8x + 7y = 83/9", "output": "6x + 1y = 209/21\n8x + 7y = 83/9\n\nUsing elimination\n8*(6x + 1y = 209/21)\n6*(8x + 7y = 83/9)\n48x + 8y = 1672/21\n48x + 42y = 166/3\nSubtract equations\n-34y = 170/7\ny = 170/7/-34\ny = -5/7\n\nSubstitute y\n6x + 1(-5/7) = 209/21\n6x = 32/3\nx = 32/3/6\nx = 16/9"} {"input": "Find x and y such that\n10x + 8y = 14\n2x + 8y = 142/5", "output": "10x + 8y = 14\n2x + 8y = 142/5\n\nUsing elimination\n2*(10x + 8y = 14)\n10*(2x + 8y = 142/5)\n20x + 16y = 28\n20x + 80y = 284\nSubtract equations\n-64y = -256\ny = -256/-64\ny = 4\n\nSubstitute y\n10x + 8(4) = 14\n10x = -18\nx = -18/10\nx = -9/5"} {"input": "Solve the equations:\n4x + 8y = 28\n4x + 2y = -2", "output": "4x + 8y = 28\n4x + 2y = -2\n\nUsing elimination\n4*(4x + 8y = 28)\n4*(4x + 2y = -2)\n16x + 32y = 112\n16x + 8y = -8\nSubtract equations\n24y = 120\ny = 120/24\ny = 5\n\nSubstitute y\n4x + 8(5) = 28\n4x = -12\nx = -12/4\nx = -3"} {"input": "Find x for x^2 + 9/2x + 7/2 = 0", "output": "x^2 + 9/2x + 7/2 = 0\n(x - -1)(x - -7/2) = 0\nx - -1 = 0 or x - -7/2 = 0\nx = -1\nx = -7/2"} {"input": "Solve the equations:\n2x + 8y = -92/5\n2x + 7y = -323/20", "output": "2x + 8y = -92/5\n2x + 7y = -323/20\n\nUsing elimination\n2*(2x + 8y = -92/5)\n2*(2x + 7y = -323/20)\n4x + 16y = -184/5\n4x + 14y = -323/10\nSubtract equations\n2y = -9/2\ny = -9/2/2\ny = -9/4\n\nSubstitute y\n2x + 8(-9/4) = -92/5\n2x = -2/5\nx = -2/5/2\nx = -1/5"} {"input": "Solve the system:\n3x + 8y = -151/20\n7x + 1y = 213/20", "output": "3x + 8y = -151/20\n7x + 1y = 213/20\n\nUsing elimination\n7*(3x + 8y = -151/20)\n3*(7x + 1y = 213/20)\n21x + 56y = -1057/20\n21x + 3y = 639/20\nSubtract equations\n53y = -424/5\ny = -424/5/53\ny = -8/5\n\nSubstitute y\n3x + 8(-8/5) = -151/20\n3x = 21/4\nx = 21/4/3\nx = 7/4"} {"input": "Find x in x^3 - 236/21x^2 + 60/7x + 800/21 = 0", "output": "x^3 - 236/21x^2 + 60/7x + 800/21 = 0\n(x - 8/3)(x - -10/7)(x - 10) = 0\nx - 8/3 = 0\nx - -10/7 = 0\nx - 10 = 0\nx = 8/3\nx = -10/7\nx = 10"} {"input": "Solve 2x - 20/9 = 0", "output": "2x - 20/9 = 0\n2x = 20/9\nx = 20/9 / 2\nx = 10/9"} {"input": "Determine x in x^2 + 11/4x + 9/8 = 0", "output": "x^2 + 11/4x + 9/8 = 0\n(x - -1/2)(x - -9/4) = 0\nx - -1/2 = 0 or x - -9/4 = 0\nx = -1/2\nx = -9/4"} {"input": "Find the solution to 8x + 160/9 = 0", "output": "8x + 160/9 = 0\n8x = -160/9\nx = -160/9 / 8\nx = -20/9"} {"input": "Find x in x^2 - 5/7x = 0", "output": "x^2 - 5/7x = 0\n(x - 5/7)(x - 0) = 0\nx - 5/7 = 0 or x - 0 = 0\nx = 5/7\nx = 0"} {"input": "Find the solution to x^3 - 14x^2 - 1469/16x - 969/16 = 0", "output": "x^3 - 14x^2 - 1469/16x - 969/16 = 0\n(x - 19)(x - -17/4)(x - -3/4) = 0\nx - 19 = 0\nx - -17/4 = 0\nx - -3/4 = 0\nx = 19\nx = -17/4\nx = -3/4"} {"input": "Solve the system:\n9x + 1y = 13/3\n7x + 9y = 43/3", "output": "9x + 1y = 13/3\n7x + 9y = 43/3\n\nUsing elimination\n7*(9x + 1y = 13/3)\n9*(7x + 9y = 43/3)\n63x + 7y = 91/3\n63x + 81y = 129\nSubtract equations\n-74y = -296/3\ny = -296/3/-74\ny = 4/3\n\nSubstitute y\n9x + 1(4/3) = 13/3\n9x = 3\nx = 3/9\nx = 1/3"} {"input": "Solve the system:\n5x + 8y = 185/6\n7x + 10y = 235/6", "output": "5x + 8y = 185/6\n7x + 10y = 235/6\n\nUsing elimination\n7*(5x + 8y = 185/6)\n5*(7x + 10y = 235/6)\n35x + 56y = 1295/6\n35x + 50y = 1175/6\nSubtract equations\n6y = 20\ny = 20/6\ny = 10/3\n\nSubstitute y\n5x + 8(10/3) = 185/6\n5x = 25/6\nx = 25/6/5\nx = 5/6"} {"input": "Find x for x^2 - 92/35x - 64/35 = 0", "output": "x^2 - 92/35x - 64/35 = 0\n(x - 16/5)(x - -4/7) = 0\nx - 16/5 = 0 or x - -4/7 = 0\nx = 16/5\nx = -4/7"} {"input": "Find x and y such that\n6x + 8y = -224/5\n4x + 7y = -171/5", "output": "6x + 8y = -224/5\n4x + 7y = -171/5\n\nUsing elimination\n4*(6x + 8y = -224/5)\n6*(4x + 7y = -171/5)\n24x + 32y = -896/5\n24x + 42y = -1026/5\nSubtract equations\n-10y = 26\ny = 26/-10\ny = -13/5\n\nSubstitute y\n6x + 8(-13/5) = -224/5\n6x = -24\nx = -24/6\nx = -4"} {"input": "Compute the solution of x^3 - 139/42x^2 - 1811/42x - 510/7 = 0", "output": "x^3 - 139/42x^2 - 1811/42x - 510/7 = 0\n(x - 9)(x - -17/6)(x - -20/7) = 0\nx - 9 = 0\nx - -17/6 = 0\nx - -20/7 = 0\nx = 9\nx = -17/6\nx = -20/7"} {"input": "Determine x in x^2 - 128/7x + 36/7 = 0", "output": "x^2 - 128/7x + 36/7 = 0\n(x - 2/7)(x - 18) = 0\nx - 2/7 = 0 or x - 18 = 0\nx = 2/7\nx = 18"} {"input": "Find x and y such that\n7x + 4y = 148/5\n4x + 1y = 46/5", "output": "7x + 4y = 148/5\n4x + 1y = 46/5\n\nUsing elimination\n4*(7x + 4y = 148/5)\n7*(4x + 1y = 46/5)\n28x + 16y = 592/5\n28x + 7y = 322/5\nSubtract equations\n9y = 54\ny = 54/9\ny = 6\n\nSubstitute y\n7x + 4(6) = 148/5\n7x = 28/5\nx = 28/5/7\nx = 4/5"} {"input": "Solve simultaneously:\n8x + 8y = -52/3\n2x + 3y = -4", "output": "8x + 8y = -52/3\n2x + 3y = -4\n\nUsing elimination\n2*(8x + 8y = -52/3)\n8*(2x + 3y = -4)\n16x + 16y = -104/3\n16x + 24y = -32\nSubtract equations\n-8y = -8/3\ny = -8/3/-8\ny = 1/3\n\nSubstitute y\n8x + 8(1/3) = -52/3\n8x = -20\nx = -20/8\nx = -5/2"} {"input": "Find the solution to 9x + 54 = 0", "output": "9x + 54 = 0\n9x = -54\nx = -54 / 9\nx = -6"} {"input": "Determine x in 3x + 9/5 = 0", "output": "3x + 9/5 = 0\n3x = -9/5\nx = -9/5 / 3\nx = -3/5"} {"input": "Solve the equations:\n2x + 9y = 49/2\n5x + 5y = 35/4", "output": "2x + 9y = 49/2\n5x + 5y = 35/4\n\nUsing elimination\n5*(2x + 9y = 49/2)\n2*(5x + 5y = 35/4)\n10x + 45y = 245/2\n10x + 10y = 35/2\nSubtract equations\n35y = 105\ny = 105/35\ny = 3\n\nSubstitute y\n2x + 9(3) = 49/2\n2x = -5/2\nx = -5/2/2\nx = -5/4"} {"input": "Solve quickly: 7x + 49/2 = 0", "output": "7x + 49/2 = 0\n7x = -49/2\nx = -49/2 / 7\nx = -7/2"} {"input": "Find the solution to x^2 - 109/36x + 20/9 = 0", "output": "x^2 - 109/36x + 20/9 = 0\n(x - 5/4)(x - 16/9) = 0\nx - 5/4 = 0 or x - 16/9 = 0\nx = 5/4\nx = 16/9"} {"input": "Find x for 9x - 90/7 = 0", "output": "9x - 90/7 = 0\n9x = 90/7\nx = 90/7 / 9\nx = 10/7"} {"input": "Solve the system:\n3x + 3y = -621/35\n8x + 10y = -1846/35", "output": "3x + 3y = -621/35\n8x + 10y = -1846/35\n\nUsing elimination\n8*(3x + 3y = -621/35)\n3*(8x + 10y = -1846/35)\n24x + 24y = -4968/35\n24x + 30y = -5538/35\nSubtract equations\n-6y = 114/7\ny = 114/7/-6\ny = -19/7\n\nSubstitute y\n3x + 3(-19/7) = -621/35\n3x = -48/5\nx = -48/5/3\nx = -16/5"} {"input": "Find x and y such that\n4x + 6y = 0\n5x + 9y = 3/7", "output": "4x + 6y = 0\n5x + 9y = 3/7\n\nUsing elimination\n5*(4x + 6y = 0)\n4*(5x + 9y = 3/7)\n20x + 30y = 0\n20x + 36y = 12/7\nSubtract equations\n-6y = -12/7\ny = -12/7/-6\ny = 2/7\n\nSubstitute y\n4x + 6(2/7) = 0\n4x = -12/7\nx = -12/7/4\nx = -3/7"} {"input": "Find the solution to x^3 - 144/35x^2 + 629/175x + 156/175 = 0", "output": "x^3 - 144/35x^2 + 629/175x + 156/175 = 0\n(x - 13/5)(x - 12/7)(x - -1/5) = 0\nx - 13/5 = 0\nx - 12/7 = 0\nx - -1/5 = 0\nx = 13/5\nx = 12/7\nx = -1/5"} {"input": "Solve simultaneously:\n8x + 6y = -28\n3x + 9y = -87/4", "output": "8x + 6y = -28\n3x + 9y = -87/4\n\nUsing elimination\n3*(8x + 6y = -28)\n8*(3x + 9y = -87/4)\n24x + 18y = -84\n24x + 72y = -174\nSubtract equations\n-54y = 90\ny = 90/-54\ny = -5/3\n\nSubstitute y\n8x + 6(-5/3) = -28\n8x = -18\nx = -18/8\nx = -9/4"} {"input": "Find x and y such that\n2x + 5y = 118/3\n5x + 4y = 125/3", "output": "2x + 5y = 118/3\n5x + 4y = 125/3\n\nUsing elimination\n5*(2x + 5y = 118/3)\n2*(5x + 4y = 125/3)\n10x + 25y = 590/3\n10x + 8y = 250/3\nSubtract equations\n17y = 340/3\ny = 340/3/17\ny = 20/3\n\nSubstitute y\n2x + 5(20/3) = 118/3\n2x = 6\nx = 6/2\nx = 3"} {"input": "Find x for x^3 + 124/7x^2 + 73/7x - 204/7 = 0", "output": "x^3 + 124/7x^2 + 73/7x - 204/7 = 0\n(x - -17)(x - 1)(x - -12/7) = 0\nx - -17 = 0\nx - 1 = 0\nx - -12/7 = 0\nx = -17\nx = 1\nx = -12/7"} {"input": "Determine x in x^2 - 31/6x - 133/18 = 0", "output": "x^2 - 31/6x - 133/18 = 0\n(x - 19/3)(x - -7/6) = 0\nx - 19/3 = 0 or x - -7/6 = 0\nx = 19/3\nx = -7/6"} {"input": "Solve 6x - 20 = 0", "output": "6x - 20 = 0\n6x = 20\nx = 20 / 6\nx = 10/3"} {"input": "Determine x in x^3 - 12/5x^2 + 3/4x + 1/10 = 0", "output": "x^3 - 12/5x^2 + 3/4x + 1/10 = 0\n(x - 1/2)(x - 2)(x - -1/10) = 0\nx - 1/2 = 0\nx - 2 = 0\nx - -1/10 = 0\nx = 1/2\nx = 2\nx = -1/10"} {"input": "Determine x in x^2 + 7/4x - 15/2 = 0", "output": "x^2 + 7/4x - 15/2 = 0\n(x - -15/4)(x - 2) = 0\nx - -15/4 = 0 or x - 2 = 0\nx = -15/4\nx = 2"} {"input": "Solve the equations:\n4x + 2y = -344/21\n5x + 6y = -274/7", "output": "4x + 2y = -344/21\n5x + 6y = -274/7\n\nUsing elimination\n5*(4x + 2y = -344/21)\n4*(5x + 6y = -274/7)\n20x + 10y = -1720/21\n20x + 24y = -1096/7\nSubtract equations\n-14y = 224/3\ny = 224/3/-14\ny = -16/3\n\nSubstitute y\n4x + 2(-16/3) = -344/21\n4x = -40/7\nx = -40/7/4\nx = -10/7"} {"input": "What value of x satisfies 7x + 35/4 = 0", "output": "7x + 35/4 = 0\n7x = -35/4\nx = -35/4 / 7\nx = -5/4"} {"input": "Compute the solution of x^3 - 217/40x^2 - 1239/40x - 54/5 = 0", "output": "x^3 - 217/40x^2 - 1239/40x - 54/5 = 0\n(x - -3/8)(x - 9)(x - -16/5) = 0\nx - -3/8 = 0\nx - 9 = 0\nx - -16/5 = 0\nx = -3/8\nx = 9\nx = -16/5"} {"input": "Find x for x^2 - 14/3x - 32/9 = 0", "output": "x^2 - 14/3x - 32/9 = 0\n(x - 16/3)(x - -2/3) = 0\nx - 16/3 = 0 or x - -2/3 = 0\nx = 16/3\nx = -2/3"} {"input": "Find x for 3x - 3/2 = 0", "output": "3x - 3/2 = 0\n3x = 3/2\nx = 3/2 / 3\nx = 1/2"} {"input": "Find the solution to x^3 - 64/3x^2 + 73/3x + 140/3 = 0", "output": "x^3 - 64/3x^2 + 73/3x + 140/3 = 0\n(x - 20)(x - 7/3)(x - -1) = 0\nx - 20 = 0\nx - 7/3 = 0\nx - -1 = 0\nx = 20\nx = 7/3\nx = -1"} {"input": "Solve the equation x^3 - 349/40x^2 - 243/80x + 81/16 = 0", "output": "x^3 - 349/40x^2 - 243/80x + 81/16 = 0\n(x - 9)(x - -9/10)(x - 5/8) = 0\nx - 9 = 0\nx - -9/10 = 0\nx - 5/8 = 0\nx = 9\nx = -9/10\nx = 5/8"} {"input": "Solve simultaneously:\n9x + 7y = -173/4\n1x + 4y = -45/4", "output": "9x + 7y = -173/4\n1x + 4y = -45/4\n\nUsing elimination\n1*(9x + 7y = -173/4)\n9*(1x + 4y = -45/4)\n9x + 7y = -173/4\n9x + 36y = -405/4\nSubtract equations\n-29y = 58\ny = 58/-29\ny = -2\n\nSubstitute y\n9x + 7(-2) = -173/4\n9x = -117/4\nx = -117/4/9\nx = -13/4"} {"input": "What value of x satisfies 4x + 13/2 = 0", "output": "4x + 13/2 = 0\n4x = -13/2\nx = -13/2 / 4\nx = -13/8"} {"input": "Solve the system:\n8x + 3y = 150\n7x + 6y = 129", "output": "8x + 3y = 150\n7x + 6y = 129\n\nUsing elimination\n7*(8x + 3y = 150)\n8*(7x + 6y = 129)\n56x + 21y = 1050\n56x + 48y = 1032\nSubtract equations\n-27y = 18\ny = 18/-27\ny = -2/3\n\nSubstitute y\n8x + 3(-2/3) = 150\n8x = 152\nx = 152/8\nx = 19"} {"input": "Find x for x^2 + 129/35x + 34/35 = 0", "output": "x^2 + 129/35x + 34/35 = 0\n(x - -2/7)(x - -17/5) = 0\nx - -2/7 = 0 or x - -17/5 = 0\nx = -2/7\nx = -17/5"} {"input": "Solve the equations:\n3x + 2y = -109/18\n3x + 1y = -77/18", "output": "3x + 2y = -109/18\n3x + 1y = -77/18\n\nUsing elimination\n3*(3x + 2y = -109/18)\n3*(3x + 1y = -77/18)\n9x + 6y = -109/6\n9x + 3y = -77/6\nSubtract equations\n3y = -16/3\ny = -16/3/3\ny = -16/9\n\nSubstitute y\n3x + 2(-16/9) = -109/18\n3x = -5/2\nx = -5/2/3\nx = -5/6"} {"input": "Solve the equations:\n8x + 8y = -108/5\n10x + 6y = -23", "output": "8x + 8y = -108/5\n10x + 6y = -23\n\nUsing elimination\n10*(8x + 8y = -108/5)\n8*(10x + 6y = -23)\n80x + 80y = -216\n80x + 48y = -184\nSubtract equations\n32y = -32\ny = -32/32\ny = -1\n\nSubstitute y\n8x + 8(-1) = -108/5\n8x = -68/5\nx = -68/5/8\nx = -17/10"} {"input": "Solve the equations:\n9x + 5y = -53\n1x + 10y = -59/2", "output": "9x + 5y = -53\n1x + 10y = -59/2\n\nUsing elimination\n1*(9x + 5y = -53)\n9*(1x + 10y = -59/2)\n9x + 5y = -53\n9x + 90y = -531/2\nSubtract equations\n-85y = 425/2\ny = 425/2/-85\ny = -5/2\n\nSubstitute y\n9x + 5(-5/2) = -53\n9x = -81/2\nx = -81/2/9\nx = -9/2"} {"input": "Solve the equation x^2 + 19/18x - 65/18 = 0", "output": "x^2 + 19/18x - 65/18 = 0\n(x - 13/9)(x - -5/2) = 0\nx - 13/9 = 0 or x - -5/2 = 0\nx = 13/9\nx = -5/2"} {"input": "Solve the equations:\n6x + 5y = 125/8\n10x + 5y = 205/8", "output": "6x + 5y = 125/8\n10x + 5y = 205/8\n\nUsing elimination\n10*(6x + 5y = 125/8)\n6*(10x + 5y = 205/8)\n60x + 50y = 625/4\n60x + 30y = 615/4\nSubtract equations\n20y = 5/2\ny = 5/2/20\ny = 1/8\n\nSubstitute y\n6x + 5(1/8) = 125/8\n6x = 15\nx = 15/6\nx = 5/2"} {"input": "Compute the solution of x^2 + 112/9x + 16/3 = 0", "output": "x^2 + 112/9x + 16/3 = 0\n(x - -4/9)(x - -12) = 0\nx - -4/9 = 0 or x - -12 = 0\nx = -4/9\nx = -12"} {"input": "Compute the solution of x^3 + 2x^2 - 1x - 2 = 0", "output": "x^3 + 2x^2 - 1x - 2 = 0\n(x - 1)(x - -1)(x - -2) = 0\nx - 1 = 0\nx - -1 = 0\nx - -2 = 0\nx = 1\nx = -1\nx = -2"} {"input": "Find x in 1x - 5/3 = 0", "output": "1x - 5/3 = 0\n1x = 5/3\nx = 5/3 / 1\nx = 5/3"} {"input": "Determine x in x^2 - 59/42x + 10/21 = 0", "output": "x^2 - 59/42x + 10/21 = 0\n(x - 5/6)(x - 4/7) = 0\nx - 5/6 = 0 or x - 4/7 = 0\nx = 5/6\nx = 4/7"} {"input": "Determine x in x^2 + 17/14x + 5/14 = 0", "output": "x^2 + 17/14x + 5/14 = 0\n(x - -1/2)(x - -5/7) = 0\nx - -1/2 = 0 or x - -5/7 = 0\nx = -1/2\nx = -5/7"} {"input": "Determine x in 6x + 27/5 = 0", "output": "6x + 27/5 = 0\n6x = -27/5\nx = -27/5 / 6\nx = -9/10"} {"input": "What value of x satisfies 10x - 5 = 0", "output": "10x - 5 = 0\n10x = 5\nx = 5 / 10\nx = 1/2"} {"input": "Find x in 9x - 30 = 0", "output": "9x - 30 = 0\n9x = 30\nx = 30 / 9\nx = 10/3"} {"input": "Find x in x^2 - 23/10x + 6/5 = 0", "output": "x^2 - 23/10x + 6/5 = 0\n(x - 4/5)(x - 3/2) = 0\nx - 4/5 = 0 or x - 3/2 = 0\nx = 4/5\nx = 3/2"} {"input": "Find x and y such that\n5x + 5y = -40/3\n3x + 2y = -12", "output": "5x + 5y = -40/3\n3x + 2y = -12\n\nUsing elimination\n3*(5x + 5y = -40/3)\n5*(3x + 2y = -12)\n15x + 15y = -40\n15x + 10y = -60\nSubtract equations\n5y = 20\ny = 20/5\ny = 4\n\nSubstitute y\n5x + 5(4) = -40/3\n5x = -100/3\nx = -100/3/5\nx = -20/3"} {"input": "Determine x in 5x - 6 = 0", "output": "5x - 6 = 0\n5x = 6\nx = 6 / 5\nx = 6/5"} {"input": "Determine x in x^2 + 20x + 36 = 0", "output": "x^2 + 20x + 36 = 0\n(x - -2)(x - -18) = 0\nx - -2 = 0 or x - -18 = 0\nx = -2\nx = -18"} {"input": "Determine x in x^2 + 2x = 0", "output": "x^2 + 2x = 0\n(x - -2)(x - 0) = 0\nx - -2 = 0 or x - 0 = 0\nx = -2\nx = 0"} {"input": "Solve simultaneously:\n4x + 5y = -95/18\n3x + 1y = -175/72", "output": "4x + 5y = -95/18\n3x + 1y = -175/72\n\nUsing elimination\n3*(4x + 5y = -95/18)\n4*(3x + 1y = -175/72)\n12x + 15y = -95/6\n12x + 4y = -175/18\nSubtract equations\n11y = -55/9\ny = -55/9/11\ny = -5/9\n\nSubstitute y\n4x + 5(-5/9) = -95/18\n4x = -5/2\nx = -5/2/4\nx = -5/8"} {"input": "What value of x satisfies 1x - 1/5 = 0", "output": "1x - 1/5 = 0\n1x = 1/5\nx = 1/5 / 1\nx = 1/5"} {"input": "What value of x satisfies 7x - 12 = 0", "output": "7x - 12 = 0\n7x = 12\nx = 12 / 7\nx = 12/7"} {"input": "Solve x^3 + 16/3x^2 - 251x + 494/3 = 0", "output": "x^3 + 16/3x^2 - 251x + 494/3 = 0\n(x - 2/3)(x - -19)(x - 13) = 0\nx - 2/3 = 0\nx - -19 = 0\nx - 13 = 0\nx = 2/3\nx = -19\nx = 13"} {"input": "Solve the system:\n8x + 5y = -231/2\n9x + 1y = -283/2", "output": "8x + 5y = -231/2\n9x + 1y = -283/2\n\nUsing elimination\n9*(8x + 5y = -231/2)\n8*(9x + 1y = -283/2)\n72x + 45y = -2079/2\n72x + 8y = -1132\nSubtract equations\n37y = 185/2\ny = 185/2/37\ny = 5/2\n\nSubstitute y\n8x + 5(5/2) = -231/2\n8x = -128\nx = -128/8\nx = -16"} {"input": "Find the solution to x^3 + 59/14x^2 + 342/175x - 162/175 = 0", "output": "x^3 + 59/14x^2 + 342/175x - 162/175 = 0\n(x - -18/5)(x - 2/7)(x - -9/10) = 0\nx - -18/5 = 0\nx - 2/7 = 0\nx - -9/10 = 0\nx = -18/5\nx = 2/7\nx = -9/10"} {"input": "Find x for x^3 - 23/10x^2 + 1/5x + 4/5 = 0", "output": "x^3 - 23/10x^2 + 1/5x + 4/5 = 0\n(x - -1/2)(x - 2)(x - 4/5) = 0\nx - -1/2 = 0\nx - 2 = 0\nx - 4/5 = 0\nx = -1/2\nx = 2\nx = 4/5"} {"input": "What value of x satisfies x^3 - 33/14x^2 - 151/7x + 585/14 = 0", "output": "x^3 - 33/14x^2 - 151/7x + 585/14 = 0\n(x - 5)(x - -9/2)(x - 13/7) = 0\nx - 5 = 0\nx - -9/2 = 0\nx - 13/7 = 0\nx = 5\nx = -9/2\nx = 13/7"} {"input": "Compute the solution of 5x - 5 = 0", "output": "5x - 5 = 0\n5x = 5\nx = 5 / 5\nx = 1"} {"input": "Determine x in x^2 + 2x - 3 = 0", "output": "x^2 + 2x - 3 = 0\n(x - 1)(x - -3) = 0\nx - 1 = 0 or x - -3 = 0\nx = 1\nx = -3"} {"input": "What value of x satisfies x^3 + 4/7x^2 - 36/7x = 0", "output": "x^3 + 4/7x^2 - 36/7x = 0\n(x - 0)(x - 2)(x - -18/7) = 0\nx - 0 = 0\nx - 2 = 0\nx - -18/7 = 0\nx = 0\nx = 2\nx = -18/7"} {"input": "Find the solution to 8x - 12/5 = 0", "output": "8x - 12/5 = 0\n8x = 12/5\nx = 12/5 / 8\nx = 3/10"} {"input": "What value of x satisfies x^3 + 17/18x^2 - 178/27x + 38/27 = 0", "output": "x^3 + 17/18x^2 - 178/27x + 38/27 = 0\n(x - 2/9)(x - 2)(x - -19/6) = 0\nx - 2/9 = 0\nx - 2 = 0\nx - -19/6 = 0\nx = 2/9\nx = 2\nx = -19/6"} {"input": "Solve the system:\n10x + 7y = 26\n8x + 10y = 216/7", "output": "10x + 7y = 26\n8x + 10y = 216/7\n\nUsing elimination\n8*(10x + 7y = 26)\n10*(8x + 10y = 216/7)\n80x + 56y = 208\n80x + 100y = 2160/7\nSubtract equations\n-44y = -704/7\ny = -704/7/-44\ny = 16/7\n\nSubstitute y\n10x + 7(16/7) = 26\n10x = 10\nx = 10/10\nx = 1"} {"input": "Solve the system:\n1x + 2y = -63/8\n3x + 9y = -291/8", "output": "1x + 2y = -63/8\n3x + 9y = -291/8\n\nUsing elimination\n3*(1x + 2y = -63/8)\n1*(3x + 9y = -291/8)\n3x + 6y = -189/8\n3x + 9y = -291/8\nSubtract equations\n-3y = 51/4\ny = 51/4/-3\ny = -17/4\n\nSubstitute y\n1x + 2(-17/4) = -63/8\n1x = 5/8\nx = 5/8/1\nx = 5/8"} {"input": "Solve the equations:\n2x + 1y = -23/12\n8x + 2y = -1/3", "output": "2x + 1y = -23/12\n8x + 2y = -1/3\n\nUsing elimination\n8*(2x + 1y = -23/12)\n2*(8x + 2y = -1/3)\n16x + 8y = -46/3\n16x + 4y = -2/3\nSubtract equations\n4y = -44/3\ny = -44/3/4\ny = -11/3\n\nSubstitute y\n2x + 1(-11/3) = -23/12\n2x = 7/4\nx = 7/4/2\nx = 7/8"} {"input": "Solve the system:\n10x + 4y = -343/15\n4x + 8y = 74/15", "output": "10x + 4y = -343/15\n4x + 8y = 74/15\n\nUsing elimination\n4*(10x + 4y = -343/15)\n10*(4x + 8y = 74/15)\n40x + 16y = -1372/15\n40x + 80y = 148/3\nSubtract equations\n-64y = -704/5\ny = -704/5/-64\ny = 11/5\n\nSubstitute y\n10x + 4(11/5) = -343/15\n10x = -95/3\nx = -95/3/10\nx = -19/6"} {"input": "Solve x^3 + 11/4x^2 - 123/2x - 189/4 = 0", "output": "x^3 + 11/4x^2 - 123/2x - 189/4 = 0\n(x - -9)(x - 7)(x - -3/4) = 0\nx - -9 = 0\nx - 7 = 0\nx - -3/4 = 0\nx = -9\nx = 7\nx = -3/4"} {"input": "Solve x^2 + 80/9x - 1 = 0", "output": "x^2 + 80/9x - 1 = 0\n(x - -9)(x - 1/9) = 0\nx - -9 = 0 or x - 1/9 = 0\nx = -9\nx = 1/9"} {"input": "Find the solution to x^2 + 16/9x - 4/9 = 0", "output": "x^2 + 16/9x - 4/9 = 0\n(x - 2/9)(x - -2) = 0\nx - 2/9 = 0 or x - -2 = 0\nx = 2/9\nx = -2"} {"input": "Solve quickly: 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve the equation 1x - 11/5 = 0", "output": "1x - 11/5 = 0\n1x = 11/5\nx = 11/5 / 1\nx = 11/5"} {"input": "Solve the equation x^2 + 1/24x - 11/6 = 0", "output": "x^2 + 1/24x - 11/6 = 0\n(x - 4/3)(x - -11/8) = 0\nx - 4/3 = 0 or x - -11/8 = 0\nx = 4/3\nx = -11/8"} {"input": "Solve the equations:\n4x + 5y = -53/12\n10x + 9y = -185/12", "output": "4x + 5y = -53/12\n10x + 9y = -185/12\n\nUsing elimination\n10*(4x + 5y = -53/12)\n4*(10x + 9y = -185/12)\n40x + 50y = -265/6\n40x + 36y = -185/3\nSubtract equations\n14y = 35/2\ny = 35/2/14\ny = 5/4\n\nSubstitute y\n4x + 5(5/4) = -53/12\n4x = -32/3\nx = -32/3/4\nx = -8/3"} {"input": "Find x in x^3 + 189/10x^2 + 321/10x - 17/5 = 0", "output": "x^3 + 189/10x^2 + 321/10x - 17/5 = 0\n(x - -2)(x - -17)(x - 1/10) = 0\nx - -2 = 0\nx - -17 = 0\nx - 1/10 = 0\nx = -2\nx = -17\nx = 1/10"} {"input": "Solve 4x + 24/5 = 0", "output": "4x + 24/5 = 0\n4x = -24/5\nx = -24/5 / 4\nx = -6/5"} {"input": "Solve the equations:\n9x + 5y = -265/6\n10x + 5y = -305/6", "output": "9x + 5y = -265/6\n10x + 5y = -305/6\n\nUsing elimination\n10*(9x + 5y = -265/6)\n9*(10x + 5y = -305/6)\n90x + 50y = -1325/3\n90x + 45y = -915/2\nSubtract equations\n5y = 95/6\ny = 95/6/5\ny = 19/6\n\nSubstitute y\n9x + 5(19/6) = -265/6\n9x = -60\nx = -60/9\nx = -20/3"} {"input": "Solve the system:\n9x + 4y = 353/8\n8x + 5y = 58", "output": "9x + 4y = 353/8\n8x + 5y = 58\n\nUsing elimination\n8*(9x + 4y = 353/8)\n9*(8x + 5y = 58)\n72x + 32y = 353\n72x + 45y = 522\nSubtract equations\n-13y = -169\ny = -169/-13\ny = 13\n\nSubstitute y\n9x + 4(13) = 353/8\n9x = -63/8\nx = -63/8/9\nx = -7/8"} {"input": "Find x in x^3 - 41/24x^2 + 59/96x - 5/96 = 0", "output": "x^3 - 41/24x^2 + 59/96x - 5/96 = 0\n(x - 5/4)(x - 1/3)(x - 1/8) = 0\nx - 5/4 = 0\nx - 1/3 = 0\nx - 1/8 = 0\nx = 5/4\nx = 1/3\nx = 1/8"} {"input": "Solve simultaneously:\n9x + 1y = -221/4\n10x + 5y = -515/12", "output": "9x + 1y = -221/4\n10x + 5y = -515/12\n\nUsing elimination\n10*(9x + 1y = -221/4)\n9*(10x + 5y = -515/12)\n90x + 10y = -1105/2\n90x + 45y = -1545/4\nSubtract equations\n-35y = -665/4\ny = -665/4/-35\ny = 19/4\n\nSubstitute y\n9x + 1(19/4) = -221/4\n9x = -60\nx = -60/9\nx = -20/3"} {"input": "Solve x^2 - 1/8x - 17/4 = 0", "output": "x^2 - 1/8x - 17/4 = 0\n(x - 17/8)(x - -2) = 0\nx - 17/8 = 0 or x - -2 = 0\nx = 17/8\nx = -2"} {"input": "What value of x satisfies x^2 + 104/21x + 128/21 = 0", "output": "x^2 + 104/21x + 128/21 = 0\n(x - -16/7)(x - -8/3) = 0\nx - -16/7 = 0 or x - -8/3 = 0\nx = -16/7\nx = -8/3"} {"input": "Solve the equations:\n6x + 1y = 8/7\n7x + 8y = -26", "output": "6x + 1y = 8/7\n7x + 8y = -26\n\nUsing elimination\n7*(6x + 1y = 8/7)\n6*(7x + 8y = -26)\n42x + 7y = 8\n42x + 48y = -156\nSubtract equations\n-41y = 164\ny = 164/-41\ny = -4\n\nSubstitute y\n6x + 1(-4) = 8/7\n6x = 36/7\nx = 36/7/6\nx = 6/7"} {"input": "What value of x satisfies x^3 + 33/10x^2 + 72/25x + 32/125 = 0", "output": "x^3 + 33/10x^2 + 72/25x + 32/125 = 0\n(x - -8/5)(x - -8/5)(x - -1/10) = 0\nx - -8/5 = 0\nx - -8/5 = 0\nx - -1/10 = 0\nx = -8/5\nx = -8/5\nx = -1/10"} {"input": "Compute the solution of x^2 - 23/6x + 5/3 = 0", "output": "x^2 - 23/6x + 5/3 = 0\n(x - 10/3)(x - 1/2) = 0\nx - 10/3 = 0 or x - 1/2 = 0\nx = 10/3\nx = 1/2"} {"input": "Solve the system:\n8x + 5y = 131/3\n7x + 9y = 184/3", "output": "8x + 5y = 131/3\n7x + 9y = 184/3\n\nUsing elimination\n7*(8x + 5y = 131/3)\n8*(7x + 9y = 184/3)\n56x + 35y = 917/3\n56x + 72y = 1472/3\nSubtract equations\n-37y = -185\ny = -185/-37\ny = 5\n\nSubstitute y\n8x + 5(5) = 131/3\n8x = 56/3\nx = 56/3/8\nx = 7/3"} {"input": "Determine x in 2x + 4 = 0", "output": "2x + 4 = 0\n2x = -4\nx = -4 / 2\nx = -2"} {"input": "Solve the equation 4x - 24/7 = 0", "output": "4x - 24/7 = 0\n4x = 24/7\nx = 24/7 / 4\nx = 6/7"} {"input": "Solve simultaneously:\n4x + 10y = 227/7\n6x + 5y = 331/14", "output": "4x + 10y = 227/7\n6x + 5y = 331/14\n\nUsing elimination\n6*(4x + 10y = 227/7)\n4*(6x + 5y = 331/14)\n24x + 60y = 1362/7\n24x + 20y = 662/7\nSubtract equations\n40y = 100\ny = 100/40\ny = 5/2\n\nSubstitute y\n4x + 10(5/2) = 227/7\n4x = 52/7\nx = 52/7/4\nx = 13/7"} {"input": "Solve the equation x^3 + 88/21x^2 + 4/7x - 160/21 = 0", "output": "x^3 + 88/21x^2 + 4/7x - 160/21 = 0\n(x - -2)(x - 8/7)(x - -10/3) = 0\nx - -2 = 0\nx - 8/7 = 0\nx - -10/3 = 0\nx = -2\nx = 8/7\nx = -10/3"} {"input": "Compute the solution of x^2 - 4/3x - 28 = 0", "output": "x^2 - 4/3x - 28 = 0\n(x - 6)(x - -14/3) = 0\nx - 6 = 0 or x - -14/3 = 0\nx = 6\nx = -14/3"} {"input": "Find the solution to x^2 + 62/21x + 32/21 = 0", "output": "x^2 + 62/21x + 32/21 = 0\n(x - -2/3)(x - -16/7) = 0\nx - -2/3 = 0 or x - -16/7 = 0\nx = -2/3\nx = -16/7"} {"input": "Compute the solution of 2x + 15 = 0", "output": "2x + 15 = 0\n2x = -15\nx = -15 / 2\nx = -15/2"} {"input": "Find x and y such that\n8x + 7y = -187/12\n1x + 10y = -217/6", "output": "8x + 7y = -187/12\n1x + 10y = -217/6\n\nUsing elimination\n1*(8x + 7y = -187/12)\n8*(1x + 10y = -217/6)\n8x + 7y = -187/12\n8x + 80y = -868/3\nSubtract equations\n-73y = 1095/4\ny = 1095/4/-73\ny = -15/4\n\nSubstitute y\n8x + 7(-15/4) = -187/12\n8x = 32/3\nx = 32/3/8\nx = 4/3"} {"input": "Find the solution to x^3 - 26/35x^2 - 53/35x + 8/35 = 0", "output": "x^3 - 26/35x^2 - 53/35x + 8/35 = 0\n(x - -1)(x - 8/5)(x - 1/7) = 0\nx - -1 = 0\nx - 8/5 = 0\nx - 1/7 = 0\nx = -1\nx = 8/5\nx = 1/7"} {"input": "What value of x satisfies 7x + 14 = 0", "output": "7x + 14 = 0\n7x = -14\nx = -14 / 7\nx = -2"} {"input": "Solve x^2 - 41/9x - 26/3 = 0", "output": "x^2 - 41/9x - 26/3 = 0\n(x - -13/9)(x - 6) = 0\nx - -13/9 = 0 or x - 6 = 0\nx = -13/9\nx = 6"} {"input": "Solve quickly: x^3 + 31/6x^2 - 62/3x + 16 = 0", "output": "x^3 + 31/6x^2 - 62/3x + 16 = 0\n(x - 4/3)(x - -8)(x - 3/2) = 0\nx - 4/3 = 0\nx - -8 = 0\nx - 3/2 = 0\nx = 4/3\nx = -8\nx = 3/2"} {"input": "Solve the system:\n7x + 10y = -89\n9x + 5y = -194/3", "output": "7x + 10y = -89\n9x + 5y = -194/3\n\nUsing elimination\n9*(7x + 10y = -89)\n7*(9x + 5y = -194/3)\n63x + 90y = -801\n63x + 35y = -1358/3\nSubtract equations\n55y = -1045/3\ny = -1045/3/55\ny = -19/3\n\nSubstitute y\n7x + 10(-19/3) = -89\n7x = -77/3\nx = -77/3/7\nx = -11/3"} {"input": "Compute the solution of x^2 - 1/3x - 14/3 = 0", "output": "x^2 - 1/3x - 14/3 = 0\n(x - 7/3)(x - -2) = 0\nx - 7/3 = 0 or x - -2 = 0\nx = 7/3\nx = -2"} {"input": "Solve quickly: x^2 - 19/4x + 45/8 = 0", "output": "x^2 - 19/4x + 45/8 = 0\n(x - 5/2)(x - 9/4) = 0\nx - 5/2 = 0 or x - 9/4 = 0\nx = 5/2\nx = 9/4"} {"input": "Find x in 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x and y such that\n6x + 9y = -144/5\n7x + 5y = -43/2", "output": "6x + 9y = -144/5\n7x + 5y = -43/2\n\nUsing elimination\n7*(6x + 9y = -144/5)\n6*(7x + 5y = -43/2)\n42x + 63y = -1008/5\n42x + 30y = -129\nSubtract equations\n33y = -363/5\ny = -363/5/33\ny = -11/5\n\nSubstitute y\n6x + 9(-11/5) = -144/5\n6x = -9\nx = -9/6\nx = -3/2"} {"input": "Compute the solution of 3x + 45/2 = 0", "output": "3x + 45/2 = 0\n3x = -45/2\nx = -45/2 / 3\nx = -15/2"} {"input": "Determine x in x^3 - 49/20x^2 - 219/40x + 459/40 = 0", "output": "x^3 - 49/20x^2 - 219/40x + 459/40 = 0\n(x - 17/10)(x - -9/4)(x - 3) = 0\nx - 17/10 = 0\nx - -9/4 = 0\nx - 3 = 0\nx = 17/10\nx = -9/4\nx = 3"} {"input": "Solve the equations:\n10x + 2y = 934/15\n1x + 5y = 59/3", "output": "10x + 2y = 934/15\n1x + 5y = 59/3\n\nUsing elimination\n1*(10x + 2y = 934/15)\n10*(1x + 5y = 59/3)\n10x + 2y = 934/15\n10x + 50y = 590/3\nSubtract equations\n-48y = -672/5\ny = -672/5/-48\ny = 14/5\n\nSubstitute y\n10x + 2(14/5) = 934/15\n10x = 170/3\nx = 170/3/10\nx = 17/3"} {"input": "Determine x in x^2 + 16/5x + 11/5 = 0", "output": "x^2 + 16/5x + 11/5 = 0\n(x - -11/5)(x - -1) = 0\nx - -11/5 = 0 or x - -1 = 0\nx = -11/5\nx = -1"} {"input": "What value of x satisfies x^2 + 44/9x - 119/27 = 0", "output": "x^2 + 44/9x - 119/27 = 0\n(x - 7/9)(x - -17/3) = 0\nx - 7/9 = 0 or x - -17/3 = 0\nx = 7/9\nx = -17/3"} {"input": "Determine x in x^2 - 211/24x + 85/6 = 0", "output": "x^2 - 211/24x + 85/6 = 0\n(x - 20/3)(x - 17/8) = 0\nx - 20/3 = 0 or x - 17/8 = 0\nx = 20/3\nx = 17/8"} {"input": "Compute the solution of x^2 + 11/8x + 3/8 = 0", "output": "x^2 + 11/8x + 3/8 = 0\n(x - -3/8)(x - -1) = 0\nx - -3/8 = 0 or x - -1 = 0\nx = -3/8\nx = -1"} {"input": "Solve the equations:\n4x + 10y = -207/7\n7x + 4y = -18", "output": "4x + 10y = -207/7\n7x + 4y = -18\n\nUsing elimination\n7*(4x + 10y = -207/7)\n4*(7x + 4y = -18)\n28x + 70y = -207\n28x + 16y = -72\nSubtract equations\n54y = -135\ny = -135/54\ny = -5/2\n\nSubstitute y\n4x + 10(-5/2) = -207/7\n4x = -32/7\nx = -32/7/4\nx = -8/7"} {"input": "Find x for x^2 + 10/3x + 1 = 0", "output": "x^2 + 10/3x + 1 = 0\n(x - -3)(x - -1/3) = 0\nx - -3 = 0 or x - -1/3 = 0\nx = -3\nx = -1/3"} {"input": "Determine x in 10x + 10 = 0", "output": "10x + 10 = 0\n10x = -10\nx = -10 / 10\nx = -1"} {"input": "Solve quickly: x^3 - 3/4x^2 - 35/18x + 25/36 = 0", "output": "x^3 - 3/4x^2 - 35/18x + 25/36 = 0\n(x - 5/3)(x - 1/3)(x - -5/4) = 0\nx - 5/3 = 0\nx - 1/3 = 0\nx - -5/4 = 0\nx = 5/3\nx = 1/3\nx = -5/4"} {"input": "Solve quickly: x^3 + 203/72x^2 + 161/162x - 95/648 = 0", "output": "x^3 + 203/72x^2 + 161/162x - 95/648 = 0\n(x - -5/9)(x - 1/9)(x - -19/8) = 0\nx - -5/9 = 0\nx - 1/9 = 0\nx - -19/8 = 0\nx = -5/9\nx = 1/9\nx = -19/8"} {"input": "Find x in 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "Find x for 1x + 15/7 = 0", "output": "1x + 15/7 = 0\n1x = -15/7\nx = -15/7 / 1\nx = -15/7"} {"input": "Solve the equation x^2 - 29/20x + 21/40 = 0", "output": "x^2 - 29/20x + 21/40 = 0\n(x - 3/4)(x - 7/10) = 0\nx - 3/4 = 0 or x - 7/10 = 0\nx = 3/4\nx = 7/10"} {"input": "Solve the equations:\n8x + 10y = 266/15\n6x + 1y = 167/15", "output": "8x + 10y = 266/15\n6x + 1y = 167/15\n\nUsing elimination\n6*(8x + 10y = 266/15)\n8*(6x + 1y = 167/15)\n48x + 60y = 532/5\n48x + 8y = 1336/15\nSubtract equations\n52y = 52/3\ny = 52/3/52\ny = 1/3\n\nSubstitute y\n8x + 10(1/3) = 266/15\n8x = 72/5\nx = 72/5/8\nx = 9/5"} {"input": "Solve quickly: 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Solve the equation x^2 - 1x - 3/4 = 0", "output": "x^2 - 1x - 3/4 = 0\n(x - 3/2)(x - -1/2) = 0\nx - 3/2 = 0 or x - -1/2 = 0\nx = 3/2\nx = -1/2"} {"input": "Find x for 10x + 45/2 = 0", "output": "10x + 45/2 = 0\n10x = -45/2\nx = -45/2 / 10\nx = -9/4"} {"input": "Find the solution to 6x - 3/2 = 0", "output": "6x - 3/2 = 0\n6x = 3/2\nx = 3/2 / 6\nx = 1/4"} {"input": "Find the solution to 1x - 13/10 = 0", "output": "1x - 13/10 = 0\n1x = 13/10\nx = 13/10 / 1\nx = 13/10"} {"input": "Solve quickly: x^3 + 4x^2 - 639/49x - 306/49 = 0", "output": "x^3 + 4x^2 - 639/49x - 306/49 = 0\n(x - 17/7)(x - -6)(x - -3/7) = 0\nx - 17/7 = 0\nx - -6 = 0\nx - -3/7 = 0\nx = 17/7\nx = -6\nx = -3/7"} {"input": "Compute the solution of 7x - 12 = 0", "output": "7x - 12 = 0\n7x = 12\nx = 12 / 7\nx = 12/7"} {"input": "Find x in 7x + 21/2 = 0", "output": "7x + 21/2 = 0\n7x = -21/2\nx = -21/2 / 7\nx = -3/2"} {"input": "Solve 6x - 8 = 0", "output": "6x - 8 = 0\n6x = 8\nx = 8 / 6\nx = 4/3"} {"input": "Find x in x^3 + 1/6x^2 - 26/3x - 10 = 0", "output": "x^3 + 1/6x^2 - 26/3x - 10 = 0\n(x - 10/3)(x - -3/2)(x - -2) = 0\nx - 10/3 = 0\nx - -3/2 = 0\nx - -2 = 0\nx = 10/3\nx = -3/2\nx = -2"} {"input": "Solve the equations:\n10x + 9y = -1367/9\n8x + 7y = -1063/9", "output": "10x + 9y = -1367/9\n8x + 7y = -1063/9\n\nUsing elimination\n8*(10x + 9y = -1367/9)\n10*(8x + 7y = -1063/9)\n80x + 72y = -10936/9\n80x + 70y = -10630/9\nSubtract equations\n2y = -34\ny = -34/2\ny = -17\n\nSubstitute y\n10x + 9(-17) = -1367/9\n10x = 10/9\nx = 10/9/10\nx = 1/9"} {"input": "Solve the equation x^3 - 5x^2 - 1x + 5 = 0", "output": "x^3 - 5x^2 - 1x + 5 = 0\n(x - 1)(x - -1)(x - 5) = 0\nx - 1 = 0\nx - -1 = 0\nx - 5 = 0\nx = 1\nx = -1\nx = 5"} {"input": "Solve the equations:\n6x + 8y = -136\n8x + 5y = -629/4", "output": "6x + 8y = -136\n8x + 5y = -629/4\n\nUsing elimination\n8*(6x + 8y = -136)\n6*(8x + 5y = -629/4)\n48x + 64y = -1088\n48x + 30y = -1887/2\nSubtract equations\n34y = -289/2\ny = -289/2/34\ny = -17/4\n\nSubstitute y\n6x + 8(-17/4) = -136\n6x = -102\nx = -102/6\nx = -17"} {"input": "Solve the equation 10x + 25 = 0", "output": "10x + 25 = 0\n10x = -25\nx = -25 / 10\nx = -5/2"} {"input": "Compute the solution of x^3 + 209/15x^2 + 842/15x + 208/3 = 0", "output": "x^3 + 209/15x^2 + 842/15x + 208/3 = 0\n(x - -13/5)(x - -10/3)(x - -8) = 0\nx - -13/5 = 0\nx - -10/3 = 0\nx - -8 = 0\nx = -13/5\nx = -10/3\nx = -8"} {"input": "Solve x^2 - 35/2x - 50 = 0", "output": "x^2 - 35/2x - 50 = 0\n(x - -5/2)(x - 20) = 0\nx - -5/2 = 0 or x - 20 = 0\nx = -5/2\nx = 20"} {"input": "Solve x^2 + 29/10x + 9/5 = 0", "output": "x^2 + 29/10x + 9/5 = 0\n(x - -2)(x - -9/10) = 0\nx - -2 = 0 or x - -9/10 = 0\nx = -2\nx = -9/10"} {"input": "Determine x in x^2 - 44/7x + 64/7 = 0", "output": "x^2 - 44/7x + 64/7 = 0\n(x - 16/7)(x - 4) = 0\nx - 16/7 = 0 or x - 4 = 0\nx = 16/7\nx = 4"} {"input": "Solve the equations:\n9x + 2y = 16\n9x + 5y = 22", "output": "9x + 2y = 16\n9x + 5y = 22\n\nUsing elimination\n9*(9x + 2y = 16)\n9*(9x + 5y = 22)\n81x + 18y = 144\n81x + 45y = 198\nSubtract equations\n-27y = -54\ny = -54/-27\ny = 2\n\nSubstitute y\n9x + 2(2) = 16\n9x = 12\nx = 12/9\nx = 4/3"} {"input": "Solve the equation x^3 - 697/180x^2 + 193/120x + 1463/360 = 0", "output": "x^3 - 697/180x^2 + 193/120x + 1463/360 = 0\n(x - -7/9)(x - 19/10)(x - 11/4) = 0\nx - -7/9 = 0\nx - 19/10 = 0\nx - 11/4 = 0\nx = -7/9\nx = 19/10\nx = 11/4"} {"input": "Solve simultaneously:\n10x + 6y = 57/2\n9x + 7y = 101/4", "output": "10x + 6y = 57/2\n9x + 7y = 101/4\n\nUsing elimination\n9*(10x + 6y = 57/2)\n10*(9x + 7y = 101/4)\n90x + 54y = 513/2\n90x + 70y = 505/2\nSubtract equations\n-16y = 4\ny = 4/-16\ny = -1/4\n\nSubstitute y\n10x + 6(-1/4) = 57/2\n10x = 30\nx = 30/10\nx = 3"} {"input": "Solve quickly: x^3 + 723/70x^2 + 991/35x + 156/7 = 0", "output": "x^3 + 723/70x^2 + 991/35x + 156/7 = 0\n(x - -12/5)(x - -13/2)(x - -10/7) = 0\nx - -12/5 = 0\nx - -13/2 = 0\nx - -10/7 = 0\nx = -12/5\nx = -13/2\nx = -10/7"} {"input": "Determine x in 1x + 19/8 = 0", "output": "1x + 19/8 = 0\n1x = -19/8\nx = -19/8 / 1\nx = -19/8"} {"input": "Solve quickly: 6x - 27 = 0", "output": "6x - 27 = 0\n6x = 27\nx = 27 / 6\nx = 9/2"} {"input": "Determine x in x^2 + 37/10x + 8/5 = 0", "output": "x^2 + 37/10x + 8/5 = 0\n(x - -16/5)(x - -1/2) = 0\nx - -16/5 = 0 or x - -1/2 = 0\nx = -16/5\nx = -1/2"} {"input": "Find x for 7x - 21 = 0", "output": "7x - 21 = 0\n7x = 21\nx = 21 / 7\nx = 3"} {"input": "Solve the equations:\n2x + 5y = 49/45\n3x + 1y = -154/45", "output": "2x + 5y = 49/45\n3x + 1y = -154/45\n\nUsing elimination\n3*(2x + 5y = 49/45)\n2*(3x + 1y = -154/45)\n6x + 15y = 49/15\n6x + 2y = -308/45\nSubtract equations\n13y = 91/9\ny = 91/9/13\ny = 7/9\n\nSubstitute y\n2x + 5(7/9) = 49/45\n2x = -14/5\nx = -14/5/2\nx = -7/5"} {"input": "Find x in 9x - 90 = 0", "output": "9x - 90 = 0\n9x = 90\nx = 90 / 9\nx = 10"} {"input": "Determine x in 3x - 57/7 = 0", "output": "3x - 57/7 = 0\n3x = 57/7\nx = 57/7 / 3\nx = 19/7"} {"input": "Find the solution to 1x + 1/8 = 0", "output": "1x + 1/8 = 0\n1x = -1/8\nx = -1/8 / 1\nx = -1/8"} {"input": "Compute the solution of x^2 - 17/63x - 10/63 = 0", "output": "x^2 - 17/63x - 10/63 = 0\n(x - 5/9)(x - -2/7) = 0\nx - 5/9 = 0 or x - -2/7 = 0\nx = 5/9\nx = -2/7"} {"input": "Solve 9x + 45/2 = 0", "output": "9x + 45/2 = 0\n9x = -45/2\nx = -45/2 / 9\nx = -5/2"} {"input": "Solve x^3 - 13/20x^2 - 221/40x + 9/4 = 0", "output": "x^3 - 13/20x^2 - 221/40x + 9/4 = 0\n(x - 2/5)(x - 5/2)(x - -9/4) = 0\nx - 2/5 = 0\nx - 5/2 = 0\nx - -9/4 = 0\nx = 2/5\nx = 5/2\nx = -9/4"} {"input": "Find the solution to x^3 + 89/18x^2 + 49/16x + 17/36 = 0", "output": "x^3 + 89/18x^2 + 49/16x + 17/36 = 0\n(x - -1/4)(x - -4/9)(x - -17/4) = 0\nx - -1/4 = 0\nx - -4/9 = 0\nx - -17/4 = 0\nx = -1/4\nx = -4/9\nx = -17/4"} {"input": "What value of x satisfies 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x and y such that\n3x + 9y = 33/2\n7x + 9y = 22", "output": "3x + 9y = 33/2\n7x + 9y = 22\n\nUsing elimination\n7*(3x + 9y = 33/2)\n3*(7x + 9y = 22)\n21x + 63y = 231/2\n21x + 27y = 66\nSubtract equations\n36y = 99/2\ny = 99/2/36\ny = 11/8\n\nSubstitute y\n3x + 9(11/8) = 33/2\n3x = 33/8\nx = 33/8/3\nx = 11/8"} {"input": "Find x for x^2 - 2/3x - 8/9 = 0", "output": "x^2 - 2/3x - 8/9 = 0\n(x - -2/3)(x - 4/3) = 0\nx - -2/3 = 0 or x - 4/3 = 0\nx = -2/3\nx = 4/3"} {"input": "What value of x satisfies 4x + 17/2 = 0", "output": "4x + 17/2 = 0\n4x = -17/2\nx = -17/2 / 4\nx = -17/8"} {"input": "Solve the equation 7x + 14/5 = 0", "output": "7x + 14/5 = 0\n7x = -14/5\nx = -14/5 / 7\nx = -2/5"} {"input": "What value of x satisfies x^3 - 16/9x^2 - 1793/144x - 95/12 = 0", "output": "x^3 - 16/9x^2 - 1793/144x - 95/12 = 0\n(x - 19/4)(x - -20/9)(x - -3/4) = 0\nx - 19/4 = 0\nx - -20/9 = 0\nx - -3/4 = 0\nx = 19/4\nx = -20/9\nx = -3/4"} {"input": "Compute the solution of 9x + 27/8 = 0", "output": "9x + 27/8 = 0\n9x = -27/8\nx = -27/8 / 9\nx = -3/8"} {"input": "Solve the equation 4x + 68 = 0", "output": "4x + 68 = 0\n4x = -68\nx = -68 / 4\nx = -17"} {"input": "What value of x satisfies 7x - 133/10 = 0", "output": "7x - 133/10 = 0\n7x = 133/10\nx = 133/10 / 7\nx = 19/10"} {"input": "Solve quickly: x^2 - 14x - 15 = 0", "output": "x^2 - 14x - 15 = 0\n(x - -1)(x - 15) = 0\nx - -1 = 0 or x - 15 = 0\nx = -1\nx = 15"} {"input": "Solve quickly: x^2 - 2/5x - 7/5 = 0", "output": "x^2 - 2/5x - 7/5 = 0\n(x - 7/5)(x - -1) = 0\nx - 7/5 = 0 or x - -1 = 0\nx = 7/5\nx = -1"} {"input": "What value of x satisfies 1x - 5 = 0", "output": "1x - 5 = 0\n1x = 5\nx = 5 / 1\nx = 5"} {"input": "Compute the solution of x^2 - 3x - 40 = 0", "output": "x^2 - 3x - 40 = 0\n(x - 8)(x - -5) = 0\nx - 8 = 0 or x - -5 = 0\nx = 8\nx = -5"} {"input": "Find the solution to x^2 + 5/7x - 48/7 = 0", "output": "x^2 + 5/7x - 48/7 = 0\n(x - -3)(x - 16/7) = 0\nx - -3 = 0 or x - 16/7 = 0\nx = -3\nx = 16/7"} {"input": "What value of x satisfies 1x - 7/6 = 0", "output": "1x - 7/6 = 0\n1x = 7/6\nx = 7/6 / 1\nx = 7/6"} {"input": "Compute the solution of 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Solve x^2 + 25/4x + 57/8 = 0", "output": "x^2 + 25/4x + 57/8 = 0\n(x - -3/2)(x - -19/4) = 0\nx - -3/2 = 0 or x - -19/4 = 0\nx = -3/2\nx = -19/4"} {"input": "Solve x^2 + 109/9x + 190/9 = 0", "output": "x^2 + 109/9x + 190/9 = 0\n(x - -19/9)(x - -10) = 0\nx - -19/9 = 0 or x - -10 = 0\nx = -19/9\nx = -10"} {"input": "Solve the equation x^2 + 77/9x + 40/9 = 0", "output": "x^2 + 77/9x + 40/9 = 0\n(x - -8)(x - -5/9) = 0\nx - -8 = 0 or x - -5/9 = 0\nx = -8\nx = -5/9"} {"input": "Solve simultaneously:\n7x + 1y = -1192/45\n2x + 10y = -292/45", "output": "7x + 1y = -1192/45\n2x + 10y = -292/45\n\nUsing elimination\n2*(7x + 1y = -1192/45)\n7*(2x + 10y = -292/45)\n14x + 2y = -2384/45\n14x + 70y = -2044/45\nSubtract equations\n-68y = -68/9\ny = -68/9/-68\ny = 1/9\n\nSubstitute y\n7x + 1(1/9) = -1192/45\n7x = -133/5\nx = -133/5/7\nx = -19/5"} {"input": "Find x for x^3 + 7/6x^2 - 66x - 459/2 = 0", "output": "x^3 + 7/6x^2 - 66x - 459/2 = 0\n(x - -9/2)(x - 9)(x - -17/3) = 0\nx - -9/2 = 0\nx - 9 = 0\nx - -17/3 = 0\nx = -9/2\nx = 9\nx = -17/3"} {"input": "Solve x^3 - 31/3x^2 + 415/12x - 75/2 = 0", "output": "x^3 - 31/3x^2 + 415/12x - 75/2 = 0\n(x - 9/2)(x - 5/2)(x - 10/3) = 0\nx - 9/2 = 0\nx - 5/2 = 0\nx - 10/3 = 0\nx = 9/2\nx = 5/2\nx = 10/3"} {"input": "Solve the equation x^3 - 529/30x^2 - 521/10x + 286/3 = 0", "output": "x^3 - 529/30x^2 - 521/10x + 286/3 = 0\n(x - 13/10)(x - -11/3)(x - 20) = 0\nx - 13/10 = 0\nx - -11/3 = 0\nx - 20 = 0\nx = 13/10\nx = -11/3\nx = 20"} {"input": "Solve x^2 + 1x - 28/9 = 0", "output": "x^2 + 1x - 28/9 = 0\n(x - 4/3)(x - -7/3) = 0\nx - 4/3 = 0 or x - -7/3 = 0\nx = 4/3\nx = -7/3"} {"input": "Solve simultaneously:\n6x + 8y = 137/6\n4x + 1y = 11/3", "output": "6x + 8y = 137/6\n4x + 1y = 11/3\n\nUsing elimination\n4*(6x + 8y = 137/6)\n6*(4x + 1y = 11/3)\n24x + 32y = 274/3\n24x + 6y = 22\nSubtract equations\n26y = 208/3\ny = 208/3/26\ny = 8/3\n\nSubstitute y\n6x + 8(8/3) = 137/6\n6x = 3/2\nx = 3/2/6\nx = 1/4"} {"input": "Find x and y such that\n1x + 6y = 281/10\n8x + 1y = 133/10", "output": "1x + 6y = 281/10\n8x + 1y = 133/10\n\nUsing elimination\n8*(1x + 6y = 281/10)\n1*(8x + 1y = 133/10)\n8x + 48y = 1124/5\n8x + 1y = 133/10\nSubtract equations\n47y = 423/2\ny = 423/2/47\ny = 9/2\n\nSubstitute y\n1x + 6(9/2) = 281/10\n1x = 11/10\nx = 11/10/1\nx = 11/10"} {"input": "Solve the equations:\n8x + 9y = 64\n4x + 3y = 20", "output": "8x + 9y = 64\n4x + 3y = 20\n\nUsing elimination\n4*(8x + 9y = 64)\n8*(4x + 3y = 20)\n32x + 36y = 256\n32x + 24y = 160\nSubtract equations\n12y = 96\ny = 96/12\ny = 8\n\nSubstitute y\n8x + 9(8) = 64\n8x = -8\nx = -8/8\nx = -1"} {"input": "Find x and y such that\n8x + 10y = 110/3\n7x + 4y = 44/3", "output": "8x + 10y = 110/3\n7x + 4y = 44/3\n\nUsing elimination\n7*(8x + 10y = 110/3)\n8*(7x + 4y = 44/3)\n56x + 70y = 770/3\n56x + 32y = 352/3\nSubtract equations\n38y = 418/3\ny = 418/3/38\ny = 11/3\n\nSubstitute y\n8x + 10(11/3) = 110/3\n8x = 0\nx = 0/8\nx = 0"} {"input": "Solve quickly: x^2 + 9/7x - 36/7 = 0", "output": "x^2 + 9/7x - 36/7 = 0\n(x - 12/7)(x - -3) = 0\nx - 12/7 = 0 or x - -3 = 0\nx = 12/7\nx = -3"} {"input": "Find x for x^3 + 89/30x^2 + 19/15x - 3/2 = 0", "output": "x^3 + 89/30x^2 + 19/15x - 3/2 = 0\n(x - -9/5)(x - 1/2)(x - -5/3) = 0\nx - -9/5 = 0\nx - 1/2 = 0\nx - -5/3 = 0\nx = -9/5\nx = 1/2\nx = -5/3"} {"input": "Find the solution to 4x + 34 = 0", "output": "4x + 34 = 0\n4x = -34\nx = -34 / 4\nx = -17/2"} {"input": "Solve the system:\n10x + 4y = 65/3\n2x + 10y = 59/3", "output": "10x + 4y = 65/3\n2x + 10y = 59/3\n\nUsing elimination\n2*(10x + 4y = 65/3)\n10*(2x + 10y = 59/3)\n20x + 8y = 130/3\n20x + 100y = 590/3\nSubtract equations\n-92y = -460/3\ny = -460/3/-92\ny = 5/3\n\nSubstitute y\n10x + 4(5/3) = 65/3\n10x = 15\nx = 15/10\nx = 3/2"} {"input": "Find the solution to x^3 - 172/35x^2 + 179/35x + 66/35 = 0", "output": "x^3 - 172/35x^2 + 179/35x + 66/35 = 0\n(x - 3)(x - -2/7)(x - 11/5) = 0\nx - 3 = 0\nx - -2/7 = 0\nx - 11/5 = 0\nx = 3\nx = -2/7\nx = 11/5"} {"input": "Find x in x^3 + 221/15x^2 + 506/15x + 56/5 = 0", "output": "x^3 + 221/15x^2 + 506/15x + 56/5 = 0\n(x - -12)(x - -2/5)(x - -7/3) = 0\nx - -12 = 0\nx - -2/5 = 0\nx - -7/3 = 0\nx = -12\nx = -2/5\nx = -7/3"} {"input": "Find x and y such that\n8x + 1y = -50/3\n3x + 1y = -35/6", "output": "8x + 1y = -50/3\n3x + 1y = -35/6\n\nUsing elimination\n3*(8x + 1y = -50/3)\n8*(3x + 1y = -35/6)\n24x + 3y = -50\n24x + 8y = -140/3\nSubtract equations\n-5y = -10/3\ny = -10/3/-5\ny = 2/3\n\nSubstitute y\n8x + 1(2/3) = -50/3\n8x = -52/3\nx = -52/3/8\nx = -13/6"} {"input": "Solve quickly: x^2 + 32/5x + 7 = 0", "output": "x^2 + 32/5x + 7 = 0\n(x - -5)(x - -7/5) = 0\nx - -5 = 0 or x - -7/5 = 0\nx = -5\nx = -7/5"} {"input": "Find the solution to x^2 - 2/3x - 8/3 = 0", "output": "x^2 - 2/3x - 8/3 = 0\n(x - 2)(x - -4/3) = 0\nx - 2 = 0 or x - -4/3 = 0\nx = 2\nx = -4/3"} {"input": "Find the solution to x^3 - 29/70x^2 - 1346/245x - 208/49 = 0", "output": "x^3 - 29/70x^2 - 1346/245x - 208/49 = 0\n(x - 20/7)(x - -13/10)(x - -8/7) = 0\nx - 20/7 = 0\nx - -13/10 = 0\nx - -8/7 = 0\nx = 20/7\nx = -13/10\nx = -8/7"} {"input": "Find x in x^2 - 17/2x - 9/2 = 0", "output": "x^2 - 17/2x - 9/2 = 0\n(x - 9)(x - -1/2) = 0\nx - 9 = 0 or x - -1/2 = 0\nx = 9\nx = -1/2"} {"input": "Solve quickly: 1x - 10 = 0", "output": "1x - 10 = 0\n1x = 10\nx = 10 / 1\nx = 10"} {"input": "Solve x^3 + 5x^2 - 274x + 520 = 0", "output": "x^3 + 5x^2 - 274x + 520 = 0\n(x - 2)(x - 13)(x - -20) = 0\nx - 2 = 0\nx - 13 = 0\nx - -20 = 0\nx = 2\nx = 13\nx = -20"} {"input": "Solve x^3 - 169/105x^2 - 187/35x + 9 = 0", "output": "x^3 - 169/105x^2 - 187/35x + 9 = 0\n(x - 9/5)(x - 15/7)(x - -7/3) = 0\nx - 9/5 = 0\nx - 15/7 = 0\nx - -7/3 = 0\nx = 9/5\nx = 15/7\nx = -7/3"} {"input": "Find the solution to x^2 - 11/3x + 8/3 = 0", "output": "x^2 - 11/3x + 8/3 = 0\n(x - 8/3)(x - 1) = 0\nx - 8/3 = 0 or x - 1 = 0\nx = 8/3\nx = 1"} {"input": "Solve simultaneously:\n3x + 8y = -22/5\n2x + 10y = -52/5", "output": "3x + 8y = -22/5\n2x + 10y = -52/5\n\nUsing elimination\n2*(3x + 8y = -22/5)\n3*(2x + 10y = -52/5)\n6x + 16y = -44/5\n6x + 30y = -156/5\nSubtract equations\n-14y = 112/5\ny = 112/5/-14\ny = -8/5\n\nSubstitute y\n3x + 8(-8/5) = -22/5\n3x = 42/5\nx = 42/5/3\nx = 14/5"} {"input": "Determine x in x^2 - 93/10x - 19/10 = 0", "output": "x^2 - 93/10x - 19/10 = 0\n(x - -1/5)(x - 19/2) = 0\nx - -1/5 = 0 or x - 19/2 = 0\nx = -1/5\nx = 19/2"} {"input": "Solve 5x - 10 = 0", "output": "5x - 10 = 0\n5x = 10\nx = 10 / 5\nx = 2"} {"input": "Find x in x^3 + 1597/360x^2 + 1451/240x + 1729/720 = 0", "output": "x^3 + 1597/360x^2 + 1451/240x + 1729/720 = 0\n(x - -19/9)(x - -13/8)(x - -7/10) = 0\nx - -19/9 = 0\nx - -13/8 = 0\nx - -7/10 = 0\nx = -19/9\nx = -13/8\nx = -7/10"} {"input": "What value of x satisfies x^3 - 37/10x^2 + 11/20x + 21/40 = 0", "output": "x^3 - 37/10x^2 + 11/20x + 21/40 = 0\n(x - 1/2)(x - -3/10)(x - 7/2) = 0\nx - 1/2 = 0\nx - -3/10 = 0\nx - 7/2 = 0\nx = 1/2\nx = -3/10\nx = 7/2"} {"input": "Solve the equation x^2 - 11/3x - 26/9 = 0", "output": "x^2 - 11/3x - 26/9 = 0\n(x - 13/3)(x - -2/3) = 0\nx - 13/3 = 0 or x - -2/3 = 0\nx = 13/3\nx = -2/3"} {"input": "Solve simultaneously:\n10x + 9y = 307/5\n6x + 5y = 37", "output": "10x + 9y = 307/5\n6x + 5y = 37\n\nUsing elimination\n6*(10x + 9y = 307/5)\n10*(6x + 5y = 37)\n60x + 54y = 1842/5\n60x + 50y = 370\nSubtract equations\n4y = -8/5\ny = -8/5/4\ny = -2/5\n\nSubstitute y\n10x + 9(-2/5) = 307/5\n10x = 65\nx = 65/10\nx = 13/2"} {"input": "Compute the solution of 7x + 21 = 0", "output": "7x + 21 = 0\n7x = -21\nx = -21 / 7\nx = -3"} {"input": "Solve x^2 - 17/3x - 76 = 0", "output": "x^2 - 17/3x - 76 = 0\n(x - 12)(x - -19/3) = 0\nx - 12 = 0 or x - -19/3 = 0\nx = 12\nx = -19/3"} {"input": "Solve quickly: x^2 + 259/72x + 209/72 = 0", "output": "x^2 + 259/72x + 209/72 = 0\n(x - -19/8)(x - -11/9) = 0\nx - -19/8 = 0 or x - -11/9 = 0\nx = -19/8\nx = -11/9"} {"input": "Solve x^2 - 4/3x - 4/3 = 0", "output": "x^2 - 4/3x - 4/3 = 0\n(x - -2/3)(x - 2) = 0\nx - -2/3 = 0 or x - 2 = 0\nx = -2/3\nx = 2"} {"input": "Solve the equation 9x + 135/7 = 0", "output": "9x + 135/7 = 0\n9x = -135/7\nx = -135/7 / 9\nx = -15/7"} {"input": "Solve the equations:\n10x + 10y = -100/3\n1x + 8y = -52/3", "output": "10x + 10y = -100/3\n1x + 8y = -52/3\n\nUsing elimination\n1*(10x + 10y = -100/3)\n10*(1x + 8y = -52/3)\n10x + 10y = -100/3\n10x + 80y = -520/3\nSubtract equations\n-70y = 140\ny = 140/-70\ny = -2\n\nSubstitute y\n10x + 10(-2) = -100/3\n10x = -40/3\nx = -40/3/10\nx = -4/3"} {"input": "Find x for x^2 + 55/4x + 323/8 = 0", "output": "x^2 + 55/4x + 323/8 = 0\n(x - -17/4)(x - -19/2) = 0\nx - -17/4 = 0 or x - -19/2 = 0\nx = -17/4\nx = -19/2"} {"input": "Solve x^2 - 7/3x - 26/3 = 0", "output": "x^2 - 7/3x - 26/3 = 0\n(x - -2)(x - 13/3) = 0\nx - -2 = 0 or x - 13/3 = 0\nx = -2\nx = 13/3"} {"input": "Compute the solution of x^2 - 13/4x - 3 = 0", "output": "x^2 - 13/4x - 3 = 0\n(x - 4)(x - -3/4) = 0\nx - 4 = 0 or x - -3/4 = 0\nx = 4\nx = -3/4"} {"input": "Solve the system:\n6x + 3y = 446/21\n7x + 3y = 1471/63", "output": "6x + 3y = 446/21\n7x + 3y = 1471/63\n\nUsing elimination\n7*(6x + 3y = 446/21)\n6*(7x + 3y = 1471/63)\n42x + 21y = 446/3\n42x + 18y = 2942/21\nSubtract equations\n3y = 60/7\ny = 60/7/3\ny = 20/7\n\nSubstitute y\n6x + 3(20/7) = 446/21\n6x = 38/3\nx = 38/3/6\nx = 19/9"} {"input": "Find x for 8x + 136/9 = 0", "output": "8x + 136/9 = 0\n8x = -136/9\nx = -136/9 / 8\nx = -17/9"} {"input": "Solve the equation x^2 - 39/40x - 1 = 0", "output": "x^2 - 39/40x - 1 = 0\n(x - 8/5)(x - -5/8) = 0\nx - 8/5 = 0 or x - -5/8 = 0\nx = 8/5\nx = -5/8"} {"input": "Solve the equation 7x + 119/4 = 0", "output": "7x + 119/4 = 0\n7x = -119/4\nx = -119/4 / 7\nx = -17/4"} {"input": "Determine x in x^2 - 71/8x - 45/4 = 0", "output": "x^2 - 71/8x - 45/4 = 0\n(x - 10)(x - -9/8) = 0\nx - 10 = 0 or x - -9/8 = 0\nx = 10\nx = -9/8"} {"input": "Solve quickly: 1x + 3/4 = 0", "output": "1x + 3/4 = 0\n1x = -3/4\nx = -3/4 / 1\nx = -3/4"} {"input": "Determine x in x^2 + 3/8x - 13/4 = 0", "output": "x^2 + 3/8x - 13/4 = 0\n(x - 13/8)(x - -2) = 0\nx - 13/8 = 0 or x - -2 = 0\nx = 13/8\nx = -2"} {"input": "Find the solution to x^2 - 15/7x = 0", "output": "x^2 - 15/7x = 0\n(x - 15/7)(x - 0) = 0\nx - 15/7 = 0 or x - 0 = 0\nx = 15/7\nx = 0"} {"input": "Find x and y such that\n9x + 4y = -98/5\n1x + 10y = -6", "output": "9x + 4y = -98/5\n1x + 10y = -6\n\nUsing elimination\n1*(9x + 4y = -98/5)\n9*(1x + 10y = -6)\n9x + 4y = -98/5\n9x + 90y = -54\nSubtract equations\n-86y = 172/5\ny = 172/5/-86\ny = -2/5\n\nSubstitute y\n9x + 4(-2/5) = -98/5\n9x = -18\nx = -18/9\nx = -2"} {"input": "Determine x in x^3 + 21x^2 + 104x = 0", "output": "x^3 + 21x^2 + 104x = 0\n(x - 0)(x - -8)(x - -13) = 0\nx - 0 = 0\nx - -8 = 0\nx - -13 = 0\nx = 0\nx = -8\nx = -13"} {"input": "Determine x in x^2 + 3/2x + 11/25 = 0", "output": "x^2 + 3/2x + 11/25 = 0\n(x - -11/10)(x - -2/5) = 0\nx - -11/10 = 0 or x - -2/5 = 0\nx = -11/10\nx = -2/5"} {"input": "Find x and y such that\n3x + 2y = 19/2\n9x + 10y = 71/2", "output": "3x + 2y = 19/2\n9x + 10y = 71/2\n\nUsing elimination\n9*(3x + 2y = 19/2)\n3*(9x + 10y = 71/2)\n27x + 18y = 171/2\n27x + 30y = 213/2\nSubtract equations\n-12y = -21\ny = -21/-12\ny = 7/4\n\nSubstitute y\n3x + 2(7/4) = 19/2\n3x = 6\nx = 6/3\nx = 2"} {"input": "Find x in 3x + 18 = 0", "output": "3x + 18 = 0\n3x = -18\nx = -18 / 3\nx = -6"} {"input": "Determine x in 8x - 40/3 = 0", "output": "8x - 40/3 = 0\n8x = 40/3\nx = 40/3 / 8\nx = 5/3"} {"input": "Find x in x^2 + 11/8x - 5/4 = 0", "output": "x^2 + 11/8x - 5/4 = 0\n(x - -2)(x - 5/8) = 0\nx - -2 = 0 or x - 5/8 = 0\nx = -2\nx = 5/8"} {"input": "Solve simultaneously:\n9x + 5y = -91/2\n9x + 3y = -93/2", "output": "9x + 5y = -91/2\n9x + 3y = -93/2\n\nUsing elimination\n9*(9x + 5y = -91/2)\n9*(9x + 3y = -93/2)\n81x + 45y = -819/2\n81x + 27y = -837/2\nSubtract equations\n18y = 9\ny = 9/18\ny = 1/2\n\nSubstitute y\n9x + 5(1/2) = -91/2\n9x = -48\nx = -48/9\nx = -16/3"} {"input": "Solve simultaneously:\n1x + 10y = -9/4\n8x + 1y = -18", "output": "1x + 10y = -9/4\n8x + 1y = -18\n\nUsing elimination\n8*(1x + 10y = -9/4)\n1*(8x + 1y = -18)\n8x + 80y = -18\n8x + 1y = -18\nSubtract equations\n79y = 0\ny = 0/79\ny = 0\n\nSubstitute y\n1x + 10(0) = -9/4\n1x = -9/4\nx = -9/4/1\nx = -9/4"} {"input": "Solve 10x + 15/2 = 0", "output": "10x + 15/2 = 0\n10x = -15/2\nx = -15/2 / 10\nx = -3/4"} {"input": "Find x for 4x - 38 = 0", "output": "4x - 38 = 0\n4x = 38\nx = 38 / 4\nx = 19/2"} {"input": "Solve quickly: x^2 + 13/4x - 3 = 0", "output": "x^2 + 13/4x - 3 = 0\n(x - 3/4)(x - -4) = 0\nx - 3/4 = 0 or x - -4 = 0\nx = 3/4\nx = -4"} {"input": "What value of x satisfies 4x + 11/2 = 0", "output": "4x + 11/2 = 0\n4x = -11/2\nx = -11/2 / 4\nx = -11/8"} {"input": "Solve 1x - 1/3 = 0", "output": "1x - 1/3 = 0\n1x = 1/3\nx = 1/3 / 1\nx = 1/3"} {"input": "What value of x satisfies x^3 + 23/3x^2 + 2x - 56/3 = 0", "output": "x^3 + 23/3x^2 + 2x - 56/3 = 0\n(x - -7)(x - -2)(x - 4/3) = 0\nx - -7 = 0\nx - -2 = 0\nx - 4/3 = 0\nx = -7\nx = -2\nx = 4/3"} {"input": "Solve quickly: 5x - 13 = 0", "output": "5x - 13 = 0\n5x = 13\nx = 13 / 5\nx = 13/5"} {"input": "Solve x^3 - 29/36x^2 - 161/54x - 49/36 = 0", "output": "x^3 - 29/36x^2 - 161/54x - 49/36 = 0\n(x - -3/4)(x - -7/9)(x - 7/3) = 0\nx - -3/4 = 0\nx - -7/9 = 0\nx - 7/3 = 0\nx = -3/4\nx = -7/9\nx = 7/3"} {"input": "Determine x in x^3 - 31/40x^2 - 361/160x + 77/80 = 0", "output": "x^3 - 31/40x^2 - 361/160x + 77/80 = 0\n(x - 7/4)(x - 2/5)(x - -11/8) = 0\nx - 7/4 = 0\nx - 2/5 = 0\nx - -11/8 = 0\nx = 7/4\nx = 2/5\nx = -11/8"} {"input": "Solve simultaneously:\n4x + 4y = 58/9\n4x + 7y = 143/18", "output": "4x + 4y = 58/9\n4x + 7y = 143/18\n\nUsing elimination\n4*(4x + 4y = 58/9)\n4*(4x + 7y = 143/18)\n16x + 16y = 232/9\n16x + 28y = 286/9\nSubtract equations\n-12y = -6\ny = -6/-12\ny = 1/2\n\nSubstitute y\n4x + 4(1/2) = 58/9\n4x = 40/9\nx = 40/9/4\nx = 10/9"} {"input": "Solve the system:\n10x + 6y = 79/7\n6x + 4y = 46/7", "output": "10x + 6y = 79/7\n6x + 4y = 46/7\n\nUsing elimination\n6*(10x + 6y = 79/7)\n10*(6x + 4y = 46/7)\n60x + 36y = 474/7\n60x + 40y = 460/7\nSubtract equations\n-4y = 2\ny = 2/-4\ny = -1/2\n\nSubstitute y\n10x + 6(-1/2) = 79/7\n10x = 100/7\nx = 100/7/10\nx = 10/7"} {"input": "Determine x in x^3 + 53/12x^2 - 52/3x + 21/4 = 0", "output": "x^3 + 53/12x^2 - 52/3x + 21/4 = 0\n(x - 9/4)(x - 1/3)(x - -7) = 0\nx - 9/4 = 0\nx - 1/3 = 0\nx - -7 = 0\nx = 9/4\nx = 1/3\nx = -7"} {"input": "Find x for x^2 - 87/8x - 27/2 = 0", "output": "x^2 - 87/8x - 27/2 = 0\n(x - -9/8)(x - 12) = 0\nx - -9/8 = 0 or x - 12 = 0\nx = -9/8\nx = 12"} {"input": "Solve quickly: x^3 - 43/70x^2 - 5/14x - 1/35 = 0", "output": "x^3 - 43/70x^2 - 5/14x - 1/35 = 0\n(x - -1/10)(x - 1)(x - -2/7) = 0\nx - -1/10 = 0\nx - 1 = 0\nx - -2/7 = 0\nx = -1/10\nx = 1\nx = -2/7"} {"input": "Find x in 8x + 40/3 = 0", "output": "8x + 40/3 = 0\n8x = -40/3\nx = -40/3 / 8\nx = -5/3"} {"input": "Find the solution to x^3 + 9/2x^2 - 9x = 0", "output": "x^3 + 9/2x^2 - 9x = 0\n(x - 0)(x - 3/2)(x - -6) = 0\nx - 0 = 0\nx - 3/2 = 0\nx - -6 = 0\nx = 0\nx = 3/2\nx = -6"} {"input": "Solve simultaneously:\n10x + 1y = -493/42\n3x + 5y = -773/42", "output": "10x + 1y = -493/42\n3x + 5y = -773/42\n\nUsing elimination\n3*(10x + 1y = -493/42)\n10*(3x + 5y = -773/42)\n30x + 3y = -493/14\n30x + 50y = -3865/21\nSubtract equations\n-47y = 893/6\ny = 893/6/-47\ny = -19/6\n\nSubstitute y\n10x + 1(-19/6) = -493/42\n10x = -60/7\nx = -60/7/10\nx = -6/7"} {"input": "Solve the equation 10x + 160 = 0", "output": "10x + 160 = 0\n10x = -160\nx = -160 / 10\nx = -16"} {"input": "Solve the equation x^2 - 19/3x - 68 = 0", "output": "x^2 - 19/3x - 68 = 0\n(x - -17/3)(x - 12) = 0\nx - -17/3 = 0 or x - 12 = 0\nx = -17/3\nx = 12"} {"input": "Find x in x^3 + 10x^2 - 1349/25x + 714/25 = 0", "output": "x^3 + 10x^2 - 1349/25x + 714/25 = 0\n(x - 17/5)(x - -14)(x - 3/5) = 0\nx - 17/5 = 0\nx - -14 = 0\nx - 3/5 = 0\nx = 17/5\nx = -14\nx = 3/5"} {"input": "Determine x in 1x - 5/3 = 0", "output": "1x - 5/3 = 0\n1x = 5/3\nx = 5/3 / 1\nx = 5/3"} {"input": "Find x and y such that\n7x + 4y = 4/3\n2x + 1y = 2/3", "output": "7x + 4y = 4/3\n2x + 1y = 2/3\n\nUsing elimination\n2*(7x + 4y = 4/3)\n7*(2x + 1y = 2/3)\n14x + 8y = 8/3\n14x + 7y = 14/3\nSubtract equations\n1y = -2\ny = -2/1\ny = -2\n\nSubstitute y\n7x + 4(-2) = 4/3\n7x = 28/3\nx = 28/3/7\nx = 4/3"} {"input": "Solve the equation x^3 - 49/4x^2 + 329/8x - 165/4 = 0", "output": "x^3 - 49/4x^2 + 329/8x - 165/4 = 0\n(x - 11/4)(x - 2)(x - 15/2) = 0\nx - 11/4 = 0\nx - 2 = 0\nx - 15/2 = 0\nx = 11/4\nx = 2\nx = 15/2"} {"input": "Find x and y such that\n3x + 9y = -933/56\n10x + 9y = -1493/56", "output": "3x + 9y = -933/56\n10x + 9y = -1493/56\n\nUsing elimination\n10*(3x + 9y = -933/56)\n3*(10x + 9y = -1493/56)\n30x + 90y = -4665/28\n30x + 27y = -4479/56\nSubtract equations\n63y = -693/8\ny = -693/8/63\ny = -11/8\n\nSubstitute y\n3x + 9(-11/8) = -933/56\n3x = -30/7\nx = -30/7/3\nx = -10/7"} {"input": "Solve x^2 - 5x - 6 = 0", "output": "x^2 - 5x - 6 = 0\n(x - -1)(x - 6) = 0\nx - -1 = 0 or x - 6 = 0\nx = -1\nx = 6"} {"input": "Solve quickly: x^2 + 25/3x + 38/3 = 0", "output": "x^2 + 25/3x + 38/3 = 0\n(x - -2)(x - -19/3) = 0\nx - -2 = 0 or x - -19/3 = 0\nx = -2\nx = -19/3"} {"input": "Solve x^3 + 454/45x^2 - 169/45x - 418/9 = 0", "output": "x^3 + 454/45x^2 - 169/45x - 418/9 = 0\n(x - -11/5)(x - 19/9)(x - -10) = 0\nx - -11/5 = 0\nx - 19/9 = 0\nx - -10 = 0\nx = -11/5\nx = 19/9\nx = -10"} {"input": "Find x in x^2 + 23/6x - 2/3 = 0", "output": "x^2 + 23/6x - 2/3 = 0\n(x - 1/6)(x - -4) = 0\nx - 1/6 = 0 or x - -4 = 0\nx = 1/6\nx = -4"} {"input": "What value of x satisfies x^3 - 11/18x^2 - 13/9x + 1/6 = 0", "output": "x^3 - 11/18x^2 - 13/9x + 1/6 = 0\n(x - 3/2)(x - -1)(x - 1/9) = 0\nx - 3/2 = 0\nx - -1 = 0\nx - 1/9 = 0\nx = 3/2\nx = -1\nx = 1/9"} {"input": "Solve the system:\n9x + 3y = 67/5\n8x + 3y = 64/5", "output": "9x + 3y = 67/5\n8x + 3y = 64/5\n\nUsing elimination\n8*(9x + 3y = 67/5)\n9*(8x + 3y = 64/5)\n72x + 24y = 536/5\n72x + 27y = 576/5\nSubtract equations\n-3y = -8\ny = -8/-3\ny = 8/3\n\nSubstitute y\n9x + 3(8/3) = 67/5\n9x = 27/5\nx = 27/5/9\nx = 3/5"} {"input": "What value of x satisfies 8x - 40 = 0", "output": "8x - 40 = 0\n8x = 40\nx = 40 / 8\nx = 5"} {"input": "Find the solution to x^2 + 2x + 3/4 = 0", "output": "x^2 + 2x + 3/4 = 0\n(x - -3/2)(x - -1/2) = 0\nx - -3/2 = 0 or x - -1/2 = 0\nx = -3/2\nx = -1/2"} {"input": "Find the solution to 10x + 26 = 0", "output": "10x + 26 = 0\n10x = -26\nx = -26 / 10\nx = -13/5"} {"input": "Find x in x^3 + 941/56x^2 - 177/8x - 297/28 = 0", "output": "x^3 + 941/56x^2 - 177/8x - 297/28 = 0\n(x - -18)(x - -3/8)(x - 11/7) = 0\nx - -18 = 0\nx - -3/8 = 0\nx - 11/7 = 0\nx = -18\nx = -3/8\nx = 11/7"} {"input": "Find the solution to x^2 - 22/5x + 17/5 = 0", "output": "x^2 - 22/5x + 17/5 = 0\n(x - 17/5)(x - 1) = 0\nx - 17/5 = 0 or x - 1 = 0\nx = 17/5\nx = 1"} {"input": "What value of x satisfies x^3 - 9/35x^2 - 34/7x - 24/35 = 0", "output": "x^3 - 9/35x^2 - 34/7x - 24/35 = 0\n(x - -2)(x - -1/7)(x - 12/5) = 0\nx - -2 = 0\nx - -1/7 = 0\nx - 12/5 = 0\nx = -2\nx = -1/7\nx = 12/5"} {"input": "Solve the equations:\n9x + 7y = 729/70\n8x + 2y = 457/35", "output": "9x + 7y = 729/70\n8x + 2y = 457/35\n\nUsing elimination\n8*(9x + 7y = 729/70)\n9*(8x + 2y = 457/35)\n72x + 56y = 2916/35\n72x + 18y = 4113/35\nSubtract equations\n38y = -171/5\ny = -171/5/38\ny = -9/10\n\nSubstitute y\n9x + 7(-9/10) = 729/70\n9x = 117/7\nx = 117/7/9\nx = 13/7"} {"input": "Solve the equation x^3 + 138/35x^2 + 113/25x + 264/175 = 0", "output": "x^3 + 138/35x^2 + 113/25x + 264/175 = 0\n(x - -11/5)(x - -8/7)(x - -3/5) = 0\nx - -11/5 = 0\nx - -8/7 = 0\nx - -3/5 = 0\nx = -11/5\nx = -8/7\nx = -3/5"} {"input": "Find x and y such that\n6x + 6y = 300/7\n7x + 9y = 60", "output": "6x + 6y = 300/7\n7x + 9y = 60\n\nUsing elimination\n7*(6x + 6y = 300/7)\n6*(7x + 9y = 60)\n42x + 42y = 300\n42x + 54y = 360\nSubtract equations\n-12y = -60\ny = -60/-12\ny = 5\n\nSubstitute y\n6x + 6(5) = 300/7\n6x = 90/7\nx = 90/7/6\nx = 15/7"} {"input": "Solve the equations:\n8x + 2y = -10/21\n6x + 10y = 766/21", "output": "8x + 2y = -10/21\n6x + 10y = 766/21\n\nUsing elimination\n6*(8x + 2y = -10/21)\n8*(6x + 10y = 766/21)\n48x + 12y = -20/7\n48x + 80y = 6128/21\nSubtract equations\n-68y = -884/3\ny = -884/3/-68\ny = 13/3\n\nSubstitute y\n8x + 2(13/3) = -10/21\n8x = -64/7\nx = -64/7/8\nx = -8/7"} {"input": "Find x in x^3 - 58/21x^2 - 19/21x + 4/7 = 0", "output": "x^3 - 58/21x^2 - 19/21x + 4/7 = 0\n(x - 1/3)(x - -4/7)(x - 3) = 0\nx - 1/3 = 0\nx - -4/7 = 0\nx - 3 = 0\nx = 1/3\nx = -4/7\nx = 3"} {"input": "Find x for x^2 - 37/10x + 21/10 = 0", "output": "x^2 - 37/10x + 21/10 = 0\n(x - 7/10)(x - 3) = 0\nx - 7/10 = 0 or x - 3 = 0\nx = 7/10\nx = 3"} {"input": "Solve the equations:\n10x + 2y = -826/9\n1x + 10y = -161/9", "output": "10x + 2y = -826/9\n1x + 10y = -161/9\n\nUsing elimination\n1*(10x + 2y = -826/9)\n10*(1x + 10y = -161/9)\n10x + 2y = -826/9\n10x + 100y = -1610/9\nSubtract equations\n-98y = 784/9\ny = 784/9/-98\ny = -8/9\n\nSubstitute y\n10x + 2(-8/9) = -826/9\n10x = -90\nx = -90/10\nx = -9"} {"input": "Solve the equations:\n4x + 10y = 472/9\n3x + 5y = 73/3", "output": "4x + 10y = 472/9\n3x + 5y = 73/3\n\nUsing elimination\n3*(4x + 10y = 472/9)\n4*(3x + 5y = 73/3)\n12x + 30y = 472/3\n12x + 20y = 292/3\nSubtract equations\n10y = 60\ny = 60/10\ny = 6\n\nSubstitute y\n4x + 10(6) = 472/9\n4x = -68/9\nx = -68/9/4\nx = -17/9"} {"input": "Find x in x^2 + 6/7x - 13/7 = 0", "output": "x^2 + 6/7x - 13/7 = 0\n(x - -13/7)(x - 1) = 0\nx - -13/7 = 0 or x - 1 = 0\nx = -13/7\nx = 1"} {"input": "Solve quickly: x^2 - 13/8x + 21/32 = 0", "output": "x^2 - 13/8x + 21/32 = 0\n(x - 7/8)(x - 3/4) = 0\nx - 7/8 = 0 or x - 3/4 = 0\nx = 7/8\nx = 3/4"} {"input": "Compute the solution of x^2 + 93/20x + 17/10 = 0", "output": "x^2 + 93/20x + 17/10 = 0\n(x - -17/4)(x - -2/5) = 0\nx - -17/4 = 0 or x - -2/5 = 0\nx = -17/4\nx = -2/5"} {"input": "Determine x in 8x + 64/5 = 0", "output": "8x + 64/5 = 0\n8x = -64/5\nx = -64/5 / 8\nx = -8/5"} {"input": "Solve simultaneously:\n1x + 5y = 155/12\n1x + 7y = 211/12", "output": "1x + 5y = 155/12\n1x + 7y = 211/12\n\nUsing elimination\n1*(1x + 5y = 155/12)\n1*(1x + 7y = 211/12)\n1x + 5y = 155/12\n1x + 7y = 211/12\nSubtract equations\n-2y = -14/3\ny = -14/3/-2\ny = 7/3\n\nSubstitute y\n1x + 5(7/3) = 155/12\n1x = 5/4\nx = 5/4/1\nx = 5/4"} {"input": "Find x for 10x - 70/3 = 0", "output": "10x - 70/3 = 0\n10x = 70/3\nx = 70/3 / 10\nx = 7/3"} {"input": "Find the solution to 7x - 112/3 = 0", "output": "7x - 112/3 = 0\n7x = 112/3\nx = 112/3 / 7\nx = 16/3"} {"input": "Find the solution to x^2 - 1/2x - 5 = 0", "output": "x^2 - 1/2x - 5 = 0\n(x - -2)(x - 5/2) = 0\nx - -2 = 0 or x - 5/2 = 0\nx = -2\nx = 5/2"} {"input": "Solve the equation 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve quickly: 5x - 65 = 0", "output": "5x - 65 = 0\n5x = 65\nx = 65 / 5\nx = 13"} {"input": "Find x in x^3 - 11/6x^2 + 61/162x + 5/27 = 0", "output": "x^3 - 11/6x^2 + 61/162x + 5/27 = 0\n(x - 3/2)(x - -2/9)(x - 5/9) = 0\nx - 3/2 = 0\nx - -2/9 = 0\nx - 5/9 = 0\nx = 3/2\nx = -2/9\nx = 5/9"} {"input": "Solve x^2 + 1/2x - 18 = 0", "output": "x^2 + 1/2x - 18 = 0\n(x - -9/2)(x - 4) = 0\nx - -9/2 = 0 or x - 4 = 0\nx = -9/2\nx = 4"} {"input": "Find the solution to 2x + 7/5 = 0", "output": "2x + 7/5 = 0\n2x = -7/5\nx = -7/5 / 2\nx = -7/10"} {"input": "Solve x^2 - 27/4x + 81/8 = 0", "output": "x^2 - 27/4x + 81/8 = 0\n(x - 9/2)(x - 9/4) = 0\nx - 9/2 = 0 or x - 9/4 = 0\nx = 9/2\nx = 9/4"} {"input": "Solve the equation 9x - 12 = 0", "output": "9x - 12 = 0\n9x = 12\nx = 12 / 9\nx = 4/3"} {"input": "Solve the equation 7x - 14 = 0", "output": "7x - 14 = 0\n7x = 14\nx = 14 / 7\nx = 2"} {"input": "What value of x satisfies x^2 - 2/3x + 5/81 = 0", "output": "x^2 - 2/3x + 5/81 = 0\n(x - 1/9)(x - 5/9) = 0\nx - 1/9 = 0 or x - 5/9 = 0\nx = 1/9\nx = 5/9"} {"input": "Find x in x^3 - 97/40x^2 + 191/160x + 11/32 = 0", "output": "x^3 - 97/40x^2 + 191/160x + 11/32 = 0\n(x - 11/8)(x - 5/4)(x - -1/5) = 0\nx - 11/8 = 0\nx - 5/4 = 0\nx - -1/5 = 0\nx = 11/8\nx = 5/4\nx = -1/5"} {"input": "Solve simultaneously:\n5x + 8y = 53/5\n1x + 10y = -13", "output": "5x + 8y = 53/5\n1x + 10y = -13\n\nUsing elimination\n1*(5x + 8y = 53/5)\n5*(1x + 10y = -13)\n5x + 8y = 53/5\n5x + 50y = -65\nSubtract equations\n-42y = 378/5\ny = 378/5/-42\ny = -9/5\n\nSubstitute y\n5x + 8(-9/5) = 53/5\n5x = 25\nx = 25/5\nx = 5"} {"input": "Solve the equations:\n9x + 3y = 33/2\n5x + 4y = 129/10", "output": "9x + 3y = 33/2\n5x + 4y = 129/10\n\nUsing elimination\n5*(9x + 3y = 33/2)\n9*(5x + 4y = 129/10)\n45x + 15y = 165/2\n45x + 36y = 1161/10\nSubtract equations\n-21y = -168/5\ny = -168/5/-21\ny = 8/5\n\nSubstitute y\n9x + 3(8/5) = 33/2\n9x = 117/10\nx = 117/10/9\nx = 13/10"} {"input": "Determine x in x^3 - 16x^2 - 76x - 80 = 0", "output": "x^3 - 16x^2 - 76x - 80 = 0\n(x - -2)(x - -2)(x - 20) = 0\nx - -2 = 0\nx - -2 = 0\nx - 20 = 0\nx = -2\nx = -2\nx = 20"} {"input": "Solve the system:\n4x + 4y = 8\n1x + 5y = 22/3", "output": "4x + 4y = 8\n1x + 5y = 22/3\n\nUsing elimination\n1*(4x + 4y = 8)\n4*(1x + 5y = 22/3)\n4x + 4y = 8\n4x + 20y = 88/3\nSubtract equations\n-16y = -64/3\ny = -64/3/-16\ny = 4/3\n\nSubstitute y\n4x + 4(4/3) = 8\n4x = 8/3\nx = 8/3/4\nx = 2/3"} {"input": "Solve simultaneously:\n4x + 5y = 61/5\n2x + 3y = 33/5", "output": "4x + 5y = 61/5\n2x + 3y = 33/5\n\nUsing elimination\n2*(4x + 5y = 61/5)\n4*(2x + 3y = 33/5)\n8x + 10y = 122/5\n8x + 12y = 132/5\nSubtract equations\n-2y = -2\ny = -2/-2\ny = 1\n\nSubstitute y\n4x + 5(1) = 61/5\n4x = 36/5\nx = 36/5/4\nx = 9/5"} {"input": "Find x in x^3 + 152/63x^2 - 281/189x - 884/189 = 0", "output": "x^3 + 152/63x^2 - 281/189x - 884/189 = 0\n(x - -13/7)(x - -17/9)(x - 4/3) = 0\nx - -13/7 = 0\nx - -17/9 = 0\nx - 4/3 = 0\nx = -13/7\nx = -17/9\nx = 4/3"} {"input": "Solve the equation x^2 - 19/8x = 0", "output": "x^2 - 19/8x = 0\n(x - 19/8)(x - 0) = 0\nx - 19/8 = 0 or x - 0 = 0\nx = 19/8\nx = 0"} {"input": "Find x in x^2 - 13/18x - 10/3 = 0", "output": "x^2 - 13/18x - 10/3 = 0\n(x - -3/2)(x - 20/9) = 0\nx - -3/2 = 0 or x - 20/9 = 0\nx = -3/2\nx = 20/9"} {"input": "Solve x^3 - 1/15x^2 - 16/3x - 64/15 = 0", "output": "x^3 - 1/15x^2 - 16/3x - 64/15 = 0\n(x - -8/5)(x - 8/3)(x - -1) = 0\nx - -8/5 = 0\nx - 8/3 = 0\nx - -1 = 0\nx = -8/5\nx = 8/3\nx = -1"} {"input": "Solve the system:\n9x + 6y = -37\n3x + 4y = -77/3", "output": "9x + 6y = -37\n3x + 4y = -77/3\n\nUsing elimination\n3*(9x + 6y = -37)\n9*(3x + 4y = -77/3)\n27x + 18y = -111\n27x + 36y = -231\nSubtract equations\n-18y = 120\ny = 120/-18\ny = -20/3\n\nSubstitute y\n9x + 6(-20/3) = -37\n9x = 3\nx = 3/9\nx = 1/3"} {"input": "Solve simultaneously:\n3x + 5y = -10\n6x + 5y = -10", "output": "3x + 5y = -10\n6x + 5y = -10\n\nUsing elimination\n6*(3x + 5y = -10)\n3*(6x + 5y = -10)\n18x + 30y = -60\n18x + 15y = -30\nSubtract equations\n15y = -30\ny = -30/15\ny = -2\n\nSubstitute y\n3x + 5(-2) = -10\n3x = 0\nx = 0/3\nx = 0"} {"input": "Find the solution to x^2 - 2x + 19/100 = 0", "output": "x^2 - 2x + 19/100 = 0\n(x - 19/10)(x - 1/10) = 0\nx - 19/10 = 0 or x - 1/10 = 0\nx = 19/10\nx = 1/10"} {"input": "Solve quickly: 5x + 10/3 = 0", "output": "5x + 10/3 = 0\n5x = -10/3\nx = -10/3 / 5\nx = -2/3"} {"input": "What value of x satisfies x^2 + 7x + 110/9 = 0", "output": "x^2 + 7x + 110/9 = 0\n(x - -11/3)(x - -10/3) = 0\nx - -11/3 = 0 or x - -10/3 = 0\nx = -11/3\nx = -10/3"} {"input": "Solve the equations:\n4x + 4y = 16/9\n3x + 10y = -86/9", "output": "4x + 4y = 16/9\n3x + 10y = -86/9\n\nUsing elimination\n3*(4x + 4y = 16/9)\n4*(3x + 10y = -86/9)\n12x + 12y = 16/3\n12x + 40y = -344/9\nSubtract equations\n-28y = 392/9\ny = 392/9/-28\ny = -14/9\n\nSubstitute y\n4x + 4(-14/9) = 16/9\n4x = 8\nx = 8/4\nx = 2"} {"input": "Find x in x^2 - 1/10x - 9/10 = 0", "output": "x^2 - 1/10x - 9/10 = 0\n(x - 1)(x - -9/10) = 0\nx - 1 = 0 or x - -9/10 = 0\nx = 1\nx = -9/10"} {"input": "Determine x in x^2 - 28/15x - 32/15 = 0", "output": "x^2 - 28/15x - 32/15 = 0\n(x - -4/5)(x - 8/3) = 0\nx - -4/5 = 0 or x - 8/3 = 0\nx = -4/5\nx = 8/3"} {"input": "Find x in 1x + 3/8 = 0", "output": "1x + 3/8 = 0\n1x = -3/8\nx = -3/8 / 1\nx = -3/8"} {"input": "Solve quickly: x^2 + 73/10x + 26/5 = 0", "output": "x^2 + 73/10x + 26/5 = 0\n(x - -13/2)(x - -4/5) = 0\nx - -13/2 = 0 or x - -4/5 = 0\nx = -13/2\nx = -4/5"} {"input": "What value of x satisfies x^2 - 107/12x + 15 = 0", "output": "x^2 - 107/12x + 15 = 0\n(x - 9/4)(x - 20/3) = 0\nx - 9/4 = 0 or x - 20/3 = 0\nx = 9/4\nx = 20/3"} {"input": "Find x in x^2 - 37/90x - 7/9 = 0", "output": "x^2 - 37/90x - 7/9 = 0\n(x - 10/9)(x - -7/10) = 0\nx - 10/9 = 0 or x - -7/10 = 0\nx = 10/9\nx = -7/10"} {"input": "What value of x satisfies x^3 + 49/60x^2 - 41/5x + 119/60 = 0", "output": "x^3 + 49/60x^2 - 41/5x + 119/60 = 0\n(x - 1/4)(x - -17/5)(x - 7/3) = 0\nx - 1/4 = 0\nx - -17/5 = 0\nx - 7/3 = 0\nx = 1/4\nx = -17/5\nx = 7/3"} {"input": "Find x and y such that\n3x + 3y = -69/2\n9x + 10y = -211/2", "output": "3x + 3y = -69/2\n9x + 10y = -211/2\n\nUsing elimination\n9*(3x + 3y = -69/2)\n3*(9x + 10y = -211/2)\n27x + 27y = -621/2\n27x + 30y = -633/2\nSubtract equations\n-3y = 6\ny = 6/-3\ny = -2\n\nSubstitute y\n3x + 3(-2) = -69/2\n3x = -57/2\nx = -57/2/3\nx = -19/2"} {"input": "Solve simultaneously:\n7x + 8y = -547/7\n8x + 10y = -626/7", "output": "7x + 8y = -547/7\n8x + 10y = -626/7\n\nUsing elimination\n8*(7x + 8y = -547/7)\n7*(8x + 10y = -626/7)\n56x + 64y = -4376/7\n56x + 70y = -626\nSubtract equations\n-6y = 6/7\ny = 6/7/-6\ny = -1/7\n\nSubstitute y\n7x + 8(-1/7) = -547/7\n7x = -77\nx = -77/7\nx = -11"} {"input": "Find the solution to x^2 + 19/5x + 18/5 = 0", "output": "x^2 + 19/5x + 18/5 = 0\n(x - -9/5)(x - -2) = 0\nx - -9/5 = 0 or x - -2 = 0\nx = -9/5\nx = -2"} {"input": "Determine x in 1x - 17 = 0", "output": "1x - 17 = 0\n1x = 17\nx = 17 / 1\nx = 17"} {"input": "Solve quickly: x^3 - 151/6x^2 + 625/6x - 50/3 = 0", "output": "x^3 - 151/6x^2 + 625/6x - 50/3 = 0\n(x - 5)(x - 20)(x - 1/6) = 0\nx - 5 = 0\nx - 20 = 0\nx - 1/6 = 0\nx = 5\nx = 20\nx = 1/6"} {"input": "Find the solution to x^2 + 37/24x + 11/48 = 0", "output": "x^2 + 37/24x + 11/48 = 0\n(x - -11/8)(x - -1/6) = 0\nx - -11/8 = 0 or x - -1/6 = 0\nx = -11/8\nx = -1/6"} {"input": "Solve the system:\n3x + 7y = 437/4\n3x + 2y = 157/4", "output": "3x + 7y = 437/4\n3x + 2y = 157/4\n\nUsing elimination\n3*(3x + 7y = 437/4)\n3*(3x + 2y = 157/4)\n9x + 21y = 1311/4\n9x + 6y = 471/4\nSubtract equations\n15y = 210\ny = 210/15\ny = 14\n\nSubstitute y\n3x + 7(14) = 437/4\n3x = 45/4\nx = 45/4/3\nx = 15/4"} {"input": "Find x and y such that\n3x + 9y = 69/5\n1x + 9y = 74/5", "output": "3x + 9y = 69/5\n1x + 9y = 74/5\n\nUsing elimination\n1*(3x + 9y = 69/5)\n3*(1x + 9y = 74/5)\n3x + 9y = 69/5\n3x + 27y = 222/5\nSubtract equations\n-18y = -153/5\ny = -153/5/-18\ny = 17/10\n\nSubstitute y\n3x + 9(17/10) = 69/5\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Solve 6x + 108/5 = 0", "output": "6x + 108/5 = 0\n6x = -108/5\nx = -108/5 / 6\nx = -18/5"} {"input": "Find the solution to 2x + 26/5 = 0", "output": "2x + 26/5 = 0\n2x = -26/5\nx = -26/5 / 2\nx = -13/5"} {"input": "Determine x in 4x + 8 = 0", "output": "4x + 8 = 0\n4x = -8\nx = -8 / 4\nx = -2"} {"input": "Compute the solution of x^2 + 4/7x - 20/7 = 0", "output": "x^2 + 4/7x - 20/7 = 0\n(x - 10/7)(x - -2) = 0\nx - 10/7 = 0 or x - -2 = 0\nx = 10/7\nx = -2"} {"input": "Solve the equations:\n4x + 8y = -64/3\n9x + 3y = 12", "output": "4x + 8y = -64/3\n9x + 3y = 12\n\nUsing elimination\n9*(4x + 8y = -64/3)\n4*(9x + 3y = 12)\n36x + 72y = -192\n36x + 12y = 48\nSubtract equations\n60y = -240\ny = -240/60\ny = -4\n\nSubstitute y\n4x + 8(-4) = -64/3\n4x = 32/3\nx = 32/3/4\nx = 8/3"} {"input": "Find the solution to x^3 + 103/45x^2 - 110/27x - 136/135 = 0", "output": "x^3 + 103/45x^2 - 110/27x - 136/135 = 0\n(x - -17/5)(x - 4/3)(x - -2/9) = 0\nx - -17/5 = 0\nx - 4/3 = 0\nx - -2/9 = 0\nx = -17/5\nx = 4/3\nx = -2/9"} {"input": "Find x in 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Find x for x^3 - 137/24x^2 + 175/24x - 11/6 = 0", "output": "x^3 - 137/24x^2 + 175/24x - 11/6 = 0\n(x - 4)(x - 1/3)(x - 11/8) = 0\nx - 4 = 0\nx - 1/3 = 0\nx - 11/8 = 0\nx = 4\nx = 1/3\nx = 11/8"} {"input": "Find x for x^3 + 47/10x^2 - 46/5x - 42/5 = 0", "output": "x^3 + 47/10x^2 - 46/5x - 42/5 = 0\n(x - 2)(x - -7/10)(x - -6) = 0\nx - 2 = 0\nx - -7/10 = 0\nx - -6 = 0\nx = 2\nx = -7/10\nx = -6"} {"input": "What value of x satisfies x^3 - 103/42x^2 - 2/21x + 65/42 = 0", "output": "x^3 - 103/42x^2 - 2/21x + 65/42 = 0\n(x - 1)(x - 13/6)(x - -5/7) = 0\nx - 1 = 0\nx - 13/6 = 0\nx - -5/7 = 0\nx = 1\nx = 13/6\nx = -5/7"} {"input": "Solve x^3 + 103/18x^2 + 22/9x - 35/6 = 0", "output": "x^3 + 103/18x^2 + 22/9x - 35/6 = 0\n(x - 7/9)(x - -3/2)(x - -5) = 0\nx - 7/9 = 0\nx - -3/2 = 0\nx - -5 = 0\nx = 7/9\nx = -3/2\nx = -5"} {"input": "Solve x^2 + 13/63x - 2/21 = 0", "output": "x^2 + 13/63x - 2/21 = 0\n(x - 2/9)(x - -3/7) = 0\nx - 2/9 = 0 or x - -3/7 = 0\nx = 2/9\nx = -3/7"} {"input": "Solve simultaneously:\n4x + 7y = 74/9\n5x + 8y = 91/9", "output": "4x + 7y = 74/9\n5x + 8y = 91/9\n\nUsing elimination\n5*(4x + 7y = 74/9)\n4*(5x + 8y = 91/9)\n20x + 35y = 370/9\n20x + 32y = 364/9\nSubtract equations\n3y = 2/3\ny = 2/3/3\ny = 2/9\n\nSubstitute y\n4x + 7(2/9) = 74/9\n4x = 20/3\nx = 20/3/4\nx = 5/3"} {"input": "Find the solution to x^2 - 269/90x + 187/90 = 0", "output": "x^2 - 269/90x + 187/90 = 0\n(x - 11/10)(x - 17/9) = 0\nx - 11/10 = 0 or x - 17/9 = 0\nx = 11/10\nx = 17/9"} {"input": "Find x for x^3 + 58/5x^2 - 63/5x - 468/5 = 0", "output": "x^3 + 58/5x^2 - 63/5x - 468/5 = 0\n(x - -13/5)(x - 3)(x - -12) = 0\nx - -13/5 = 0\nx - 3 = 0\nx - -12 = 0\nx = -13/5\nx = 3\nx = -12"} {"input": "Find x for x^3 - 39/10x^2 + 1699/405x - 304/405 = 0", "output": "x^3 - 39/10x^2 + 1699/405x - 304/405 = 0\n(x - 19/10)(x - 16/9)(x - 2/9) = 0\nx - 19/10 = 0\nx - 16/9 = 0\nx - 2/9 = 0\nx = 19/10\nx = 16/9\nx = 2/9"} {"input": "Solve simultaneously:\n2x + 1y = -38/21\n5x + 7y = -536/21", "output": "2x + 1y = -38/21\n5x + 7y = -536/21\n\nUsing elimination\n5*(2x + 1y = -38/21)\n2*(5x + 7y = -536/21)\n10x + 5y = -190/21\n10x + 14y = -1072/21\nSubtract equations\n-9y = 42\ny = 42/-9\ny = -14/3\n\nSubstitute y\n2x + 1(-14/3) = -38/21\n2x = 20/7\nx = 20/7/2\nx = 10/7"} {"input": "Solve the equation 4x - 24 = 0", "output": "4x - 24 = 0\n4x = 24\nx = 24 / 4\nx = 6"} {"input": "Find x in 1x - 9 = 0", "output": "1x - 9 = 0\n1x = 9\nx = 9 / 1\nx = 9"} {"input": "What value of x satisfies x^3 - 11/2x^2 + 10x - 6 = 0", "output": "x^3 - 11/2x^2 + 10x - 6 = 0\n(x - 2)(x - 3/2)(x - 2) = 0\nx - 2 = 0\nx - 3/2 = 0\nx - 2 = 0\nx = 2\nx = 3/2\nx = 2"} {"input": "Determine x in x^3 + 1/9x^2 - 20/27x + 4/27 = 0", "output": "x^3 + 1/9x^2 - 20/27x + 4/27 = 0\n(x - 2/9)(x - 2/3)(x - -1) = 0\nx - 2/9 = 0\nx - 2/3 = 0\nx - -1 = 0\nx = 2/9\nx = 2/3\nx = -1"} {"input": "Solve x^2 + 65/28x + 33/28 = 0", "output": "x^2 + 65/28x + 33/28 = 0\n(x - -3/4)(x - -11/7) = 0\nx - -3/4 = 0 or x - -11/7 = 0\nx = -3/4\nx = -11/7"} {"input": "What value of x satisfies 8x - 11 = 0", "output": "8x - 11 = 0\n8x = 11\nx = 11 / 8\nx = 11/8"} {"input": "Compute the solution of 7x + 49/2 = 0", "output": "7x + 49/2 = 0\n7x = -49/2\nx = -49/2 / 7\nx = -7/2"} {"input": "Solve 1x - 17 = 0", "output": "1x - 17 = 0\n1x = 17\nx = 17 / 1\nx = 17"} {"input": "What value of x satisfies 4x - 68/9 = 0", "output": "4x - 68/9 = 0\n4x = 68/9\nx = 68/9 / 4\nx = 17/9"} {"input": "Solve the equations:\n2x + 2y = -105/4\n1x + 10y = 15/4", "output": "2x + 2y = -105/4\n1x + 10y = 15/4\n\nUsing elimination\n1*(2x + 2y = -105/4)\n2*(1x + 10y = 15/4)\n2x + 2y = -105/4\n2x + 20y = 15/2\nSubtract equations\n-18y = -135/4\ny = -135/4/-18\ny = 15/8\n\nSubstitute y\n2x + 2(15/8) = -105/4\n2x = -30\nx = -30/2\nx = -15"} {"input": "Find x and y such that\n1x + 10y = -38/3\n3x + 6y = -10", "output": "1x + 10y = -38/3\n3x + 6y = -10\n\nUsing elimination\n3*(1x + 10y = -38/3)\n1*(3x + 6y = -10)\n3x + 30y = -38\n3x + 6y = -10\nSubtract equations\n24y = -28\ny = -28/24\ny = -7/6\n\nSubstitute y\n1x + 10(-7/6) = -38/3\n1x = -1\nx = -1/1\nx = -1"} {"input": "Solve 10x - 6 = 0", "output": "10x - 6 = 0\n10x = 6\nx = 6 / 10\nx = 3/5"} {"input": "Determine x in x^2 + 53/21x - 8/21 = 0", "output": "x^2 + 53/21x - 8/21 = 0\n(x - -8/3)(x - 1/7) = 0\nx - -8/3 = 0 or x - 1/7 = 0\nx = -8/3\nx = 1/7"} {"input": "Solve x^2 - 5x - 6 = 0", "output": "x^2 - 5x - 6 = 0\n(x - -1)(x - 6) = 0\nx - -1 = 0 or x - 6 = 0\nx = -1\nx = 6"} {"input": "Compute the solution of x^3 - 62/15x^2 + 73/15x - 6/5 = 0", "output": "x^3 - 62/15x^2 + 73/15x - 6/5 = 0\n(x - 2)(x - 1/3)(x - 9/5) = 0\nx - 2 = 0\nx - 1/3 = 0\nx - 9/5 = 0\nx = 2\nx = 1/3\nx = 9/5"} {"input": "Solve the equation 2x - 7/3 = 0", "output": "2x - 7/3 = 0\n2x = 7/3\nx = 7/3 / 2\nx = 7/6"} {"input": "Solve x^2 - 17/5x + 14/5 = 0", "output": "x^2 - 17/5x + 14/5 = 0\n(x - 7/5)(x - 2) = 0\nx - 7/5 = 0 or x - 2 = 0\nx = 7/5\nx = 2"} {"input": "Solve simultaneously:\n6x + 4y = 21/5\n1x + 7y = -587/30", "output": "6x + 4y = 21/5\n1x + 7y = -587/30\n\nUsing elimination\n1*(6x + 4y = 21/5)\n6*(1x + 7y = -587/30)\n6x + 4y = 21/5\n6x + 42y = -587/5\nSubtract equations\n-38y = 608/5\ny = 608/5/-38\ny = -16/5\n\nSubstitute y\n6x + 4(-16/5) = 21/5\n6x = 17\nx = 17/6\nx = 17/6"} {"input": "Find the solution to x^2 + 38/5x + 48/5 = 0", "output": "x^2 + 38/5x + 48/5 = 0\n(x - -8/5)(x - -6) = 0\nx - -8/5 = 0 or x - -6 = 0\nx = -8/5\nx = -6"} {"input": "Solve the equation x^3 + 37/10x^2 + 3/25x - 297/50 = 0", "output": "x^3 + 37/10x^2 + 3/25x - 297/50 = 0\n(x - -3)(x - 11/10)(x - -9/5) = 0\nx - -3 = 0\nx - 11/10 = 0\nx - -9/5 = 0\nx = -3\nx = 11/10\nx = -9/5"} {"input": "Solve quickly: 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Find x in 5x - 85/7 = 0", "output": "5x - 85/7 = 0\n5x = 85/7\nx = 85/7 / 5\nx = 17/7"} {"input": "Find the solution to x^3 + 13/18x^2 - 190/27x + 50/9 = 0", "output": "x^3 + 13/18x^2 - 190/27x + 50/9 = 0\n(x - -10/3)(x - 10/9)(x - 3/2) = 0\nx - -10/3 = 0\nx - 10/9 = 0\nx - 3/2 = 0\nx = -10/3\nx = 10/9\nx = 3/2"} {"input": "Solve x^3 + 14x^2 + 23x - 110 = 0", "output": "x^3 + 14x^2 + 23x - 110 = 0\n(x - 2)(x - -11)(x - -5) = 0\nx - 2 = 0\nx - -11 = 0\nx - -5 = 0\nx = 2\nx = -11\nx = -5"} {"input": "Find x in x^3 + 9/2x^2 - 16x - 39/2 = 0", "output": "x^3 + 9/2x^2 - 16x - 39/2 = 0\n(x - -1)(x - 3)(x - -13/2) = 0\nx - -1 = 0\nx - 3 = 0\nx - -13/2 = 0\nx = -1\nx = 3\nx = -13/2"} {"input": "Find the solution to x^3 + 14x^2 + 151/4x - 45/2 = 0", "output": "x^3 + 14x^2 + 151/4x - 45/2 = 0\n(x - 1/2)(x - -9/2)(x - -10) = 0\nx - 1/2 = 0\nx - -9/2 = 0\nx - -10 = 0\nx = 1/2\nx = -9/2\nx = -10"} {"input": "Find the solution to x^2 + 9/4x - 45/8 = 0", "output": "x^2 + 9/4x - 45/8 = 0\n(x - -15/4)(x - 3/2) = 0\nx - -15/4 = 0 or x - 3/2 = 0\nx = -15/4\nx = 3/2"} {"input": "Solve the equations:\n6x + 8y = 413/5\n2x + 4y = 211/5", "output": "6x + 8y = 413/5\n2x + 4y = 211/5\n\nUsing elimination\n2*(6x + 8y = 413/5)\n6*(2x + 4y = 211/5)\n12x + 16y = 826/5\n12x + 24y = 1266/5\nSubtract equations\n-8y = -88\ny = -88/-8\ny = 11\n\nSubstitute y\n6x + 8(11) = 413/5\n6x = -27/5\nx = -27/5/6\nx = -9/10"} {"input": "What value of x satisfies x^3 - 15/4x^2 + 783/200x - 19/25 = 0", "output": "x^3 - 15/4x^2 + 783/200x - 19/25 = 0\n(x - 1/4)(x - 8/5)(x - 19/10) = 0\nx - 1/4 = 0\nx - 8/5 = 0\nx - 19/10 = 0\nx = 1/4\nx = 8/5\nx = 19/10"} {"input": "Find x for x^2 + 19x + 34 = 0", "output": "x^2 + 19x + 34 = 0\n(x - -17)(x - -2) = 0\nx - -17 = 0 or x - -2 = 0\nx = -17\nx = -2"} {"input": "Find the solution to x^3 + 13/6x^2 - 83/6x - 15 = 0", "output": "x^3 + 13/6x^2 - 83/6x - 15 = 0\n(x - -1)(x - 10/3)(x - -9/2) = 0\nx - -1 = 0\nx - 10/3 = 0\nx - -9/2 = 0\nx = -1\nx = 10/3\nx = -9/2"} {"input": "Find x in x^2 + 161/36x + 143/36 = 0", "output": "x^2 + 161/36x + 143/36 = 0\n(x - -13/4)(x - -11/9) = 0\nx - -13/4 = 0 or x - -11/9 = 0\nx = -13/4\nx = -11/9"} {"input": "Determine x in x^2 - 19/5x + 78/25 = 0", "output": "x^2 - 19/5x + 78/25 = 0\n(x - 6/5)(x - 13/5) = 0\nx - 6/5 = 0 or x - 13/5 = 0\nx = 6/5\nx = 13/5"} {"input": "Find x and y such that\n3x + 1y = -13/4\n8x + 10y = -217/6", "output": "3x + 1y = -13/4\n8x + 10y = -217/6\n\nUsing elimination\n8*(3x + 1y = -13/4)\n3*(8x + 10y = -217/6)\n24x + 8y = -26\n24x + 30y = -217/2\nSubtract equations\n-22y = 165/2\ny = 165/2/-22\ny = -15/4\n\nSubstitute y\n3x + 1(-15/4) = -13/4\n3x = 1/2\nx = 1/2/3\nx = 1/6"} {"input": "Find x and y such that\n9x + 7y = -91/8\n10x + 10y = -265/28", "output": "9x + 7y = -91/8\n10x + 10y = -265/28\n\nUsing elimination\n10*(9x + 7y = -91/8)\n9*(10x + 10y = -265/28)\n90x + 70y = -455/4\n90x + 90y = -2385/28\nSubtract equations\n-20y = -200/7\ny = -200/7/-20\ny = 10/7\n\nSubstitute y\n9x + 7(10/7) = -91/8\n9x = -171/8\nx = -171/8/9\nx = -19/8"} {"input": "Solve simultaneously:\n6x + 2y = 98/15\n10x + 8y = 70/3", "output": "6x + 2y = 98/15\n10x + 8y = 70/3\n\nUsing elimination\n10*(6x + 2y = 98/15)\n6*(10x + 8y = 70/3)\n60x + 20y = 196/3\n60x + 48y = 140\nSubtract equations\n-28y = -224/3\ny = -224/3/-28\ny = 8/3\n\nSubstitute y\n6x + 2(8/3) = 98/15\n6x = 6/5\nx = 6/5/6\nx = 1/5"} {"input": "Find the solution to 2x + 20/3 = 0", "output": "2x + 20/3 = 0\n2x = -20/3\nx = -20/3 / 2\nx = -10/3"} {"input": "Find the solution to 3x + 3/2 = 0", "output": "3x + 3/2 = 0\n3x = -3/2\nx = -3/2 / 3\nx = -1/2"} {"input": "Compute the solution of x^3 - 11/3x^2 - 577/12x - 209/3 = 0", "output": "x^3 - 11/3x^2 - 577/12x - 209/3 = 0\n(x - 19/2)(x - -11/6)(x - -4) = 0\nx - 19/2 = 0\nx - -11/6 = 0\nx - -4 = 0\nx = 19/2\nx = -11/6\nx = -4"} {"input": "Solve x^2 + 7/3x - 10/3 = 0", "output": "x^2 + 7/3x - 10/3 = 0\n(x - -10/3)(x - 1) = 0\nx - -10/3 = 0 or x - 1 = 0\nx = -10/3\nx = 1"} {"input": "Find x for x^3 - 43/10x^2 + 211/45x - 68/45 = 0", "output": "x^3 - 43/10x^2 + 211/45x - 68/45 = 0\n(x - 4/5)(x - 2/3)(x - 17/6) = 0\nx - 4/5 = 0\nx - 2/3 = 0\nx - 17/6 = 0\nx = 4/5\nx = 2/3\nx = 17/6"} {"input": "Solve simultaneously:\n1x + 1y = -65/9\n10x + 7y = -515/9", "output": "1x + 1y = -65/9\n10x + 7y = -515/9\n\nUsing elimination\n10*(1x + 1y = -65/9)\n1*(10x + 7y = -515/9)\n10x + 10y = -650/9\n10x + 7y = -515/9\nSubtract equations\n3y = -15\ny = -15/3\ny = -5\n\nSubstitute y\n1x + 1(-5) = -65/9\n1x = -20/9\nx = -20/9/1\nx = -20/9"} {"input": "Solve 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Find the solution to x^3 - 6/5x^2 - 549/20x - 81/10 = 0", "output": "x^3 - 6/5x^2 - 549/20x - 81/10 = 0\n(x - 6)(x - -9/2)(x - -3/10) = 0\nx - 6 = 0\nx - -9/2 = 0\nx - -3/10 = 0\nx = 6\nx = -9/2\nx = -3/10"} {"input": "Find x in x^2 - 146/9x - 119/9 = 0", "output": "x^2 - 146/9x - 119/9 = 0\n(x - 17)(x - -7/9) = 0\nx - 17 = 0 or x - -7/9 = 0\nx = 17\nx = -7/9"} {"input": "Find x and y such that\n4x + 7y = -79/10\n2x + 7y = -99/10", "output": "4x + 7y = -79/10\n2x + 7y = -99/10\n\nUsing elimination\n2*(4x + 7y = -79/10)\n4*(2x + 7y = -99/10)\n8x + 14y = -79/5\n8x + 28y = -198/5\nSubtract equations\n-14y = 119/5\ny = 119/5/-14\ny = -17/10\n\nSubstitute y\n4x + 7(-17/10) = -79/10\n4x = 4\nx = 4/4\nx = 1"} {"input": "Solve simultaneously:\n3x + 8y = 59/3\n4x + 5y = 134/9", "output": "3x + 8y = 59/3\n4x + 5y = 134/9\n\nUsing elimination\n4*(3x + 8y = 59/3)\n3*(4x + 5y = 134/9)\n12x + 32y = 236/3\n12x + 15y = 134/3\nSubtract equations\n17y = 34\ny = 34/17\ny = 2\n\nSubstitute y\n3x + 8(2) = 59/3\n3x = 11/3\nx = 11/3/3\nx = 11/9"} {"input": "What value of x satisfies x^2 - 25/4x - 21/4 = 0", "output": "x^2 - 25/4x - 21/4 = 0\n(x - -3/4)(x - 7) = 0\nx - -3/4 = 0 or x - 7 = 0\nx = -3/4\nx = 7"} {"input": "Solve the equation 6x - 15 = 0", "output": "6x - 15 = 0\n6x = 15\nx = 15 / 6\nx = 5/2"} {"input": "Find x in x^2 + 13/12x - 15/2 = 0", "output": "x^2 + 13/12x - 15/2 = 0\n(x - -10/3)(x - 9/4) = 0\nx - -10/3 = 0 or x - 9/4 = 0\nx = -10/3\nx = 9/4"} {"input": "Compute the solution of x^3 - 43/40x^2 - 29/160x + 3/80 = 0", "output": "x^3 - 43/40x^2 - 29/160x + 3/80 = 0\n(x - 1/8)(x - 6/5)(x - -1/4) = 0\nx - 1/8 = 0\nx - 6/5 = 0\nx - -1/4 = 0\nx = 1/8\nx = 6/5\nx = -1/4"} {"input": "Find x in 8x - 160/3 = 0", "output": "8x - 160/3 = 0\n8x = 160/3\nx = 160/3 / 8\nx = 20/3"} {"input": "Find x and y such that\n4x + 5y = -67/9\n4x + 3y = -11/3", "output": "4x + 5y = -67/9\n4x + 3y = -11/3\n\nUsing elimination\n4*(4x + 5y = -67/9)\n4*(4x + 3y = -11/3)\n16x + 20y = -268/9\n16x + 12y = -44/3\nSubtract equations\n8y = -136/9\ny = -136/9/8\ny = -17/9\n\nSubstitute y\n4x + 5(-17/9) = -67/9\n4x = 2\nx = 2/4\nx = 1/2"} {"input": "Solve the equation x^2 - 6x - 133/4 = 0", "output": "x^2 - 6x - 133/4 = 0\n(x - -7/2)(x - 19/2) = 0\nx - -7/2 = 0 or x - 19/2 = 0\nx = -7/2\nx = 19/2"} {"input": "Solve 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x for x^2 + 21x + 20 = 0", "output": "x^2 + 21x + 20 = 0\n(x - -20)(x - -1) = 0\nx - -20 = 0 or x - -1 = 0\nx = -20\nx = -1"} {"input": "Solve quickly: x^3 + 194/35x^2 + 353/35x + 6 = 0", "output": "x^3 + 194/35x^2 + 353/35x + 6 = 0\n(x - -7/5)(x - -2)(x - -15/7) = 0\nx - -7/5 = 0\nx - -2 = 0\nx - -15/7 = 0\nx = -7/5\nx = -2\nx = -15/7"} {"input": "Find x and y such that\n3x + 2y = 18/5\n4x + 6y = -26/5", "output": "3x + 2y = 18/5\n4x + 6y = -26/5\n\nUsing elimination\n4*(3x + 2y = 18/5)\n3*(4x + 6y = -26/5)\n12x + 8y = 72/5\n12x + 18y = -78/5\nSubtract equations\n-10y = 30\ny = 30/-10\ny = -3\n\nSubstitute y\n3x + 2(-3) = 18/5\n3x = 48/5\nx = 48/5/3\nx = 16/5"} {"input": "Solve the equations:\n5x + 8y = 121/6\n7x + 9y = 55/2", "output": "5x + 8y = 121/6\n7x + 9y = 55/2\n\nUsing elimination\n7*(5x + 8y = 121/6)\n5*(7x + 9y = 55/2)\n35x + 56y = 847/6\n35x + 45y = 275/2\nSubtract equations\n11y = 11/3\ny = 11/3/11\ny = 1/3\n\nSubstitute y\n5x + 8(1/3) = 121/6\n5x = 35/2\nx = 35/2/5\nx = 7/2"} {"input": "Determine x in x^2 - 43/18x - 19/2 = 0", "output": "x^2 - 43/18x - 19/2 = 0\n(x - 9/2)(x - -19/9) = 0\nx - 9/2 = 0 or x - -19/9 = 0\nx = 9/2\nx = -19/9"} {"input": "Solve simultaneously:\n7x + 3y = -206/63\n3x + 8y = -110/21", "output": "7x + 3y = -206/63\n3x + 8y = -110/21\n\nUsing elimination\n3*(7x + 3y = -206/63)\n7*(3x + 8y = -110/21)\n21x + 9y = -206/21\n21x + 56y = -110/3\nSubtract equations\n-47y = 188/7\ny = 188/7/-47\ny = -4/7\n\nSubstitute y\n7x + 3(-4/7) = -206/63\n7x = -14/9\nx = -14/9/7\nx = -2/9"} {"input": "Compute the solution of x^3 - 17/12x^2 - 247/18x + 169/36 = 0", "output": "x^3 - 17/12x^2 - 247/18x + 169/36 = 0\n(x - 13/3)(x - 1/3)(x - -13/4) = 0\nx - 13/3 = 0\nx - 1/3 = 0\nx - -13/4 = 0\nx = 13/3\nx = 1/3\nx = -13/4"} {"input": "Find x and y such that\n7x + 3y = -361/63\n2x + 4y = -584/63", "output": "7x + 3y = -361/63\n2x + 4y = -584/63\n\nUsing elimination\n2*(7x + 3y = -361/63)\n7*(2x + 4y = -584/63)\n14x + 6y = -722/63\n14x + 28y = -584/9\nSubtract equations\n-22y = 374/7\ny = 374/7/-22\ny = -17/7\n\nSubstitute y\n7x + 3(-17/7) = -361/63\n7x = 14/9\nx = 14/9/7\nx = 2/9"} {"input": "What value of x satisfies x^2 + 157/8x - 15/2 = 0", "output": "x^2 + 157/8x - 15/2 = 0\n(x - 3/8)(x - -20) = 0\nx - 3/8 = 0 or x - -20 = 0\nx = 3/8\nx = -20"} {"input": "Find the solution to 7x - 56/5 = 0", "output": "7x - 56/5 = 0\n7x = 56/5\nx = 56/5 / 7\nx = 8/5"} {"input": "Solve the system:\n3x + 6y = -173/21\n6x + 1y = -730/63", "output": "3x + 6y = -173/21\n6x + 1y = -730/63\n\nUsing elimination\n6*(3x + 6y = -173/21)\n3*(6x + 1y = -730/63)\n18x + 36y = -346/7\n18x + 3y = -730/21\nSubtract equations\n33y = -44/3\ny = -44/3/33\ny = -4/9\n\nSubstitute y\n3x + 6(-4/9) = -173/21\n3x = -39/7\nx = -39/7/3\nx = -13/7"} {"input": "Solve simultaneously:\n10x + 6y = 130/9\n1x + 1y = 25/9", "output": "10x + 6y = 130/9\n1x + 1y = 25/9\n\nUsing elimination\n1*(10x + 6y = 130/9)\n10*(1x + 1y = 25/9)\n10x + 6y = 130/9\n10x + 10y = 250/9\nSubtract equations\n-4y = -40/3\ny = -40/3/-4\ny = 10/3\n\nSubstitute y\n10x + 6(10/3) = 130/9\n10x = -50/9\nx = -50/9/10\nx = -5/9"} {"input": "Solve the equations:\n8x + 2y = 38\n1x + 9y = 719/4", "output": "8x + 2y = 38\n1x + 9y = 719/4\n\nUsing elimination\n1*(8x + 2y = 38)\n8*(1x + 9y = 719/4)\n8x + 2y = 38\n8x + 72y = 1438\nSubtract equations\n-70y = -1400\ny = -1400/-70\ny = 20\n\nSubstitute y\n8x + 2(20) = 38\n8x = -2\nx = -2/8\nx = -1/4"} {"input": "Find x for 10x + 20/3 = 0", "output": "10x + 20/3 = 0\n10x = -20/3\nx = -20/3 / 10\nx = -2/3"} {"input": "Find x for 6x - 51/2 = 0", "output": "6x - 51/2 = 0\n6x = 51/2\nx = 51/2 / 6\nx = 17/4"} {"input": "Solve the equations:\n6x + 9y = -48/5\n5x + 5y = -11/2", "output": "6x + 9y = -48/5\n5x + 5y = -11/2\n\nUsing elimination\n5*(6x + 9y = -48/5)\n6*(5x + 5y = -11/2)\n30x + 45y = -48\n30x + 30y = -33\nSubtract equations\n15y = -15\ny = -15/15\ny = -1\n\nSubstitute y\n6x + 9(-1) = -48/5\n6x = -3/5\nx = -3/5/6\nx = -1/10"} {"input": "Solve 1x + 5/9 = 0", "output": "1x + 5/9 = 0\n1x = -5/9\nx = -5/9 / 1\nx = -5/9"} {"input": "Find the solution to x^3 + 11/12x^2 - 19/8x - 15/8 = 0", "output": "x^3 + 11/12x^2 - 19/8x - 15/8 = 0\n(x - -3/4)(x - 3/2)(x - -5/3) = 0\nx - -3/4 = 0\nx - 3/2 = 0\nx - -5/3 = 0\nx = -3/4\nx = 3/2\nx = -5/3"} {"input": "Solve quickly: x^3 + 159/8x^2 + 285/32x - 4693/32 = 0", "output": "x^3 + 159/8x^2 + 285/32x - 4693/32 = 0\n(x - -13/4)(x - -19)(x - 19/8) = 0\nx - -13/4 = 0\nx - -19 = 0\nx - 19/8 = 0\nx = -13/4\nx = -19\nx = 19/8"} {"input": "Find x and y such that\n10x + 10y = -75/2\n10x + 7y = -33", "output": "10x + 10y = -75/2\n10x + 7y = -33\n\nUsing elimination\n10*(10x + 10y = -75/2)\n10*(10x + 7y = -33)\n100x + 100y = -375\n100x + 70y = -330\nSubtract equations\n30y = -45\ny = -45/30\ny = -3/2\n\nSubstitute y\n10x + 10(-3/2) = -75/2\n10x = -45/2\nx = -45/2/10\nx = -9/4"} {"input": "Determine x in x^2 - 3x - 10 = 0", "output": "x^2 - 3x - 10 = 0\n(x - 5)(x - -2) = 0\nx - 5 = 0 or x - -2 = 0\nx = 5\nx = -2"} {"input": "What value of x satisfies x^3 - 49/10x^2 + 72/5 = 0", "output": "x^3 - 49/10x^2 + 72/5 = 0\n(x - -3/2)(x - 4)(x - 12/5) = 0\nx - -3/2 = 0\nx - 4 = 0\nx - 12/5 = 0\nx = -3/2\nx = 4\nx = 12/5"} {"input": "Solve the system:\n9x + 10y = -109/4\n1x + 8y = -53/3", "output": "9x + 10y = -109/4\n1x + 8y = -53/3\n\nUsing elimination\n1*(9x + 10y = -109/4)\n9*(1x + 8y = -53/3)\n9x + 10y = -109/4\n9x + 72y = -159\nSubtract equations\n-62y = 527/4\ny = 527/4/-62\ny = -17/8\n\nSubstitute y\n9x + 10(-17/8) = -109/4\n9x = -6\nx = -6/9\nx = -2/3"} {"input": "What value of x satisfies x^3 - 24/5x^2 + 3x + 4/5 = 0", "output": "x^3 - 24/5x^2 + 3x + 4/5 = 0\n(x - -1/5)(x - 4)(x - 1) = 0\nx - -1/5 = 0\nx - 4 = 0\nx - 1 = 0\nx = -1/5\nx = 4\nx = 1"} {"input": "Solve the system:\n10x + 9y = -30\n5x + 9y = -20", "output": "10x + 9y = -30\n5x + 9y = -20\n\nUsing elimination\n5*(10x + 9y = -30)\n10*(5x + 9y = -20)\n50x + 45y = -150\n50x + 90y = -200\nSubtract equations\n-45y = 50\ny = 50/-45\ny = -10/9\n\nSubstitute y\n10x + 9(-10/9) = -30\n10x = -20\nx = -20/10\nx = -2"} {"input": "Compute the solution of 4x - 20/3 = 0", "output": "4x - 20/3 = 0\n4x = 20/3\nx = 20/3 / 4\nx = 5/3"} {"input": "Solve the equation x^2 + 19/8x + 21/16 = 0", "output": "x^2 + 19/8x + 21/16 = 0\n(x - -7/8)(x - -3/2) = 0\nx - -7/8 = 0 or x - -3/2 = 0\nx = -7/8\nx = -3/2"} {"input": "Solve simultaneously:\n2x + 3y = 7/2\n5x + 3y = 71/4", "output": "2x + 3y = 7/2\n5x + 3y = 71/4\n\nUsing elimination\n5*(2x + 3y = 7/2)\n2*(5x + 3y = 71/4)\n10x + 15y = 35/2\n10x + 6y = 71/2\nSubtract equations\n9y = -18\ny = -18/9\ny = -2\n\nSubstitute y\n2x + 3(-2) = 7/2\n2x = 19/2\nx = 19/2/2\nx = 19/4"} {"input": "Solve quickly: 3x + 42 = 0", "output": "3x + 42 = 0\n3x = -42\nx = -42 / 3\nx = -14"} {"input": "Solve quickly: 3x + 7 = 0", "output": "3x + 7 = 0\n3x = -7\nx = -7 / 3\nx = -7/3"} {"input": "Solve the equations:\n10x + 1y = -335/9\n6x + 2y = -956/45", "output": "10x + 1y = -335/9\n6x + 2y = -956/45\n\nUsing elimination\n6*(10x + 1y = -335/9)\n10*(6x + 2y = -956/45)\n60x + 6y = -670/3\n60x + 20y = -1912/9\nSubtract equations\n-14y = -98/9\ny = -98/9/-14\ny = 7/9\n\nSubstitute y\n10x + 1(7/9) = -335/9\n10x = -38\nx = -38/10\nx = -19/5"} {"input": "Determine x in 9x + 81/10 = 0", "output": "9x + 81/10 = 0\n9x = -81/10\nx = -81/10 / 9\nx = -9/10"} {"input": "Find x and y such that\n10x + 7y = 76\n3x + 1y = 64/3", "output": "10x + 7y = 76\n3x + 1y = 64/3\n\nUsing elimination\n3*(10x + 7y = 76)\n10*(3x + 1y = 64/3)\n30x + 21y = 228\n30x + 10y = 640/3\nSubtract equations\n11y = 44/3\ny = 44/3/11\ny = 4/3\n\nSubstitute y\n10x + 7(4/3) = 76\n10x = 200/3\nx = 200/3/10\nx = 20/3"} {"input": "Solve the equations:\n3x + 4y = 45/2\n1x + 1y = 13/2", "output": "3x + 4y = 45/2\n1x + 1y = 13/2\n\nUsing elimination\n1*(3x + 4y = 45/2)\n3*(1x + 1y = 13/2)\n3x + 4y = 45/2\n3x + 3y = 39/2\nSubtract equations\n1y = 3\ny = 3/1\ny = 3\n\nSubstitute y\n3x + 4(3) = 45/2\n3x = 21/2\nx = 21/2/3\nx = 7/2"} {"input": "Solve x^2 - 9x - 90 = 0", "output": "x^2 - 9x - 90 = 0\n(x - -6)(x - 15) = 0\nx - -6 = 0 or x - 15 = 0\nx = -6\nx = 15"} {"input": "Find x for x^3 + 173/18x^2 - 371/9x + 221/6 = 0", "output": "x^3 + 173/18x^2 - 371/9x + 221/6 = 0\n(x - -13)(x - 3/2)(x - 17/9) = 0\nx - -13 = 0\nx - 3/2 = 0\nx - 17/9 = 0\nx = -13\nx = 3/2\nx = 17/9"} {"input": "Solve the equations:\n2x + 3y = -31/7\n7x + 5y = -81/7", "output": "2x + 3y = -31/7\n7x + 5y = -81/7\n\nUsing elimination\n7*(2x + 3y = -31/7)\n2*(7x + 5y = -81/7)\n14x + 21y = -31\n14x + 10y = -162/7\nSubtract equations\n11y = -55/7\ny = -55/7/11\ny = -5/7\n\nSubstitute y\n2x + 3(-5/7) = -31/7\n2x = -16/7\nx = -16/7/2\nx = -8/7"} {"input": "Find x in 6x + 90/7 = 0", "output": "6x + 90/7 = 0\n6x = -90/7\nx = -90/7 / 6\nx = -15/7"} {"input": "Find x in x^3 - 82/7x^2 - 1205/7x + 900/7 = 0", "output": "x^3 - 82/7x^2 - 1205/7x + 900/7 = 0\n(x - 20)(x - -9)(x - 5/7) = 0\nx - 20 = 0\nx - -9 = 0\nx - 5/7 = 0\nx = 20\nx = -9\nx = 5/7"} {"input": "Find the solution to 5x - 95/4 = 0", "output": "5x - 95/4 = 0\n5x = 95/4\nx = 95/4 / 5\nx = 19/4"} {"input": "Solve the equations:\n2x + 9y = -67/4\n7x + 3y = -343/24", "output": "2x + 9y = -67/4\n7x + 3y = -343/24\n\nUsing elimination\n7*(2x + 9y = -67/4)\n2*(7x + 3y = -343/24)\n14x + 63y = -469/4\n14x + 6y = -343/12\nSubtract equations\n57y = -266/3\ny = -266/3/57\ny = -14/9\n\nSubstitute y\n2x + 9(-14/9) = -67/4\n2x = -11/4\nx = -11/4/2\nx = -11/8"} {"input": "Compute the solution of 2x - 3 = 0", "output": "2x - 3 = 0\n2x = 3\nx = 3 / 2\nx = 3/2"} {"input": "Solve quickly: x^2 - 16 = 0", "output": "x^2 - 16 = 0\n(x - 4)(x - -4) = 0\nx - 4 = 0 or x - -4 = 0\nx = 4\nx = -4"} {"input": "Solve quickly: x^2 + 89/40x + 99/80 = 0", "output": "x^2 + 89/40x + 99/80 = 0\n(x - -9/8)(x - -11/10) = 0\nx - -9/8 = 0 or x - -11/10 = 0\nx = -9/8\nx = -11/10"} {"input": "Find the solution to 7x + 119/8 = 0", "output": "7x + 119/8 = 0\n7x = -119/8\nx = -119/8 / 7\nx = -17/8"} {"input": "Solve the equation x^3 + 108/35x^2 + 387/140x + 81/140 = 0", "output": "x^3 + 108/35x^2 + 387/140x + 81/140 = 0\n(x - -9/7)(x - -3/2)(x - -3/10) = 0\nx - -9/7 = 0\nx - -3/2 = 0\nx - -3/10 = 0\nx = -9/7\nx = -3/2\nx = -3/10"} {"input": "Solve the system:\n10x + 3y = 146\n8x + 9y = 130", "output": "10x + 3y = 146\n8x + 9y = 130\n\nUsing elimination\n8*(10x + 3y = 146)\n10*(8x + 9y = 130)\n80x + 24y = 1168\n80x + 90y = 1300\nSubtract equations\n-66y = -132\ny = -132/-66\ny = 2\n\nSubstitute y\n10x + 3(2) = 146\n10x = 140\nx = 140/10\nx = 14"} {"input": "Solve x^3 + 29/45x^2 - 1564/405x - 64/81 = 0", "output": "x^3 + 29/45x^2 - 1564/405x - 64/81 = 0\n(x - 16/9)(x - -1/5)(x - -20/9) = 0\nx - 16/9 = 0\nx - -1/5 = 0\nx - -20/9 = 0\nx = 16/9\nx = -1/5\nx = -20/9"} {"input": "Find x and y such that\n2x + 6y = 29/4\n5x + 10y = 95/8", "output": "2x + 6y = 29/4\n5x + 10y = 95/8\n\nUsing elimination\n5*(2x + 6y = 29/4)\n2*(5x + 10y = 95/8)\n10x + 30y = 145/4\n10x + 20y = 95/4\nSubtract equations\n10y = 25/2\ny = 25/2/10\ny = 5/4\n\nSubstitute y\n2x + 6(5/4) = 29/4\n2x = -1/4\nx = -1/4/2\nx = -1/8"} {"input": "Compute the solution of 8x - 24 = 0", "output": "8x - 24 = 0\n8x = 24\nx = 24 / 8\nx = 3"} {"input": "Find x for x^3 - 163/24x^2 + 233/24x - 15/4 = 0", "output": "x^3 - 163/24x^2 + 233/24x - 15/4 = 0\n(x - 5)(x - 9/8)(x - 2/3) = 0\nx - 5 = 0\nx - 9/8 = 0\nx - 2/3 = 0\nx = 5\nx = 9/8\nx = 2/3"} {"input": "Determine x in x^3 - 274/9x^2 + 2087/9x - 2470/9 = 0", "output": "x^3 - 274/9x^2 + 2087/9x - 2470/9 = 0\n(x - 10)(x - 13/9)(x - 19) = 0\nx - 10 = 0\nx - 13/9 = 0\nx - 19 = 0\nx = 10\nx = 13/9\nx = 19"} {"input": "Solve quickly: 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "Solve simultaneously:\n9x + 9y = 9/5\n3x + 1y = -17/5", "output": "9x + 9y = 9/5\n3x + 1y = -17/5\n\nUsing elimination\n3*(9x + 9y = 9/5)\n9*(3x + 1y = -17/5)\n27x + 27y = 27/5\n27x + 9y = -153/5\nSubtract equations\n18y = 36\ny = 36/18\ny = 2\n\nSubstitute y\n9x + 9(2) = 9/5\n9x = -81/5\nx = -81/5/9\nx = -9/5"} {"input": "Solve the equations:\n6x + 7y = -25/3\n5x + 2y = -28/9", "output": "6x + 7y = -25/3\n5x + 2y = -28/9\n\nUsing elimination\n5*(6x + 7y = -25/3)\n6*(5x + 2y = -28/9)\n30x + 35y = -125/3\n30x + 12y = -56/3\nSubtract equations\n23y = -23\ny = -23/23\ny = -1\n\nSubstitute y\n6x + 7(-1) = -25/3\n6x = -4/3\nx = -4/3/6\nx = -2/9"} {"input": "Find x in x^3 + 81/20x^2 + 141/40x - 7/8 = 0", "output": "x^3 + 81/20x^2 + 141/40x - 7/8 = 0\n(x - 1/5)(x - -5/2)(x - -7/4) = 0\nx - 1/5 = 0\nx - -5/2 = 0\nx - -7/4 = 0\nx = 1/5\nx = -5/2\nx = -7/4"} {"input": "Find the solution to x^3 - 3/2x^2 - 35/2x + 18 = 0", "output": "x^3 - 3/2x^2 - 35/2x + 18 = 0\n(x - 9/2)(x - -4)(x - 1) = 0\nx - 9/2 = 0\nx - -4 = 0\nx - 1 = 0\nx = 9/2\nx = -4\nx = 1"} {"input": "Find the solution to x^3 + 125/18x^2 - 175/6x + 125/9 = 0", "output": "x^3 + 125/18x^2 - 175/6x + 125/9 = 0\n(x - 5/2)(x - -10)(x - 5/9) = 0\nx - 5/2 = 0\nx - -10 = 0\nx - 5/9 = 0\nx = 5/2\nx = -10\nx = 5/9"} {"input": "Find x in x^2 + 1x = 0", "output": "x^2 + 1x = 0\n(x - -1)(x - 0) = 0\nx - -1 = 0 or x - 0 = 0\nx = -1\nx = 0"} {"input": "Solve the equation x^3 + 5/2x^2 - 57/4x + 99/8 = 0", "output": "x^3 + 5/2x^2 - 57/4x + 99/8 = 0\n(x - 3/2)(x - -11/2)(x - 3/2) = 0\nx - 3/2 = 0\nx - -11/2 = 0\nx - 3/2 = 0\nx = 3/2\nx = -11/2\nx = 3/2"} {"input": "Solve the equation x^2 - 6x + 5 = 0", "output": "x^2 - 6x + 5 = 0\n(x - 1)(x - 5) = 0\nx - 1 = 0 or x - 5 = 0\nx = 1\nx = 5"} {"input": "Find the solution to 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Find x in x^2 + 1/42x - 1/42 = 0", "output": "x^2 + 1/42x - 1/42 = 0\n(x - -1/6)(x - 1/7) = 0\nx - -1/6 = 0 or x - 1/7 = 0\nx = -1/6\nx = 1/7"} {"input": "Solve quickly: x^2 + 3/2x - 1 = 0", "output": "x^2 + 3/2x - 1 = 0\n(x - -2)(x - 1/2) = 0\nx - -2 = 0 or x - 1/2 = 0\nx = -2\nx = 1/2"} {"input": "Determine x in 2x - 7 = 0", "output": "2x - 7 = 0\n2x = 7\nx = 7 / 2\nx = 7/2"} {"input": "Find x and y such that\n5x + 7y = -11/2\n7x + 2y = 59/5", "output": "5x + 7y = -11/2\n7x + 2y = 59/5\n\nUsing elimination\n7*(5x + 7y = -11/2)\n5*(7x + 2y = 59/5)\n35x + 49y = -77/2\n35x + 10y = 59\nSubtract equations\n39y = -195/2\ny = -195/2/39\ny = -5/2\n\nSubstitute y\n5x + 7(-5/2) = -11/2\n5x = 12\nx = 12/5\nx = 12/5"} {"input": "What value of x satisfies x^2 + 2x - 8 = 0", "output": "x^2 + 2x - 8 = 0\n(x - 2)(x - -4) = 0\nx - 2 = 0 or x - -4 = 0\nx = 2\nx = -4"} {"input": "Find the solution to 1x - 4/9 = 0", "output": "1x - 4/9 = 0\n1x = 4/9\nx = 4/9 / 1\nx = 4/9"} {"input": "Solve the equation x^2 + 26/5x + 1 = 0", "output": "x^2 + 26/5x + 1 = 0\n(x - -1/5)(x - -5) = 0\nx - -1/5 = 0 or x - -5 = 0\nx = -1/5\nx = -5"} {"input": "Solve quickly: 1x + 10 = 0", "output": "1x + 10 = 0\n1x = -10\nx = -10 / 1\nx = -10"} {"input": "Solve the system:\n10x + 3y = 12\n7x + 7y = 7/2", "output": "10x + 3y = 12\n7x + 7y = 7/2\n\nUsing elimination\n7*(10x + 3y = 12)\n10*(7x + 7y = 7/2)\n70x + 21y = 84\n70x + 70y = 35\nSubtract equations\n-49y = 49\ny = 49/-49\ny = -1\n\nSubstitute y\n10x + 3(-1) = 12\n10x = 15\nx = 15/10\nx = 3/2"} {"input": "Solve 10x - 75 = 0", "output": "10x - 75 = 0\n10x = 75\nx = 75 / 10\nx = 15/2"} {"input": "Compute the solution of x^2 + 37/10x - 6/5 = 0", "output": "x^2 + 37/10x - 6/5 = 0\n(x - -4)(x - 3/10) = 0\nx - -4 = 0 or x - 3/10 = 0\nx = -4\nx = 3/10"} {"input": "Compute the solution of x^3 - 19/42x^2 - 193/21x + 80/7 = 0", "output": "x^3 - 19/42x^2 - 193/21x + 80/7 = 0\n(x - 16/7)(x - -10/3)(x - 3/2) = 0\nx - 16/7 = 0\nx - -10/3 = 0\nx - 3/2 = 0\nx = 16/7\nx = -10/3\nx = 3/2"} {"input": "Find x in x^3 + 29/24x^2 - 221/48x = 0", "output": "x^3 + 29/24x^2 - 221/48x = 0\n(x - 0)(x - -17/6)(x - 13/8) = 0\nx - 0 = 0\nx - -17/6 = 0\nx - 13/8 = 0\nx = 0\nx = -17/6\nx = 13/8"} {"input": "Solve the equation x^2 - 49/6x - 17/6 = 0", "output": "x^2 - 49/6x - 17/6 = 0\n(x - 17/2)(x - -1/3) = 0\nx - 17/2 = 0 or x - -1/3 = 0\nx = 17/2\nx = -1/3"} {"input": "Solve x^3 - 77/12x^2 + 4x + 17/12 = 0", "output": "x^3 - 77/12x^2 + 4x + 17/12 = 0\n(x - 1)(x - -1/4)(x - 17/3) = 0\nx - 1 = 0\nx - -1/4 = 0\nx - 17/3 = 0\nx = 1\nx = -1/4\nx = 17/3"} {"input": "Solve simultaneously:\n3x + 6y = -5\n10x + 4y = -10/3", "output": "3x + 6y = -5\n10x + 4y = -10/3\n\nUsing elimination\n10*(3x + 6y = -5)\n3*(10x + 4y = -10/3)\n30x + 60y = -50\n30x + 12y = -10\nSubtract equations\n48y = -40\ny = -40/48\ny = -5/6\n\nSubstitute y\n3x + 6(-5/6) = -5\n3x = 0\nx = 0/3\nx = 0"} {"input": "Compute the solution of x^3 - 4x^2 - 52x - 80 = 0", "output": "x^3 - 4x^2 - 52x - 80 = 0\n(x - -2)(x - -4)(x - 10) = 0\nx - -2 = 0\nx - -4 = 0\nx - 10 = 0\nx = -2\nx = -4\nx = 10"} {"input": "Find x in 9x + 13 = 0", "output": "9x + 13 = 0\n9x = -13\nx = -13 / 9\nx = -13/9"} {"input": "Determine x in x^3 + 53/9x^2 + 862/81x + 160/27 = 0", "output": "x^3 + 53/9x^2 + 862/81x + 160/27 = 0\n(x - -3)(x - -16/9)(x - -10/9) = 0\nx - -3 = 0\nx - -16/9 = 0\nx - -10/9 = 0\nx = -3\nx = -16/9\nx = -10/9"} {"input": "Find x and y such that\n2x + 4y = -46/9\n7x + 5y = -233/9", "output": "2x + 4y = -46/9\n7x + 5y = -233/9\n\nUsing elimination\n7*(2x + 4y = -46/9)\n2*(7x + 5y = -233/9)\n14x + 28y = -322/9\n14x + 10y = -466/9\nSubtract equations\n18y = 16\ny = 16/18\ny = 8/9\n\nSubstitute y\n2x + 4(8/9) = -46/9\n2x = -26/3\nx = -26/3/2\nx = -13/3"} {"input": "Find x in 10x - 180/7 = 0", "output": "10x - 180/7 = 0\n10x = 180/7\nx = 180/7 / 10\nx = 18/7"} {"input": "Solve quickly: x^2 + 1/10x = 0", "output": "x^2 + 1/10x = 0\n(x - 0)(x - -1/10) = 0\nx - 0 = 0 or x - -1/10 = 0\nx = 0\nx = -1/10"} {"input": "Find x and y such that\n5x + 1y = -13/6\n5x + 9y = -23/2", "output": "5x + 1y = -13/6\n5x + 9y = -23/2\n\nUsing elimination\n5*(5x + 1y = -13/6)\n5*(5x + 9y = -23/2)\n25x + 5y = -65/6\n25x + 45y = -115/2\nSubtract equations\n-40y = 140/3\ny = 140/3/-40\ny = -7/6\n\nSubstitute y\n5x + 1(-7/6) = -13/6\n5x = -1\nx = -1/5\nx = -1/5"} {"input": "Determine x in x^2 - 115/6x + 221/6 = 0", "output": "x^2 - 115/6x + 221/6 = 0\n(x - 17)(x - 13/6) = 0\nx - 17 = 0 or x - 13/6 = 0\nx = 17\nx = 13/6"} {"input": "Find the solution to x^3 - 31/20x^2 - 6/5x + 27/20 = 0", "output": "x^3 - 31/20x^2 - 6/5x + 27/20 = 0\n(x - 3/4)(x - 9/5)(x - -1) = 0\nx - 3/4 = 0\nx - 9/5 = 0\nx - -1 = 0\nx = 3/4\nx = 9/5\nx = -1"} {"input": "Solve x^2 + 22/5x + 63/20 = 0", "output": "x^2 + 22/5x + 63/20 = 0\n(x - -9/10)(x - -7/2) = 0\nx - -9/10 = 0 or x - -7/2 = 0\nx = -9/10\nx = -7/2"} {"input": "Find x in x^2 + 3x + 182/81 = 0", "output": "x^2 + 3x + 182/81 = 0\n(x - -13/9)(x - -14/9) = 0\nx - -13/9 = 0 or x - -14/9 = 0\nx = -13/9\nx = -14/9"} {"input": "Solve quickly: x^3 - 287/60x^2 + 97/24x - 5/8 = 0", "output": "x^3 - 287/60x^2 + 97/24x - 5/8 = 0\n(x - 15/4)(x - 5/6)(x - 1/5) = 0\nx - 15/4 = 0\nx - 5/6 = 0\nx - 1/5 = 0\nx = 15/4\nx = 5/6\nx = 1/5"} {"input": "Find the solution to x^3 - 115/36x^2 + 73/36x + 13/18 = 0", "output": "x^3 - 115/36x^2 + 73/36x + 13/18 = 0\n(x - 13/9)(x - 2)(x - -1/4) = 0\nx - 13/9 = 0\nx - 2 = 0\nx - -1/4 = 0\nx = 13/9\nx = 2\nx = -1/4"} {"input": "Compute the solution of x^3 + 51/4x^2 + 159/8x + 55/8 = 0", "output": "x^3 + 51/4x^2 + 159/8x + 55/8 = 0\n(x - -1/2)(x - -5/4)(x - -11) = 0\nx - -1/2 = 0\nx - -5/4 = 0\nx - -11 = 0\nx = -1/2\nx = -5/4\nx = -11"} {"input": "Solve quickly: 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Solve the equations:\n8x + 10y = 662/9\n1x + 7y = 445/9", "output": "8x + 10y = 662/9\n1x + 7y = 445/9\n\nUsing elimination\n1*(8x + 10y = 662/9)\n8*(1x + 7y = 445/9)\n8x + 10y = 662/9\n8x + 56y = 3560/9\nSubtract equations\n-46y = -322\ny = -322/-46\ny = 7\n\nSubstitute y\n8x + 10(7) = 662/9\n8x = 32/9\nx = 32/9/8\nx = 4/9"} {"input": "Find x for 2x - 10/3 = 0", "output": "2x - 10/3 = 0\n2x = 10/3\nx = 10/3 / 2\nx = 5/3"} {"input": "Find x in x^3 - 53/6x^2 - 109/3x - 20 = 0", "output": "x^3 - 53/6x^2 - 109/3x - 20 = 0\n(x - 12)(x - -2/3)(x - -5/2) = 0\nx - 12 = 0\nx - -2/3 = 0\nx - -5/2 = 0\nx = 12\nx = -2/3\nx = -5/2"} {"input": "Solve the equations:\n2x + 8y = 482/63\n1x + 8y = 349/63", "output": "2x + 8y = 482/63\n1x + 8y = 349/63\n\nUsing elimination\n1*(2x + 8y = 482/63)\n2*(1x + 8y = 349/63)\n2x + 8y = 482/63\n2x + 16y = 698/63\nSubtract equations\n-8y = -24/7\ny = -24/7/-8\ny = 3/7\n\nSubstitute y\n2x + 8(3/7) = 482/63\n2x = 38/9\nx = 38/9/2\nx = 19/9"} {"input": "Solve the equations:\n3x + 6y = 156/5\n3x + 5y = 131/5", "output": "3x + 6y = 156/5\n3x + 5y = 131/5\n\nUsing elimination\n3*(3x + 6y = 156/5)\n3*(3x + 5y = 131/5)\n9x + 18y = 468/5\n9x + 15y = 393/5\nSubtract equations\n3y = 15\ny = 15/3\ny = 5\n\nSubstitute y\n3x + 6(5) = 156/5\n3x = 6/5\nx = 6/5/3\nx = 2/5"} {"input": "Determine x in x^2 + 45/7x + 68/7 = 0", "output": "x^2 + 45/7x + 68/7 = 0\n(x - -4)(x - -17/7) = 0\nx - -4 = 0 or x - -17/7 = 0\nx = -4\nx = -17/7"} {"input": "What value of x satisfies 9x + 117/8 = 0", "output": "9x + 117/8 = 0\n9x = -117/8\nx = -117/8 / 9\nx = -13/8"} {"input": "Determine x in x^3 - 97/15x^2 + 56/5x - 16/3 = 0", "output": "x^3 - 97/15x^2 + 56/5x - 16/3 = 0\n(x - 5/3)(x - 4/5)(x - 4) = 0\nx - 5/3 = 0\nx - 4/5 = 0\nx - 4 = 0\nx = 5/3\nx = 4/5\nx = 4"} {"input": "Solve quickly: x^3 + 61/45x^2 - 61/45x - 1 = 0", "output": "x^3 + 61/45x^2 - 61/45x - 1 = 0\n(x - -5/9)(x - -9/5)(x - 1) = 0\nx - -5/9 = 0\nx - -9/5 = 0\nx - 1 = 0\nx = -5/9\nx = -9/5\nx = 1"} {"input": "Solve simultaneously:\n4x + 1y = 67/9\n5x + 10y = 1265/9", "output": "4x + 1y = 67/9\n5x + 10y = 1265/9\n\nUsing elimination\n5*(4x + 1y = 67/9)\n4*(5x + 10y = 1265/9)\n20x + 5y = 335/9\n20x + 40y = 5060/9\nSubtract equations\n-35y = -525\ny = -525/-35\ny = 15\n\nSubstitute y\n4x + 1(15) = 67/9\n4x = -68/9\nx = -68/9/4\nx = -17/9"} {"input": "Solve the equation x^2 + 3/2x - 27 = 0", "output": "x^2 + 3/2x - 27 = 0\n(x - 9/2)(x - -6) = 0\nx - 9/2 = 0 or x - -6 = 0\nx = 9/2\nx = -6"} {"input": "Compute the solution of x^2 + 17/2x - 15 = 0", "output": "x^2 + 17/2x - 15 = 0\n(x - -10)(x - 3/2) = 0\nx - -10 = 0 or x - 3/2 = 0\nx = -10\nx = 3/2"} {"input": "Find the solution to 7x - 7 = 0", "output": "7x - 7 = 0\n7x = 7\nx = 7 / 7\nx = 1"} {"input": "Solve the equations:\n8x + 10y = 34\n4x + 2y = 67/5", "output": "8x + 10y = 34\n4x + 2y = 67/5\n\nUsing elimination\n4*(8x + 10y = 34)\n8*(4x + 2y = 67/5)\n32x + 40y = 136\n32x + 16y = 536/5\nSubtract equations\n24y = 144/5\ny = 144/5/24\ny = 6/5\n\nSubstitute y\n8x + 10(6/5) = 34\n8x = 22\nx = 22/8\nx = 11/4"} {"input": "Determine x in x^2 + 4x - 77 = 0", "output": "x^2 + 4x - 77 = 0\n(x - 7)(x - -11) = 0\nx - 7 = 0 or x - -11 = 0\nx = 7\nx = -11"} {"input": "What value of x satisfies x^3 - 101/45x^2 + 52/45x = 0", "output": "x^3 - 101/45x^2 + 52/45x = 0\n(x - 13/9)(x - 0)(x - 4/5) = 0\nx - 13/9 = 0\nx - 0 = 0\nx - 4/5 = 0\nx = 13/9\nx = 0\nx = 4/5"} {"input": "Find x for x^3 - 32/63x^2 - 43/7x - 4 = 0", "output": "x^3 - 32/63x^2 - 43/7x - 4 = 0\n(x - 3)(x - -7/9)(x - -12/7) = 0\nx - 3 = 0\nx - -7/9 = 0\nx - -12/7 = 0\nx = 3\nx = -7/9\nx = -12/7"} {"input": "What value of x satisfies x^3 + 4x^2 - 243/4x - 765/4 = 0", "output": "x^3 + 4x^2 - 243/4x - 765/4 = 0\n(x - -3)(x - -17/2)(x - 15/2) = 0\nx - -3 = 0\nx - -17/2 = 0\nx - 15/2 = 0\nx = -3\nx = -17/2\nx = 15/2"} {"input": "Compute the solution of x^3 + 13/7x^2 - 2/7x = 0", "output": "x^3 + 13/7x^2 - 2/7x = 0\n(x - 1/7)(x - 0)(x - -2) = 0\nx - 1/7 = 0\nx - 0 = 0\nx - -2 = 0\nx = 1/7\nx = 0\nx = -2"} {"input": "Solve 2x - 32/5 = 0", "output": "2x - 32/5 = 0\n2x = 32/5\nx = 32/5 / 2\nx = 16/5"} {"input": "Find x and y such that\n5x + 4y = 42/5\n1x + 8y = -78/5", "output": "5x + 4y = 42/5\n1x + 8y = -78/5\n\nUsing elimination\n1*(5x + 4y = 42/5)\n5*(1x + 8y = -78/5)\n5x + 4y = 42/5\n5x + 40y = -78\nSubtract equations\n-36y = 432/5\ny = 432/5/-36\ny = -12/5\n\nSubstitute y\n5x + 4(-12/5) = 42/5\n5x = 18\nx = 18/5\nx = 18/5"} {"input": "Determine x in x^2 - 3/2x + 1/2 = 0", "output": "x^2 - 3/2x + 1/2 = 0\n(x - 1/2)(x - 1) = 0\nx - 1/2 = 0 or x - 1 = 0\nx = 1/2\nx = 1"} {"input": "Solve x^3 + 49/5x^2 + 72/5x = 0", "output": "x^3 + 49/5x^2 + 72/5x = 0\n(x - -9/5)(x - 0)(x - -8) = 0\nx - -9/5 = 0\nx - 0 = 0\nx - -8 = 0\nx = -9/5\nx = 0\nx = -8"} {"input": "Solve quickly: x^3 - 4x = 0", "output": "x^3 - 4x = 0\n(x - -2)(x - 2)(x - 0) = 0\nx - -2 = 0\nx - 2 = 0\nx - 0 = 0\nx = -2\nx = 2\nx = 0"} {"input": "Solve the equation x^2 + 31/2x + 55 = 0", "output": "x^2 + 31/2x + 55 = 0\n(x - -11/2)(x - -10) = 0\nx - -11/2 = 0 or x - -10 = 0\nx = -11/2\nx = -10"} {"input": "Find the solution to x^3 - 47/42x^2 - 16/21x + 2/7 = 0", "output": "x^3 - 47/42x^2 - 16/21x + 2/7 = 0\n(x - 2/7)(x - -2/3)(x - 3/2) = 0\nx - 2/7 = 0\nx - -2/3 = 0\nx - 3/2 = 0\nx = 2/7\nx = -2/3\nx = 3/2"} {"input": "Solve the system:\n9x + 2y = -1441/72\n5x + 1y = -797/72", "output": "9x + 2y = -1441/72\n5x + 1y = -797/72\n\nUsing elimination\n5*(9x + 2y = -1441/72)\n9*(5x + 1y = -797/72)\n45x + 10y = -7205/72\n45x + 9y = -797/8\nSubtract equations\n1y = -4/9\ny = -4/9/1\ny = -4/9\n\nSubstitute y\n9x + 2(-4/9) = -1441/72\n9x = -153/8\nx = -153/8/9\nx = -17/8"} {"input": "Find x in 8x - 10 = 0", "output": "8x - 10 = 0\n8x = 10\nx = 10 / 8\nx = 5/4"} {"input": "Solve the system:\n10x + 10y = 1/3\n4x + 6y = 4/5", "output": "10x + 10y = 1/3\n4x + 6y = 4/5\n\nUsing elimination\n4*(10x + 10y = 1/3)\n10*(4x + 6y = 4/5)\n40x + 40y = 4/3\n40x + 60y = 8\nSubtract equations\n-20y = -20/3\ny = -20/3/-20\ny = 1/3\n\nSubstitute y\n10x + 10(1/3) = 1/3\n10x = -3\nx = -3/10\nx = -3/10"} {"input": "Find the solution to x^2 + 101/7x - 60/7 = 0", "output": "x^2 + 101/7x - 60/7 = 0\n(x - 4/7)(x - -15) = 0\nx - 4/7 = 0 or x - -15 = 0\nx = 4/7\nx = -15"} {"input": "Find the solution to 8x - 36 = 0", "output": "8x - 36 = 0\n8x = 36\nx = 36 / 8\nx = 9/2"} {"input": "Solve simultaneously:\n1x + 8y = 43/3\n5x + 7y = 17/3", "output": "1x + 8y = 43/3\n5x + 7y = 17/3\n\nUsing elimination\n5*(1x + 8y = 43/3)\n1*(5x + 7y = 17/3)\n5x + 40y = 215/3\n5x + 7y = 17/3\nSubtract equations\n33y = 66\ny = 66/33\ny = 2\n\nSubstitute y\n1x + 8(2) = 43/3\n1x = -5/3\nx = -5/3/1\nx = -5/3"} {"input": "Solve the equations:\n1x + 1y = -13/2\n6x + 10y = -73", "output": "1x + 1y = -13/2\n6x + 10y = -73\n\nUsing elimination\n6*(1x + 1y = -13/2)\n1*(6x + 10y = -73)\n6x + 6y = -39\n6x + 10y = -73\nSubtract equations\n-4y = 34\ny = 34/-4\ny = -17/2\n\nSubstitute y\n1x + 1(-17/2) = -13/2\n1x = 2\nx = 2/1\nx = 2"} {"input": "Compute the solution of 1x - 7/2 = 0", "output": "1x - 7/2 = 0\n1x = 7/2\nx = 7/2 / 1\nx = 7/2"} {"input": "Compute the solution of x^2 + 8x + 12 = 0", "output": "x^2 + 8x + 12 = 0\n(x - -6)(x - -2) = 0\nx - -6 = 0 or x - -2 = 0\nx = -6\nx = -2"} {"input": "Solve simultaneously:\n9x + 4y = 133\n10x + 1y = 165", "output": "9x + 4y = 133\n10x + 1y = 165\n\nUsing elimination\n10*(9x + 4y = 133)\n9*(10x + 1y = 165)\n90x + 40y = 1330\n90x + 9y = 1485\nSubtract equations\n31y = -155\ny = -155/31\ny = -5\n\nSubstitute y\n9x + 4(-5) = 133\n9x = 153\nx = 153/9\nx = 17"} {"input": "Solve the equations:\n7x + 10y = 80/9\n7x + 6y = 16/3", "output": "7x + 10y = 80/9\n7x + 6y = 16/3\n\nUsing elimination\n7*(7x + 10y = 80/9)\n7*(7x + 6y = 16/3)\n49x + 70y = 560/9\n49x + 42y = 112/3\nSubtract equations\n28y = 224/9\ny = 224/9/28\ny = 8/9\n\nSubstitute y\n7x + 10(8/9) = 80/9\n7x = 0\nx = 0/7\nx = 0"} {"input": "Solve the equations:\n1x + 2y = -4\n4x + 4y = -14", "output": "1x + 2y = -4\n4x + 4y = -14\n\nUsing elimination\n4*(1x + 2y = -4)\n1*(4x + 4y = -14)\n4x + 8y = -16\n4x + 4y = -14\nSubtract equations\n4y = -2\ny = -2/4\ny = -1/2\n\nSubstitute y\n1x + 2(-1/2) = -4\n1x = -3\nx = -3/1\nx = -3"} {"input": "Solve the system:\n2x + 6y = 97/6\n5x + 8y = 1091/36", "output": "2x + 6y = 97/6\n5x + 8y = 1091/36\n\nUsing elimination\n5*(2x + 6y = 97/6)\n2*(5x + 8y = 1091/36)\n10x + 30y = 485/6\n10x + 16y = 1091/18\nSubtract equations\n14y = 182/9\ny = 182/9/14\ny = 13/9\n\nSubstitute y\n2x + 6(13/9) = 97/6\n2x = 15/2\nx = 15/2/2\nx = 15/4"} {"input": "Solve the system:\n10x + 4y = 73/3\n4x + 6y = 20", "output": "10x + 4y = 73/3\n4x + 6y = 20\n\nUsing elimination\n4*(10x + 4y = 73/3)\n10*(4x + 6y = 20)\n40x + 16y = 292/3\n40x + 60y = 200\nSubtract equations\n-44y = -308/3\ny = -308/3/-44\ny = 7/3\n\nSubstitute y\n10x + 4(7/3) = 73/3\n10x = 15\nx = 15/10\nx = 3/2"} {"input": "Solve quickly: x^2 - 35/9x - 4/9 = 0", "output": "x^2 - 35/9x - 4/9 = 0\n(x - -1/9)(x - 4) = 0\nx - -1/9 = 0 or x - 4 = 0\nx = -1/9\nx = 4"} {"input": "Find the solution to 1x - 1/5 = 0", "output": "1x - 1/5 = 0\n1x = 1/5\nx = 1/5 / 1\nx = 1/5"} {"input": "Solve quickly: x^2 - 5/2x - 6 = 0", "output": "x^2 - 5/2x - 6 = 0\n(x - -3/2)(x - 4) = 0\nx - -3/2 = 0 or x - 4 = 0\nx = -3/2\nx = 4"} {"input": "Find x in x^2 - 3/8x - 11/8 = 0", "output": "x^2 - 3/8x - 11/8 = 0\n(x - -1)(x - 11/8) = 0\nx - -1 = 0 or x - 11/8 = 0\nx = -1\nx = 11/8"} {"input": "Solve the equations:\n9x + 10y = -34\n8x + 6y = -23", "output": "9x + 10y = -34\n8x + 6y = -23\n\nUsing elimination\n8*(9x + 10y = -34)\n9*(8x + 6y = -23)\n72x + 80y = -272\n72x + 54y = -207\nSubtract equations\n26y = -65\ny = -65/26\ny = -5/2\n\nSubstitute y\n9x + 10(-5/2) = -34\n9x = -9\nx = -9/9\nx = -1"} {"input": "Find x and y such that\n8x + 6y = 24\n8x + 3y = 17", "output": "8x + 6y = 24\n8x + 3y = 17\n\nUsing elimination\n8*(8x + 6y = 24)\n8*(8x + 3y = 17)\n64x + 48y = 192\n64x + 24y = 136\nSubtract equations\n24y = 56\ny = 56/24\ny = 7/3\n\nSubstitute y\n8x + 6(7/3) = 24\n8x = 10\nx = 10/8\nx = 5/4"} {"input": "Solve x^2 + 13/9x - 16/27 = 0", "output": "x^2 + 13/9x - 16/27 = 0\n(x - 1/3)(x - -16/9) = 0\nx - 1/3 = 0 or x - -16/9 = 0\nx = 1/3\nx = -16/9"} {"input": "Determine x in x^3 + 8/5x^2 - 447/5x - 54 = 0", "output": "x^3 + 8/5x^2 - 447/5x - 54 = 0\n(x - -10)(x - -3/5)(x - 9) = 0\nx - -10 = 0\nx - -3/5 = 0\nx - 9 = 0\nx = -10\nx = -3/5\nx = 9"} {"input": "Determine x in 3x - 6 = 0", "output": "3x - 6 = 0\n3x = 6\nx = 6 / 3\nx = 2"} {"input": "Determine x in 2x - 10/9 = 0", "output": "2x - 10/9 = 0\n2x = 10/9\nx = 10/9 / 2\nx = 5/9"} {"input": "Find x for 2x - 19 = 0", "output": "2x - 19 = 0\n2x = 19\nx = 19 / 2\nx = 19/2"} {"input": "What value of x satisfies 4x - 32/5 = 0", "output": "4x - 32/5 = 0\n4x = 32/5\nx = 32/5 / 4\nx = 8/5"} {"input": "What value of x satisfies 6x - 6 = 0", "output": "6x - 6 = 0\n6x = 6\nx = 6 / 6\nx = 1"} {"input": "Find x in x^2 - 13/5x - 48/25 = 0", "output": "x^2 - 13/5x - 48/25 = 0\n(x - -3/5)(x - 16/5) = 0\nx - -3/5 = 0 or x - 16/5 = 0\nx = -3/5\nx = 16/5"} {"input": "Solve simultaneously:\n5x + 10y = -120\n4x + 9y = -109", "output": "5x + 10y = -120\n4x + 9y = -109\n\nUsing elimination\n4*(5x + 10y = -120)\n5*(4x + 9y = -109)\n20x + 40y = -480\n20x + 45y = -545\nSubtract equations\n-5y = 65\ny = 65/-5\ny = -13\n\nSubstitute y\n5x + 10(-13) = -120\n5x = 10\nx = 10/5\nx = 2"} {"input": "What value of x satisfies x^2 + 5/3x - 50/3 = 0", "output": "x^2 + 5/3x - 50/3 = 0\n(x - 10/3)(x - -5) = 0\nx - 10/3 = 0 or x - -5 = 0\nx = 10/3\nx = -5"} {"input": "Solve quickly: x^3 - 22x^2 + 67x + 90 = 0", "output": "x^3 - 22x^2 + 67x + 90 = 0\n(x - 18)(x - 5)(x - -1) = 0\nx - 18 = 0\nx - 5 = 0\nx - -1 = 0\nx = 18\nx = 5\nx = -1"} {"input": "Solve simultaneously:\n2x + 7y = 43/5\n8x + 7y = 5", "output": "2x + 7y = 43/5\n8x + 7y = 5\n\nUsing elimination\n8*(2x + 7y = 43/5)\n2*(8x + 7y = 5)\n16x + 56y = 344/5\n16x + 14y = 10\nSubtract equations\n42y = 294/5\ny = 294/5/42\ny = 7/5\n\nSubstitute y\n2x + 7(7/5) = 43/5\n2x = -6/5\nx = -6/5/2\nx = -3/5"} {"input": "Solve the system:\n3x + 8y = 91/5\n2x + 10y = 119/5", "output": "3x + 8y = 91/5\n2x + 10y = 119/5\n\nUsing elimination\n2*(3x + 8y = 91/5)\n3*(2x + 10y = 119/5)\n6x + 16y = 182/5\n6x + 30y = 357/5\nSubtract equations\n-14y = -35\ny = -35/-14\ny = 5/2\n\nSubstitute y\n3x + 8(5/2) = 91/5\n3x = -9/5\nx = -9/5/3\nx = -3/5"} {"input": "Solve x^3 - 19/4x^2 + 57/8x - 27/8 = 0", "output": "x^3 - 19/4x^2 + 57/8x - 27/8 = 0\n(x - 9/4)(x - 1)(x - 3/2) = 0\nx - 9/4 = 0\nx - 1 = 0\nx - 3/2 = 0\nx = 9/4\nx = 1\nx = 3/2"} {"input": "Solve the equation x^3 - 121/20x^2 + 57/5x - 27/4 = 0", "output": "x^3 - 121/20x^2 + 57/5x - 27/4 = 0\n(x - 3)(x - 9/5)(x - 5/4) = 0\nx - 3 = 0\nx - 9/5 = 0\nx - 5/4 = 0\nx = 3\nx = 9/5\nx = 5/4"} {"input": "Find x in x^2 + 104/15x + 169/15 = 0", "output": "x^2 + 104/15x + 169/15 = 0\n(x - -13/3)(x - -13/5) = 0\nx - -13/3 = 0 or x - -13/5 = 0\nx = -13/3\nx = -13/5"} {"input": "Determine x in 9x + 16 = 0", "output": "9x + 16 = 0\n9x = -16\nx = -16 / 9\nx = -16/9"} {"input": "Solve the equations:\n9x + 9y = 99/35\n9x + 6y = 24/35", "output": "9x + 9y = 99/35\n9x + 6y = 24/35\n\nUsing elimination\n9*(9x + 9y = 99/35)\n9*(9x + 6y = 24/35)\n81x + 81y = 891/35\n81x + 54y = 216/35\nSubtract equations\n27y = 135/7\ny = 135/7/27\ny = 5/7\n\nSubstitute y\n9x + 9(5/7) = 99/35\n9x = -18/5\nx = -18/5/9\nx = -2/5"} {"input": "Determine x in x^2 - 13/2x + 15/2 = 0", "output": "x^2 - 13/2x + 15/2 = 0\n(x - 3/2)(x - 5) = 0\nx - 3/2 = 0 or x - 5 = 0\nx = 3/2\nx = 5"} {"input": "Find x for x^2 - 109/10x + 51/2 = 0", "output": "x^2 - 109/10x + 51/2 = 0\n(x - 15/2)(x - 17/5) = 0\nx - 15/2 = 0 or x - 17/5 = 0\nx = 15/2\nx = 17/5"} {"input": "What value of x satisfies x^3 + 5/42x^2 - 253/42x - 95/21 = 0", "output": "x^3 + 5/42x^2 - 253/42x - 95/21 = 0\n(x - 19/7)(x - -2)(x - -5/6) = 0\nx - 19/7 = 0\nx - -2 = 0\nx - -5/6 = 0\nx = 19/7\nx = -2\nx = -5/6"} {"input": "Solve the system:\n8x + 4y = 272/7\n2x + 3y = 64/7", "output": "8x + 4y = 272/7\n2x + 3y = 64/7\n\nUsing elimination\n2*(8x + 4y = 272/7)\n8*(2x + 3y = 64/7)\n16x + 8y = 544/7\n16x + 24y = 512/7\nSubtract equations\n-16y = 32/7\ny = 32/7/-16\ny = -2/7\n\nSubstitute y\n8x + 4(-2/7) = 272/7\n8x = 40\nx = 40/8\nx = 5"} {"input": "Solve quickly: x^3 + 1273/252x^2 + 601/84x + 143/63 = 0", "output": "x^3 + 1273/252x^2 + 601/84x + 143/63 = 0\n(x - -13/7)(x - -11/4)(x - -4/9) = 0\nx - -13/7 = 0\nx - -11/4 = 0\nx - -4/9 = 0\nx = -13/7\nx = -11/4\nx = -4/9"} {"input": "Compute the solution of x^3 + 157/20x^2 - 59/4x - 198/5 = 0", "output": "x^3 + 157/20x^2 - 59/4x - 198/5 = 0\n(x - 11/4)(x - -8/5)(x - -9) = 0\nx - 11/4 = 0\nx - -8/5 = 0\nx - -9 = 0\nx = 11/4\nx = -8/5\nx = -9"} {"input": "Solve simultaneously:\n10x + 4y = 289/6\n2x + 3y = 10", "output": "10x + 4y = 289/6\n2x + 3y = 10\n\nUsing elimination\n2*(10x + 4y = 289/6)\n10*(2x + 3y = 10)\n20x + 8y = 289/3\n20x + 30y = 100\nSubtract equations\n-22y = -11/3\ny = -11/3/-22\ny = 1/6\n\nSubstitute y\n10x + 4(1/6) = 289/6\n10x = 95/2\nx = 95/2/10\nx = 19/4"} {"input": "Solve quickly: x^3 - 51/10x^2 - 733/10x - 114 = 0", "output": "x^3 - 51/10x^2 - 733/10x - 114 = 0\n(x - -5)(x - 12)(x - -19/10) = 0\nx - -5 = 0\nx - 12 = 0\nx - -19/10 = 0\nx = -5\nx = 12\nx = -19/10"} {"input": "What value of x satisfies x^3 - 337/126x^2 - 505/63x + 323/18 = 0", "output": "x^3 - 337/126x^2 - 505/63x + 323/18 = 0\n(x - 17/9)(x - 7/2)(x - -19/7) = 0\nx - 17/9 = 0\nx - 7/2 = 0\nx - -19/7 = 0\nx = 17/9\nx = 7/2\nx = -19/7"} {"input": "Determine x in x^3 - 1/3x^2 - 10/3x = 0", "output": "x^3 - 1/3x^2 - 10/3x = 0\n(x - 2)(x - 0)(x - -5/3) = 0\nx - 2 = 0\nx - 0 = 0\nx - -5/3 = 0\nx = 2\nx = 0\nx = -5/3"} {"input": "Solve the equations:\n1x + 7y = 142/9\n9x + 2y = -43/7", "output": "1x + 7y = 142/9\n9x + 2y = -43/7\n\nUsing elimination\n9*(1x + 7y = 142/9)\n1*(9x + 2y = -43/7)\n9x + 63y = 142\n9x + 2y = -43/7\nSubtract equations\n61y = 1037/7\ny = 1037/7/61\ny = 17/7\n\nSubstitute y\n1x + 7(17/7) = 142/9\n1x = -11/9\nx = -11/9/1\nx = -11/9"} {"input": "Find x for x^2 - 79/8x + 285/16 = 0", "output": "x^2 - 79/8x + 285/16 = 0\n(x - 19/8)(x - 15/2) = 0\nx - 19/8 = 0 or x - 15/2 = 0\nx = 19/8\nx = 15/2"} {"input": "Find x for x^3 + 25/8x^2 + 1/8x - 17/4 = 0", "output": "x^3 + 25/8x^2 + 1/8x - 17/4 = 0\n(x - -2)(x - 1)(x - -17/8) = 0\nx - -2 = 0\nx - 1 = 0\nx - -17/8 = 0\nx = -2\nx = 1\nx = -17/8"} {"input": "Find x for x^3 - 161/20x^2 + 2097/100x - 891/50 = 0", "output": "x^3 - 161/20x^2 + 2097/100x - 891/50 = 0\n(x - 11/5)(x - 18/5)(x - 9/4) = 0\nx - 11/5 = 0\nx - 18/5 = 0\nx - 9/4 = 0\nx = 11/5\nx = 18/5\nx = 9/4"} {"input": "What value of x satisfies x^2 - 2x + 3/4 = 0", "output": "x^2 - 2x + 3/4 = 0\n(x - 3/2)(x - 1/2) = 0\nx - 3/2 = 0 or x - 1/2 = 0\nx = 3/2\nx = 1/2"} {"input": "Find x in x^2 - 49/12x - 57/4 = 0", "output": "x^2 - 49/12x - 57/4 = 0\n(x - 19/3)(x - -9/4) = 0\nx - 19/3 = 0 or x - -9/4 = 0\nx = 19/3\nx = -9/4"} {"input": "Find the solution to 7x - 70 = 0", "output": "7x - 70 = 0\n7x = 70\nx = 70 / 7\nx = 10"} {"input": "Find x in x^2 - 28/15x - 323/15 = 0", "output": "x^2 - 28/15x - 323/15 = 0\n(x - -19/5)(x - 17/3) = 0\nx - -19/5 = 0 or x - 17/3 = 0\nx = -19/5\nx = 17/3"} {"input": "What value of x satisfies x^2 - 9/7x - 36/7 = 0", "output": "x^2 - 9/7x - 36/7 = 0\n(x - 3)(x - -12/7) = 0\nx - 3 = 0 or x - -12/7 = 0\nx = 3\nx = -12/7"} {"input": "Solve x^2 - 23/3x - 12 = 0", "output": "x^2 - 23/3x - 12 = 0\n(x - -4/3)(x - 9) = 0\nx - -4/3 = 0 or x - 9 = 0\nx = -4/3\nx = 9"} {"input": "Solve simultaneously:\n5x + 7y = -141/2\n1x + 4y = -18", "output": "5x + 7y = -141/2\n1x + 4y = -18\n\nUsing elimination\n1*(5x + 7y = -141/2)\n5*(1x + 4y = -18)\n5x + 7y = -141/2\n5x + 20y = -90\nSubtract equations\n-13y = 39/2\ny = 39/2/-13\ny = -3/2\n\nSubstitute y\n5x + 7(-3/2) = -141/2\n5x = -60\nx = -60/5\nx = -12"} {"input": "Find the solution to x^3 + 41/12x^2 + 667/192x + 35/32 = 0", "output": "x^3 + 41/12x^2 + 667/192x + 35/32 = 0\n(x - -2/3)(x - -15/8)(x - -7/8) = 0\nx - -2/3 = 0\nx - -15/8 = 0\nx - -7/8 = 0\nx = -2/3\nx = -15/8\nx = -7/8"} {"input": "Find the solution to x^2 - 7/2x - 15 = 0", "output": "x^2 - 7/2x - 15 = 0\n(x - 6)(x - -5/2) = 0\nx - 6 = 0 or x - -5/2 = 0\nx = 6\nx = -5/2"} {"input": "Solve the equations:\n8x + 2y = 196/15\n3x + 6y = 7/5", "output": "8x + 2y = 196/15\n3x + 6y = 7/5\n\nUsing elimination\n3*(8x + 2y = 196/15)\n8*(3x + 6y = 7/5)\n24x + 6y = 196/5\n24x + 48y = 56/5\nSubtract equations\n-42y = 28\ny = 28/-42\ny = -2/3\n\nSubstitute y\n8x + 2(-2/3) = 196/15\n8x = 72/5\nx = 72/5/8\nx = 9/5"} {"input": "Solve simultaneously:\n5x + 7y = -573/35\n3x + 1y = -299/35", "output": "5x + 7y = -573/35\n3x + 1y = -299/35\n\nUsing elimination\n3*(5x + 7y = -573/35)\n5*(3x + 1y = -299/35)\n15x + 21y = -1719/35\n15x + 5y = -299/7\nSubtract equations\n16y = -32/5\ny = -32/5/16\ny = -2/5\n\nSubstitute y\n5x + 7(-2/5) = -573/35\n5x = -95/7\nx = -95/7/5\nx = -19/7"} {"input": "Solve the equation x^2 + 31/3x + 238/9 = 0", "output": "x^2 + 31/3x + 238/9 = 0\n(x - -14/3)(x - -17/3) = 0\nx - -14/3 = 0 or x - -17/3 = 0\nx = -14/3\nx = -17/3"} {"input": "Find the solution to 2x - 7/5 = 0", "output": "2x - 7/5 = 0\n2x = 7/5\nx = 7/5 / 2\nx = 7/10"} {"input": "Solve the equation x^2 - 43/15x - 16/15 = 0", "output": "x^2 - 43/15x - 16/15 = 0\n(x - 16/5)(x - -1/3) = 0\nx - 16/5 = 0 or x - -1/3 = 0\nx = 16/5\nx = -1/3"} {"input": "Find x in x^3 + 1157/56x^2 + 523/8x + 374/7 = 0", "output": "x^3 + 1157/56x^2 + 523/8x + 374/7 = 0\n(x - -11/8)(x - -17)(x - -16/7) = 0\nx - -11/8 = 0\nx - -17 = 0\nx - -16/7 = 0\nx = -11/8\nx = -17\nx = -16/7"} {"input": "Find x for x^3 - 73/5x^2 + 427/20x - 143/20 = 0", "output": "x^3 - 73/5x^2 + 427/20x - 143/20 = 0\n(x - 11/10)(x - 13)(x - 1/2) = 0\nx - 11/10 = 0\nx - 13 = 0\nx - 1/2 = 0\nx = 11/10\nx = 13\nx = 1/2"} {"input": "Find x for x^3 + 35/6x^2 + 1/2x - 22/3 = 0", "output": "x^3 + 35/6x^2 + 1/2x - 22/3 = 0\n(x - -11/2)(x - 1)(x - -4/3) = 0\nx - -11/2 = 0\nx - 1 = 0\nx - -4/3 = 0\nx = -11/2\nx = 1\nx = -4/3"} {"input": "Find the solution to x^3 - 10/7x^2 - 277/49x + 442/49 = 0", "output": "x^3 - 10/7x^2 - 277/49x + 442/49 = 0\n(x - 13/7)(x - 2)(x - -17/7) = 0\nx - 13/7 = 0\nx - 2 = 0\nx - -17/7 = 0\nx = 13/7\nx = 2\nx = -17/7"} {"input": "Solve quickly: x^2 + 7/5x = 0", "output": "x^2 + 7/5x = 0\n(x - -7/5)(x - 0) = 0\nx - -7/5 = 0 or x - 0 = 0\nx = -7/5\nx = 0"} {"input": "What value of x satisfies x^2 + 17/7x - 12/7 = 0", "output": "x^2 + 17/7x - 12/7 = 0\n(x - -3)(x - 4/7) = 0\nx - -3 = 0 or x - 4/7 = 0\nx = -3\nx = 4/7"} {"input": "Determine x in x^2 - 1/9x - 34/9 = 0", "output": "x^2 - 1/9x - 34/9 = 0\n(x - -17/9)(x - 2) = 0\nx - -17/9 = 0 or x - 2 = 0\nx = -17/9\nx = 2"} {"input": "Find x and y such that\n3x + 5y = 221/4\n3x + 7y = 301/4", "output": "3x + 5y = 221/4\n3x + 7y = 301/4\n\nUsing elimination\n3*(3x + 5y = 221/4)\n3*(3x + 7y = 301/4)\n9x + 15y = 663/4\n9x + 21y = 903/4\nSubtract equations\n-6y = -60\ny = -60/-6\ny = 10\n\nSubstitute y\n3x + 5(10) = 221/4\n3x = 21/4\nx = 21/4/3\nx = 7/4"} {"input": "Determine x in 4x + 32/3 = 0", "output": "4x + 32/3 = 0\n4x = -32/3\nx = -32/3 / 4\nx = -8/3"} {"input": "Find x for x^2 + 39/7x + 44/7 = 0", "output": "x^2 + 39/7x + 44/7 = 0\n(x - -11/7)(x - -4) = 0\nx - -11/7 = 0 or x - -4 = 0\nx = -11/7\nx = -4"} {"input": "Compute the solution of 7x - 56 = 0", "output": "7x - 56 = 0\n7x = 56\nx = 56 / 7\nx = 8"} {"input": "Solve quickly: x^3 + 3x^2 - 64x + 60 = 0", "output": "x^3 + 3x^2 - 64x + 60 = 0\n(x - -10)(x - 1)(x - 6) = 0\nx - -10 = 0\nx - 1 = 0\nx - 6 = 0\nx = -10\nx = 1\nx = 6"} {"input": "Compute the solution of 7x + 91/8 = 0", "output": "7x + 91/8 = 0\n7x = -91/8\nx = -91/8 / 7\nx = -13/8"} {"input": "Determine x in x^2 + 43/2x + 30 = 0", "output": "x^2 + 43/2x + 30 = 0\n(x - -3/2)(x - -20) = 0\nx - -3/2 = 0 or x - -20 = 0\nx = -3/2\nx = -20"} {"input": "Find x for x^2 - 1/2x - 3 = 0", "output": "x^2 - 1/2x - 3 = 0\n(x - 2)(x - -3/2) = 0\nx - 2 = 0 or x - -3/2 = 0\nx = 2\nx = -3/2"} {"input": "Find x for x^2 - 59/18x + 8/3 = 0", "output": "x^2 - 59/18x + 8/3 = 0\n(x - 16/9)(x - 3/2) = 0\nx - 16/9 = 0 or x - 3/2 = 0\nx = 16/9\nx = 3/2"} {"input": "Solve x^3 - 46/3x^2 + 113/3x + 110 = 0", "output": "x^3 - 46/3x^2 + 113/3x + 110 = 0\n(x - 6)(x - 11)(x - -5/3) = 0\nx - 6 = 0\nx - 11 = 0\nx - -5/3 = 0\nx = 6\nx = 11\nx = -5/3"} {"input": "Find x and y such that\n5x + 4y = -184/15\n5x + 6y = -226/15", "output": "5x + 4y = -184/15\n5x + 6y = -226/15\n\nUsing elimination\n5*(5x + 4y = -184/15)\n5*(5x + 6y = -226/15)\n25x + 20y = -184/3\n25x + 30y = -226/3\nSubtract equations\n-10y = 14\ny = 14/-10\ny = -7/5\n\nSubstitute y\n5x + 4(-7/5) = -184/15\n5x = -20/3\nx = -20/3/5\nx = -4/3"} {"input": "Find the solution to x^2 + 13/8x = 0", "output": "x^2 + 13/8x = 0\n(x - 0)(x - -13/8) = 0\nx - 0 = 0 or x - -13/8 = 0\nx = 0\nx = -13/8"} {"input": "Solve the equation x^2 + 3/4x - 135/8 = 0", "output": "x^2 + 3/4x - 135/8 = 0\n(x - 15/4)(x - -9/2) = 0\nx - 15/4 = 0 or x - -9/2 = 0\nx = 15/4\nx = -9/2"} {"input": "Solve quickly: x^3 + 469/45x^2 + 196/15x + 12/5 = 0", "output": "x^3 + 469/45x^2 + 196/15x + 12/5 = 0\n(x - -9)(x - -2/9)(x - -6/5) = 0\nx - -9 = 0\nx - -2/9 = 0\nx - -6/5 = 0\nx = -9\nx = -2/9\nx = -6/5"} {"input": "Solve x^3 + 13/18x^2 - 19/9x - 11/6 = 0", "output": "x^3 + 13/18x^2 - 19/9x - 11/6 = 0\n(x - 3/2)(x - -1)(x - -11/9) = 0\nx - 3/2 = 0\nx - -1 = 0\nx - -11/9 = 0\nx = 3/2\nx = -1\nx = -11/9"} {"input": "What value of x satisfies 4x - 20 = 0", "output": "4x - 20 = 0\n4x = 20\nx = 20 / 4\nx = 5"} {"input": "Find x and y such that\n7x + 3y = -24\n6x + 10y = -188/3", "output": "7x + 3y = -24\n6x + 10y = -188/3\n\nUsing elimination\n6*(7x + 3y = -24)\n7*(6x + 10y = -188/3)\n42x + 18y = -144\n42x + 70y = -1316/3\nSubtract equations\n-52y = 884/3\ny = 884/3/-52\ny = -17/3\n\nSubstitute y\n7x + 3(-17/3) = -24\n7x = -7\nx = -7/7\nx = -1"} {"input": "Solve the equations:\n4x + 4y = -32/7\n7x + 4y = 1/7", "output": "4x + 4y = -32/7\n7x + 4y = 1/7\n\nUsing elimination\n7*(4x + 4y = -32/7)\n4*(7x + 4y = 1/7)\n28x + 28y = -32\n28x + 16y = 4/7\nSubtract equations\n12y = -228/7\ny = -228/7/12\ny = -19/7\n\nSubstitute y\n4x + 4(-19/7) = -32/7\n4x = 44/7\nx = 44/7/4\nx = 11/7"} {"input": "Solve 4x + 64/5 = 0", "output": "4x + 64/5 = 0\n4x = -64/5\nx = -64/5 / 4\nx = -16/5"} {"input": "Solve the equation 1x - 3 = 0", "output": "1x - 3 = 0\n1x = 3\nx = 3 / 1\nx = 3"} {"input": "What value of x satisfies 3x - 15 = 0", "output": "3x - 15 = 0\n3x = 15\nx = 15 / 3\nx = 5"} {"input": "Determine x in x^2 + 23x + 120 = 0", "output": "x^2 + 23x + 120 = 0\n(x - -15)(x - -8) = 0\nx - -15 = 0 or x - -8 = 0\nx = -15\nx = -8"} {"input": "Compute the solution of 6x - 114 = 0", "output": "6x - 114 = 0\n6x = 114\nx = 114 / 6\nx = 19"} {"input": "What value of x satisfies x^2 - 3/2x + 2/9 = 0", "output": "x^2 - 3/2x + 2/9 = 0\n(x - 1/6)(x - 4/3) = 0\nx - 1/6 = 0 or x - 4/3 = 0\nx = 1/6\nx = 4/3"} {"input": "Solve the system:\n8x + 7y = -29\n8x + 9y = -35", "output": "8x + 7y = -29\n8x + 9y = -35\n\nUsing elimination\n8*(8x + 7y = -29)\n8*(8x + 9y = -35)\n64x + 56y = -232\n64x + 72y = -280\nSubtract equations\n-16y = 48\ny = 48/-16\ny = -3\n\nSubstitute y\n8x + 7(-3) = -29\n8x = -8\nx = -8/8\nx = -1"} {"input": "Find x in x^3 - 241/180x^2 + 9/20x - 2/45 = 0", "output": "x^3 - 241/180x^2 + 9/20x - 2/45 = 0\n(x - 8/9)(x - 1/4)(x - 1/5) = 0\nx - 8/9 = 0\nx - 1/4 = 0\nx - 1/5 = 0\nx = 8/9\nx = 1/4\nx = 1/5"} {"input": "Solve the equation 8x - 128/5 = 0", "output": "8x - 128/5 = 0\n8x = 128/5\nx = 128/5 / 8\nx = 16/5"} {"input": "Solve the equation 5x + 55/9 = 0", "output": "5x + 55/9 = 0\n5x = -55/9\nx = -55/9 / 5\nx = -11/9"} {"input": "Determine x in x^3 + 93/56x^2 - 85/112x - 75/112 = 0", "output": "x^3 + 93/56x^2 - 85/112x - 75/112 = 0\n(x - -15/8)(x - 5/7)(x - -1/2) = 0\nx - -15/8 = 0\nx - 5/7 = 0\nx - -1/2 = 0\nx = -15/8\nx = 5/7\nx = -1/2"} {"input": "Find x for x^3 - 296/35x^2 + 111/7x - 234/35 = 0", "output": "x^3 - 296/35x^2 + 111/7x - 234/35 = 0\n(x - 6)(x - 13/7)(x - 3/5) = 0\nx - 6 = 0\nx - 13/7 = 0\nx - 3/5 = 0\nx = 6\nx = 13/7\nx = 3/5"} {"input": "Find x in 7x + 56/5 = 0", "output": "7x + 56/5 = 0\n7x = -56/5\nx = -56/5 / 7\nx = -8/5"} {"input": "What value of x satisfies 9x + 90 = 0", "output": "9x + 90 = 0\n9x = -90\nx = -90 / 9\nx = -10"} {"input": "Find x for 3x + 15/7 = 0", "output": "3x + 15/7 = 0\n3x = -15/7\nx = -15/7 / 3\nx = -5/7"} {"input": "Find x and y such that\n1x + 9y = 13\n7x + 8y = -281/9", "output": "1x + 9y = 13\n7x + 8y = -281/9\n\nUsing elimination\n7*(1x + 9y = 13)\n1*(7x + 8y = -281/9)\n7x + 63y = 91\n7x + 8y = -281/9\nSubtract equations\n55y = 1100/9\ny = 1100/9/55\ny = 20/9\n\nSubstitute y\n1x + 9(20/9) = 13\n1x = -7\nx = -7/1\nx = -7"} {"input": "Solve the equations:\n7x + 1y = 113/4\n2x + 9y = 41/4", "output": "7x + 1y = 113/4\n2x + 9y = 41/4\n\nUsing elimination\n2*(7x + 1y = 113/4)\n7*(2x + 9y = 41/4)\n14x + 2y = 113/2\n14x + 63y = 287/4\nSubtract equations\n-61y = -61/4\ny = -61/4/-61\ny = 1/4\n\nSubstitute y\n7x + 1(1/4) = 113/4\n7x = 28\nx = 28/7\nx = 4"} {"input": "Find x in x^3 + 153/20x^2 + 107/10x - 51/4 = 0", "output": "x^3 + 153/20x^2 + 107/10x - 51/4 = 0\n(x - 3/4)(x - -5)(x - -17/5) = 0\nx - 3/4 = 0\nx - -5 = 0\nx - -17/5 = 0\nx = 3/4\nx = -5\nx = -17/5"} {"input": "Compute the solution of x^2 + 17/9x - 10/3 = 0", "output": "x^2 + 17/9x - 10/3 = 0\n(x - -3)(x - 10/9) = 0\nx - -3 = 0 or x - 10/9 = 0\nx = -3\nx = 10/9"} {"input": "Find x in x^2 + 87/35x + 54/35 = 0", "output": "x^2 + 87/35x + 54/35 = 0\n(x - -6/5)(x - -9/7) = 0\nx - -6/5 = 0 or x - -9/7 = 0\nx = -6/5\nx = -9/7"} {"input": "Find x for 7x - 21/2 = 0", "output": "7x - 21/2 = 0\n7x = 21/2\nx = 21/2 / 7\nx = 3/2"} {"input": "Determine x in x^3 - 301/90x^2 - 493/135x + 3179/270 = 0", "output": "x^3 - 301/90x^2 - 493/135x + 3179/270 = 0\n(x - -17/9)(x - 17/5)(x - 11/6) = 0\nx - -17/9 = 0\nx - 17/5 = 0\nx - 11/6 = 0\nx = -17/9\nx = 17/5\nx = 11/6"} {"input": "Solve x^3 - 47/10x^2 + 397/80x - 13/16 = 0", "output": "x^3 - 47/10x^2 + 397/80x - 13/16 = 0\n(x - 1/5)(x - 5/4)(x - 13/4) = 0\nx - 1/5 = 0\nx - 5/4 = 0\nx - 13/4 = 0\nx = 1/5\nx = 5/4\nx = 13/4"} {"input": "Compute the solution of x^2 - 37/4x + 51/8 = 0", "output": "x^2 - 37/4x + 51/8 = 0\n(x - 17/2)(x - 3/4) = 0\nx - 17/2 = 0 or x - 3/4 = 0\nx = 17/2\nx = 3/4"} {"input": "Solve the equation x^3 - 29/2x^2 - 47/2x - 8 = 0", "output": "x^3 - 29/2x^2 - 47/2x - 8 = 0\n(x - 16)(x - -1)(x - -1/2) = 0\nx - 16 = 0\nx - -1 = 0\nx - -1/2 = 0\nx = 16\nx = -1\nx = -1/2"} {"input": "Solve the equations:\n4x + 9y = -28/3\n7x + 6y = 1", "output": "4x + 9y = -28/3\n7x + 6y = 1\n\nUsing elimination\n7*(4x + 9y = -28/3)\n4*(7x + 6y = 1)\n28x + 63y = -196/3\n28x + 24y = 4\nSubtract equations\n39y = -208/3\ny = -208/3/39\ny = -16/9\n\nSubstitute y\n4x + 9(-16/9) = -28/3\n4x = 20/3\nx = 20/3/4\nx = 5/3"} {"input": "Solve the system:\n4x + 2y = -75\n3x + 6y = -63", "output": "4x + 2y = -75\n3x + 6y = -63\n\nUsing elimination\n3*(4x + 2y = -75)\n4*(3x + 6y = -63)\n12x + 6y = -225\n12x + 24y = -252\nSubtract equations\n-18y = 27\ny = 27/-18\ny = -3/2\n\nSubstitute y\n4x + 2(-3/2) = -75\n4x = -72\nx = -72/4\nx = -18"} {"input": "Solve quickly: x^2 + 11/3x - 4/3 = 0", "output": "x^2 + 11/3x - 4/3 = 0\n(x - 1/3)(x - -4) = 0\nx - 1/3 = 0 or x - -4 = 0\nx = 1/3\nx = -4"} {"input": "Find x in x^3 - 719/35x^2 + 981/35x + 171/7 = 0", "output": "x^3 - 719/35x^2 + 981/35x + 171/7 = 0\n(x - -3/5)(x - 19)(x - 15/7) = 0\nx - -3/5 = 0\nx - 19 = 0\nx - 15/7 = 0\nx = -3/5\nx = 19\nx = 15/7"} {"input": "Find x for x^3 - 601/40x^2 + 221/20x + 231/5 = 0", "output": "x^3 - 601/40x^2 + 221/20x + 231/5 = 0\n(x - -11/8)(x - 12/5)(x - 14) = 0\nx - -11/8 = 0\nx - 12/5 = 0\nx - 14 = 0\nx = -11/8\nx = 12/5\nx = 14"} {"input": "Solve the system:\n8x + 4y = 140/3\n3x + 7y = 45", "output": "8x + 4y = 140/3\n3x + 7y = 45\n\nUsing elimination\n3*(8x + 4y = 140/3)\n8*(3x + 7y = 45)\n24x + 12y = 140\n24x + 56y = 360\nSubtract equations\n-44y = -220\ny = -220/-44\ny = 5\n\nSubstitute y\n8x + 4(5) = 140/3\n8x = 80/3\nx = 80/3/8\nx = 10/3"} {"input": "Solve the system:\n4x + 5y = -43/2\n8x + 9y = -71/2", "output": "4x + 5y = -43/2\n8x + 9y = -71/2\n\nUsing elimination\n8*(4x + 5y = -43/2)\n4*(8x + 9y = -71/2)\n32x + 40y = -172\n32x + 36y = -142\nSubtract equations\n4y = -30\ny = -30/4\ny = -15/2\n\nSubstitute y\n4x + 5(-15/2) = -43/2\n4x = 16\nx = 16/4\nx = 4"} {"input": "Find the solution to 2x - 6 = 0", "output": "2x - 6 = 0\n2x = 6\nx = 6 / 2\nx = 3"} {"input": "Solve quickly: x^2 + 87/10x - 13 = 0", "output": "x^2 + 87/10x - 13 = 0\n(x - -10)(x - 13/10) = 0\nx - -10 = 0 or x - 13/10 = 0\nx = -10\nx = 13/10"} {"input": "Find the solution to 3x - 27/10 = 0", "output": "3x - 27/10 = 0\n3x = 27/10\nx = 27/10 / 3\nx = 9/10"} {"input": "Find x for x^2 - 67/18x + 187/54 = 0", "output": "x^2 - 67/18x + 187/54 = 0\n(x - 11/6)(x - 17/9) = 0\nx - 11/6 = 0 or x - 17/9 = 0\nx = 11/6\nx = 17/9"} {"input": "Solve x^2 - 35/9x + 98/27 = 0", "output": "x^2 - 35/9x + 98/27 = 0\n(x - 7/3)(x - 14/9) = 0\nx - 7/3 = 0 or x - 14/9 = 0\nx = 7/3\nx = 14/9"} {"input": "Find x for 9x - 54 = 0", "output": "9x - 54 = 0\n9x = 54\nx = 54 / 9\nx = 6"} {"input": "Solve x^3 + 67/20x^2 + 9/40x - 99/40 = 0", "output": "x^3 + 67/20x^2 + 9/40x - 99/40 = 0\n(x - 3/4)(x - -3)(x - -11/10) = 0\nx - 3/4 = 0\nx - -3 = 0\nx - -11/10 = 0\nx = 3/4\nx = -3\nx = -11/10"} {"input": "Solve the system:\n5x + 3y = 217/6\n4x + 5y = 197/6", "output": "5x + 3y = 217/6\n4x + 5y = 197/6\n\nUsing elimination\n4*(5x + 3y = 217/6)\n5*(4x + 5y = 197/6)\n20x + 12y = 434/3\n20x + 25y = 985/6\nSubtract equations\n-13y = -39/2\ny = -39/2/-13\ny = 3/2\n\nSubstitute y\n5x + 3(3/2) = 217/6\n5x = 95/3\nx = 95/3/5\nx = 19/3"} {"input": "Solve the equation 10x + 10 = 0", "output": "10x + 10 = 0\n10x = -10\nx = -10 / 10\nx = -1"} {"input": "Solve quickly: x^3 - 89/36x^2 - 1121/54x - 2527/108 = 0", "output": "x^3 - 89/36x^2 - 1121/54x - 2527/108 = 0\n(x - 19/3)(x - -7/4)(x - -19/9) = 0\nx - 19/3 = 0\nx - -7/4 = 0\nx - -19/9 = 0\nx = 19/3\nx = -7/4\nx = -19/9"} {"input": "Compute the solution of x^3 - 29/30x^2 - 57/25x - 52/75 = 0", "output": "x^3 - 29/30x^2 - 57/25x - 52/75 = 0\n(x - -2/5)(x - -4/5)(x - 13/6) = 0\nx - -2/5 = 0\nx - -4/5 = 0\nx - 13/6 = 0\nx = -2/5\nx = -4/5\nx = 13/6"} {"input": "Determine x in x^3 - 29/12x^2 - 215/24x + 119/24 = 0", "output": "x^3 - 29/12x^2 - 215/24x + 119/24 = 0\n(x - 1/2)(x - -7/3)(x - 17/4) = 0\nx - 1/2 = 0\nx - -7/3 = 0\nx - 17/4 = 0\nx = 1/2\nx = -7/3\nx = 17/4"} {"input": "Find the solution to x^3 + 24/7x^2 - 127/63x - 680/63 = 0", "output": "x^3 + 24/7x^2 - 127/63x - 680/63 = 0\n(x - -17/7)(x - 5/3)(x - -8/3) = 0\nx - -17/7 = 0\nx - 5/3 = 0\nx - -8/3 = 0\nx = -17/7\nx = 5/3\nx = -8/3"} {"input": "Solve the equations:\n5x + 6y = -325/28\n7x + 6y = -311/28", "output": "5x + 6y = -325/28\n7x + 6y = -311/28\n\nUsing elimination\n7*(5x + 6y = -325/28)\n5*(7x + 6y = -311/28)\n35x + 42y = -325/4\n35x + 30y = -1555/28\nSubtract equations\n12y = -180/7\ny = -180/7/12\ny = -15/7\n\nSubstitute y\n5x + 6(-15/7) = -325/28\n5x = 5/4\nx = 5/4/5\nx = 1/4"} {"input": "Solve the equations:\n8x + 1y = -95/7\n5x + 7y = -461/7", "output": "8x + 1y = -95/7\n5x + 7y = -461/7\n\nUsing elimination\n5*(8x + 1y = -95/7)\n8*(5x + 7y = -461/7)\n40x + 5y = -475/7\n40x + 56y = -3688/7\nSubtract equations\n-51y = 459\ny = 459/-51\ny = -9\n\nSubstitute y\n8x + 1(-9) = -95/7\n8x = -32/7\nx = -32/7/8\nx = -4/7"} {"input": "Solve the system:\n6x + 5y = 96/5\n4x + 10y = 64/5", "output": "6x + 5y = 96/5\n4x + 10y = 64/5\n\nUsing elimination\n4*(6x + 5y = 96/5)\n6*(4x + 10y = 64/5)\n24x + 20y = 384/5\n24x + 60y = 384/5\nSubtract equations\n-40y = 0\ny = 0/-40\ny = 0\n\nSubstitute y\n6x + 5(0) = 96/5\n6x = 96/5\nx = 96/5/6\nx = 16/5"} {"input": "Determine x in x^3 - 19/8x^2 - 289/100x + 5491/800 = 0", "output": "x^3 - 19/8x^2 - 289/100x + 5491/800 = 0\n(x - 17/10)(x - -17/10)(x - 19/8) = 0\nx - 17/10 = 0\nx - -17/10 = 0\nx - 19/8 = 0\nx = 17/10\nx = -17/10\nx = 19/8"} {"input": "Find the solution to 4x - 6 = 0", "output": "4x - 6 = 0\n4x = 6\nx = 6 / 4\nx = 3/2"} {"input": "Solve quickly: x^3 + 2/5x^2 - 49/20x - 6/5 = 0", "output": "x^3 + 2/5x^2 - 49/20x - 6/5 = 0\n(x - -3/2)(x - -1/2)(x - 8/5) = 0\nx - -3/2 = 0\nx - -1/2 = 0\nx - 8/5 = 0\nx = -3/2\nx = -1/2\nx = 8/5"} {"input": "Compute the solution of x^2 - 53/14x + 24/7 = 0", "output": "x^2 - 53/14x + 24/7 = 0\n(x - 3/2)(x - 16/7) = 0\nx - 3/2 = 0 or x - 16/7 = 0\nx = 3/2\nx = 16/7"} {"input": "Solve quickly: x^2 - 61/9x + 20/27 = 0", "output": "x^2 - 61/9x + 20/27 = 0\n(x - 1/9)(x - 20/3) = 0\nx - 1/9 = 0 or x - 20/3 = 0\nx = 1/9\nx = 20/3"} {"input": "Find x in x^2 - 24/7x + 17/7 = 0", "output": "x^2 - 24/7x + 17/7 = 0\n(x - 1)(x - 17/7) = 0\nx - 1 = 0 or x - 17/7 = 0\nx = 1\nx = 17/7"} {"input": "Solve the equations:\n4x + 1y = 0\n5x + 3y = -63/8", "output": "4x + 1y = 0\n5x + 3y = -63/8\n\nUsing elimination\n5*(4x + 1y = 0)\n4*(5x + 3y = -63/8)\n20x + 5y = 0\n20x + 12y = -63/2\nSubtract equations\n-7y = 63/2\ny = 63/2/-7\ny = -9/2\n\nSubstitute y\n4x + 1(-9/2) = 0\n4x = 9/2\nx = 9/2/4\nx = 9/8"} {"input": "Solve 8x - 28/3 = 0", "output": "8x - 28/3 = 0\n8x = 28/3\nx = 28/3 / 8\nx = 7/6"} {"input": "Find x in 9x - 108/7 = 0", "output": "9x - 108/7 = 0\n9x = 108/7\nx = 108/7 / 9\nx = 12/7"} {"input": "Find x for x^3 + 1x^2 - 40/81x - 16/243 = 0", "output": "x^3 + 1x^2 - 40/81x - 16/243 = 0\n(x - -4/3)(x - 4/9)(x - -1/9) = 0\nx - -4/3 = 0\nx - 4/9 = 0\nx - -1/9 = 0\nx = -4/3\nx = 4/9\nx = -1/9"} {"input": "Solve the equations:\n2x + 3y = 9/2\n3x + 4y = 31/5", "output": "2x + 3y = 9/2\n3x + 4y = 31/5\n\nUsing elimination\n3*(2x + 3y = 9/2)\n2*(3x + 4y = 31/5)\n6x + 9y = 27/2\n6x + 8y = 62/5\nSubtract equations\n1y = 11/10\ny = 11/10/1\ny = 11/10\n\nSubstitute y\n2x + 3(11/10) = 9/2\n2x = 6/5\nx = 6/5/2\nx = 3/5"} {"input": "Solve simultaneously:\n7x + 5y = -7\n7x + 9y = -7", "output": "7x + 5y = -7\n7x + 9y = -7\n\nUsing elimination\n7*(7x + 5y = -7)\n7*(7x + 9y = -7)\n49x + 35y = -49\n49x + 63y = -49\nSubtract equations\n-28y = 0\ny = 0/-28\ny = 0\n\nSubstitute y\n7x + 5(0) = -7\n7x = -7\nx = -7/7\nx = -1"} {"input": "Find x in 6x - 45 = 0", "output": "6x - 45 = 0\n6x = 45\nx = 45 / 6\nx = 15/2"} {"input": "Find x and y such that\n5x + 2y = -179/6\n7x + 6y = -107/2", "output": "5x + 2y = -179/6\n7x + 6y = -107/2\n\nUsing elimination\n7*(5x + 2y = -179/6)\n5*(7x + 6y = -107/2)\n35x + 14y = -1253/6\n35x + 30y = -535/2\nSubtract equations\n-16y = 176/3\ny = 176/3/-16\ny = -11/3\n\nSubstitute y\n5x + 2(-11/3) = -179/6\n5x = -45/2\nx = -45/2/5\nx = -9/2"} {"input": "Solve the equations:\n1x + 8y = 61/3\n9x + 3y = -1", "output": "1x + 8y = 61/3\n9x + 3y = -1\n\nUsing elimination\n9*(1x + 8y = 61/3)\n1*(9x + 3y = -1)\n9x + 72y = 183\n9x + 3y = -1\nSubtract equations\n69y = 184\ny = 184/69\ny = 8/3\n\nSubstitute y\n1x + 8(8/3) = 61/3\n1x = -1\nx = -1/1\nx = -1"} {"input": "Solve x^2 + 31/5x + 77/20 = 0", "output": "x^2 + 31/5x + 77/20 = 0\n(x - -7/10)(x - -11/2) = 0\nx - -7/10 = 0 or x - -11/2 = 0\nx = -7/10\nx = -11/2"} {"input": "Find x and y such that\n6x + 5y = -16/5\n8x + 10y = -48/5", "output": "6x + 5y = -16/5\n8x + 10y = -48/5\n\nUsing elimination\n8*(6x + 5y = -16/5)\n6*(8x + 10y = -48/5)\n48x + 40y = -128/5\n48x + 60y = -288/5\nSubtract equations\n-20y = 32\ny = 32/-20\ny = -8/5\n\nSubstitute y\n6x + 5(-8/5) = -16/5\n6x = 24/5\nx = 24/5/6\nx = 4/5"} {"input": "Solve the equation 9x - 99/8 = 0", "output": "9x - 99/8 = 0\n9x = 99/8\nx = 99/8 / 9\nx = 11/8"} {"input": "Find x for x^2 + 15/8x + 13/32 = 0", "output": "x^2 + 15/8x + 13/32 = 0\n(x - -13/8)(x - -1/4) = 0\nx - -13/8 = 0 or x - -1/4 = 0\nx = -13/8\nx = -1/4"} {"input": "Determine x in x^2 - 22/15x - 56/15 = 0", "output": "x^2 - 22/15x - 56/15 = 0\n(x - -4/3)(x - 14/5) = 0\nx - -4/3 = 0 or x - 14/5 = 0\nx = -4/3\nx = 14/5"} {"input": "Solve the equations:\n8x + 2y = -206/9\n7x + 9y = -898/9", "output": "8x + 2y = -206/9\n7x + 9y = -898/9\n\nUsing elimination\n7*(8x + 2y = -206/9)\n8*(7x + 9y = -898/9)\n56x + 14y = -1442/9\n56x + 72y = -7184/9\nSubtract equations\n-58y = 638\ny = 638/-58\ny = -11\n\nSubstitute y\n8x + 2(-11) = -206/9\n8x = -8/9\nx = -8/9/8\nx = -1/9"} {"input": "Compute the solution of x^3 - 17/5x^2 - 33/20x + 171/20 = 0", "output": "x^3 - 17/5x^2 - 33/20x + 171/20 = 0\n(x - 19/10)(x - -3/2)(x - 3) = 0\nx - 19/10 = 0\nx - -3/2 = 0\nx - 3 = 0\nx = 19/10\nx = -3/2\nx = 3"} {"input": "Solve the equation x^2 + 4/5x = 0", "output": "x^2 + 4/5x = 0\n(x - -4/5)(x - 0) = 0\nx - -4/5 = 0 or x - 0 = 0\nx = -4/5\nx = 0"} {"input": "Solve the equation 1x - 4/7 = 0", "output": "1x - 4/7 = 0\n1x = 4/7\nx = 4/7 / 1\nx = 4/7"} {"input": "Solve simultaneously:\n10x + 8y = -134/9\n1x + 6y = -109/15", "output": "10x + 8y = -134/9\n1x + 6y = -109/15\n\nUsing elimination\n1*(10x + 8y = -134/9)\n10*(1x + 6y = -109/15)\n10x + 8y = -134/9\n10x + 60y = -218/3\nSubtract equations\n-52y = 520/9\ny = 520/9/-52\ny = -10/9\n\nSubstitute y\n10x + 8(-10/9) = -134/9\n10x = -6\nx = -6/10\nx = -3/5"} {"input": "Find the solution to 1x + 3/5 = 0", "output": "1x + 3/5 = 0\n1x = -3/5\nx = -3/5 / 1\nx = -3/5"} {"input": "What value of x satisfies x^3 - 291/40x^2 + 97/8x - 15/4 = 0", "output": "x^3 - 291/40x^2 + 97/8x - 15/4 = 0\n(x - 2/5)(x - 15/8)(x - 5) = 0\nx - 2/5 = 0\nx - 15/8 = 0\nx - 5 = 0\nx = 2/5\nx = 15/8\nx = 5"} {"input": "Find x and y such that\n4x + 2y = -50/3\n9x + 6y = -83/2", "output": "4x + 2y = -50/3\n9x + 6y = -83/2\n\nUsing elimination\n9*(4x + 2y = -50/3)\n4*(9x + 6y = -83/2)\n36x + 18y = -150\n36x + 24y = -166\nSubtract equations\n-6y = 16\ny = 16/-6\ny = -8/3\n\nSubstitute y\n4x + 2(-8/3) = -50/3\n4x = -34/3\nx = -34/3/4\nx = -17/6"} {"input": "Compute the solution of x^2 + 13/40x - 187/80 = 0", "output": "x^2 + 13/40x - 187/80 = 0\n(x - -17/10)(x - 11/8) = 0\nx - -17/10 = 0 or x - 11/8 = 0\nx = -17/10\nx = 11/8"} {"input": "Find x for x^2 + 45/8x - 225/16 = 0", "output": "x^2 + 45/8x - 225/16 = 0\n(x - 15/8)(x - -15/2) = 0\nx - 15/8 = 0 or x - -15/2 = 0\nx = 15/8\nx = -15/2"} {"input": "Find x for 7x - 7/4 = 0", "output": "7x - 7/4 = 0\n7x = 7/4\nx = 7/4 / 7\nx = 1/4"} {"input": "Find the solution to x^3 + 89/56x^2 + 1/2x - 5/56 = 0", "output": "x^3 + 89/56x^2 + 1/2x - 5/56 = 0\n(x - -1)(x - -5/7)(x - 1/8) = 0\nx - -1 = 0\nx - -5/7 = 0\nx - 1/8 = 0\nx = -1\nx = -5/7\nx = 1/8"} {"input": "Find x in x^2 + 196/45x + 196/45 = 0", "output": "x^2 + 196/45x + 196/45 = 0\n(x - -14/9)(x - -14/5) = 0\nx - -14/9 = 0 or x - -14/5 = 0\nx = -14/9\nx = -14/5"} {"input": "Solve simultaneously:\n5x + 9y = -35/4\n9x + 10y = 15/2", "output": "5x + 9y = -35/4\n9x + 10y = 15/2\n\nUsing elimination\n9*(5x + 9y = -35/4)\n5*(9x + 10y = 15/2)\n45x + 81y = -315/4\n45x + 50y = 75/2\nSubtract equations\n31y = -465/4\ny = -465/4/31\ny = -15/4\n\nSubstitute y\n5x + 9(-15/4) = -35/4\n5x = 25\nx = 25/5\nx = 5"} {"input": "Solve quickly: x^2 + 103/7x + 10 = 0", "output": "x^2 + 103/7x + 10 = 0\n(x - -14)(x - -5/7) = 0\nx - -14 = 0 or x - -5/7 = 0\nx = -14\nx = -5/7"} {"input": "What value of x satisfies 9x - 51 = 0", "output": "9x - 51 = 0\n9x = 51\nx = 51 / 9\nx = 17/3"} {"input": "Determine x in x^2 - 163/21x + 190/21 = 0", "output": "x^2 - 163/21x + 190/21 = 0\n(x - 19/3)(x - 10/7) = 0\nx - 19/3 = 0 or x - 10/7 = 0\nx = 19/3\nx = 10/7"} {"input": "Find x in 2x + 9/4 = 0", "output": "2x + 9/4 = 0\n2x = -9/4\nx = -9/4 / 2\nx = -9/8"} {"input": "What value of x satisfies x^2 - 11/7x + 4/7 = 0", "output": "x^2 - 11/7x + 4/7 = 0\n(x - 4/7)(x - 1) = 0\nx - 4/7 = 0 or x - 1 = 0\nx = 4/7\nx = 1"} {"input": "Determine x in 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Find x and y such that\n10x + 5y = -50\n8x + 1y = -31", "output": "10x + 5y = -50\n8x + 1y = -31\n\nUsing elimination\n8*(10x + 5y = -50)\n10*(8x + 1y = -31)\n80x + 40y = -400\n80x + 10y = -310\nSubtract equations\n30y = -90\ny = -90/30\ny = -3\n\nSubstitute y\n10x + 5(-3) = -50\n10x = -35\nx = -35/10\nx = -7/2"} {"input": "Solve the system:\n10x + 5y = 1085/6\n9x + 9y = 309/2", "output": "10x + 5y = 1085/6\n9x + 9y = 309/2\n\nUsing elimination\n9*(10x + 5y = 1085/6)\n10*(9x + 9y = 309/2)\n90x + 45y = 3255/2\n90x + 90y = 1545\nSubtract equations\n-45y = 165/2\ny = 165/2/-45\ny = -11/6\n\nSubstitute y\n10x + 5(-11/6) = 1085/6\n10x = 190\nx = 190/10\nx = 19"} {"input": "Determine x in x^3 + 81/7x^2 + 240/7x + 16 = 0", "output": "x^3 + 81/7x^2 + 240/7x + 16 = 0\n(x - -7)(x - -4)(x - -4/7) = 0\nx - -7 = 0\nx - -4 = 0\nx - -4/7 = 0\nx = -7\nx = -4\nx = -4/7"} {"input": "Solve the system:\n3x + 9y = 51/7\n1x + 8y = 57/7", "output": "3x + 9y = 51/7\n1x + 8y = 57/7\n\nUsing elimination\n1*(3x + 9y = 51/7)\n3*(1x + 8y = 57/7)\n3x + 9y = 51/7\n3x + 24y = 171/7\nSubtract equations\n-15y = -120/7\ny = -120/7/-15\ny = 8/7\n\nSubstitute y\n3x + 9(8/7) = 51/7\n3x = -3\nx = -3/3\nx = -1"} {"input": "Solve the system:\n6x + 10y = -69\n3x + 6y = -33", "output": "6x + 10y = -69\n3x + 6y = -33\n\nUsing elimination\n3*(6x + 10y = -69)\n6*(3x + 6y = -33)\n18x + 30y = -207\n18x + 36y = -198\nSubtract equations\n-6y = -9\ny = -9/-6\ny = 3/2\n\nSubstitute y\n6x + 10(3/2) = -69\n6x = -84\nx = -84/6\nx = -14"} {"input": "Solve the equation 7x - 35/8 = 0", "output": "7x - 35/8 = 0\n7x = 35/8\nx = 35/8 / 7\nx = 5/8"} {"input": "Find x and y such that\n5x + 5y = 75/4\n8x + 5y = 39/2", "output": "5x + 5y = 75/4\n8x + 5y = 39/2\n\nUsing elimination\n8*(5x + 5y = 75/4)\n5*(8x + 5y = 39/2)\n40x + 40y = 150\n40x + 25y = 195/2\nSubtract equations\n15y = 105/2\ny = 105/2/15\ny = 7/2\n\nSubstitute y\n5x + 5(7/2) = 75/4\n5x = 5/4\nx = 5/4/5\nx = 1/4"} {"input": "What value of x satisfies x^3 - 94/35x^2 + 3/5x + 54/35 = 0", "output": "x^3 - 94/35x^2 + 3/5x + 54/35 = 0\n(x - 2)(x - 9/7)(x - -3/5) = 0\nx - 2 = 0\nx - 9/7 = 0\nx - -3/5 = 0\nx = 2\nx = 9/7\nx = -3/5"} {"input": "Solve x^3 + 113/45x^2 + 16/15x + 4/45 = 0", "output": "x^3 + 113/45x^2 + 16/15x + 4/45 = 0\n(x - -2)(x - -2/5)(x - -1/9) = 0\nx - -2 = 0\nx - -2/5 = 0\nx - -1/9 = 0\nx = -2\nx = -2/5\nx = -1/9"} {"input": "Solve simultaneously:\n2x + 5y = -62/3\n10x + 5y = -290/3", "output": "2x + 5y = -62/3\n10x + 5y = -290/3\n\nUsing elimination\n10*(2x + 5y = -62/3)\n2*(10x + 5y = -290/3)\n20x + 50y = -620/3\n20x + 10y = -580/3\nSubtract equations\n40y = -40/3\ny = -40/3/40\ny = -1/3\n\nSubstitute y\n2x + 5(-1/3) = -62/3\n2x = -19\nx = -19/2\nx = -19/2"} {"input": "Solve the equation x^3 + 43/6x^2 + 97/6x + 35/3 = 0", "output": "x^3 + 43/6x^2 + 97/6x + 35/3 = 0\n(x - -2)(x - -7/2)(x - -5/3) = 0\nx - -2 = 0\nx - -7/2 = 0\nx - -5/3 = 0\nx = -2\nx = -7/2\nx = -5/3"} {"input": "Solve 2x - 24 = 0", "output": "2x - 24 = 0\n2x = 24\nx = 24 / 2\nx = 12"} {"input": "Find the solution to 5x + 75/8 = 0", "output": "5x + 75/8 = 0\n5x = -75/8\nx = -75/8 / 5\nx = -15/8"} {"input": "Find x and y such that\n6x + 9y = 205/24\n6x + 5y = 121/24", "output": "6x + 9y = 205/24\n6x + 5y = 121/24\n\nUsing elimination\n6*(6x + 9y = 205/24)\n6*(6x + 5y = 121/24)\n36x + 54y = 205/4\n36x + 30y = 121/4\nSubtract equations\n24y = 21\ny = 21/24\ny = 7/8\n\nSubstitute y\n6x + 9(7/8) = 205/24\n6x = 2/3\nx = 2/3/6\nx = 1/9"} {"input": "Find x and y such that\n7x + 4y = -302/9\n9x + 4y = -386/9", "output": "7x + 4y = -302/9\n9x + 4y = -386/9\n\nUsing elimination\n9*(7x + 4y = -302/9)\n7*(9x + 4y = -386/9)\n63x + 36y = -302\n63x + 28y = -2702/9\nSubtract equations\n8y = -16/9\ny = -16/9/8\ny = -2/9\n\nSubstitute y\n7x + 4(-2/9) = -302/9\n7x = -98/3\nx = -98/3/7\nx = -14/3"} {"input": "Solve the equation x^3 + 19/20x^2 - 251/20x - 209/10 = 0", "output": "x^3 + 19/20x^2 - 251/20x - 209/10 = 0\n(x - -2)(x - -11/4)(x - 19/5) = 0\nx - -2 = 0\nx - -11/4 = 0\nx - 19/5 = 0\nx = -2\nx = -11/4\nx = 19/5"} {"input": "Find x and y such that\n7x + 9y = 79/4\n10x + 10y = 485/18", "output": "7x + 9y = 79/4\n10x + 10y = 485/18\n\nUsing elimination\n10*(7x + 9y = 79/4)\n7*(10x + 10y = 485/18)\n70x + 90y = 395/2\n70x + 70y = 3395/18\nSubtract equations\n20y = 80/9\ny = 80/9/20\ny = 4/9\n\nSubstitute y\n7x + 9(4/9) = 79/4\n7x = 63/4\nx = 63/4/7\nx = 9/4"} {"input": "Find x in 4x + 8 = 0", "output": "4x + 8 = 0\n4x = -8\nx = -8 / 4\nx = -2"} {"input": "Solve quickly: 9x + 36 = 0", "output": "9x + 36 = 0\n9x = -36\nx = -36 / 9\nx = -4"} {"input": "Find x for x^3 + 31/6x^2 - 73/18x - 110/9 = 0", "output": "x^3 + 31/6x^2 - 73/18x - 110/9 = 0\n(x - -4/3)(x - -11/2)(x - 5/3) = 0\nx - -4/3 = 0\nx - -11/2 = 0\nx - 5/3 = 0\nx = -4/3\nx = -11/2\nx = 5/3"} {"input": "Find x in x^3 + 205/24x^2 - 53x + 1547/24 = 0", "output": "x^3 + 205/24x^2 - 53x + 1547/24 = 0\n(x - 7/3)(x - -13)(x - 17/8) = 0\nx - 7/3 = 0\nx - -13 = 0\nx - 17/8 = 0\nx = 7/3\nx = -13\nx = 17/8"} {"input": "Solve 9x - 54/7 = 0", "output": "9x - 54/7 = 0\n9x = 54/7\nx = 54/7 / 9\nx = 6/7"} {"input": "Find x for 1x + 5/2 = 0", "output": "1x + 5/2 = 0\n1x = -5/2\nx = -5/2 / 1\nx = -5/2"} {"input": "Compute the solution of x^3 - 5x^2 - 12x + 36 = 0", "output": "x^3 - 5x^2 - 12x + 36 = 0\n(x - 6)(x - 2)(x - -3) = 0\nx - 6 = 0\nx - 2 = 0\nx - -3 = 0\nx = 6\nx = 2\nx = -3"} {"input": "Solve the equations:\n7x + 8y = 38/3\n8x + 7y = 22/3", "output": "7x + 8y = 38/3\n8x + 7y = 22/3\n\nUsing elimination\n8*(7x + 8y = 38/3)\n7*(8x + 7y = 22/3)\n56x + 64y = 304/3\n56x + 49y = 154/3\nSubtract equations\n15y = 50\ny = 50/15\ny = 10/3\n\nSubstitute y\n7x + 8(10/3) = 38/3\n7x = -14\nx = -14/7\nx = -2"} {"input": "Determine x in 7x - 28/3 = 0", "output": "7x - 28/3 = 0\n7x = 28/3\nx = 28/3 / 7\nx = 4/3"} {"input": "What value of x satisfies 8x + 28/3 = 0", "output": "8x + 28/3 = 0\n8x = -28/3\nx = -28/3 / 8\nx = -7/6"} {"input": "What value of x satisfies x^2 + 47/6x - 17/3 = 0", "output": "x^2 + 47/6x - 17/3 = 0\n(x - -17/2)(x - 2/3) = 0\nx - -17/2 = 0 or x - 2/3 = 0\nx = -17/2\nx = 2/3"} {"input": "Find x for x^3 - 29/6x^2 - 19/6x + 21 = 0", "output": "x^3 - 29/6x^2 - 19/6x + 21 = 0\n(x - 9/2)(x - 7/3)(x - -2) = 0\nx - 9/2 = 0\nx - 7/3 = 0\nx - -2 = 0\nx = 9/2\nx = 7/3\nx = -2"} {"input": "Solve simultaneously:\n7x + 8y = 79/9\n10x + 8y = 106/9", "output": "7x + 8y = 79/9\n10x + 8y = 106/9\n\nUsing elimination\n10*(7x + 8y = 79/9)\n7*(10x + 8y = 106/9)\n70x + 80y = 790/9\n70x + 56y = 742/9\nSubtract equations\n24y = 16/3\ny = 16/3/24\ny = 2/9\n\nSubstitute y\n7x + 8(2/9) = 79/9\n7x = 7\nx = 7/7\nx = 1"} {"input": "Solve 1x + 2 = 0", "output": "1x + 2 = 0\n1x = -2\nx = -2 / 1\nx = -2"} {"input": "Determine x in x^3 + 29/2x^2 - 41x + 51/2 = 0", "output": "x^3 + 29/2x^2 - 41x + 51/2 = 0\n(x - -17)(x - 1)(x - 3/2) = 0\nx - -17 = 0\nx - 1 = 0\nx - 3/2 = 0\nx = -17\nx = 1\nx = 3/2"} {"input": "Solve quickly: x^3 - 25/3x^2 + 14/3x + 152/3 = 0", "output": "x^3 - 25/3x^2 + 14/3x + 152/3 = 0\n(x - 19/3)(x - 4)(x - -2) = 0\nx - 19/3 = 0\nx - 4 = 0\nx - -2 = 0\nx = 19/3\nx = 4\nx = -2"} {"input": "What value of x satisfies x^3 - 41/24x^2 - 13/48x + 7/8 = 0", "output": "x^3 - 41/24x^2 - 13/48x + 7/8 = 0\n(x - 7/8)(x - 3/2)(x - -2/3) = 0\nx - 7/8 = 0\nx - 3/2 = 0\nx - -2/3 = 0\nx = 7/8\nx = 3/2\nx = -2/3"} {"input": "Solve quickly: x^2 - 13/8x + 9/16 = 0", "output": "x^2 - 13/8x + 9/16 = 0\n(x - 1/2)(x - 9/8) = 0\nx - 1/2 = 0 or x - 9/8 = 0\nx = 1/2\nx = 9/8"} {"input": "Solve the equations:\n2x + 9y = 12\n9x + 4y = 559/9", "output": "2x + 9y = 12\n9x + 4y = 559/9\n\nUsing elimination\n9*(2x + 9y = 12)\n2*(9x + 4y = 559/9)\n18x + 81y = 108\n18x + 8y = 1118/9\nSubtract equations\n73y = -146/9\ny = -146/9/73\ny = -2/9\n\nSubstitute y\n2x + 9(-2/9) = 12\n2x = 14\nx = 14/2\nx = 7"} {"input": "Solve 1x + 5/9 = 0", "output": "1x + 5/9 = 0\n1x = -5/9\nx = -5/9 / 1\nx = -5/9"} {"input": "Find x in x^3 - 5/168x^2 - 911/168x + 33/7 = 0", "output": "x^3 - 5/168x^2 - 911/168x + 33/7 = 0\n(x - 11/7)(x - 9/8)(x - -8/3) = 0\nx - 11/7 = 0\nx - 9/8 = 0\nx - -8/3 = 0\nx = 11/7\nx = 9/8\nx = -8/3"} {"input": "Find x and y such that\n6x + 2y = -200/9\n6x + 1y = -190/9", "output": "6x + 2y = -200/9\n6x + 1y = -190/9\n\nUsing elimination\n6*(6x + 2y = -200/9)\n6*(6x + 1y = -190/9)\n36x + 12y = -400/3\n36x + 6y = -380/3\nSubtract equations\n6y = -20/3\ny = -20/3/6\ny = -10/9\n\nSubstitute y\n6x + 2(-10/9) = -200/9\n6x = -20\nx = -20/6\nx = -10/3"} {"input": "Find x for x^2 + 37/6x + 19/2 = 0", "output": "x^2 + 37/6x + 19/2 = 0\n(x - -19/6)(x - -3) = 0\nx - -19/6 = 0 or x - -3 = 0\nx = -19/6\nx = -3"} {"input": "Solve the equations:\n10x + 5y = 5\n7x + 6y = 1", "output": "10x + 5y = 5\n7x + 6y = 1\n\nUsing elimination\n7*(10x + 5y = 5)\n10*(7x + 6y = 1)\n70x + 35y = 35\n70x + 60y = 10\nSubtract equations\n-25y = 25\ny = 25/-25\ny = -1\n\nSubstitute y\n10x + 5(-1) = 5\n10x = 10\nx = 10/10\nx = 1"} {"input": "What value of x satisfies x^2 - 6x + 8 = 0", "output": "x^2 - 6x + 8 = 0\n(x - 4)(x - 2) = 0\nx - 4 = 0 or x - 2 = 0\nx = 4\nx = 2"} {"input": "Find the solution to x^2 + 85/36x + 25/18 = 0", "output": "x^2 + 85/36x + 25/18 = 0\n(x - -5/4)(x - -10/9) = 0\nx - -5/4 = 0 or x - -10/9 = 0\nx = -5/4\nx = -10/9"} {"input": "Solve simultaneously:\n1x + 4y = 16/7\n1x + 8y = 44/7", "output": "1x + 4y = 16/7\n1x + 8y = 44/7\n\nUsing elimination\n1*(1x + 4y = 16/7)\n1*(1x + 8y = 44/7)\n1x + 4y = 16/7\n1x + 8y = 44/7\nSubtract equations\n-4y = -4\ny = -4/-4\ny = 1\n\nSubstitute y\n1x + 4(1) = 16/7\n1x = -12/7\nx = -12/7/1\nx = -12/7"} {"input": "Solve the system:\n7x + 8y = 112/5\n4x + 4y = 66/5", "output": "7x + 8y = 112/5\n4x + 4y = 66/5\n\nUsing elimination\n4*(7x + 8y = 112/5)\n7*(4x + 4y = 66/5)\n28x + 32y = 448/5\n28x + 28y = 462/5\nSubtract equations\n4y = -14/5\ny = -14/5/4\ny = -7/10\n\nSubstitute y\n7x + 8(-7/10) = 112/5\n7x = 28\nx = 28/7\nx = 4"} {"input": "Find x for x^3 - 37/8x^2 - 3/2x + 297/32 = 0", "output": "x^3 - 37/8x^2 - 3/2x + 297/32 = 0\n(x - 3/2)(x - 9/2)(x - -11/8) = 0\nx - 3/2 = 0\nx - 9/2 = 0\nx - -11/8 = 0\nx = 3/2\nx = 9/2\nx = -11/8"} {"input": "Find x in 5x - 80/9 = 0", "output": "5x - 80/9 = 0\n5x = 80/9\nx = 80/9 / 5\nx = 16/9"} {"input": "Determine x in x^2 - 3x - 27/4 = 0", "output": "x^2 - 3x - 27/4 = 0\n(x - 9/2)(x - -3/2) = 0\nx - 9/2 = 0 or x - -3/2 = 0\nx = 9/2\nx = -3/2"} {"input": "Find x for 10x + 100 = 0", "output": "10x + 100 = 0\n10x = -100\nx = -100 / 10\nx = -10"} {"input": "Find x for x^2 + 3/4x - 27/4 = 0", "output": "x^2 + 3/4x - 27/4 = 0\n(x - -3)(x - 9/4) = 0\nx - -3 = 0 or x - 9/4 = 0\nx = -3\nx = 9/4"} {"input": "Solve simultaneously:\n10x + 9y = -1473/10\n2x + 9y = -273/10", "output": "10x + 9y = -1473/10\n2x + 9y = -273/10\n\nUsing elimination\n2*(10x + 9y = -1473/10)\n10*(2x + 9y = -273/10)\n20x + 18y = -1473/5\n20x + 90y = -273\nSubtract equations\n-72y = -108/5\ny = -108/5/-72\ny = 3/10\n\nSubstitute y\n10x + 9(3/10) = -1473/10\n10x = -150\nx = -150/10\nx = -15"} {"input": "Find x for x^2 + 43/40x - 3/20 = 0", "output": "x^2 + 43/40x - 3/20 = 0\n(x - 1/8)(x - -6/5) = 0\nx - 1/8 = 0 or x - -6/5 = 0\nx = 1/8\nx = -6/5"} {"input": "Solve simultaneously:\n1x + 9y = 86/5\n8x + 10y = 26", "output": "1x + 9y = 86/5\n8x + 10y = 26\n\nUsing elimination\n8*(1x + 9y = 86/5)\n1*(8x + 10y = 26)\n8x + 72y = 688/5\n8x + 10y = 26\nSubtract equations\n62y = 558/5\ny = 558/5/62\ny = 9/5\n\nSubstitute y\n1x + 9(9/5) = 86/5\n1x = 1\nx = 1/1\nx = 1"} {"input": "Solve x^3 - 293/20x^2 - 111/20x + 9/2 = 0", "output": "x^3 - 293/20x^2 - 111/20x + 9/2 = 0\n(x - -3/4)(x - 15)(x - 2/5) = 0\nx - -3/4 = 0\nx - 15 = 0\nx - 2/5 = 0\nx = -3/4\nx = 15\nx = 2/5"} {"input": "Solve the equations:\n1x + 5y = -251/8\n7x + 10y = -557/8", "output": "1x + 5y = -251/8\n7x + 10y = -557/8\n\nUsing elimination\n7*(1x + 5y = -251/8)\n1*(7x + 10y = -557/8)\n7x + 35y = -1757/8\n7x + 10y = -557/8\nSubtract equations\n25y = -150\ny = -150/25\ny = -6\n\nSubstitute y\n1x + 5(-6) = -251/8\n1x = -11/8\nx = -11/8/1\nx = -11/8"} {"input": "What value of x satisfies 4x - 68/9 = 0", "output": "4x - 68/9 = 0\n4x = 68/9\nx = 68/9 / 4\nx = 17/9"} {"input": "Solve x^2 + 1/4x = 0", "output": "x^2 + 1/4x = 0\n(x - -1/4)(x - 0) = 0\nx - -1/4 = 0 or x - 0 = 0\nx = -1/4\nx = 0"} {"input": "What value of x satisfies x^2 + 43/28x - 12/7 = 0", "output": "x^2 + 43/28x - 12/7 = 0\n(x - -16/7)(x - 3/4) = 0\nx - -16/7 = 0 or x - 3/4 = 0\nx = -16/7\nx = 3/4"} {"input": "Find the solution to 2x + 8/3 = 0", "output": "2x + 8/3 = 0\n2x = -8/3\nx = -8/3 / 2\nx = -4/3"} {"input": "Compute the solution of x^3 - 7/3x^2 + 5/3x - 1/3 = 0", "output": "x^3 - 7/3x^2 + 5/3x - 1/3 = 0\n(x - 1/3)(x - 1)(x - 1) = 0\nx - 1/3 = 0\nx - 1 = 0\nx - 1 = 0\nx = 1/3\nx = 1\nx = 1"} {"input": "Solve 5x + 65/6 = 0", "output": "5x + 65/6 = 0\n5x = -65/6\nx = -65/6 / 5\nx = -13/6"} {"input": "Find x in x^3 - 131/10x^2 + 723/20x + 351/8 = 0", "output": "x^3 - 131/10x^2 + 723/20x + 351/8 = 0\n(x - 15/2)(x - -9/10)(x - 13/2) = 0\nx - 15/2 = 0\nx - -9/10 = 0\nx - 13/2 = 0\nx = 15/2\nx = -9/10\nx = 13/2"} {"input": "Solve x^3 - 26/63x^2 - 275/63x + 50/21 = 0", "output": "x^3 - 26/63x^2 - 275/63x + 50/21 = 0\n(x - -15/7)(x - 5/9)(x - 2) = 0\nx - -15/7 = 0\nx - 5/9 = 0\nx - 2 = 0\nx = -15/7\nx = 5/9\nx = 2"} {"input": "Find x and y such that\n2x + 6y = -8\n8x + 1y = 37", "output": "2x + 6y = -8\n8x + 1y = 37\n\nUsing elimination\n8*(2x + 6y = -8)\n2*(8x + 1y = 37)\n16x + 48y = -64\n16x + 2y = 74\nSubtract equations\n46y = -138\ny = -138/46\ny = -3\n\nSubstitute y\n2x + 6(-3) = -8\n2x = 10\nx = 10/2\nx = 5"} {"input": "Compute the solution of x^3 + 1313/315x^2 + 1222/315x + 8/21 = 0", "output": "x^3 + 1313/315x^2 + 1222/315x + 8/21 = 0\n(x - -1/9)(x - -6/5)(x - -20/7) = 0\nx - -1/9 = 0\nx - -6/5 = 0\nx - -20/7 = 0\nx = -1/9\nx = -6/5\nx = -20/7"} {"input": "Compute the solution of x^2 - 43/18x - 35/9 = 0", "output": "x^2 - 43/18x - 35/9 = 0\n(x - 7/2)(x - -10/9) = 0\nx - 7/2 = 0 or x - -10/9 = 0\nx = 7/2\nx = -10/9"} {"input": "Solve x^2 + 31/9x + 4/3 = 0", "output": "x^2 + 31/9x + 4/3 = 0\n(x - -4/9)(x - -3) = 0\nx - -4/9 = 0 or x - -3 = 0\nx = -4/9\nx = -3"} {"input": "Find x in x^3 + 35/2x^2 + 596/25x - 64/25 = 0", "output": "x^3 + 35/2x^2 + 596/25x - 64/25 = 0\n(x - 1/10)(x - -16)(x - -8/5) = 0\nx - 1/10 = 0\nx - -16 = 0\nx - -8/5 = 0\nx = 1/10\nx = -16\nx = -8/5"} {"input": "What value of x satisfies x^2 - 17/2x - 15 = 0", "output": "x^2 - 17/2x - 15 = 0\n(x - 10)(x - -3/2) = 0\nx - 10 = 0 or x - -3/2 = 0\nx = 10\nx = -3/2"} {"input": "Find x in x^3 - 247/90x^2 - 559/135x + 133/270 = 0", "output": "x^3 - 247/90x^2 - 559/135x + 133/270 = 0\n(x - 19/5)(x - 1/9)(x - -7/6) = 0\nx - 19/5 = 0\nx - 1/9 = 0\nx - -7/6 = 0\nx = 19/5\nx = 1/9\nx = -7/6"} {"input": "Find x for 3x - 2/3 = 0", "output": "3x - 2/3 = 0\n3x = 2/3\nx = 2/3 / 3\nx = 2/9"} {"input": "Determine x in x^3 + 226/45x^2 + 1832/225x + 64/15 = 0", "output": "x^3 + 226/45x^2 + 1832/225x + 64/15 = 0\n(x - -8/5)(x - -6/5)(x - -20/9) = 0\nx - -8/5 = 0\nx - -6/5 = 0\nx - -20/9 = 0\nx = -8/5\nx = -6/5\nx = -20/9"} {"input": "Find x in 3x - 57/4 = 0", "output": "3x - 57/4 = 0\n3x = 57/4\nx = 57/4 / 3\nx = 19/4"} {"input": "Solve the equations:\n9x + 3y = 129/4\n3x + 3y = 63/4", "output": "9x + 3y = 129/4\n3x + 3y = 63/4\n\nUsing elimination\n3*(9x + 3y = 129/4)\n9*(3x + 3y = 63/4)\n27x + 9y = 387/4\n27x + 27y = 567/4\nSubtract equations\n-18y = -45\ny = -45/-18\ny = 5/2\n\nSubstitute y\n9x + 3(5/2) = 129/4\n9x = 99/4\nx = 99/4/9\nx = 11/4"} {"input": "Solve the equations:\n1x + 1y = -2\n8x + 6y = -34/3", "output": "1x + 1y = -2\n8x + 6y = -34/3\n\nUsing elimination\n8*(1x + 1y = -2)\n1*(8x + 6y = -34/3)\n8x + 8y = -16\n8x + 6y = -34/3\nSubtract equations\n2y = -14/3\ny = -14/3/2\ny = -7/3\n\nSubstitute y\n1x + 1(-7/3) = -2\n1x = 1/3\nx = 1/3/1\nx = 1/3"} {"input": "Solve 7x + 28 = 0", "output": "7x + 28 = 0\n7x = -28\nx = -28 / 7\nx = -4"} {"input": "Solve 5x - 85/4 = 0", "output": "5x - 85/4 = 0\n5x = 85/4\nx = 85/4 / 5\nx = 17/4"} {"input": "Find x in x^2 + 33/5x + 54/5 = 0", "output": "x^2 + 33/5x + 54/5 = 0\n(x - -3)(x - -18/5) = 0\nx - -3 = 0 or x - -18/5 = 0\nx = -3\nx = -18/5"} {"input": "What value of x satisfies 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Solve quickly: x^2 - 184/63x + 5/3 = 0", "output": "x^2 - 184/63x + 5/3 = 0\n(x - 7/9)(x - 15/7) = 0\nx - 7/9 = 0 or x - 15/7 = 0\nx = 7/9\nx = 15/7"} {"input": "What value of x satisfies 8x + 16/3 = 0", "output": "8x + 16/3 = 0\n8x = -16/3\nx = -16/3 / 8\nx = -2/3"} {"input": "Solve the equation x^2 + 17/3x - 2 = 0", "output": "x^2 + 17/3x - 2 = 0\n(x - 1/3)(x - -6) = 0\nx - 1/3 = 0 or x - -6 = 0\nx = 1/3\nx = -6"} {"input": "Find x for 7x + 105/2 = 0", "output": "7x + 105/2 = 0\n7x = -105/2\nx = -105/2 / 7\nx = -15/2"} {"input": "Determine x in x^3 - 211/14x^2 + 400/7x - 450/7 = 0", "output": "x^3 - 211/14x^2 + 400/7x - 450/7 = 0\n(x - 5/2)(x - 10)(x - 18/7) = 0\nx - 5/2 = 0\nx - 10 = 0\nx - 18/7 = 0\nx = 5/2\nx = 10\nx = 18/7"} {"input": "Solve simultaneously:\n5x + 6y = 75/4\n6x + 10y = 73/2", "output": "5x + 6y = 75/4\n6x + 10y = 73/2\n\nUsing elimination\n6*(5x + 6y = 75/4)\n5*(6x + 10y = 73/2)\n30x + 36y = 225/2\n30x + 50y = 365/2\nSubtract equations\n-14y = -70\ny = -70/-14\ny = 5\n\nSubstitute y\n5x + 6(5) = 75/4\n5x = -45/4\nx = -45/4/5\nx = -9/4"} {"input": "Find the solution to x^2 - 10/3x + 17/12 = 0", "output": "x^2 - 10/3x + 17/12 = 0\n(x - 17/6)(x - 1/2) = 0\nx - 17/6 = 0 or x - 1/2 = 0\nx = 17/6\nx = 1/2"} {"input": "What value of x satisfies 6x + 8 = 0", "output": "6x + 8 = 0\n6x = -8\nx = -8 / 6\nx = -4/3"} {"input": "Solve simultaneously:\n6x + 6y = -21\n3x + 5y = -39/2", "output": "6x + 6y = -21\n3x + 5y = -39/2\n\nUsing elimination\n3*(6x + 6y = -21)\n6*(3x + 5y = -39/2)\n18x + 18y = -63\n18x + 30y = -117\nSubtract equations\n-12y = 54\ny = 54/-12\ny = -9/2\n\nSubstitute y\n6x + 6(-9/2) = -21\n6x = 6\nx = 6/6\nx = 1"} {"input": "Compute the solution of 2x + 16/3 = 0", "output": "2x + 16/3 = 0\n2x = -16/3\nx = -16/3 / 2\nx = -8/3"} {"input": "Solve 7x + 2 = 0", "output": "7x + 2 = 0\n7x = -2\nx = -2 / 7\nx = -2/7"} {"input": "Solve x^3 + 65/9x^2 + 100/9x = 0", "output": "x^3 + 65/9x^2 + 100/9x = 0\n(x - -20/9)(x - 0)(x - -5) = 0\nx - -20/9 = 0\nx - 0 = 0\nx - -5 = 0\nx = -20/9\nx = 0\nx = -5"} {"input": "Find x for x^3 - 1/4x^2 - 35/72x + 1/12 = 0", "output": "x^3 - 1/4x^2 - 35/72x + 1/12 = 0\n(x - -2/3)(x - 3/4)(x - 1/6) = 0\nx - -2/3 = 0\nx - 3/4 = 0\nx - 1/6 = 0\nx = -2/3\nx = 3/4\nx = 1/6"} {"input": "Solve the equation 2x + 16/5 = 0", "output": "2x + 16/5 = 0\n2x = -16/5\nx = -16/5 / 2\nx = -8/5"} {"input": "Find x and y such that\n3x + 9y = 99/28\n8x + 6y = 69/14", "output": "3x + 9y = 99/28\n8x + 6y = 69/14\n\nUsing elimination\n8*(3x + 9y = 99/28)\n3*(8x + 6y = 69/14)\n24x + 72y = 198/7\n24x + 18y = 207/14\nSubtract equations\n54y = 27/2\ny = 27/2/54\ny = 1/4\n\nSubstitute y\n3x + 9(1/4) = 99/28\n3x = 9/7\nx = 9/7/3\nx = 3/7"} {"input": "Find x and y such that\n10x + 10y = -45/4\n3x + 5y = -15/8", "output": "10x + 10y = -45/4\n3x + 5y = -15/8\n\nUsing elimination\n3*(10x + 10y = -45/4)\n10*(3x + 5y = -15/8)\n30x + 30y = -135/4\n30x + 50y = -75/4\nSubtract equations\n-20y = -15\ny = -15/-20\ny = 3/4\n\nSubstitute y\n10x + 10(3/4) = -45/4\n10x = -75/4\nx = -75/4/10\nx = -15/8"} {"input": "Solve quickly: x^3 + 13/2x^2 - 109/4x + 95/8 = 0", "output": "x^3 + 13/2x^2 - 109/4x + 95/8 = 0\n(x - 1/2)(x - -19/2)(x - 5/2) = 0\nx - 1/2 = 0\nx - -19/2 = 0\nx - 5/2 = 0\nx = 1/2\nx = -19/2\nx = 5/2"} {"input": "Solve the equation x^3 - 163/35x^2 - 276/35x - 36/35 = 0", "output": "x^3 - 163/35x^2 - 276/35x - 36/35 = 0\n(x - -6/5)(x - -1/7)(x - 6) = 0\nx - -6/5 = 0\nx - -1/7 = 0\nx - 6 = 0\nx = -6/5\nx = -1/7\nx = 6"} {"input": "Find x and y such that\n9x + 3y = -144\n9x + 4y = -138", "output": "9x + 3y = -144\n9x + 4y = -138\n\nUsing elimination\n9*(9x + 3y = -144)\n9*(9x + 4y = -138)\n81x + 27y = -1296\n81x + 36y = -1242\nSubtract equations\n-9y = -54\ny = -54/-9\ny = 6\n\nSubstitute y\n9x + 3(6) = -144\n9x = -162\nx = -162/9\nx = -18"} {"input": "Find x and y such that\n6x + 3y = 3/2\n1x + 3y = 3/2", "output": "6x + 3y = 3/2\n1x + 3y = 3/2\n\nUsing elimination\n1*(6x + 3y = 3/2)\n6*(1x + 3y = 3/2)\n6x + 3y = 3/2\n6x + 18y = 9\nSubtract equations\n-15y = -15/2\ny = -15/2/-15\ny = 1/2\n\nSubstitute y\n6x + 3(1/2) = 3/2\n6x = 0\nx = 0/6\nx = 0"} {"input": "Solve the equation 2x + 12/5 = 0", "output": "2x + 12/5 = 0\n2x = -12/5\nx = -12/5 / 2\nx = -6/5"} {"input": "Find x for x^3 - 388/45x^2 - 167/45x + 14/5 = 0", "output": "x^3 - 388/45x^2 - 167/45x + 14/5 = 0\n(x - -7/9)(x - 9)(x - 2/5) = 0\nx - -7/9 = 0\nx - 9 = 0\nx - 2/5 = 0\nx = -7/9\nx = 9\nx = 2/5"} {"input": "Solve the system:\n8x + 9y = 32/3\n6x + 8y = 13", "output": "8x + 9y = 32/3\n6x + 8y = 13\n\nUsing elimination\n6*(8x + 9y = 32/3)\n8*(6x + 8y = 13)\n48x + 54y = 64\n48x + 64y = 104\nSubtract equations\n-10y = -40\ny = -40/-10\ny = 4\n\nSubstitute y\n8x + 9(4) = 32/3\n8x = -76/3\nx = -76/3/8\nx = -19/6"} {"input": "Solve quickly: x^2 + 1/8x - 9/8 = 0", "output": "x^2 + 1/8x - 9/8 = 0\n(x - 1)(x - -9/8) = 0\nx - 1 = 0 or x - -9/8 = 0\nx = 1\nx = -9/8"} {"input": "Solve the equation x^2 + 16/3x + 7 = 0", "output": "x^2 + 16/3x + 7 = 0\n(x - -7/3)(x - -3) = 0\nx - -7/3 = 0 or x - -3 = 0\nx = -7/3\nx = -3"} {"input": "Find x in x^2 - 7/9x - 20/3 = 0", "output": "x^2 - 7/9x - 20/3 = 0\n(x - 3)(x - -20/9) = 0\nx - 3 = 0 or x - -20/9 = 0\nx = 3\nx = -20/9"} {"input": "Solve quickly: 8x - 19 = 0", "output": "8x - 19 = 0\n8x = 19\nx = 19 / 8\nx = 19/8"} {"input": "What value of x satisfies 10x + 85 = 0", "output": "10x + 85 = 0\n10x = -85\nx = -85 / 10\nx = -17/2"} {"input": "Solve the system:\n8x + 9y = 49/15\n9x + 5y = -7/2", "output": "8x + 9y = 49/15\n9x + 5y = -7/2\n\nUsing elimination\n9*(8x + 9y = 49/15)\n8*(9x + 5y = -7/2)\n72x + 81y = 147/5\n72x + 40y = -28\nSubtract equations\n41y = 287/5\ny = 287/5/41\ny = 7/5\n\nSubstitute y\n8x + 9(7/5) = 49/15\n8x = -28/3\nx = -28/3/8\nx = -7/6"} {"input": "Compute the solution of x^2 + 59/3x + 38/3 = 0", "output": "x^2 + 59/3x + 38/3 = 0\n(x - -2/3)(x - -19) = 0\nx - -2/3 = 0 or x - -19 = 0\nx = -2/3\nx = -19"} {"input": "Find x in x^2 - 217/36x + 68/9 = 0", "output": "x^2 - 217/36x + 68/9 = 0\n(x - 17/4)(x - 16/9) = 0\nx - 17/4 = 0 or x - 16/9 = 0\nx = 17/4\nx = 16/9"} {"input": "Find x in x^2 + 39/4x + 27/4 = 0", "output": "x^2 + 39/4x + 27/4 = 0\n(x - -3/4)(x - -9) = 0\nx - -3/4 = 0 or x - -9 = 0\nx = -3/4\nx = -9"} {"input": "Solve the equations:\n4x + 9y = 38/7\n7x + 4y = 90/7", "output": "4x + 9y = 38/7\n7x + 4y = 90/7\n\nUsing elimination\n7*(4x + 9y = 38/7)\n4*(7x + 4y = 90/7)\n28x + 63y = 38\n28x + 16y = 360/7\nSubtract equations\n47y = -94/7\ny = -94/7/47\ny = -2/7\n\nSubstitute y\n4x + 9(-2/7) = 38/7\n4x = 8\nx = 8/4\nx = 2"} {"input": "Solve the system:\n4x + 9y = -163/2\n9x + 6y = -162", "output": "4x + 9y = -163/2\n9x + 6y = -162\n\nUsing elimination\n9*(4x + 9y = -163/2)\n4*(9x + 6y = -162)\n36x + 81y = -1467/2\n36x + 24y = -648\nSubtract equations\n57y = -171/2\ny = -171/2/57\ny = -3/2\n\nSubstitute y\n4x + 9(-3/2) = -163/2\n4x = -68\nx = -68/4\nx = -17"} {"input": "Find the solution to 7x + 2 = 0", "output": "7x + 2 = 0\n7x = -2\nx = -2 / 7\nx = -2/7"} {"input": "Solve the system:\n6x + 4y = -104\n7x + 2y = -104", "output": "6x + 4y = -104\n7x + 2y = -104\n\nUsing elimination\n7*(6x + 4y = -104)\n6*(7x + 2y = -104)\n42x + 28y = -728\n42x + 12y = -624\nSubtract equations\n16y = -104\ny = -104/16\ny = -13/2\n\nSubstitute y\n6x + 4(-13/2) = -104\n6x = -78\nx = -78/6\nx = -13"} {"input": "Solve the equations:\n10x + 5y = -170\n10x + 8y = -164", "output": "10x + 5y = -170\n10x + 8y = -164\n\nUsing elimination\n10*(10x + 5y = -170)\n10*(10x + 8y = -164)\n100x + 50y = -1700\n100x + 80y = -1640\nSubtract equations\n-30y = -60\ny = -60/-30\ny = 2\n\nSubstitute y\n10x + 5(2) = -170\n10x = -180\nx = -180/10\nx = -18"} {"input": "Find x for x^2 + 29/10x + 9/5 = 0", "output": "x^2 + 29/10x + 9/5 = 0\n(x - -2)(x - -9/10) = 0\nx - -2 = 0 or x - -9/10 = 0\nx = -2\nx = -9/10"} {"input": "Compute the solution of x^3 + 187/21x^2 + 515/21x + 143/7 = 0", "output": "x^3 + 187/21x^2 + 515/21x + 143/7 = 0\n(x - -3)(x - -13/3)(x - -11/7) = 0\nx - -3 = 0\nx - -13/3 = 0\nx - -11/7 = 0\nx = -3\nx = -13/3\nx = -11/7"} {"input": "Solve quickly: x^3 - 53/36x^2 - 115/36x + 77/18 = 0", "output": "x^3 - 53/36x^2 - 115/36x + 77/18 = 0\n(x - 2)(x - 11/9)(x - -7/4) = 0\nx - 2 = 0\nx - 11/9 = 0\nx - -7/4 = 0\nx = 2\nx = 11/9\nx = -7/4"} {"input": "Solve the equation x^2 + 85/28x - 75/28 = 0", "output": "x^2 + 85/28x - 75/28 = 0\n(x - 5/7)(x - -15/4) = 0\nx - 5/7 = 0 or x - -15/4 = 0\nx = 5/7\nx = -15/4"} {"input": "Find x for x^3 + 233/56x^2 + 347/112x - 19/7 = 0", "output": "x^3 + 233/56x^2 + 347/112x - 19/7 = 0\n(x - -19/8)(x - 1/2)(x - -16/7) = 0\nx - -19/8 = 0\nx - 1/2 = 0\nx - -16/7 = 0\nx = -19/8\nx = 1/2\nx = -16/7"} {"input": "Find x and y such that\n6x + 9y = -303/35\n1x + 4y = -351/70", "output": "6x + 9y = -303/35\n1x + 4y = -351/70\n\nUsing elimination\n1*(6x + 9y = -303/35)\n6*(1x + 4y = -351/70)\n6x + 9y = -303/35\n6x + 24y = -1053/35\nSubtract equations\n-15y = 150/7\ny = 150/7/-15\ny = -10/7\n\nSubstitute y\n6x + 9(-10/7) = -303/35\n6x = 21/5\nx = 21/5/6\nx = 7/10"} {"input": "Find the solution to 1x + 7/4 = 0", "output": "1x + 7/4 = 0\n1x = -7/4\nx = -7/4 / 1\nx = -7/4"} {"input": "Find x and y such that\n2x + 1y = -27/20\n8x + 1y = -243/20", "output": "2x + 1y = -27/20\n8x + 1y = -243/20\n\nUsing elimination\n8*(2x + 1y = -27/20)\n2*(8x + 1y = -243/20)\n16x + 8y = -54/5\n16x + 2y = -243/10\nSubtract equations\n6y = 27/2\ny = 27/2/6\ny = 9/4\n\nSubstitute y\n2x + 1(9/4) = -27/20\n2x = -18/5\nx = -18/5/2\nx = -9/5"} {"input": "Solve the equation 5x - 80 = 0", "output": "5x - 80 = 0\n5x = 80\nx = 80 / 5\nx = 16"} {"input": "Solve x^3 - 253/84x^2 + 73/84x + 5/3 = 0", "output": "x^3 - 253/84x^2 + 73/84x + 5/3 = 0\n(x - -4/7)(x - 7/3)(x - 5/4) = 0\nx - -4/7 = 0\nx - 7/3 = 0\nx - 5/4 = 0\nx = -4/7\nx = 7/3\nx = 5/4"} {"input": "Compute the solution of x^2 + 34/35x - 33/35 = 0", "output": "x^2 + 34/35x - 33/35 = 0\n(x - -11/7)(x - 3/5) = 0\nx - -11/7 = 0 or x - 3/5 = 0\nx = -11/7\nx = 3/5"} {"input": "Determine x in x^2 + 34/15x - 16/15 = 0", "output": "x^2 + 34/15x - 16/15 = 0\n(x - -8/3)(x - 2/5) = 0\nx - -8/3 = 0 or x - 2/5 = 0\nx = -8/3\nx = 2/5"} {"input": "Solve x^2 - 21/40x - 143/80 = 0", "output": "x^2 - 21/40x - 143/80 = 0\n(x - -11/10)(x - 13/8) = 0\nx - -11/10 = 0 or x - 13/8 = 0\nx = -11/10\nx = 13/8"} {"input": "What value of x satisfies x^3 + 13/2x^2 + 213/16x + 135/16 = 0", "output": "x^3 + 13/2x^2 + 213/16x + 135/16 = 0\n(x - -5/4)(x - -3)(x - -9/4) = 0\nx - -5/4 = 0\nx - -3 = 0\nx - -9/4 = 0\nx = -5/4\nx = -3\nx = -9/4"} {"input": "Solve quickly: x^3 - 29/6x^2 - 21/2x + 19/3 = 0", "output": "x^3 - 29/6x^2 - 21/2x + 19/3 = 0\n(x - 1/2)(x - 19/3)(x - -2) = 0\nx - 1/2 = 0\nx - 19/3 = 0\nx - -2 = 0\nx = 1/2\nx = 19/3\nx = -2"} {"input": "Solve quickly: 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "Find x in x^2 + 89/10x + 133/10 = 0", "output": "x^2 + 89/10x + 133/10 = 0\n(x - -7)(x - -19/10) = 0\nx - -7 = 0 or x - -19/10 = 0\nx = -7\nx = -19/10"} {"input": "Solve the system:\n4x + 5y = -114/7\n1x + 5y = -207/14", "output": "4x + 5y = -114/7\n1x + 5y = -207/14\n\nUsing elimination\n1*(4x + 5y = -114/7)\n4*(1x + 5y = -207/14)\n4x + 5y = -114/7\n4x + 20y = -414/7\nSubtract equations\n-15y = 300/7\ny = 300/7/-15\ny = -20/7\n\nSubstitute y\n4x + 5(-20/7) = -114/7\n4x = -2\nx = -2/4\nx = -1/2"} {"input": "Find the solution to 10x - 40 = 0", "output": "10x - 40 = 0\n10x = 40\nx = 40 / 10\nx = 4"} {"input": "Solve the system:\n3x + 6y = -175/6\n6x + 1y = -205/12", "output": "3x + 6y = -175/6\n6x + 1y = -205/12\n\nUsing elimination\n6*(3x + 6y = -175/6)\n3*(6x + 1y = -205/12)\n18x + 36y = -175\n18x + 3y = -205/4\nSubtract equations\n33y = -495/4\ny = -495/4/33\ny = -15/4\n\nSubstitute y\n3x + 6(-15/4) = -175/6\n3x = -20/3\nx = -20/3/3\nx = -20/9"} {"input": "Compute the solution of x^2 + 23/4x - 85/2 = 0", "output": "x^2 + 23/4x - 85/2 = 0\n(x - -10)(x - 17/4) = 0\nx - -10 = 0 or x - 17/4 = 0\nx = -10\nx = 17/4"} {"input": "Solve simultaneously:\n9x + 8y = -571/20\n10x + 7y = -287/10", "output": "9x + 8y = -571/20\n10x + 7y = -287/10\n\nUsing elimination\n10*(9x + 8y = -571/20)\n9*(10x + 7y = -287/10)\n90x + 80y = -571/2\n90x + 63y = -2583/10\nSubtract equations\n17y = -136/5\ny = -136/5/17\ny = -8/5\n\nSubstitute y\n9x + 8(-8/5) = -571/20\n9x = -63/4\nx = -63/4/9\nx = -7/4"} {"input": "Find x for 3x - 45/2 = 0", "output": "3x - 45/2 = 0\n3x = 45/2\nx = 45/2 / 3\nx = 15/2"} {"input": "What value of x satisfies x^2 - 123/10x + 133/5 = 0", "output": "x^2 - 123/10x + 133/5 = 0\n(x - 19/2)(x - 14/5) = 0\nx - 19/2 = 0 or x - 14/5 = 0\nx = 19/2\nx = 14/5"} {"input": "Solve the equation 4x + 64/7 = 0", "output": "4x + 64/7 = 0\n4x = -64/7\nx = -64/7 / 4\nx = -16/7"} {"input": "Determine x in 2x - 36/5 = 0", "output": "2x - 36/5 = 0\n2x = 36/5\nx = 36/5 / 2\nx = 18/5"} {"input": "Compute the solution of x^2 + 20/3x + 4 = 0", "output": "x^2 + 20/3x + 4 = 0\n(x - -6)(x - -2/3) = 0\nx - -6 = 0 or x - -2/3 = 0\nx = -6\nx = -2/3"} {"input": "Solve the system:\n2x + 5y = -126\n5x + 8y = -225", "output": "2x + 5y = -126\n5x + 8y = -225\n\nUsing elimination\n5*(2x + 5y = -126)\n2*(5x + 8y = -225)\n10x + 25y = -630\n10x + 16y = -450\nSubtract equations\n9y = -180\ny = -180/9\ny = -20\n\nSubstitute y\n2x + 5(-20) = -126\n2x = -26\nx = -26/2\nx = -13"} {"input": "Determine x in x^2 + 23/3x + 14 = 0", "output": "x^2 + 23/3x + 14 = 0\n(x - -14/3)(x - -3) = 0\nx - -14/3 = 0 or x - -3 = 0\nx = -14/3\nx = -3"} {"input": "Solve the equations:\n7x + 5y = -17/2\n7x + 8y = -25", "output": "7x + 5y = -17/2\n7x + 8y = -25\n\nUsing elimination\n7*(7x + 5y = -17/2)\n7*(7x + 8y = -25)\n49x + 35y = -119/2\n49x + 56y = -175\nSubtract equations\n-21y = 231/2\ny = 231/2/-21\ny = -11/2\n\nSubstitute y\n7x + 5(-11/2) = -17/2\n7x = 19\nx = 19/7\nx = 19/7"} {"input": "Find x for x^2 + 19/5x + 18/5 = 0", "output": "x^2 + 19/5x + 18/5 = 0\n(x - -9/5)(x - -2) = 0\nx - -9/5 = 0 or x - -2 = 0\nx = -9/5\nx = -2"} {"input": "Solve the equations:\n6x + 4y = -110/9\n5x + 8y = -115/9", "output": "6x + 4y = -110/9\n5x + 8y = -115/9\n\nUsing elimination\n5*(6x + 4y = -110/9)\n6*(5x + 8y = -115/9)\n30x + 20y = -550/9\n30x + 48y = -230/3\nSubtract equations\n-28y = 140/9\ny = 140/9/-28\ny = -5/9\n\nSubstitute y\n6x + 4(-5/9) = -110/9\n6x = -10\nx = -10/6\nx = -5/3"} {"input": "Solve the system:\n6x + 10y = -242/7\n5x + 4y = -527/21", "output": "6x + 10y = -242/7\n5x + 4y = -527/21\n\nUsing elimination\n5*(6x + 10y = -242/7)\n6*(5x + 4y = -527/21)\n30x + 50y = -1210/7\n30x + 24y = -1054/7\nSubtract equations\n26y = -156/7\ny = -156/7/26\ny = -6/7\n\nSubstitute y\n6x + 10(-6/7) = -242/7\n6x = -26\nx = -26/6\nx = -13/3"} {"input": "Find x in x^2 + 108/35x + 81/35 = 0", "output": "x^2 + 108/35x + 81/35 = 0\n(x - -9/7)(x - -9/5) = 0\nx - -9/7 = 0 or x - -9/5 = 0\nx = -9/7\nx = -9/5"} {"input": "Find the solution to 5x - 65/6 = 0", "output": "5x - 65/6 = 0\n5x = 65/6\nx = 65/6 / 5\nx = 13/6"} {"input": "Compute the solution of x^2 + 3/7x - 40/49 = 0", "output": "x^2 + 3/7x - 40/49 = 0\n(x - -8/7)(x - 5/7) = 0\nx - -8/7 = 0 or x - 5/7 = 0\nx = -8/7\nx = 5/7"} {"input": "Solve simultaneously:\n3x + 10y = 512/15\n2x + 9y = 141/5", "output": "3x + 10y = 512/15\n2x + 9y = 141/5\n\nUsing elimination\n2*(3x + 10y = 512/15)\n3*(2x + 9y = 141/5)\n6x + 20y = 1024/15\n6x + 27y = 423/5\nSubtract equations\n-7y = -49/3\ny = -49/3/-7\ny = 7/3\n\nSubstitute y\n3x + 10(7/3) = 512/15\n3x = 54/5\nx = 54/5/3\nx = 18/5"} {"input": "Find the solution to x^2 + 4x - 32 = 0", "output": "x^2 + 4x - 32 = 0\n(x - -8)(x - 4) = 0\nx - -8 = 0 or x - 4 = 0\nx = -8\nx = 4"} {"input": "Find x and y such that\n4x + 5y = 21/4\n5x + 4y = 15/4", "output": "4x + 5y = 21/4\n5x + 4y = 15/4\n\nUsing elimination\n5*(4x + 5y = 21/4)\n4*(5x + 4y = 15/4)\n20x + 25y = 105/4\n20x + 16y = 15\nSubtract equations\n9y = 45/4\ny = 45/4/9\ny = 5/4\n\nSubstitute y\n4x + 5(5/4) = 21/4\n4x = -1\nx = -1/4\nx = -1/4"} {"input": "Determine x in x^3 + 103/45x^2 - 44/45x - 28/9 = 0", "output": "x^3 + 103/45x^2 - 44/45x - 28/9 = 0\n(x - 10/9)(x - -2)(x - -7/5) = 0\nx - 10/9 = 0\nx - -2 = 0\nx - -7/5 = 0\nx = 10/9\nx = -2\nx = -7/5"} {"input": "Solve x^2 - 28/15x - 64/15 = 0", "output": "x^2 - 28/15x - 64/15 = 0\n(x - -4/3)(x - 16/5) = 0\nx - -4/3 = 0 or x - 16/5 = 0\nx = -4/3\nx = 16/5"} {"input": "Find x and y such that\n1x + 7y = 73/6\n1x + 2y = 211/42", "output": "1x + 7y = 73/6\n1x + 2y = 211/42\n\nUsing elimination\n1*(1x + 7y = 73/6)\n1*(1x + 2y = 211/42)\n1x + 7y = 73/6\n1x + 2y = 211/42\nSubtract equations\n5y = 50/7\ny = 50/7/5\ny = 10/7\n\nSubstitute y\n1x + 7(10/7) = 73/6\n1x = 13/6\nx = 13/6/1\nx = 13/6"} {"input": "Solve the equation x^2 + 6/5x - 17/20 = 0", "output": "x^2 + 6/5x - 17/20 = 0\n(x - 1/2)(x - -17/10) = 0\nx - 1/2 = 0 or x - -17/10 = 0\nx = 1/2\nx = -17/10"} {"input": "Solve x^3 - 23/3x^2 - 32/3x + 64 = 0", "output": "x^3 - 23/3x^2 - 32/3x + 64 = 0\n(x - 8)(x - 8/3)(x - -3) = 0\nx - 8 = 0\nx - 8/3 = 0\nx - -3 = 0\nx = 8\nx = 8/3\nx = -3"} {"input": "Solve x^3 + 149/90x^2 - 67/54x - 55/27 = 0", "output": "x^3 + 149/90x^2 - 67/54x - 55/27 = 0\n(x - 10/9)(x - -11/10)(x - -5/3) = 0\nx - 10/9 = 0\nx - -11/10 = 0\nx - -5/3 = 0\nx = 10/9\nx = -11/10\nx = -5/3"} {"input": "Solve x^3 + 103/10x^2 - 103/10x - 143/5 = 0", "output": "x^3 + 103/10x^2 - 103/10x - 143/5 = 0\n(x - -13/10)(x - 2)(x - -11) = 0\nx - -13/10 = 0\nx - 2 = 0\nx - -11 = 0\nx = -13/10\nx = 2\nx = -11"} {"input": "Find x in x^2 + 13/40x - 3/16 = 0", "output": "x^2 + 13/40x - 3/16 = 0\n(x - 3/10)(x - -5/8) = 0\nx - 3/10 = 0 or x - -5/8 = 0\nx = 3/10\nx = -5/8"} {"input": "Find x for 7x - 35/3 = 0", "output": "7x - 35/3 = 0\n7x = 35/3\nx = 35/3 / 7\nx = 5/3"} {"input": "Find x for x^3 + 529/42x^2 + 272/7x + 1445/42 = 0", "output": "x^3 + 529/42x^2 + 272/7x + 1445/42 = 0\n(x - -17/2)(x - -5/3)(x - -17/7) = 0\nx - -17/2 = 0\nx - -5/3 = 0\nx - -17/7 = 0\nx = -17/2\nx = -5/3\nx = -17/7"} {"input": "Solve the system:\n4x + 9y = 91/18\n8x + 10y = -17/9", "output": "4x + 9y = 91/18\n8x + 10y = -17/9\n\nUsing elimination\n8*(4x + 9y = 91/18)\n4*(8x + 10y = -17/9)\n32x + 72y = 364/9\n32x + 40y = -68/9\nSubtract equations\n32y = 48\ny = 48/32\ny = 3/2\n\nSubstitute y\n4x + 9(3/2) = 91/18\n4x = -76/9\nx = -76/9/4\nx = -19/9"} {"input": "Compute the solution of 8x - 8/9 = 0", "output": "8x - 8/9 = 0\n8x = 8/9\nx = 8/9 / 8\nx = 1/9"} {"input": "Find the solution to x^2 + 18/7x = 0", "output": "x^2 + 18/7x = 0\n(x - -18/7)(x - 0) = 0\nx - -18/7 = 0 or x - 0 = 0\nx = -18/7\nx = 0"} {"input": "Solve the equations:\n1x + 10y = -59/2\n9x + 2y = -3/2", "output": "1x + 10y = -59/2\n9x + 2y = -3/2\n\nUsing elimination\n9*(1x + 10y = -59/2)\n1*(9x + 2y = -3/2)\n9x + 90y = -531/2\n9x + 2y = -3/2\nSubtract equations\n88y = -264\ny = -264/88\ny = -3\n\nSubstitute y\n1x + 10(-3) = -59/2\n1x = 1/2\nx = 1/2/1\nx = 1/2"} {"input": "Find the solution to x^2 + 161/30x + 104/15 = 0", "output": "x^2 + 161/30x + 104/15 = 0\n(x - -13/6)(x - -16/5) = 0\nx - -13/6 = 0 or x - -16/5 = 0\nx = -13/6\nx = -16/5"} {"input": "Solve quickly: 7x - 133/3 = 0", "output": "7x - 133/3 = 0\n7x = 133/3\nx = 133/3 / 7\nx = 19/3"} {"input": "Solve 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "Solve quickly: x^3 - 65/24x^2 - 647/144x + 221/18 = 0", "output": "x^3 - 65/24x^2 - 647/144x + 221/18 = 0\n(x - 8/3)(x - 13/6)(x - -17/8) = 0\nx - 8/3 = 0\nx - 13/6 = 0\nx - -17/8 = 0\nx = 8/3\nx = 13/6\nx = -17/8"} {"input": "Find x for 4x + 52 = 0", "output": "4x + 52 = 0\n4x = -52\nx = -52 / 4\nx = -13"} {"input": "Determine x in x^3 + 13/14x^2 - 13/2x - 45/7 = 0", "output": "x^3 + 13/14x^2 - 13/2x - 45/7 = 0\n(x - -5/2)(x - 18/7)(x - -1) = 0\nx - -5/2 = 0\nx - 18/7 = 0\nx - -1 = 0\nx = -5/2\nx = 18/7\nx = -1"} {"input": "What value of x satisfies 8x + 36 = 0", "output": "8x + 36 = 0\n8x = -36\nx = -36 / 8\nx = -9/2"} {"input": "Find x and y such that\n8x + 5y = -17/2\n10x + 7y = -23/2", "output": "8x + 5y = -17/2\n10x + 7y = -23/2\n\nUsing elimination\n10*(8x + 5y = -17/2)\n8*(10x + 7y = -23/2)\n80x + 50y = -85\n80x + 56y = -92\nSubtract equations\n-6y = 7\ny = 7/-6\ny = -7/6\n\nSubstitute y\n8x + 5(-7/6) = -17/2\n8x = -8/3\nx = -8/3/8\nx = -1/3"} {"input": "Solve quickly: x^2 - 49/8x + 55/16 = 0", "output": "x^2 - 49/8x + 55/16 = 0\n(x - 5/8)(x - 11/2) = 0\nx - 5/8 = 0 or x - 11/2 = 0\nx = 5/8\nx = 11/2"} {"input": "Find x in 10x - 180/7 = 0", "output": "10x - 180/7 = 0\n10x = 180/7\nx = 180/7 / 10\nx = 18/7"} {"input": "Solve quickly: 2x + 11/3 = 0", "output": "2x + 11/3 = 0\n2x = -11/3\nx = -11/3 / 2\nx = -11/6"} {"input": "Compute the solution of x^3 + 317/140x^2 - 979/280x - 247/40 = 0", "output": "x^3 + 317/140x^2 - 979/280x - 247/40 = 0\n(x - -13/10)(x - -19/7)(x - 7/4) = 0\nx - -13/10 = 0\nx - -19/7 = 0\nx - 7/4 = 0\nx = -13/10\nx = -19/7\nx = 7/4"} {"input": "Determine x in x^2 - 34/7x + 39/7 = 0", "output": "x^2 - 34/7x + 39/7 = 0\n(x - 3)(x - 13/7) = 0\nx - 3 = 0 or x - 13/7 = 0\nx = 3\nx = 13/7"} {"input": "Solve the equation x^3 + 25/6x^2 - 7/6x - 11 = 0", "output": "x^3 + 25/6x^2 - 7/6x - 11 = 0\n(x - -11/3)(x - -2)(x - 3/2) = 0\nx - -11/3 = 0\nx - -2 = 0\nx - 3/2 = 0\nx = -11/3\nx = -2\nx = 3/2"} {"input": "Determine x in x^2 + 85/21x + 50/21 = 0", "output": "x^2 + 85/21x + 50/21 = 0\n(x - -10/3)(x - -5/7) = 0\nx - -10/3 = 0 or x - -5/7 = 0\nx = -10/3\nx = -5/7"} {"input": "Determine x in 9x - 39 = 0", "output": "9x - 39 = 0\n9x = 39\nx = 39 / 9\nx = 13/3"} {"input": "Solve the equation x^3 + 97/30x^2 - 37/15x - 19/2 = 0", "output": "x^3 + 97/30x^2 - 37/15x - 19/2 = 0\n(x - 5/3)(x - -19/10)(x - -3) = 0\nx - 5/3 = 0\nx - -19/10 = 0\nx - -3 = 0\nx = 5/3\nx = -19/10\nx = -3"} {"input": "Solve simultaneously:\n7x + 10y = -547/28\n9x + 9y = -549/28", "output": "7x + 10y = -547/28\n9x + 9y = -549/28\n\nUsing elimination\n9*(7x + 10y = -547/28)\n7*(9x + 9y = -549/28)\n63x + 90y = -4923/28\n63x + 63y = -549/4\nSubtract equations\n27y = -270/7\ny = -270/7/27\ny = -10/7\n\nSubstitute y\n7x + 10(-10/7) = -547/28\n7x = -21/4\nx = -21/4/7\nx = -3/4"} {"input": "Find x in x^2 + 16/5x = 0", "output": "x^2 + 16/5x = 0\n(x - 0)(x - -16/5) = 0\nx - 0 = 0 or x - -16/5 = 0\nx = 0\nx = -16/5"} {"input": "Find the solution to x^2 - 6/5x - 8/5 = 0", "output": "x^2 - 6/5x - 8/5 = 0\n(x - 2)(x - -4/5) = 0\nx - 2 = 0 or x - -4/5 = 0\nx = 2\nx = -4/5"} {"input": "Solve quickly: x^2 + 89/5x + 266/5 = 0", "output": "x^2 + 89/5x + 266/5 = 0\n(x - -19/5)(x - -14) = 0\nx - -19/5 = 0 or x - -14 = 0\nx = -19/5\nx = -14"} {"input": "Solve the equation x^3 + 331/140x^2 - 463/140x + 51/70 = 0", "output": "x^3 + 331/140x^2 - 463/140x + 51/70 = 0\n(x - -17/5)(x - 3/4)(x - 2/7) = 0\nx - -17/5 = 0\nx - 3/4 = 0\nx - 2/7 = 0\nx = -17/5\nx = 3/4\nx = 2/7"} {"input": "Find x for x^3 + 31/12x^2 - 205/12x - 25 = 0", "output": "x^3 + 31/12x^2 - 205/12x - 25 = 0\n(x - -5)(x - 15/4)(x - -4/3) = 0\nx - -5 = 0\nx - 15/4 = 0\nx - -4/3 = 0\nx = -5\nx = 15/4\nx = -4/3"} {"input": "Find x in x^3 + 9/4x^2 - 317/8x + 51 = 0", "output": "x^3 + 9/4x^2 - 317/8x + 51 = 0\n(x - -8)(x - 17/4)(x - 3/2) = 0\nx - -8 = 0\nx - 17/4 = 0\nx - 3/2 = 0\nx = -8\nx = 17/4\nx = 3/2"} {"input": "Solve the equations:\n3x + 4y = 41/2\n10x + 8y = 157/3", "output": "3x + 4y = 41/2\n10x + 8y = 157/3\n\nUsing elimination\n10*(3x + 4y = 41/2)\n3*(10x + 8y = 157/3)\n30x + 40y = 205\n30x + 24y = 157\nSubtract equations\n16y = 48\ny = 48/16\ny = 3\n\nSubstitute y\n3x + 4(3) = 41/2\n3x = 17/2\nx = 17/2/3\nx = 17/6"} {"input": "Find x for x^3 - 193/40x^2 + 38/5x - 39/10 = 0", "output": "x^3 - 193/40x^2 + 38/5x - 39/10 = 0\n(x - 13/8)(x - 6/5)(x - 2) = 0\nx - 13/8 = 0\nx - 6/5 = 0\nx - 2 = 0\nx = 13/8\nx = 6/5\nx = 2"} {"input": "Compute the solution of 9x - 171/8 = 0", "output": "9x - 171/8 = 0\n9x = 171/8\nx = 171/8 / 9\nx = 19/8"} {"input": "What value of x satisfies x^3 - 49/30x^2 - 127/30x + 91/15 = 0", "output": "x^3 - 49/30x^2 - 127/30x + 91/15 = 0\n(x - -2)(x - 7/3)(x - 13/10) = 0\nx - -2 = 0\nx - 7/3 = 0\nx - 13/10 = 0\nx = -2\nx = 7/3\nx = 13/10"} {"input": "Compute the solution of x^2 + 21/5x - 4 = 0", "output": "x^2 + 21/5x - 4 = 0\n(x - -5)(x - 4/5) = 0\nx - -5 = 0 or x - 4/5 = 0\nx = -5\nx = 4/5"} {"input": "Solve the equation x^2 - 47/5x - 6 = 0", "output": "x^2 - 47/5x - 6 = 0\n(x - 10)(x - -3/5) = 0\nx - 10 = 0 or x - -3/5 = 0\nx = 10\nx = -3/5"} {"input": "What value of x satisfies x^3 - 7/5x^2 - 188/25x - 36/25 = 0", "output": "x^3 - 7/5x^2 - 188/25x - 36/25 = 0\n(x - -1/5)(x - 18/5)(x - -2) = 0\nx - -1/5 = 0\nx - 18/5 = 0\nx - -2 = 0\nx = -1/5\nx = 18/5\nx = -2"} {"input": "Find x and y such that\n1x + 9y = -187/10\n2x + 1y = 0", "output": "1x + 9y = -187/10\n2x + 1y = 0\n\nUsing elimination\n2*(1x + 9y = -187/10)\n1*(2x + 1y = 0)\n2x + 18y = -187/5\n2x + 1y = 0\nSubtract equations\n17y = -187/5\ny = -187/5/17\ny = -11/5\n\nSubstitute y\n1x + 9(-11/5) = -187/10\n1x = 11/10\nx = 11/10/1\nx = 11/10"} {"input": "Solve the system:\n6x + 9y = 199/2\n5x + 3y = 295/6", "output": "6x + 9y = 199/2\n5x + 3y = 295/6\n\nUsing elimination\n5*(6x + 9y = 199/2)\n6*(5x + 3y = 295/6)\n30x + 45y = 995/2\n30x + 18y = 295\nSubtract equations\n27y = 405/2\ny = 405/2/27\ny = 15/2\n\nSubstitute y\n6x + 9(15/2) = 199/2\n6x = 32\nx = 32/6\nx = 16/3"} {"input": "Solve simultaneously:\n2x + 3y = 165/7\n9x + 6y = 750/7", "output": "2x + 3y = 165/7\n9x + 6y = 750/7\n\nUsing elimination\n9*(2x + 3y = 165/7)\n2*(9x + 6y = 750/7)\n18x + 27y = 1485/7\n18x + 12y = 1500/7\nSubtract equations\n15y = -15/7\ny = -15/7/15\ny = -1/7\n\nSubstitute y\n2x + 3(-1/7) = 165/7\n2x = 24\nx = 24/2\nx = 12"} {"input": "Solve the equation x^3 + 3/28x^2 - 149/56x + 3/8 = 0", "output": "x^3 + 3/28x^2 - 149/56x + 3/8 = 0\n(x - 3/2)(x - 1/7)(x - -7/4) = 0\nx - 3/2 = 0\nx - 1/7 = 0\nx - -7/4 = 0\nx = 3/2\nx = 1/7\nx = -7/4"} {"input": "Compute the solution of x^2 + 7/6x - 51/2 = 0", "output": "x^2 + 7/6x - 51/2 = 0\n(x - 9/2)(x - -17/3) = 0\nx - 9/2 = 0 or x - -17/3 = 0\nx = 9/2\nx = -17/3"} {"input": "Solve quickly: 5x + 20/9 = 0", "output": "5x + 20/9 = 0\n5x = -20/9\nx = -20/9 / 5\nx = -4/9"} {"input": "Solve the system:\n9x + 9y = -180/7\n4x + 9y = -115/7", "output": "9x + 9y = -180/7\n4x + 9y = -115/7\n\nUsing elimination\n4*(9x + 9y = -180/7)\n9*(4x + 9y = -115/7)\n36x + 36y = -720/7\n36x + 81y = -1035/7\nSubtract equations\n-45y = 45\ny = 45/-45\ny = -1\n\nSubstitute y\n9x + 9(-1) = -180/7\n9x = -117/7\nx = -117/7/9\nx = -13/7"} {"input": "Solve quickly: 2x - 38/3 = 0", "output": "2x - 38/3 = 0\n2x = 38/3\nx = 38/3 / 2\nx = 19/3"} {"input": "Determine x in x^3 + 5x^2 - 17x - 21 = 0", "output": "x^3 + 5x^2 - 17x - 21 = 0\n(x - -1)(x - 3)(x - -7) = 0\nx - -1 = 0\nx - 3 = 0\nx - -7 = 0\nx = -1\nx = 3\nx = -7"} {"input": "Solve x^2 - 58/21x + 17/21 = 0", "output": "x^2 - 58/21x + 17/21 = 0\n(x - 1/3)(x - 17/7) = 0\nx - 1/3 = 0 or x - 17/7 = 0\nx = 1/3\nx = 17/7"} {"input": "Solve the system:\n8x + 4y = -140/3\n6x + 1y = -5", "output": "8x + 4y = -140/3\n6x + 1y = -5\n\nUsing elimination\n6*(8x + 4y = -140/3)\n8*(6x + 1y = -5)\n48x + 24y = -280\n48x + 8y = -40\nSubtract equations\n16y = -240\ny = -240/16\ny = -15\n\nSubstitute y\n8x + 4(-15) = -140/3\n8x = 40/3\nx = 40/3/8\nx = 5/3"} {"input": "Find the solution to 9x + 27 = 0", "output": "9x + 27 = 0\n9x = -27\nx = -27 / 9\nx = -3"} {"input": "Find x and y such that\n1x + 10y = 3/2\n5x + 2y = -21/10", "output": "1x + 10y = 3/2\n5x + 2y = -21/10\n\nUsing elimination\n5*(1x + 10y = 3/2)\n1*(5x + 2y = -21/10)\n5x + 50y = 15/2\n5x + 2y = -21/10\nSubtract equations\n48y = 48/5\ny = 48/5/48\ny = 1/5\n\nSubstitute y\n1x + 10(1/5) = 3/2\n1x = -1/2\nx = -1/2/1\nx = -1/2"} {"input": "Solve 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Find the solution to x^2 + 11/35x - 6/35 = 0", "output": "x^2 + 11/35x - 6/35 = 0\n(x - 2/7)(x - -3/5) = 0\nx - 2/7 = 0 or x - -3/5 = 0\nx = 2/7\nx = -3/5"} {"input": "Determine x in x^2 - 13/6x = 0", "output": "x^2 - 13/6x = 0\n(x - 13/6)(x - 0) = 0\nx - 13/6 = 0 or x - 0 = 0\nx = 13/6\nx = 0"} {"input": "Find x and y such that\n10x + 3y = -5\n5x + 4y = -65/6", "output": "10x + 3y = -5\n5x + 4y = -65/6\n\nUsing elimination\n5*(10x + 3y = -5)\n10*(5x + 4y = -65/6)\n50x + 15y = -25\n50x + 40y = -325/3\nSubtract equations\n-25y = 250/3\ny = 250/3/-25\ny = -10/3\n\nSubstitute y\n10x + 3(-10/3) = -5\n10x = 5\nx = 5/10\nx = 1/2"} {"input": "Find x in 7x - 35 = 0", "output": "7x - 35 = 0\n7x = 35\nx = 35 / 7\nx = 5"} {"input": "Compute the solution of x^3 - 277/56x^2 - 3043/112x - 1445/56 = 0", "output": "x^3 - 277/56x^2 - 3043/112x - 1445/56 = 0\n(x - -17/8)(x - 17/2)(x - -10/7) = 0\nx - -17/8 = 0\nx - 17/2 = 0\nx - -10/7 = 0\nx = -17/8\nx = 17/2\nx = -10/7"} {"input": "Find x for x^3 + 43/6x^2 + 61/6x - 7 = 0", "output": "x^3 + 43/6x^2 + 61/6x - 7 = 0\n(x - -3)(x - -14/3)(x - 1/2) = 0\nx - -3 = 0\nx - -14/3 = 0\nx - 1/2 = 0\nx = -3\nx = -14/3\nx = 1/2"} {"input": "Compute the solution of x^2 + 23/2x + 51/2 = 0", "output": "x^2 + 23/2x + 51/2 = 0\n(x - -17/2)(x - -3) = 0\nx - -17/2 = 0 or x - -3 = 0\nx = -17/2\nx = -3"} {"input": "Find x for 10x - 10/7 = 0", "output": "10x - 10/7 = 0\n10x = 10/7\nx = 10/7 / 10\nx = 1/7"} {"input": "Solve quickly: x^3 + 41/6x^2 + 275/48x - 475/24 = 0", "output": "x^3 + 41/6x^2 + 275/48x - 475/24 = 0\n(x - -19/4)(x - -10/3)(x - 5/4) = 0\nx - -19/4 = 0\nx - -10/3 = 0\nx - 5/4 = 0\nx = -19/4\nx = -10/3\nx = 5/4"} {"input": "Solve quickly: x^2 + 1x - 15/4 = 0", "output": "x^2 + 1x - 15/4 = 0\n(x - 3/2)(x - -5/2) = 0\nx - 3/2 = 0 or x - -5/2 = 0\nx = 3/2\nx = -5/2"} {"input": "Solve the system:\n8x + 10y = 221/2\n4x + 8y = 62", "output": "8x + 10y = 221/2\n4x + 8y = 62\n\nUsing elimination\n4*(8x + 10y = 221/2)\n8*(4x + 8y = 62)\n32x + 40y = 442\n32x + 64y = 496\nSubtract equations\n-24y = -54\ny = -54/-24\ny = 9/4\n\nSubstitute y\n8x + 10(9/4) = 221/2\n8x = 88\nx = 88/8\nx = 11"} {"input": "Solve the equation x^2 - 79/15x + 14/5 = 0", "output": "x^2 - 79/15x + 14/5 = 0\n(x - 3/5)(x - 14/3) = 0\nx - 3/5 = 0 or x - 14/3 = 0\nx = 3/5\nx = 14/3"} {"input": "Solve the equations:\n3x + 5y = -5/3\n3x + 8y = -8/3", "output": "3x + 5y = -5/3\n3x + 8y = -8/3\n\nUsing elimination\n3*(3x + 5y = -5/3)\n3*(3x + 8y = -8/3)\n9x + 15y = -5\n9x + 24y = -8\nSubtract equations\n-9y = 3\ny = 3/-9\ny = -1/3\n\nSubstitute y\n3x + 5(-1/3) = -5/3\n3x = 0\nx = 0/3\nx = 0"} {"input": "Solve simultaneously:\n1x + 6y = -20/3\n8x + 7y = -316/9", "output": "1x + 6y = -20/3\n8x + 7y = -316/9\n\nUsing elimination\n8*(1x + 6y = -20/3)\n1*(8x + 7y = -316/9)\n8x + 48y = -160/3\n8x + 7y = -316/9\nSubtract equations\n41y = -164/9\ny = -164/9/41\ny = -4/9\n\nSubstitute y\n1x + 6(-4/9) = -20/3\n1x = -4\nx = -4/1\nx = -4"} {"input": "Find x for 1x - 9/5 = 0", "output": "1x - 9/5 = 0\n1x = 9/5\nx = 9/5 / 1\nx = 9/5"} {"input": "Find the solution to x^2 - 37/10x + 21/10 = 0", "output": "x^2 - 37/10x + 21/10 = 0\n(x - 3)(x - 7/10) = 0\nx - 3 = 0 or x - 7/10 = 0\nx = 3\nx = 7/10"} {"input": "Solve simultaneously:\n2x + 4y = -42\n8x + 2y = -84", "output": "2x + 4y = -42\n8x + 2y = -84\n\nUsing elimination\n8*(2x + 4y = -42)\n2*(8x + 2y = -84)\n16x + 32y = -336\n16x + 4y = -168\nSubtract equations\n28y = -168\ny = -168/28\ny = -6\n\nSubstitute y\n2x + 4(-6) = -42\n2x = -18\nx = -18/2\nx = -9"} {"input": "Find the solution to 6x - 3 = 0", "output": "6x - 3 = 0\n6x = 3\nx = 3 / 6\nx = 1/2"} {"input": "Solve the equations:\n4x + 8y = 88\n3x + 7y = 78", "output": "4x + 8y = 88\n3x + 7y = 78\n\nUsing elimination\n3*(4x + 8y = 88)\n4*(3x + 7y = 78)\n12x + 24y = 264\n12x + 28y = 312\nSubtract equations\n-4y = -48\ny = -48/-4\ny = 12\n\nSubstitute y\n4x + 8(12) = 88\n4x = -8\nx = -8/4\nx = -2"} {"input": "Solve the equation 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "What value of x satisfies x^2 - 177/35x + 44/7 = 0", "output": "x^2 - 177/35x + 44/7 = 0\n(x - 20/7)(x - 11/5) = 0\nx - 20/7 = 0 or x - 11/5 = 0\nx = 20/7\nx = 11/5"} {"input": "Find x in 2x + 8 = 0", "output": "2x + 8 = 0\n2x = -8\nx = -8 / 2\nx = -4"} {"input": "Solve the equation x^3 - 37/20x^2 - 203/320x + 17/160 = 0", "output": "x^3 - 37/20x^2 - 203/320x + 17/160 = 0\n(x - -2/5)(x - 17/8)(x - 1/8) = 0\nx - -2/5 = 0\nx - 17/8 = 0\nx - 1/8 = 0\nx = -2/5\nx = 17/8\nx = 1/8"} {"input": "Solve quickly: x^3 - 1077/56x^2 + 45/2x - 81/14 = 0", "output": "x^3 - 1077/56x^2 + 45/2x - 81/14 = 0\n(x - 6/7)(x - 18)(x - 3/8) = 0\nx - 6/7 = 0\nx - 18 = 0\nx - 3/8 = 0\nx = 6/7\nx = 18\nx = 3/8"} {"input": "Compute the solution of x^3 - 25/2x^2 - 19/2x + 39 = 0", "output": "x^3 - 25/2x^2 - 19/2x + 39 = 0\n(x - 3/2)(x - 13)(x - -2) = 0\nx - 3/2 = 0\nx - 13 = 0\nx - -2 = 0\nx = 3/2\nx = 13\nx = -2"} {"input": "Find the solution to 3x - 17/2 = 0", "output": "3x - 17/2 = 0\n3x = 17/2\nx = 17/2 / 3\nx = 17/6"} {"input": "What value of x satisfies x^3 - 32/15x^2 + 7/5x - 4/15 = 0", "output": "x^3 - 32/15x^2 + 7/5x - 4/15 = 0\n(x - 1)(x - 4/5)(x - 1/3) = 0\nx - 1 = 0\nx - 4/5 = 0\nx - 1/3 = 0\nx = 1\nx = 4/5\nx = 1/3"} {"input": "Determine x in x^2 - 1/15x - 8/3 = 0", "output": "x^2 - 1/15x - 8/3 = 0\n(x - -8/5)(x - 5/3) = 0\nx - -8/5 = 0 or x - 5/3 = 0\nx = -8/5\nx = 5/3"} {"input": "Find x for 7x - 63/5 = 0", "output": "7x - 63/5 = 0\n7x = 63/5\nx = 63/5 / 7\nx = 9/5"} {"input": "Solve the equation x^3 + 293/56x^2 + 725/112x - 25/28 = 0", "output": "x^3 + 293/56x^2 + 725/112x - 25/28 = 0\n(x - -5/2)(x - -20/7)(x - 1/8) = 0\nx - -5/2 = 0\nx - -20/7 = 0\nx - 1/8 = 0\nx = -5/2\nx = -20/7\nx = 1/8"} {"input": "Find x for x^3 - 117/10x^2 + 6x + 187/10 = 0", "output": "x^3 - 117/10x^2 + 6x + 187/10 = 0\n(x - 11)(x - 17/10)(x - -1) = 0\nx - 11 = 0\nx - 17/10 = 0\nx - -1 = 0\nx = 11\nx = 17/10\nx = -1"} {"input": "Find x in x^3 - 15/4x^2 - 83/8x + 165/8 = 0", "output": "x^3 - 15/4x^2 - 83/8x + 165/8 = 0\n(x - 3/2)(x - -11/4)(x - 5) = 0\nx - 3/2 = 0\nx - -11/4 = 0\nx - 5 = 0\nx = 3/2\nx = -11/4\nx = 5"} {"input": "Determine x in x^2 + 7/8x + 3/16 = 0", "output": "x^2 + 7/8x + 3/16 = 0\n(x - -1/2)(x - -3/8) = 0\nx - -1/2 = 0 or x - -3/8 = 0\nx = -1/2\nx = -3/8"} {"input": "What value of x satisfies x^3 + 3x^2 - 4x - 12 = 0", "output": "x^3 + 3x^2 - 4x - 12 = 0\n(x - -3)(x - -2)(x - 2) = 0\nx - -3 = 0\nx - -2 = 0\nx - 2 = 0\nx = -3\nx = -2\nx = 2"} {"input": "What value of x satisfies x^3 - 253/70x^2 + 271/70x - 9/7 = 0", "output": "x^3 - 253/70x^2 + 271/70x - 9/7 = 0\n(x - 9/10)(x - 2)(x - 5/7) = 0\nx - 9/10 = 0\nx - 2 = 0\nx - 5/7 = 0\nx = 9/10\nx = 2\nx = 5/7"} {"input": "Find x for x^2 - 13/9x + 22/81 = 0", "output": "x^2 - 13/9x + 22/81 = 0\n(x - 11/9)(x - 2/9) = 0\nx - 11/9 = 0 or x - 2/9 = 0\nx = 11/9\nx = 2/9"} {"input": "What value of x satisfies x^3 + 47/24x^2 + 7/6x + 5/24 = 0", "output": "x^3 + 47/24x^2 + 7/6x + 5/24 = 0\n(x - -1)(x - -5/8)(x - -1/3) = 0\nx - -1 = 0\nx - -5/8 = 0\nx - -1/3 = 0\nx = -1\nx = -5/8\nx = -1/3"} {"input": "Determine x in x^2 + 24/7x + 143/49 = 0", "output": "x^2 + 24/7x + 143/49 = 0\n(x - -13/7)(x - -11/7) = 0\nx - -13/7 = 0 or x - -11/7 = 0\nx = -13/7\nx = -11/7"} {"input": "Determine x in 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "Determine x in x^2 + 22/5x - 9/20 = 0", "output": "x^2 + 22/5x - 9/20 = 0\n(x - 1/10)(x - -9/2) = 0\nx - 1/10 = 0 or x - -9/2 = 0\nx = 1/10\nx = -9/2"} {"input": "Solve the equation 1x - 7/6 = 0", "output": "1x - 7/6 = 0\n1x = 7/6\nx = 7/6 / 1\nx = 7/6"} {"input": "Solve simultaneously:\n10x + 1y = -17\n9x + 6y = -357/10", "output": "10x + 1y = -17\n9x + 6y = -357/10\n\nUsing elimination\n9*(10x + 1y = -17)\n10*(9x + 6y = -357/10)\n90x + 9y = -153\n90x + 60y = -357\nSubtract equations\n-51y = 204\ny = 204/-51\ny = -4\n\nSubstitute y\n10x + 1(-4) = -17\n10x = -13\nx = -13/10\nx = -13/10"} {"input": "Determine x in x^3 - 20x^2 - 9x + 180 = 0", "output": "x^3 - 20x^2 - 9x + 180 = 0\n(x - -3)(x - 3)(x - 20) = 0\nx - -3 = 0\nx - 3 = 0\nx - 20 = 0\nx = -3\nx = 3\nx = 20"} {"input": "Solve the equation 1x + 15/2 = 0", "output": "1x + 15/2 = 0\n1x = -15/2\nx = -15/2 / 1\nx = -15/2"} {"input": "Solve simultaneously:\n3x + 7y = -109/2\n9x + 7y = -75/2", "output": "3x + 7y = -109/2\n9x + 7y = -75/2\n\nUsing elimination\n9*(3x + 7y = -109/2)\n3*(9x + 7y = -75/2)\n27x + 63y = -981/2\n27x + 21y = -225/2\nSubtract equations\n42y = -378\ny = -378/42\ny = -9\n\nSubstitute y\n3x + 7(-9) = -109/2\n3x = 17/2\nx = 17/2/3\nx = 17/6"} {"input": "Solve simultaneously:\n10x + 4y = -524/9\n8x + 5y = -646/9", "output": "10x + 4y = -524/9\n8x + 5y = -646/9\n\nUsing elimination\n8*(10x + 4y = -524/9)\n10*(8x + 5y = -646/9)\n80x + 32y = -4192/9\n80x + 50y = -6460/9\nSubtract equations\n-18y = 252\ny = 252/-18\ny = -14\n\nSubstitute y\n10x + 4(-14) = -524/9\n10x = -20/9\nx = -20/9/10\nx = -2/9"} {"input": "Compute the solution of 8x + 8/5 = 0", "output": "8x + 8/5 = 0\n8x = -8/5\nx = -8/5 / 8\nx = -1/5"} {"input": "Find the solution to 4x + 32/3 = 0", "output": "4x + 32/3 = 0\n4x = -32/3\nx = -32/3 / 4\nx = -8/3"} {"input": "Find x for x^3 - 227/30x^2 + 41/10x + 38/3 = 0", "output": "x^3 - 227/30x^2 + 41/10x + 38/3 = 0\n(x - 19/10)(x - 20/3)(x - -1) = 0\nx - 19/10 = 0\nx - 20/3 = 0\nx - -1 = 0\nx = 19/10\nx = 20/3\nx = -1"} {"input": "Solve simultaneously:\n6x + 3y = 81/2\n7x + 5y = 279/4", "output": "6x + 3y = 81/2\n7x + 5y = 279/4\n\nUsing elimination\n7*(6x + 3y = 81/2)\n6*(7x + 5y = 279/4)\n42x + 21y = 567/2\n42x + 30y = 837/2\nSubtract equations\n-9y = -135\ny = -135/-9\ny = 15\n\nSubstitute y\n6x + 3(15) = 81/2\n6x = -9/2\nx = -9/2/6\nx = -3/4"} {"input": "What value of x satisfies 4x + 4 = 0", "output": "4x + 4 = 0\n4x = -4\nx = -4 / 4\nx = -1"} {"input": "Find the solution to x^2 - 169 = 0", "output": "x^2 - 169 = 0\n(x - -13)(x - 13) = 0\nx - -13 = 0 or x - 13 = 0\nx = -13\nx = 13"} {"input": "What value of x satisfies 7x - 35 = 0", "output": "7x - 35 = 0\n7x = 35\nx = 35 / 7\nx = 5"} {"input": "What value of x satisfies x^3 - 157/36x^2 + 211/36x - 5/2 = 0", "output": "x^3 - 157/36x^2 + 211/36x - 5/2 = 0\n(x - 1)(x - 9/4)(x - 10/9) = 0\nx - 1 = 0\nx - 9/4 = 0\nx - 10/9 = 0\nx = 1\nx = 9/4\nx = 10/9"} {"input": "Solve the equations:\n6x + 3y = 102/5\n3x + 8y = 246/5", "output": "6x + 3y = 102/5\n3x + 8y = 246/5\n\nUsing elimination\n3*(6x + 3y = 102/5)\n6*(3x + 8y = 246/5)\n18x + 9y = 306/5\n18x + 48y = 1476/5\nSubtract equations\n-39y = -234\ny = -234/-39\ny = 6\n\nSubstitute y\n6x + 3(6) = 102/5\n6x = 12/5\nx = 12/5/6\nx = 2/5"} {"input": "Determine x in x^2 + 5/21x - 50/21 = 0", "output": "x^2 + 5/21x - 50/21 = 0\n(x - -5/3)(x - 10/7) = 0\nx - -5/3 = 0 or x - 10/7 = 0\nx = -5/3\nx = 10/7"} {"input": "Solve simultaneously:\n2x + 7y = -41/8\n6x + 3y = 3/8", "output": "2x + 7y = -41/8\n6x + 3y = 3/8\n\nUsing elimination\n6*(2x + 7y = -41/8)\n2*(6x + 3y = 3/8)\n12x + 42y = -123/4\n12x + 6y = 3/4\nSubtract equations\n36y = -63/2\ny = -63/2/36\ny = -7/8\n\nSubstitute y\n2x + 7(-7/8) = -41/8\n2x = 1\nx = 1/2\nx = 1/2"} {"input": "Find x in x^2 + 8/5x - 48/5 = 0", "output": "x^2 + 8/5x - 48/5 = 0\n(x - -4)(x - 12/5) = 0\nx - -4 = 0 or x - 12/5 = 0\nx = -4\nx = 12/5"} {"input": "Solve 5x - 85/4 = 0", "output": "5x - 85/4 = 0\n5x = 85/4\nx = 85/4 / 5\nx = 17/4"} {"input": "Find x in 7x + 56/3 = 0", "output": "7x + 56/3 = 0\n7x = -56/3\nx = -56/3 / 7\nx = -8/3"} {"input": "Solve quickly: 2x + 11/3 = 0", "output": "2x + 11/3 = 0\n2x = -11/3\nx = -11/3 / 2\nx = -11/6"} {"input": "Solve quickly: x^2 + 77/30x + 49/30 = 0", "output": "x^2 + 77/30x + 49/30 = 0\n(x - -7/6)(x - -7/5) = 0\nx - -7/6 = 0 or x - -7/5 = 0\nx = -7/6\nx = -7/5"} {"input": "Solve the system:\n4x + 6y = -103/20\n8x + 9y = -277/40", "output": "4x + 6y = -103/20\n8x + 9y = -277/40\n\nUsing elimination\n8*(4x + 6y = -103/20)\n4*(8x + 9y = -277/40)\n32x + 48y = -206/5\n32x + 36y = -277/10\nSubtract equations\n12y = -27/2\ny = -27/2/12\ny = -9/8\n\nSubstitute y\n4x + 6(-9/8) = -103/20\n4x = 8/5\nx = 8/5/4\nx = 2/5"} {"input": "Find x for 7x - 14 = 0", "output": "7x - 14 = 0\n7x = 14\nx = 14 / 7\nx = 2"} {"input": "Find the solution to 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "Find x for 2x - 4 = 0", "output": "2x - 4 = 0\n2x = 4\nx = 4 / 2\nx = 2"} {"input": "Compute the solution of 1x + 17/3 = 0", "output": "1x + 17/3 = 0\n1x = -17/3\nx = -17/3 / 1\nx = -17/3"} {"input": "Solve the system:\n1x + 6y = 1\n7x + 3y = 67/4", "output": "1x + 6y = 1\n7x + 3y = 67/4\n\nUsing elimination\n7*(1x + 6y = 1)\n1*(7x + 3y = 67/4)\n7x + 42y = 7\n7x + 3y = 67/4\nSubtract equations\n39y = -39/4\ny = -39/4/39\ny = -1/4\n\nSubstitute y\n1x + 6(-1/4) = 1\n1x = 5/2\nx = 5/2/1\nx = 5/2"} {"input": "Determine x in x^3 + 65/8x^2 + 337/16x + 273/16 = 0", "output": "x^3 + 65/8x^2 + 337/16x + 273/16 = 0\n(x - -13/8)(x - -3)(x - -7/2) = 0\nx - -13/8 = 0\nx - -3 = 0\nx - -7/2 = 0\nx = -13/8\nx = -3\nx = -7/2"} {"input": "Solve the equation x^3 + 29/7x^2 - 247/63x - 845/63 = 0", "output": "x^3 + 29/7x^2 - 247/63x - 845/63 = 0\n(x - -13/3)(x - -5/3)(x - 13/7) = 0\nx - -13/3 = 0\nx - -5/3 = 0\nx - 13/7 = 0\nx = -13/3\nx = -5/3\nx = 13/7"} {"input": "Find the solution to 1x - 16 = 0", "output": "1x - 16 = 0\n1x = 16\nx = 16 / 1\nx = 16"} {"input": "What value of x satisfies x^3 + 29/8x^2 - 271/32x - 255/32 = 0", "output": "x^3 + 29/8x^2 - 271/32x - 255/32 = 0\n(x - -3/4)(x - 17/8)(x - -5) = 0\nx - -3/4 = 0\nx - 17/8 = 0\nx - -5 = 0\nx = -3/4\nx = 17/8\nx = -5"} {"input": "Find the solution to 8x - 19 = 0", "output": "8x - 19 = 0\n8x = 19\nx = 19 / 8\nx = 19/8"} {"input": "Find x and y such that\n5x + 7y = -53/8\n1x + 8y = -37/8", "output": "5x + 7y = -53/8\n1x + 8y = -37/8\n\nUsing elimination\n1*(5x + 7y = -53/8)\n5*(1x + 8y = -37/8)\n5x + 7y = -53/8\n5x + 40y = -185/8\nSubtract equations\n-33y = 33/2\ny = 33/2/-33\ny = -1/2\n\nSubstitute y\n5x + 7(-1/2) = -53/8\n5x = -25/8\nx = -25/8/5\nx = -5/8"} {"input": "Find x and y such that\n6x + 8y = 47/3\n10x + 5y = 115/6", "output": "6x + 8y = 47/3\n10x + 5y = 115/6\n\nUsing elimination\n10*(6x + 8y = 47/3)\n6*(10x + 5y = 115/6)\n60x + 80y = 470/3\n60x + 30y = 115\nSubtract equations\n50y = 125/3\ny = 125/3/50\ny = 5/6\n\nSubstitute y\n6x + 8(5/6) = 47/3\n6x = 9\nx = 9/6\nx = 3/2"} {"input": "Determine x in 9x - 12 = 0", "output": "9x - 12 = 0\n9x = 12\nx = 12 / 9\nx = 4/3"} {"input": "Find x for x^3 - 28/3x^2 + 32/3x = 0", "output": "x^3 - 28/3x^2 + 32/3x = 0\n(x - 4/3)(x - 8)(x - 0) = 0\nx - 4/3 = 0\nx - 8 = 0\nx - 0 = 0\nx = 4/3\nx = 8\nx = 0"} {"input": "Find x and y such that\n8x + 10y = 47/2\n8x + 6y = 41/2", "output": "8x + 10y = 47/2\n8x + 6y = 41/2\n\nUsing elimination\n8*(8x + 10y = 47/2)\n8*(8x + 6y = 41/2)\n64x + 80y = 188\n64x + 48y = 164\nSubtract equations\n32y = 24\ny = 24/32\ny = 3/4\n\nSubstitute y\n8x + 10(3/4) = 47/2\n8x = 16\nx = 16/8\nx = 2"} {"input": "Solve the system:\n5x + 7y = 91/12\n10x + 3y = 17", "output": "5x + 7y = 91/12\n10x + 3y = 17\n\nUsing elimination\n10*(5x + 7y = 91/12)\n5*(10x + 3y = 17)\n50x + 70y = 455/6\n50x + 15y = 85\nSubtract equations\n55y = -55/6\ny = -55/6/55\ny = -1/6\n\nSubstitute y\n5x + 7(-1/6) = 91/12\n5x = 35/4\nx = 35/4/5\nx = 7/4"} {"input": "Solve simultaneously:\n3x + 2y = 47/4\n4x + 5y = 43/2", "output": "3x + 2y = 47/4\n4x + 5y = 43/2\n\nUsing elimination\n4*(3x + 2y = 47/4)\n3*(4x + 5y = 43/2)\n12x + 8y = 47\n12x + 15y = 129/2\nSubtract equations\n-7y = -35/2\ny = -35/2/-7\ny = 5/2\n\nSubstitute y\n3x + 2(5/2) = 47/4\n3x = 27/4\nx = 27/4/3\nx = 9/4"} {"input": "Find the solution to x^3 - 161/15x^2 - 1174/15x - 96 = 0", "output": "x^3 - 161/15x^2 - 1174/15x - 96 = 0\n(x - -5/3)(x - 16)(x - -18/5) = 0\nx - -5/3 = 0\nx - 16 = 0\nx - -18/5 = 0\nx = -5/3\nx = 16\nx = -18/5"} {"input": "Solve simultaneously:\n7x + 3y = -288/5\n10x + 7y = -387/5", "output": "7x + 3y = -288/5\n10x + 7y = -387/5\n\nUsing elimination\n10*(7x + 3y = -288/5)\n7*(10x + 7y = -387/5)\n70x + 30y = -576\n70x + 49y = -2709/5\nSubtract equations\n-19y = -171/5\ny = -171/5/-19\ny = 9/5\n\nSubstitute y\n7x + 3(9/5) = -288/5\n7x = -63\nx = -63/7\nx = -9"} {"input": "Solve the equation 5x - 60/7 = 0", "output": "5x - 60/7 = 0\n5x = 60/7\nx = 60/7 / 5\nx = 12/7"} {"input": "Solve the equations:\n6x + 4y = 12\n6x + 2y = 11", "output": "6x + 4y = 12\n6x + 2y = 11\n\nUsing elimination\n6*(6x + 4y = 12)\n6*(6x + 2y = 11)\n36x + 24y = 72\n36x + 12y = 66\nSubtract equations\n12y = 6\ny = 6/12\ny = 1/2\n\nSubstitute y\n6x + 4(1/2) = 12\n6x = 10\nx = 10/6\nx = 5/3"} {"input": "Solve simultaneously:\n7x + 2y = -134/35\n8x + 9y = 384/35", "output": "7x + 2y = -134/35\n8x + 9y = 384/35\n\nUsing elimination\n8*(7x + 2y = -134/35)\n7*(8x + 9y = 384/35)\n56x + 16y = -1072/35\n56x + 63y = 384/5\nSubtract equations\n-47y = -752/7\ny = -752/7/-47\ny = 16/7\n\nSubstitute y\n7x + 2(16/7) = -134/35\n7x = -42/5\nx = -42/5/7\nx = -6/5"} {"input": "Solve the equation x^2 + 13/6x + 5/6 = 0", "output": "x^2 + 13/6x + 5/6 = 0\n(x - -1/2)(x - -5/3) = 0\nx - -1/2 = 0 or x - -5/3 = 0\nx = -1/2\nx = -5/3"} {"input": "Find x and y such that\n7x + 7y = 539/15\n3x + 1y = 69/5", "output": "7x + 7y = 539/15\n3x + 1y = 69/5\n\nUsing elimination\n3*(7x + 7y = 539/15)\n7*(3x + 1y = 69/5)\n21x + 21y = 539/5\n21x + 7y = 483/5\nSubtract equations\n14y = 56/5\ny = 56/5/14\ny = 4/5\n\nSubstitute y\n7x + 7(4/5) = 539/15\n7x = 91/3\nx = 91/3/7\nx = 13/3"} {"input": "Compute the solution of x^3 + 61/3x^2 + 256/3x + 80 = 0", "output": "x^3 + 61/3x^2 + 256/3x + 80 = 0\n(x - -15)(x - -4/3)(x - -4) = 0\nx - -15 = 0\nx - -4/3 = 0\nx - -4 = 0\nx = -15\nx = -4/3\nx = -4"} {"input": "Solve quickly: x^3 - 664/63x^2 + 1297/63x - 136/63 = 0", "output": "x^3 - 664/63x^2 + 1297/63x - 136/63 = 0\n(x - 17/7)(x - 8)(x - 1/9) = 0\nx - 17/7 = 0\nx - 8 = 0\nx - 1/9 = 0\nx = 17/7\nx = 8\nx = 1/9"} {"input": "Solve the equation 10x + 140/3 = 0", "output": "10x + 140/3 = 0\n10x = -140/3\nx = -140/3 / 10\nx = -14/3"} {"input": "Find the solution to x^3 - 34/15x^2 - 113/15x + 44/5 = 0", "output": "x^3 - 34/15x^2 - 113/15x + 44/5 = 0\n(x - 1)(x - 11/3)(x - -12/5) = 0\nx - 1 = 0\nx - 11/3 = 0\nx - -12/5 = 0\nx = 1\nx = 11/3\nx = -12/5"} {"input": "Solve 6x + 78 = 0", "output": "6x + 78 = 0\n6x = -78\nx = -78 / 6\nx = -13"} {"input": "Find x and y such that\n4x + 6y = -48\n10x + 2y = 10", "output": "4x + 6y = -48\n10x + 2y = 10\n\nUsing elimination\n10*(4x + 6y = -48)\n4*(10x + 2y = 10)\n40x + 60y = -480\n40x + 8y = 40\nSubtract equations\n52y = -520\ny = -520/52\ny = -10\n\nSubstitute y\n4x + 6(-10) = -48\n4x = 12\nx = 12/4\nx = 3"} {"input": "Determine x in 9x - 4 = 0", "output": "9x - 4 = 0\n9x = 4\nx = 4 / 9\nx = 4/9"} {"input": "Solve the equations:\n9x + 6y = 380/21\n7x + 4y = 124/9", "output": "9x + 6y = 380/21\n7x + 4y = 124/9\n\nUsing elimination\n7*(9x + 6y = 380/21)\n9*(7x + 4y = 124/9)\n63x + 42y = 380/3\n63x + 36y = 124\nSubtract equations\n6y = 8/3\ny = 8/3/6\ny = 4/9\n\nSubstitute y\n9x + 6(4/9) = 380/21\n9x = 108/7\nx = 108/7/9\nx = 12/7"} {"input": "Solve quickly: x^3 - 57/10x^2 - 2071/10x - 1287/5 = 0", "output": "x^3 - 57/10x^2 - 2071/10x - 1287/5 = 0\n(x - 18)(x - -13/10)(x - -11) = 0\nx - 18 = 0\nx - -13/10 = 0\nx - -11 = 0\nx = 18\nx = -13/10\nx = -11"} {"input": "Determine x in 3x - 18 = 0", "output": "3x - 18 = 0\n3x = 18\nx = 18 / 3\nx = 6"} {"input": "Solve the equation x^2 + 3x - 28 = 0", "output": "x^2 + 3x - 28 = 0\n(x - 4)(x - -7) = 0\nx - 4 = 0 or x - -7 = 0\nx = 4\nx = -7"} {"input": "Determine x in 2x - 34/9 = 0", "output": "2x - 34/9 = 0\n2x = 34/9\nx = 34/9 / 2\nx = 17/9"} {"input": "Solve simultaneously:\n5x + 1y = -119/2\n7x + 9y = -311/2", "output": "5x + 1y = -119/2\n7x + 9y = -311/2\n\nUsing elimination\n7*(5x + 1y = -119/2)\n5*(7x + 9y = -311/2)\n35x + 7y = -833/2\n35x + 45y = -1555/2\nSubtract equations\n-38y = 361\ny = 361/-38\ny = -19/2\n\nSubstitute y\n5x + 1(-19/2) = -119/2\n5x = -50\nx = -50/5\nx = -10"} {"input": "Solve x^2 - 20x + 36 = 0", "output": "x^2 - 20x + 36 = 0\n(x - 18)(x - 2) = 0\nx - 18 = 0 or x - 2 = 0\nx = 18\nx = 2"} {"input": "Determine x in x^3 - 71/18x^2 + 253/54x - 40/27 = 0", "output": "x^3 - 71/18x^2 + 253/54x - 40/27 = 0\n(x - 16/9)(x - 5/3)(x - 1/2) = 0\nx - 16/9 = 0\nx - 5/3 = 0\nx - 1/2 = 0\nx = 16/9\nx = 5/3\nx = 1/2"} {"input": "Solve x^2 + 133/9x + 208/9 = 0", "output": "x^2 + 133/9x + 208/9 = 0\n(x - -16/9)(x - -13) = 0\nx - -16/9 = 0 or x - -13 = 0\nx = -16/9\nx = -13"} {"input": "Solve the equation 10x + 20/3 = 0", "output": "10x + 20/3 = 0\n10x = -20/3\nx = -20/3 / 10\nx = -2/3"} {"input": "Compute the solution of x^2 - 31/24x - 13/24 = 0", "output": "x^2 - 31/24x - 13/24 = 0\n(x - 13/8)(x - -1/3) = 0\nx - 13/8 = 0 or x - -1/3 = 0\nx = 13/8\nx = -1/3"} {"input": "Solve the equation 2x - 12/5 = 0", "output": "2x - 12/5 = 0\n2x = 12/5\nx = 12/5 / 2\nx = 6/5"} {"input": "Solve the system:\n4x + 4y = 28\n1x + 6y = 32", "output": "4x + 4y = 28\n1x + 6y = 32\n\nUsing elimination\n1*(4x + 4y = 28)\n4*(1x + 6y = 32)\n4x + 4y = 28\n4x + 24y = 128\nSubtract equations\n-20y = -100\ny = -100/-20\ny = 5\n\nSubstitute y\n4x + 4(5) = 28\n4x = 8\nx = 8/4\nx = 2"} {"input": "Solve simultaneously:\n5x + 7y = 14\n9x + 4y = -46/5", "output": "5x + 7y = 14\n9x + 4y = -46/5\n\nUsing elimination\n9*(5x + 7y = 14)\n5*(9x + 4y = -46/5)\n45x + 63y = 126\n45x + 20y = -46\nSubtract equations\n43y = 172\ny = 172/43\ny = 4\n\nSubstitute y\n5x + 7(4) = 14\n5x = -14\nx = -14/5\nx = -14/5"} {"input": "What value of x satisfies x^2 + 25/14x - 8/7 = 0", "output": "x^2 + 25/14x - 8/7 = 0\n(x - -16/7)(x - 1/2) = 0\nx - -16/7 = 0 or x - 1/2 = 0\nx = -16/7\nx = 1/2"} {"input": "Solve 7x - 77/9 = 0", "output": "7x - 77/9 = 0\n7x = 77/9\nx = 77/9 / 7\nx = 11/9"} {"input": "What value of x satisfies 9x - 21/2 = 0", "output": "9x - 21/2 = 0\n9x = 21/2\nx = 21/2 / 9\nx = 7/6"} {"input": "Solve the equation x^2 - 33/5x - 14/5 = 0", "output": "x^2 - 33/5x - 14/5 = 0\n(x - -2/5)(x - 7) = 0\nx - -2/5 = 0 or x - 7 = 0\nx = -2/5\nx = 7"} {"input": "Solve quickly: x^2 + 1/15x - 28/5 = 0", "output": "x^2 + 1/15x - 28/5 = 0\n(x - 7/3)(x - -12/5) = 0\nx - 7/3 = 0 or x - -12/5 = 0\nx = 7/3\nx = -12/5"} {"input": "Solve x^2 - 24/7x + 20/7 = 0", "output": "x^2 - 24/7x + 20/7 = 0\n(x - 2)(x - 10/7) = 0\nx - 2 = 0 or x - 10/7 = 0\nx = 2\nx = 10/7"} {"input": "Solve quickly: x^2 + 13/7x - 24/7 = 0", "output": "x^2 + 13/7x - 24/7 = 0\n(x - 8/7)(x - -3) = 0\nx - 8/7 = 0 or x - -3 = 0\nx = 8/7\nx = -3"} {"input": "Solve quickly: 7x + 133 = 0", "output": "7x + 133 = 0\n7x = -133\nx = -133 / 7\nx = -19"} {"input": "Find x and y such that\n7x + 9y = 167/2\n5x + 3y = 37/2", "output": "7x + 9y = 167/2\n5x + 3y = 37/2\n\nUsing elimination\n5*(7x + 9y = 167/2)\n7*(5x + 3y = 37/2)\n35x + 45y = 835/2\n35x + 21y = 259/2\nSubtract equations\n24y = 288\ny = 288/24\ny = 12\n\nSubstitute y\n7x + 9(12) = 167/2\n7x = -49/2\nx = -49/2/7\nx = -7/2"} {"input": "Find x for x^2 + 7/10x - 13/5 = 0", "output": "x^2 + 7/10x - 13/5 = 0\n(x - -2)(x - 13/10) = 0\nx - -2 = 0 or x - 13/10 = 0\nx = -2\nx = 13/10"} {"input": "Compute the solution of 7x + 70/9 = 0", "output": "7x + 70/9 = 0\n7x = -70/9\nx = -70/9 / 7\nx = -10/9"} {"input": "Find x in x^2 + 104/9x - 169/9 = 0", "output": "x^2 + 104/9x - 169/9 = 0\n(x - -13)(x - 13/9) = 0\nx - -13 = 0 or x - 13/9 = 0\nx = -13\nx = 13/9"} {"input": "Solve quickly: 3x - 39/10 = 0", "output": "3x - 39/10 = 0\n3x = 39/10\nx = 39/10 / 3\nx = 13/10"} {"input": "Find x for x^2 + 8x + 15 = 0", "output": "x^2 + 8x + 15 = 0\n(x - -3)(x - -5) = 0\nx - -3 = 0 or x - -5 = 0\nx = -3\nx = -5"} {"input": "Compute the solution of 3x - 3/10 = 0", "output": "3x - 3/10 = 0\n3x = 3/10\nx = 3/10 / 3\nx = 1/10"} {"input": "Solve simultaneously:\n1x + 3y = 159/14\n3x + 3y = 239/14", "output": "1x + 3y = 159/14\n3x + 3y = 239/14\n\nUsing elimination\n3*(1x + 3y = 159/14)\n1*(3x + 3y = 239/14)\n3x + 9y = 477/14\n3x + 3y = 239/14\nSubtract equations\n6y = 17\ny = 17/6\ny = 17/6\n\nSubstitute y\n1x + 3(17/6) = 159/14\n1x = 20/7\nx = 20/7/1\nx = 20/7"} {"input": "Find the solution to x^3 - 43/6x^2 - 208/3x - 169/2 = 0", "output": "x^3 - 43/6x^2 - 208/3x - 169/2 = 0\n(x - -3/2)(x - -13/3)(x - 13) = 0\nx - -3/2 = 0\nx - -13/3 = 0\nx - 13 = 0\nx = -3/2\nx = -13/3\nx = 13"} {"input": "Compute the solution of x^3 + 175/36x^2 + 17/9x - 56/9 = 0", "output": "x^3 + 175/36x^2 + 17/9x - 56/9 = 0\n(x - -7/4)(x - -4)(x - 8/9) = 0\nx - -7/4 = 0\nx - -4 = 0\nx - 8/9 = 0\nx = -7/4\nx = -4\nx = 8/9"} {"input": "Solve the equations:\n10x + 2y = -88/5\n6x + 7y = -123/10", "output": "10x + 2y = -88/5\n6x + 7y = -123/10\n\nUsing elimination\n6*(10x + 2y = -88/5)\n10*(6x + 7y = -123/10)\n60x + 12y = -528/5\n60x + 70y = -123\nSubtract equations\n-58y = 87/5\ny = 87/5/-58\ny = -3/10\n\nSubstitute y\n10x + 2(-3/10) = -88/5\n10x = -17\nx = -17/10\nx = -17/10"} {"input": "Solve simultaneously:\n5x + 10y = 85/4\n9x + 9y = 63/4", "output": "5x + 10y = 85/4\n9x + 9y = 63/4\n\nUsing elimination\n9*(5x + 10y = 85/4)\n5*(9x + 9y = 63/4)\n45x + 90y = 765/4\n45x + 45y = 315/4\nSubtract equations\n45y = 225/2\ny = 225/2/45\ny = 5/2\n\nSubstitute y\n5x + 10(5/2) = 85/4\n5x = -15/4\nx = -15/4/5\nx = -3/4"} {"input": "Find x in x^2 - 9/10x - 4 = 0", "output": "x^2 - 9/10x - 4 = 0\n(x - -8/5)(x - 5/2) = 0\nx - -8/5 = 0 or x - 5/2 = 0\nx = -8/5\nx = 5/2"} {"input": "What value of x satisfies x^3 + 25/7x^2 - 83/7x - 165/7 = 0", "output": "x^3 + 25/7x^2 - 83/7x - 165/7 = 0\n(x - -5)(x - -11/7)(x - 3) = 0\nx - -5 = 0\nx - -11/7 = 0\nx - 3 = 0\nx = -5\nx = -11/7\nx = 3"} {"input": "Solve the equation 1x + 19/10 = 0", "output": "1x + 19/10 = 0\n1x = -19/10\nx = -19/10 / 1\nx = -19/10"} {"input": "Find the solution to 10x - 5 = 0", "output": "10x - 5 = 0\n10x = 5\nx = 5 / 10\nx = 1/2"} {"input": "Solve quickly: x^2 + 19/9x - 40/27 = 0", "output": "x^2 + 19/9x - 40/27 = 0\n(x - 5/9)(x - -8/3) = 0\nx - 5/9 = 0 or x - -8/3 = 0\nx = 5/9\nx = -8/3"} {"input": "Find x in x^2 - 101/24x + 209/48 = 0", "output": "x^2 - 101/24x + 209/48 = 0\n(x - 19/8)(x - 11/6) = 0\nx - 19/8 = 0 or x - 11/6 = 0\nx = 19/8\nx = 11/6"} {"input": "Find the solution to x^3 - 41/12x^2 - 223/12x + 119/2 = 0", "output": "x^3 - 41/12x^2 - 223/12x + 119/2 = 0\n(x - 3)(x - -17/4)(x - 14/3) = 0\nx - 3 = 0\nx - -17/4 = 0\nx - 14/3 = 0\nx = 3\nx = -17/4\nx = 14/3"} {"input": "Solve the equation x^2 - 14x + 24 = 0", "output": "x^2 - 14x + 24 = 0\n(x - 12)(x - 2) = 0\nx - 12 = 0 or x - 2 = 0\nx = 12\nx = 2"} {"input": "Find x for x^2 + 121/9x + 52/3 = 0", "output": "x^2 + 121/9x + 52/3 = 0\n(x - -13/9)(x - -12) = 0\nx - -13/9 = 0 or x - -12 = 0\nx = -13/9\nx = -12"} {"input": "Compute the solution of x^3 - 213/8x^2 + 1039/8x + 105/2 = 0", "output": "x^3 - 213/8x^2 + 1039/8x + 105/2 = 0\n(x - -3/8)(x - 7)(x - 20) = 0\nx - -3/8 = 0\nx - 7 = 0\nx - 20 = 0\nx = -3/8\nx = 7\nx = 20"} {"input": "Solve simultaneously:\n6x + 4y = -538/9\n2x + 7y = -253/9", "output": "6x + 4y = -538/9\n2x + 7y = -253/9\n\nUsing elimination\n2*(6x + 4y = -538/9)\n6*(2x + 7y = -253/9)\n12x + 8y = -1076/9\n12x + 42y = -506/3\nSubtract equations\n-34y = 442/9\ny = 442/9/-34\ny = -13/9\n\nSubstitute y\n6x + 4(-13/9) = -538/9\n6x = -54\nx = -54/6\nx = -9"} {"input": "Find x for x^2 - 2x - 8 = 0", "output": "x^2 - 2x - 8 = 0\n(x - -2)(x - 4) = 0\nx - -2 = 0 or x - 4 = 0\nx = -2\nx = 4"} {"input": "Find the solution to 5x + 65/6 = 0", "output": "5x + 65/6 = 0\n5x = -65/6\nx = -65/6 / 5\nx = -13/6"} {"input": "What value of x satisfies x^3 + 12/7x^2 - 655/448x + 57/224 = 0", "output": "x^3 + 12/7x^2 - 655/448x + 57/224 = 0\n(x - -19/8)(x - 3/8)(x - 2/7) = 0\nx - -19/8 = 0\nx - 3/8 = 0\nx - 2/7 = 0\nx = -19/8\nx = 3/8\nx = 2/7"} {"input": "Find the solution to 3x + 51/8 = 0", "output": "3x + 51/8 = 0\n3x = -51/8\nx = -51/8 / 3\nx = -17/8"} {"input": "Solve the system:\n6x + 8y = -164/3\n4x + 6y = -37", "output": "6x + 8y = -164/3\n4x + 6y = -37\n\nUsing elimination\n4*(6x + 8y = -164/3)\n6*(4x + 6y = -37)\n24x + 32y = -656/3\n24x + 36y = -222\nSubtract equations\n-4y = 10/3\ny = 10/3/-4\ny = -5/6\n\nSubstitute y\n6x + 8(-5/6) = -164/3\n6x = -48\nx = -48/6\nx = -8"} {"input": "Solve quickly: x^2 + 15x - 76 = 0", "output": "x^2 + 15x - 76 = 0\n(x - -19)(x - 4) = 0\nx - -19 = 0 or x - 4 = 0\nx = -19\nx = 4"} {"input": "Find the solution to x^2 + 3x + 20/49 = 0", "output": "x^2 + 3x + 20/49 = 0\n(x - -20/7)(x - -1/7) = 0\nx - -20/7 = 0 or x - -1/7 = 0\nx = -20/7\nx = -1/7"} {"input": "What value of x satisfies 7x - 7/3 = 0", "output": "7x - 7/3 = 0\n7x = 7/3\nx = 7/3 / 7\nx = 1/3"} {"input": "Solve 9x + 4 = 0", "output": "9x + 4 = 0\n9x = -4\nx = -4 / 9\nx = -4/9"} {"input": "Find x for x^3 - 71/4x^2 + 115/4x - 12 = 0", "output": "x^3 - 71/4x^2 + 115/4x - 12 = 0\n(x - 16)(x - 3/4)(x - 1) = 0\nx - 16 = 0\nx - 3/4 = 0\nx - 1 = 0\nx = 16\nx = 3/4\nx = 1"} {"input": "Find x for 8x + 160 = 0", "output": "8x + 160 = 0\n8x = -160\nx = -160 / 8\nx = -20"} {"input": "Find x in x^2 - 53/35x - 114/35 = 0", "output": "x^2 - 53/35x - 114/35 = 0\n(x - 19/7)(x - -6/5) = 0\nx - 19/7 = 0 or x - -6/5 = 0\nx = 19/7\nx = -6/5"} {"input": "Find x in x^2 - 3x - 10/9 = 0", "output": "x^2 - 3x - 10/9 = 0\n(x - -1/3)(x - 10/3) = 0\nx - -1/3 = 0 or x - 10/3 = 0\nx = -1/3\nx = 10/3"} {"input": "Solve the equation 6x + 10 = 0", "output": "6x + 10 = 0\n6x = -10\nx = -10 / 6\nx = -5/3"} {"input": "Solve the equation 4x + 68/7 = 0", "output": "4x + 68/7 = 0\n4x = -68/7\nx = -68/7 / 4\nx = -17/7"} {"input": "Solve simultaneously:\n5x + 6y = -12\n2x + 9y = -13/5", "output": "5x + 6y = -12\n2x + 9y = -13/5\n\nUsing elimination\n2*(5x + 6y = -12)\n5*(2x + 9y = -13/5)\n10x + 12y = -24\n10x + 45y = -13\nSubtract equations\n-33y = -11\ny = -11/-33\ny = 1/3\n\nSubstitute y\n5x + 6(1/3) = -12\n5x = -14\nx = -14/5\nx = -14/5"} {"input": "Solve simultaneously:\n1x + 7y = -129/8\n6x + 10y = -131/4", "output": "1x + 7y = -129/8\n6x + 10y = -131/4\n\nUsing elimination\n6*(1x + 7y = -129/8)\n1*(6x + 10y = -131/4)\n6x + 42y = -387/4\n6x + 10y = -131/4\nSubtract equations\n32y = -64\ny = -64/32\ny = -2\n\nSubstitute y\n1x + 7(-2) = -129/8\n1x = -17/8\nx = -17/8/1\nx = -17/8"} {"input": "Find the solution to 4x - 8/3 = 0", "output": "4x - 8/3 = 0\n4x = 8/3\nx = 8/3 / 4\nx = 2/3"} {"input": "What value of x satisfies x^3 + 27/10x^2 + 2x + 3/10 = 0", "output": "x^3 + 27/10x^2 + 2x + 3/10 = 0\n(x - -3/2)(x - -1/5)(x - -1) = 0\nx - -3/2 = 0\nx - -1/5 = 0\nx - -1 = 0\nx = -3/2\nx = -1/5\nx = -1"} {"input": "Solve simultaneously:\n3x + 8y = -20/3\n3x + 9y = -15/2", "output": "3x + 8y = -20/3\n3x + 9y = -15/2\n\nUsing elimination\n3*(3x + 8y = -20/3)\n3*(3x + 9y = -15/2)\n9x + 24y = -20\n9x + 27y = -45/2\nSubtract equations\n-3y = 5/2\ny = 5/2/-3\ny = -5/6\n\nSubstitute y\n3x + 8(-5/6) = -20/3\n3x = 0\nx = 0/3\nx = 0"} {"input": "Find the solution to x^3 + 36/5x^2 + 37/5x + 6/5 = 0", "output": "x^3 + 36/5x^2 + 37/5x + 6/5 = 0\n(x - -6)(x - -1/5)(x - -1) = 0\nx - -6 = 0\nx - -1/5 = 0\nx - -1 = 0\nx = -6\nx = -1/5\nx = -1"} {"input": "Find x for x^2 + 33/2x + 54 = 0", "output": "x^2 + 33/2x + 54 = 0\n(x - -9/2)(x - -12) = 0\nx - -9/2 = 0 or x - -12 = 0\nx = -9/2\nx = -12"} {"input": "Solve the equation x^3 - 39/20x^2 - 173/20x + 9/5 = 0", "output": "x^3 - 39/20x^2 - 173/20x + 9/5 = 0\n(x - 4)(x - -9/4)(x - 1/5) = 0\nx - 4 = 0\nx - -9/4 = 0\nx - 1/5 = 0\nx = 4\nx = -9/4\nx = 1/5"} {"input": "Find the solution to x^2 - 21/4x + 5 = 0", "output": "x^2 - 21/4x + 5 = 0\n(x - 4)(x - 5/4) = 0\nx - 4 = 0 or x - 5/4 = 0\nx = 4\nx = 5/4"} {"input": "Find x for x^3 - 113/63x^2 - 865/189x + 209/27 = 0", "output": "x^3 - 113/63x^2 - 865/189x + 209/27 = 0\n(x - 11/7)(x - 7/3)(x - -19/9) = 0\nx - 11/7 = 0\nx - 7/3 = 0\nx - -19/9 = 0\nx = 11/7\nx = 7/3\nx = -19/9"} {"input": "Find x and y such that\n10x + 2y = 166/3\n2x + 8y = -20/3", "output": "10x + 2y = 166/3\n2x + 8y = -20/3\n\nUsing elimination\n2*(10x + 2y = 166/3)\n10*(2x + 8y = -20/3)\n20x + 4y = 332/3\n20x + 80y = -200/3\nSubtract equations\n-76y = 532/3\ny = 532/3/-76\ny = -7/3\n\nSubstitute y\n10x + 2(-7/3) = 166/3\n10x = 60\nx = 60/10\nx = 6"} {"input": "Compute the solution of x^2 - 33/2x - 95/2 = 0", "output": "x^2 - 33/2x - 95/2 = 0\n(x - 19)(x - -5/2) = 0\nx - 19 = 0 or x - -5/2 = 0\nx = 19\nx = -5/2"} {"input": "Solve quickly: 3x + 14/3 = 0", "output": "3x + 14/3 = 0\n3x = -14/3\nx = -14/3 / 3\nx = -14/9"} {"input": "Solve 10x - 40/3 = 0", "output": "10x - 40/3 = 0\n10x = 40/3\nx = 40/3 / 10\nx = 4/3"} {"input": "Find the solution to x^2 - 62/3x + 48 = 0", "output": "x^2 - 62/3x + 48 = 0\n(x - 18)(x - 8/3) = 0\nx - 18 = 0 or x - 8/3 = 0\nx = 18\nx = 8/3"} {"input": "Solve the equation 5x + 55 = 0", "output": "5x + 55 = 0\n5x = -55\nx = -55 / 5\nx = -11"} {"input": "Find the solution to x^2 + 7/6x - 13/6 = 0", "output": "x^2 + 7/6x - 13/6 = 0\n(x - -13/6)(x - 1) = 0\nx - -13/6 = 0 or x - 1 = 0\nx = -13/6\nx = 1"} {"input": "Find x in 1x - 1/2 = 0", "output": "1x - 1/2 = 0\n1x = 1/2\nx = 1/2 / 1\nx = 1/2"} {"input": "Find x in x^3 - 49/12x^2 + 5/6x + 25/16 = 0", "output": "x^3 - 49/12x^2 + 5/6x + 25/16 = 0\n(x - 15/4)(x - -1/2)(x - 5/6) = 0\nx - 15/4 = 0\nx - -1/2 = 0\nx - 5/6 = 0\nx = 15/4\nx = -1/2\nx = 5/6"} {"input": "Solve the system:\n4x + 6y = 191/15\n3x + 5y = 21/2", "output": "4x + 6y = 191/15\n3x + 5y = 21/2\n\nUsing elimination\n3*(4x + 6y = 191/15)\n4*(3x + 5y = 21/2)\n12x + 18y = 191/5\n12x + 20y = 42\nSubtract equations\n-2y = -19/5\ny = -19/5/-2\ny = 19/10\n\nSubstitute y\n4x + 6(19/10) = 191/15\n4x = 4/3\nx = 4/3/4\nx = 1/3"} {"input": "Find x for x^2 + 1/2x - 1/2 = 0", "output": "x^2 + 1/2x - 1/2 = 0\n(x - -1)(x - 1/2) = 0\nx - -1 = 0 or x - 1/2 = 0\nx = -1\nx = 1/2"} {"input": "Find x for x^2 - 16/3x + 20/3 = 0", "output": "x^2 - 16/3x + 20/3 = 0\n(x - 2)(x - 10/3) = 0\nx - 2 = 0 or x - 10/3 = 0\nx = 2\nx = 10/3"} {"input": "What value of x satisfies x^2 + 52/45x - 32/45 = 0", "output": "x^2 + 52/45x - 32/45 = 0\n(x - 4/9)(x - -8/5) = 0\nx - 4/9 = 0 or x - -8/5 = 0\nx = 4/9\nx = -8/5"} {"input": "Solve quickly: x^3 + 1075/56x^2 - 1109/56x - 1045/14 = 0", "output": "x^3 + 1075/56x^2 - 1109/56x - 1045/14 = 0\n(x - 19/8)(x - -11/7)(x - -20) = 0\nx - 19/8 = 0\nx - -11/7 = 0\nx - -20 = 0\nx = 19/8\nx = -11/7\nx = -20"} {"input": "Find x and y such that\n6x + 5y = -38/5\n5x + 3y = -19/10", "output": "6x + 5y = -38/5\n5x + 3y = -19/10\n\nUsing elimination\n5*(6x + 5y = -38/5)\n6*(5x + 3y = -19/10)\n30x + 25y = -38\n30x + 18y = -57/5\nSubtract equations\n7y = -133/5\ny = -133/5/7\ny = -19/5\n\nSubstitute y\n6x + 5(-19/5) = -38/5\n6x = 57/5\nx = 57/5/6\nx = 19/10"} {"input": "Find x and y such that\n3x + 5y = 253/24\n4x + 9y = 1411/72", "output": "3x + 5y = 253/24\n4x + 9y = 1411/72\n\nUsing elimination\n4*(3x + 5y = 253/24)\n3*(4x + 9y = 1411/72)\n12x + 20y = 253/6\n12x + 27y = 1411/24\nSubtract equations\n-7y = -133/8\ny = -133/8/-7\ny = 19/8\n\nSubstitute y\n3x + 5(19/8) = 253/24\n3x = -4/3\nx = -4/3/3\nx = -4/9"} {"input": "Solve the system:\n4x + 4y = 16/15\n4x + 7y = 91/15", "output": "4x + 4y = 16/15\n4x + 7y = 91/15\n\nUsing elimination\n4*(4x + 4y = 16/15)\n4*(4x + 7y = 91/15)\n16x + 16y = 64/15\n16x + 28y = 364/15\nSubtract equations\n-12y = -20\ny = -20/-12\ny = 5/3\n\nSubstitute y\n4x + 4(5/3) = 16/15\n4x = -28/5\nx = -28/5/4\nx = -7/5"} {"input": "Solve the system:\n7x + 10y = -1304/45\n6x + 1y = -512/45", "output": "7x + 10y = -1304/45\n6x + 1y = -512/45\n\nUsing elimination\n6*(7x + 10y = -1304/45)\n7*(6x + 1y = -512/45)\n42x + 60y = -2608/15\n42x + 7y = -3584/45\nSubtract equations\n53y = -848/9\ny = -848/9/53\ny = -16/9\n\nSubstitute y\n7x + 10(-16/9) = -1304/45\n7x = -56/5\nx = -56/5/7\nx = -8/5"} {"input": "Find the solution to x^3 - 386/63x^2 + 311/63x + 220/63 = 0", "output": "x^3 - 386/63x^2 + 311/63x + 220/63 = 0\n(x - 5)(x - 11/7)(x - -4/9) = 0\nx - 5 = 0\nx - 11/7 = 0\nx - -4/9 = 0\nx = 5\nx = 11/7\nx = -4/9"} {"input": "Compute the solution of x^2 + 94/15x - 8/3 = 0", "output": "x^2 + 94/15x - 8/3 = 0\n(x - 2/5)(x - -20/3) = 0\nx - 2/5 = 0 or x - -20/3 = 0\nx = 2/5\nx = -20/3"} {"input": "Find x and y such that\n4x + 6y = -18\n5x + 10y = -45/2", "output": "4x + 6y = -18\n5x + 10y = -45/2\n\nUsing elimination\n5*(4x + 6y = -18)\n4*(5x + 10y = -45/2)\n20x + 30y = -90\n20x + 40y = -90\nSubtract equations\n-10y = 0\ny = 0/-10\ny = 0\n\nSubstitute y\n4x + 6(0) = -18\n4x = -18\nx = -18/4\nx = -9/2"} {"input": "Solve the equations:\n1x + 8y = -179/10\n9x + 8y = -331/10", "output": "1x + 8y = -179/10\n9x + 8y = -331/10\n\nUsing elimination\n9*(1x + 8y = -179/10)\n1*(9x + 8y = -331/10)\n9x + 72y = -1611/10\n9x + 8y = -331/10\nSubtract equations\n64y = -128\ny = -128/64\ny = -2\n\nSubstitute y\n1x + 8(-2) = -179/10\n1x = -19/10\nx = -19/10/1\nx = -19/10"} {"input": "Determine x in x^3 + 46/5x^2 - 197/25x + 6/5 = 0", "output": "x^3 + 46/5x^2 - 197/25x + 6/5 = 0\n(x - 3/5)(x - -10)(x - 1/5) = 0\nx - 3/5 = 0\nx - -10 = 0\nx - 1/5 = 0\nx = 3/5\nx = -10\nx = 1/5"} {"input": "Find the solution to 5x - 85/9 = 0", "output": "5x - 85/9 = 0\n5x = 85/9\nx = 85/9 / 5\nx = 17/9"} {"input": "Find x in x^3 + 587/105x^2 + 338/35x + 24/5 = 0", "output": "x^3 + 587/105x^2 + 338/35x + 24/5 = 0\n(x - -7/3)(x - -6/7)(x - -12/5) = 0\nx - -7/3 = 0\nx - -6/7 = 0\nx - -12/5 = 0\nx = -7/3\nx = -6/7\nx = -12/5"} {"input": "Find x for x^3 - 16/15x^2 - 37/60x - 1/20 = 0", "output": "x^3 - 16/15x^2 - 37/60x - 1/20 = 0\n(x - 3/2)(x - -1/3)(x - -1/10) = 0\nx - 3/2 = 0\nx - -1/3 = 0\nx - -1/10 = 0\nx = 3/2\nx = -1/3\nx = -1/10"} {"input": "What value of x satisfies x^3 + 61/18x^2 - 64/9x - 19/2 = 0", "output": "x^3 + 61/18x^2 - 64/9x - 19/2 = 0\n(x - -9/2)(x - 19/9)(x - -1) = 0\nx - -9/2 = 0\nx - 19/9 = 0\nx - -1 = 0\nx = -9/2\nx = 19/9\nx = -1"} {"input": "Solve quickly: x^2 - 51/4x + 38 = 0", "output": "x^2 - 51/4x + 38 = 0\n(x - 8)(x - 19/4) = 0\nx - 8 = 0 or x - 19/4 = 0\nx = 8\nx = 19/4"} {"input": "Solve the equations:\n10x + 5y = 37/4\n6x + 7y = 291/20", "output": "10x + 5y = 37/4\n6x + 7y = 291/20\n\nUsing elimination\n6*(10x + 5y = 37/4)\n10*(6x + 7y = 291/20)\n60x + 30y = 111/2\n60x + 70y = 291/2\nSubtract equations\n-40y = -90\ny = -90/-40\ny = 9/4\n\nSubstitute y\n10x + 5(9/4) = 37/4\n10x = -2\nx = -2/10\nx = -1/5"} {"input": "What value of x satisfies 1x + 4 = 0", "output": "1x + 4 = 0\n1x = -4\nx = -4 / 1\nx = -4"} {"input": "Solve the system:\n3x + 5y = -311/35\n10x + 9y = -215/7", "output": "3x + 5y = -311/35\n10x + 9y = -215/7\n\nUsing elimination\n10*(3x + 5y = -311/35)\n3*(10x + 9y = -215/7)\n30x + 50y = -622/7\n30x + 27y = -645/7\nSubtract equations\n23y = 23/7\ny = 23/7/23\ny = 1/7\n\nSubstitute y\n3x + 5(1/7) = -311/35\n3x = -48/5\nx = -48/5/3\nx = -16/5"} {"input": "Solve simultaneously:\n4x + 5y = -101/6\n9x + 9y = -42", "output": "4x + 5y = -101/6\n9x + 9y = -42\n\nUsing elimination\n9*(4x + 5y = -101/6)\n4*(9x + 9y = -42)\n36x + 45y = -303/2\n36x + 36y = -168\nSubtract equations\n9y = 33/2\ny = 33/2/9\ny = 11/6\n\nSubstitute y\n4x + 5(11/6) = -101/6\n4x = -26\nx = -26/4\nx = -13/2"} {"input": "Solve simultaneously:\n8x + 9y = -128/3\n8x + 1y = -32/3", "output": "8x + 9y = -128/3\n8x + 1y = -32/3\n\nUsing elimination\n8*(8x + 9y = -128/3)\n8*(8x + 1y = -32/3)\n64x + 72y = -1024/3\n64x + 8y = -256/3\nSubtract equations\n64y = -256\ny = -256/64\ny = -4\n\nSubstitute y\n8x + 9(-4) = -128/3\n8x = -20/3\nx = -20/3/8\nx = -5/6"} {"input": "Determine x in 8x + 8/3 = 0", "output": "8x + 8/3 = 0\n8x = -8/3\nx = -8/3 / 8\nx = -1/3"} {"input": "Determine x in x^3 - 59/4x^2 + 35x + 275/4 = 0", "output": "x^3 - 59/4x^2 + 35x + 275/4 = 0\n(x - 11)(x - -5/4)(x - 5) = 0\nx - 11 = 0\nx - -5/4 = 0\nx - 5 = 0\nx = 11\nx = -5/4\nx = 5"} {"input": "What value of x satisfies x^2 + 30/7x + 27/7 = 0", "output": "x^2 + 30/7x + 27/7 = 0\n(x - -9/7)(x - -3) = 0\nx - -9/7 = 0 or x - -3 = 0\nx = -9/7\nx = -3"} {"input": "Compute the solution of 6x - 3/4 = 0", "output": "6x - 3/4 = 0\n6x = 3/4\nx = 3/4 / 6\nx = 1/8"} {"input": "Solve quickly: 4x + 28 = 0", "output": "4x + 28 = 0\n4x = -28\nx = -28 / 4\nx = -7"} {"input": "What value of x satisfies 7x + 28 = 0", "output": "7x + 28 = 0\n7x = -28\nx = -28 / 7\nx = -4"} {"input": "Determine x in 1x - 19/10 = 0", "output": "1x - 19/10 = 0\n1x = 19/10\nx = 19/10 / 1\nx = 19/10"} {"input": "Compute the solution of x^2 + 19/6x + 5/2 = 0", "output": "x^2 + 19/6x + 5/2 = 0\n(x - -5/3)(x - -3/2) = 0\nx - -5/3 = 0 or x - -3/2 = 0\nx = -5/3\nx = -3/2"} {"input": "Solve the equations:\n9x + 1y = 181/12\n3x + 5y = 23/12", "output": "9x + 1y = 181/12\n3x + 5y = 23/12\n\nUsing elimination\n3*(9x + 1y = 181/12)\n9*(3x + 5y = 23/12)\n27x + 3y = 181/4\n27x + 45y = 69/4\nSubtract equations\n-42y = 28\ny = 28/-42\ny = -2/3\n\nSubstitute y\n9x + 1(-2/3) = 181/12\n9x = 63/4\nx = 63/4/9\nx = 7/4"} {"input": "Find x and y such that\n4x + 2y = 268/9\n9x + 7y = 102", "output": "4x + 2y = 268/9\n9x + 7y = 102\n\nUsing elimination\n9*(4x + 2y = 268/9)\n4*(9x + 7y = 102)\n36x + 18y = 268\n36x + 28y = 408\nSubtract equations\n-10y = -140\ny = -140/-10\ny = 14\n\nSubstitute y\n4x + 2(14) = 268/9\n4x = 16/9\nx = 16/9/4\nx = 4/9"} {"input": "What value of x satisfies 8x - 128/3 = 0", "output": "8x - 128/3 = 0\n8x = 128/3\nx = 128/3 / 8\nx = 16/3"} {"input": "Find x for x^3 + 27/5x^2 - 29/5x - 39 = 0", "output": "x^3 + 27/5x^2 - 29/5x - 39 = 0\n(x - 13/5)(x - -3)(x - -5) = 0\nx - 13/5 = 0\nx - -3 = 0\nx - -5 = 0\nx = 13/5\nx = -3\nx = -5"} {"input": "Compute the solution of x^2 + 4/5x - 33/100 = 0", "output": "x^2 + 4/5x - 33/100 = 0\n(x - 3/10)(x - -11/10) = 0\nx - 3/10 = 0 or x - -11/10 = 0\nx = 3/10\nx = -11/10"} {"input": "Solve x^2 - 67/8x - 17/16 = 0", "output": "x^2 - 67/8x - 17/16 = 0\n(x - -1/8)(x - 17/2) = 0\nx - -1/8 = 0 or x - 17/2 = 0\nx = -1/8\nx = 17/2"} {"input": "Solve the equation x^2 + 223/63x + 190/63 = 0", "output": "x^2 + 223/63x + 190/63 = 0\n(x - -19/9)(x - -10/7) = 0\nx - -19/9 = 0 or x - -10/7 = 0\nx = -19/9\nx = -10/7"} {"input": "Solve the system:\n1x + 10y = 22/3\n3x + 1y = 15/2", "output": "1x + 10y = 22/3\n3x + 1y = 15/2\n\nUsing elimination\n3*(1x + 10y = 22/3)\n1*(3x + 1y = 15/2)\n3x + 30y = 22\n3x + 1y = 15/2\nSubtract equations\n29y = 29/2\ny = 29/2/29\ny = 1/2\n\nSubstitute y\n1x + 10(1/2) = 22/3\n1x = 7/3\nx = 7/3/1\nx = 7/3"} {"input": "Determine x in x^3 - 121/60x^2 - 323/24x + 2023/120 = 0", "output": "x^3 - 121/60x^2 - 323/24x + 2023/120 = 0\n(x - 7/6)(x - 17/4)(x - -17/5) = 0\nx - 7/6 = 0\nx - 17/4 = 0\nx - -17/5 = 0\nx = 7/6\nx = 17/4\nx = -17/5"} {"input": "Find x in x^2 + 3/7x - 34/7 = 0", "output": "x^2 + 3/7x - 34/7 = 0\n(x - -17/7)(x - 2) = 0\nx - -17/7 = 0 or x - 2 = 0\nx = -17/7\nx = 2"} {"input": "Find x in 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Solve quickly: x^3 - 479/120x^2 + 27/10x - 133/480 = 0", "output": "x^3 - 479/120x^2 + 27/10x - 133/480 = 0\n(x - 7/10)(x - 1/8)(x - 19/6) = 0\nx - 7/10 = 0\nx - 1/8 = 0\nx - 19/6 = 0\nx = 7/10\nx = 1/8\nx = 19/6"} {"input": "Find x in x^3 + 19/6x^2 + 7/3x = 0", "output": "x^3 + 19/6x^2 + 7/3x = 0\n(x - -7/6)(x - -2)(x - 0) = 0\nx - -7/6 = 0\nx - -2 = 0\nx - 0 = 0\nx = -7/6\nx = -2\nx = 0"} {"input": "Solve the equations:\n6x + 2y = -267/20\n5x + 10y = -7/4", "output": "6x + 2y = -267/20\n5x + 10y = -7/4\n\nUsing elimination\n5*(6x + 2y = -267/20)\n6*(5x + 10y = -7/4)\n30x + 10y = -267/4\n30x + 60y = -21/2\nSubtract equations\n-50y = -225/4\ny = -225/4/-50\ny = 9/8\n\nSubstitute y\n6x + 2(9/8) = -267/20\n6x = -78/5\nx = -78/5/6\nx = -13/5"} {"input": "Find the solution to x^3 - 131/15x^2 - 69/20x + 189/20 = 0", "output": "x^3 - 131/15x^2 - 69/20x + 189/20 = 0\n(x - -7/6)(x - 9)(x - 9/10) = 0\nx - -7/6 = 0\nx - 9 = 0\nx - 9/10 = 0\nx = -7/6\nx = 9\nx = 9/10"} {"input": "What value of x satisfies x^2 - 21x + 38 = 0", "output": "x^2 - 21x + 38 = 0\n(x - 2)(x - 19) = 0\nx - 2 = 0 or x - 19 = 0\nx = 2\nx = 19"} {"input": "Find x in x^2 - 41/15x - 114/5 = 0", "output": "x^2 - 41/15x - 114/5 = 0\n(x - 19/3)(x - -18/5) = 0\nx - 19/3 = 0 or x - -18/5 = 0\nx = 19/3\nx = -18/5"} {"input": "Find x in x^3 + 147/8x^2 - 117/8x - 209/4 = 0", "output": "x^3 + 147/8x^2 - 117/8x - 209/4 = 0\n(x - 2)(x - -11/8)(x - -19) = 0\nx - 2 = 0\nx - -11/8 = 0\nx - -19 = 0\nx = 2\nx = -11/8\nx = -19"} {"input": "What value of x satisfies x^3 - 1007/315x^2 - 83/35x + 19/63 = 0", "output": "x^3 - 1007/315x^2 - 83/35x + 19/63 = 0\n(x - 1/9)(x - -5/7)(x - 19/5) = 0\nx - 1/9 = 0\nx - -5/7 = 0\nx - 19/5 = 0\nx = 1/9\nx = -5/7\nx = 19/5"} {"input": "What value of x satisfies 7x + 7/10 = 0", "output": "7x + 7/10 = 0\n7x = -7/10\nx = -7/10 / 7\nx = -1/10"} {"input": "Compute the solution of 6x - 102/5 = 0", "output": "6x - 102/5 = 0\n6x = 102/5\nx = 102/5 / 6\nx = 17/5"} {"input": "Determine x in x^3 + 71/12x^2 + 55/9x - 25/3 = 0", "output": "x^3 + 71/12x^2 + 55/9x - 25/3 = 0\n(x - 3/4)(x - -10/3)(x - -10/3) = 0\nx - 3/4 = 0\nx - -10/3 = 0\nx - -10/3 = 0\nx = 3/4\nx = -10/3\nx = -10/3"} {"input": "Find x in 10x - 20/3 = 0", "output": "10x - 20/3 = 0\n10x = 20/3\nx = 20/3 / 10\nx = 2/3"} {"input": "Find the solution to x^2 - 14/5x = 0", "output": "x^2 - 14/5x = 0\n(x - 0)(x - 14/5) = 0\nx - 0 = 0 or x - 14/5 = 0\nx = 0\nx = 14/5"} {"input": "Solve the equations:\n2x + 1y = 21/5\n2x + 4y = 69/5", "output": "2x + 1y = 21/5\n2x + 4y = 69/5\n\nUsing elimination\n2*(2x + 1y = 21/5)\n2*(2x + 4y = 69/5)\n4x + 2y = 42/5\n4x + 8y = 138/5\nSubtract equations\n-6y = -96/5\ny = -96/5/-6\ny = 16/5\n\nSubstitute y\n2x + 1(16/5) = 21/5\n2x = 1\nx = 1/2\nx = 1/2"} {"input": "Solve the equations:\n8x + 6y = -45\n5x + 8y = -61/3", "output": "8x + 6y = -45\n5x + 8y = -61/3\n\nUsing elimination\n5*(8x + 6y = -45)\n8*(5x + 8y = -61/3)\n40x + 30y = -225\n40x + 64y = -488/3\nSubtract equations\n-34y = -187/3\ny = -187/3/-34\ny = 11/6\n\nSubstitute y\n8x + 6(11/6) = -45\n8x = -56\nx = -56/8\nx = -7"} {"input": "Solve the equations:\n7x + 9y = 27/4\n7x + 5y = 15/4", "output": "7x + 9y = 27/4\n7x + 5y = 15/4\n\nUsing elimination\n7*(7x + 9y = 27/4)\n7*(7x + 5y = 15/4)\n49x + 63y = 189/4\n49x + 35y = 105/4\nSubtract equations\n28y = 21\ny = 21/28\ny = 3/4\n\nSubstitute y\n7x + 9(3/4) = 27/4\n7x = 0\nx = 0/7\nx = 0"} {"input": "Find x and y such that\n3x + 10y = -67/4\n5x + 1y = -57/20", "output": "3x + 10y = -67/4\n5x + 1y = -57/20\n\nUsing elimination\n5*(3x + 10y = -67/4)\n3*(5x + 1y = -57/20)\n15x + 50y = -335/4\n15x + 3y = -171/20\nSubtract equations\n47y = -376/5\ny = -376/5/47\ny = -8/5\n\nSubstitute y\n3x + 10(-8/5) = -67/4\n3x = -3/4\nx = -3/4/3\nx = -1/4"} {"input": "Solve quickly: 7x - 112/5 = 0", "output": "7x - 112/5 = 0\n7x = 112/5\nx = 112/5 / 7\nx = 16/5"} {"input": "Solve quickly: x^2 - 3/70x - 247/70 = 0", "output": "x^2 - 3/70x - 247/70 = 0\n(x - 19/10)(x - -13/7) = 0\nx - 19/10 = 0 or x - -13/7 = 0\nx = 19/10\nx = -13/7"} {"input": "Compute the solution of 6x - 102/7 = 0", "output": "6x - 102/7 = 0\n6x = 102/7\nx = 102/7 / 6\nx = 17/7"} {"input": "Find x in x^3 - 11/3x^2 - 28/3x + 32 = 0", "output": "x^3 - 11/3x^2 - 28/3x + 32 = 0\n(x - 8/3)(x - 4)(x - -3) = 0\nx - 8/3 = 0\nx - 4 = 0\nx - -3 = 0\nx = 8/3\nx = 4\nx = -3"} {"input": "Solve x^3 - 9/4x^2 - 95/8x = 0", "output": "x^3 - 9/4x^2 - 95/8x = 0\n(x - 0)(x - 19/4)(x - -5/2) = 0\nx - 0 = 0\nx - 19/4 = 0\nx - -5/2 = 0\nx = 0\nx = 19/4\nx = -5/2"} {"input": "Find the solution to x^2 - 23x + 76 = 0", "output": "x^2 - 23x + 76 = 0\n(x - 4)(x - 19) = 0\nx - 4 = 0 or x - 19 = 0\nx = 4\nx = 19"} {"input": "Find x and y such that\n5x + 4y = 761/56\n6x + 2y = 423/28", "output": "5x + 4y = 761/56\n6x + 2y = 423/28\n\nUsing elimination\n6*(5x + 4y = 761/56)\n5*(6x + 2y = 423/28)\n30x + 24y = 2283/28\n30x + 10y = 2115/28\nSubtract equations\n14y = 6\ny = 6/14\ny = 3/7\n\nSubstitute y\n5x + 4(3/7) = 761/56\n5x = 95/8\nx = 95/8/5\nx = 19/8"} {"input": "Solve the equations:\n10x + 5y = -295/9\n4x + 4y = -92/9", "output": "10x + 5y = -295/9\n4x + 4y = -92/9\n\nUsing elimination\n4*(10x + 5y = -295/9)\n10*(4x + 4y = -92/9)\n40x + 20y = -1180/9\n40x + 40y = -920/9\nSubtract equations\n-20y = -260/9\ny = -260/9/-20\ny = 13/9\n\nSubstitute y\n10x + 5(13/9) = -295/9\n10x = -40\nx = -40/10\nx = -4"} {"input": "Find x in x^2 + 6x + 5 = 0", "output": "x^2 + 6x + 5 = 0\n(x - -1)(x - -5) = 0\nx - -1 = 0 or x - -5 = 0\nx = -1\nx = -5"} {"input": "Compute the solution of x^2 - 37/12x - 12 = 0", "output": "x^2 - 37/12x - 12 = 0\n(x - -9/4)(x - 16/3) = 0\nx - -9/4 = 0 or x - 16/3 = 0\nx = -9/4\nx = 16/3"} {"input": "Solve the equations:\n3x + 5y = -91/5\n9x + 1y = -98/5", "output": "3x + 5y = -91/5\n9x + 1y = -98/5\n\nUsing elimination\n9*(3x + 5y = -91/5)\n3*(9x + 1y = -98/5)\n27x + 45y = -819/5\n27x + 3y = -294/5\nSubtract equations\n42y = -105\ny = -105/42\ny = -5/2\n\nSubstitute y\n3x + 5(-5/2) = -91/5\n3x = -57/10\nx = -57/10/3\nx = -19/10"} {"input": "Find x and y such that\n8x + 9y = -723/14\n7x + 5y = -53/2", "output": "8x + 9y = -723/14\n7x + 5y = -53/2\n\nUsing elimination\n7*(8x + 9y = -723/14)\n8*(7x + 5y = -53/2)\n56x + 63y = -723/2\n56x + 40y = -212\nSubtract equations\n23y = -299/2\ny = -299/2/23\ny = -13/2\n\nSubstitute y\n8x + 9(-13/2) = -723/14\n8x = 48/7\nx = 48/7/8\nx = 6/7"} {"input": "What value of x satisfies 5x + 5 = 0", "output": "5x + 5 = 0\n5x = -5\nx = -5 / 5\nx = -1"} {"input": "Solve the system:\n3x + 2y = -41/6\n3x + 7y = -247/12", "output": "3x + 2y = -41/6\n3x + 7y = -247/12\n\nUsing elimination\n3*(3x + 2y = -41/6)\n3*(3x + 7y = -247/12)\n9x + 6y = -41/2\n9x + 21y = -247/4\nSubtract equations\n-15y = 165/4\ny = 165/4/-15\ny = -11/4\n\nSubstitute y\n3x + 2(-11/4) = -41/6\n3x = -4/3\nx = -4/3/3\nx = -4/9"} {"input": "Solve x^3 - 2/9x^2 - 565/27x - 304/9 = 0", "output": "x^3 - 2/9x^2 - 565/27x - 304/9 = 0\n(x - -3)(x - 16/3)(x - -19/9) = 0\nx - -3 = 0\nx - 16/3 = 0\nx - -19/9 = 0\nx = -3\nx = 16/3\nx = -19/9"} {"input": "Solve quickly: x^2 - 2/15x - 187/60 = 0", "output": "x^2 - 2/15x - 187/60 = 0\n(x - -17/10)(x - 11/6) = 0\nx - -17/10 = 0 or x - 11/6 = 0\nx = -17/10\nx = 11/6"} {"input": "Find x in 4x + 28 = 0", "output": "4x + 28 = 0\n4x = -28\nx = -28 / 4\nx = -7"} {"input": "Determine x in x^2 + 54/5x - 72/5 = 0", "output": "x^2 + 54/5x - 72/5 = 0\n(x - 6/5)(x - -12) = 0\nx - 6/5 = 0 or x - -12 = 0\nx = 6/5\nx = -12"} {"input": "Find the solution to x^2 + 7/2x + 5/2 = 0", "output": "x^2 + 7/2x + 5/2 = 0\n(x - -1)(x - -5/2) = 0\nx - -1 = 0 or x - -5/2 = 0\nx = -1\nx = -5/2"} {"input": "What value of x satisfies x^3 - 103/18x^2 + 694/81x - 224/81 = 0", "output": "x^3 - 103/18x^2 + 694/81x - 224/81 = 0\n(x - 7/2)(x - 16/9)(x - 4/9) = 0\nx - 7/2 = 0\nx - 16/9 = 0\nx - 4/9 = 0\nx = 7/2\nx = 16/9\nx = 4/9"} {"input": "Find x in 7x - 63/10 = 0", "output": "7x - 63/10 = 0\n7x = 63/10\nx = 63/10 / 7\nx = 9/10"} {"input": "What value of x satisfies x^2 - 13/8x + 11/32 = 0", "output": "x^2 - 13/8x + 11/32 = 0\n(x - 11/8)(x - 1/4) = 0\nx - 11/8 = 0 or x - 1/4 = 0\nx = 11/8\nx = 1/4"} {"input": "Solve the equation x^3 - 41/5x^2 + 22x - 96/5 = 0", "output": "x^3 - 41/5x^2 + 22x - 96/5 = 0\n(x - 2)(x - 3)(x - 16/5) = 0\nx - 2 = 0\nx - 3 = 0\nx - 16/5 = 0\nx = 2\nx = 3\nx = 16/5"} {"input": "Solve the equation x^3 - 54/5x^2 + 67/5x + 462/5 = 0", "output": "x^3 - 54/5x^2 + 67/5x + 462/5 = 0\n(x - 6)(x - 7)(x - -11/5) = 0\nx - 6 = 0\nx - 7 = 0\nx - -11/5 = 0\nx = 6\nx = 7\nx = -11/5"} {"input": "Find x for x^3 - 152/21x^2 + 47/3x - 66/7 = 0", "output": "x^3 - 152/21x^2 + 47/3x - 66/7 = 0\n(x - 1)(x - 18/7)(x - 11/3) = 0\nx - 1 = 0\nx - 18/7 = 0\nx - 11/3 = 0\nx = 1\nx = 18/7\nx = 11/3"} {"input": "Find x in 7x - 112 = 0", "output": "7x - 112 = 0\n7x = 112\nx = 112 / 7\nx = 16"} {"input": "Find x and y such that\n8x + 10y = -11\n9x + 10y = -31/2", "output": "8x + 10y = -11\n9x + 10y = -31/2\n\nUsing elimination\n9*(8x + 10y = -11)\n8*(9x + 10y = -31/2)\n72x + 90y = -99\n72x + 80y = -124\nSubtract equations\n10y = 25\ny = 25/10\ny = 5/2\n\nSubstitute y\n8x + 10(5/2) = -11\n8x = -36\nx = -36/8\nx = -9/2"} {"input": "Solve simultaneously:\n2x + 5y = 82/9\n7x + 2y = 256/9", "output": "2x + 5y = 82/9\n7x + 2y = 256/9\n\nUsing elimination\n7*(2x + 5y = 82/9)\n2*(7x + 2y = 256/9)\n14x + 35y = 574/9\n14x + 4y = 512/9\nSubtract equations\n31y = 62/9\ny = 62/9/31\ny = 2/9\n\nSubstitute y\n2x + 5(2/9) = 82/9\n2x = 8\nx = 8/2\nx = 4"} {"input": "Compute the solution of x^2 - 17/10x + 7/10 = 0", "output": "x^2 - 17/10x + 7/10 = 0\n(x - 1)(x - 7/10) = 0\nx - 1 = 0 or x - 7/10 = 0\nx = 1\nx = 7/10"} {"input": "Solve simultaneously:\n7x + 7y = 301/2\n10x + 1y = 385/2", "output": "7x + 7y = 301/2\n10x + 1y = 385/2\n\nUsing elimination\n10*(7x + 7y = 301/2)\n7*(10x + 1y = 385/2)\n70x + 70y = 1505\n70x + 7y = 2695/2\nSubtract equations\n63y = 315/2\ny = 315/2/63\ny = 5/2\n\nSubstitute y\n7x + 7(5/2) = 301/2\n7x = 133\nx = 133/7\nx = 19"} {"input": "Solve the equation x^2 + 29/2x + 39/2 = 0", "output": "x^2 + 29/2x + 39/2 = 0\n(x - -3/2)(x - -13) = 0\nx - -3/2 = 0 or x - -13 = 0\nx = -3/2\nx = -13"} {"input": "Find x for 6x + 8 = 0", "output": "6x + 8 = 0\n6x = -8\nx = -8 / 6\nx = -4/3"} {"input": "Solve 7x + 70/3 = 0", "output": "7x + 70/3 = 0\n7x = -70/3\nx = -70/3 / 7\nx = -10/3"} {"input": "Find x and y such that\n8x + 10y = -29\n5x + 1y = -31/2", "output": "8x + 10y = -29\n5x + 1y = -31/2\n\nUsing elimination\n5*(8x + 10y = -29)\n8*(5x + 1y = -31/2)\n40x + 50y = -145\n40x + 8y = -124\nSubtract equations\n42y = -21\ny = -21/42\ny = -1/2\n\nSubstitute y\n8x + 10(-1/2) = -29\n8x = -24\nx = -24/8\nx = -3"} {"input": "What value of x satisfies x^3 - 97/6x^2 - 55/3x + 425/6 = 0", "output": "x^3 - 97/6x^2 - 55/3x + 425/6 = 0\n(x - 17)(x - 5/3)(x - -5/2) = 0\nx - 17 = 0\nx - 5/3 = 0\nx - -5/2 = 0\nx = 17\nx = 5/3\nx = -5/2"} {"input": "Find x and y such that\n9x + 8y = -20\n9x + 3y = -115/8", "output": "9x + 8y = -20\n9x + 3y = -115/8\n\nUsing elimination\n9*(9x + 8y = -20)\n9*(9x + 3y = -115/8)\n81x + 72y = -180\n81x + 27y = -1035/8\nSubtract equations\n45y = -405/8\ny = -405/8/45\ny = -9/8\n\nSubstitute y\n9x + 8(-9/8) = -20\n9x = -11\nx = -11/9\nx = -11/9"} {"input": "Solve the equations:\n7x + 8y = 1699/56\n5x + 4y = 1049/56", "output": "7x + 8y = 1699/56\n5x + 4y = 1049/56\n\nUsing elimination\n5*(7x + 8y = 1699/56)\n7*(5x + 4y = 1049/56)\n35x + 40y = 8495/56\n35x + 28y = 1049/8\nSubtract equations\n12y = 144/7\ny = 144/7/12\ny = 12/7\n\nSubstitute y\n7x + 8(12/7) = 1699/56\n7x = 133/8\nx = 133/8/7\nx = 19/8"} {"input": "Solve the system:\n4x + 2y = 0\n1x + 1y = 3/8", "output": "4x + 2y = 0\n1x + 1y = 3/8\n\nUsing elimination\n1*(4x + 2y = 0)\n4*(1x + 1y = 3/8)\n4x + 2y = 0\n4x + 4y = 3/2\nSubtract equations\n-2y = -3/2\ny = -3/2/-2\ny = 3/4\n\nSubstitute y\n4x + 2(3/4) = 0\n4x = -3/2\nx = -3/2/4\nx = -3/8"} {"input": "Find the solution to 5x + 50 = 0", "output": "5x + 50 = 0\n5x = -50\nx = -50 / 5\nx = -10"} {"input": "Solve simultaneously:\n10x + 9y = -105/2\n3x + 5y = -43/2", "output": "10x + 9y = -105/2\n3x + 5y = -43/2\n\nUsing elimination\n3*(10x + 9y = -105/2)\n10*(3x + 5y = -43/2)\n30x + 27y = -315/2\n30x + 50y = -215\nSubtract equations\n-23y = 115/2\ny = 115/2/-23\ny = -5/2\n\nSubstitute y\n10x + 9(-5/2) = -105/2\n10x = -30\nx = -30/10\nx = -3"} {"input": "What value of x satisfies x^3 - 22/3x^2 - 47/3x + 6 = 0", "output": "x^3 - 22/3x^2 - 47/3x + 6 = 0\n(x - -2)(x - 1/3)(x - 9) = 0\nx - -2 = 0\nx - 1/3 = 0\nx - 9 = 0\nx = -2\nx = 1/3\nx = 9"} {"input": "Find the solution to x^3 - 83/14x^2 + 69/7x - 45/14 = 0", "output": "x^3 - 83/14x^2 + 69/7x - 45/14 = 0\n(x - 3/7)(x - 5/2)(x - 3) = 0\nx - 3/7 = 0\nx - 5/2 = 0\nx - 3 = 0\nx = 3/7\nx = 5/2\nx = 3"} {"input": "Find x and y such that\n9x + 1y = 1287/70\n5x + 4y = 205/14", "output": "9x + 1y = 1287/70\n5x + 4y = 205/14\n\nUsing elimination\n5*(9x + 1y = 1287/70)\n9*(5x + 4y = 205/14)\n45x + 5y = 1287/14\n45x + 36y = 1845/14\nSubtract equations\n-31y = -279/7\ny = -279/7/-31\ny = 9/7\n\nSubstitute y\n9x + 1(9/7) = 1287/70\n9x = 171/10\nx = 171/10/9\nx = 19/10"} {"input": "Find x in x^3 - 17/30x^2 - 1/10x + 1/15 = 0", "output": "x^3 - 17/30x^2 - 1/10x + 1/15 = 0\n(x - 2/5)(x - -1/3)(x - 1/2) = 0\nx - 2/5 = 0\nx - -1/3 = 0\nx - 1/2 = 0\nx = 2/5\nx = -1/3\nx = 1/2"} {"input": "Solve the equation x^3 + 25/6x^2 - 1/6x - 10/3 = 0", "output": "x^3 + 25/6x^2 - 1/6x - 10/3 = 0\n(x - 5/6)(x - -1)(x - -4) = 0\nx - 5/6 = 0\nx - -1 = 0\nx - -4 = 0\nx = 5/6\nx = -1\nx = -4"} {"input": "Solve the equations:\n5x + 7y = 761/20\n7x + 2y = 691/20", "output": "5x + 7y = 761/20\n7x + 2y = 691/20\n\nUsing elimination\n7*(5x + 7y = 761/20)\n5*(7x + 2y = 691/20)\n35x + 49y = 5327/20\n35x + 10y = 691/4\nSubtract equations\n39y = 468/5\ny = 468/5/39\ny = 12/5\n\nSubstitute y\n5x + 7(12/5) = 761/20\n5x = 85/4\nx = 85/4/5\nx = 17/4"} {"input": "Solve the system:\n6x + 9y = 129/5\n1x + 3y = -7/5", "output": "6x + 9y = 129/5\n1x + 3y = -7/5\n\nUsing elimination\n1*(6x + 9y = 129/5)\n6*(1x + 3y = -7/5)\n6x + 9y = 129/5\n6x + 18y = -42/5\nSubtract equations\n-9y = 171/5\ny = 171/5/-9\ny = -19/5\n\nSubstitute y\n6x + 9(-19/5) = 129/5\n6x = 60\nx = 60/6\nx = 10"} {"input": "Find x in x^2 + 16x - 57 = 0", "output": "x^2 + 16x - 57 = 0\n(x - 3)(x - -19) = 0\nx - 3 = 0 or x - -19 = 0\nx = 3\nx = -19"} {"input": "Compute the solution of x^2 + 17/18x - 13/18 = 0", "output": "x^2 + 17/18x - 13/18 = 0\n(x - 1/2)(x - -13/9) = 0\nx - 1/2 = 0 or x - -13/9 = 0\nx = 1/2\nx = -13/9"} {"input": "Solve quickly: 7x - 91/8 = 0", "output": "7x - 91/8 = 0\n7x = 91/8\nx = 91/8 / 7\nx = 13/8"} {"input": "Solve the equation x^3 - 23/9x^2 + 100/81x + 100/243 = 0", "output": "x^3 - 23/9x^2 + 100/81x + 100/243 = 0\n(x - -2/9)(x - 10/9)(x - 5/3) = 0\nx - -2/9 = 0\nx - 10/9 = 0\nx - 5/3 = 0\nx = -2/9\nx = 10/9\nx = 5/3"} {"input": "Find x in x^3 + 122/45x^2 + 79/60x + 19/180 = 0", "output": "x^3 + 122/45x^2 + 79/60x + 19/180 = 0\n(x - -1/2)(x - -19/9)(x - -1/10) = 0\nx - -1/2 = 0\nx - -19/9 = 0\nx - -1/10 = 0\nx = -1/2\nx = -19/9\nx = -1/10"} {"input": "Solve the equations:\n7x + 9y = -531/10\n8x + 3y = -687/10", "output": "7x + 9y = -531/10\n8x + 3y = -687/10\n\nUsing elimination\n8*(7x + 9y = -531/10)\n7*(8x + 3y = -687/10)\n56x + 72y = -2124/5\n56x + 21y = -4809/10\nSubtract equations\n51y = 561/10\ny = 561/10/51\ny = 11/10\n\nSubstitute y\n7x + 9(11/10) = -531/10\n7x = -63\nx = -63/7\nx = -9"} {"input": "Compute the solution of x^2 + 15x + 50 = 0", "output": "x^2 + 15x + 50 = 0\n(x - -10)(x - -5) = 0\nx - -10 = 0 or x - -5 = 0\nx = -10\nx = -5"} {"input": "Solve x^3 + 283/60x^2 + 31/5x + 117/80 = 0", "output": "x^3 + 283/60x^2 + 31/5x + 117/80 = 0\n(x - -9/4)(x - -13/6)(x - -3/10) = 0\nx - -9/4 = 0\nx - -13/6 = 0\nx - -3/10 = 0\nx = -9/4\nx = -13/6\nx = -3/10"} {"input": "Solve quickly: x^2 + 73/42x + 2/3 = 0", "output": "x^2 + 73/42x + 2/3 = 0\n(x - -7/6)(x - -4/7) = 0\nx - -7/6 = 0 or x - -4/7 = 0\nx = -7/6\nx = -4/7"} {"input": "Solve x^2 - 34/7x - 48/7 = 0", "output": "x^2 - 34/7x - 48/7 = 0\n(x - -8/7)(x - 6) = 0\nx - -8/7 = 0 or x - 6 = 0\nx = -8/7\nx = 6"} {"input": "Find x in x^2 + 1x - 6 = 0", "output": "x^2 + 1x - 6 = 0\n(x - -3)(x - 2) = 0\nx - -3 = 0 or x - 2 = 0\nx = -3\nx = 2"} {"input": "Find x in 6x - 32 = 0", "output": "6x - 32 = 0\n6x = 32\nx = 32 / 6\nx = 16/3"} {"input": "Find x for x^3 + 8/5x^2 - 143/20x + 2299/500 = 0", "output": "x^3 + 8/5x^2 - 143/20x + 2299/500 = 0\n(x - -19/5)(x - 11/10)(x - 11/10) = 0\nx - -19/5 = 0\nx - 11/10 = 0\nx - 11/10 = 0\nx = -19/5\nx = 11/10\nx = 11/10"} {"input": "Compute the solution of x^3 + 176/9x^2 + 257/9x + 10 = 0", "output": "x^3 + 176/9x^2 + 257/9x + 10 = 0\n(x - -1)(x - -5/9)(x - -18) = 0\nx - -1 = 0\nx - -5/9 = 0\nx - -18 = 0\nx = -1\nx = -5/9\nx = -18"} {"input": "Solve the equations:\n4x + 2y = -4/9\n5x + 8y = 193/9", "output": "4x + 2y = -4/9\n5x + 8y = 193/9\n\nUsing elimination\n5*(4x + 2y = -4/9)\n4*(5x + 8y = 193/9)\n20x + 10y = -20/9\n20x + 32y = 772/9\nSubtract equations\n-22y = -88\ny = -88/-22\ny = 4\n\nSubstitute y\n4x + 2(4) = -4/9\n4x = -76/9\nx = -76/9/4\nx = -19/9"} {"input": "Determine x in x^3 - 19/20x^2 - 43/2x + 165/4 = 0", "output": "x^3 - 19/20x^2 - 43/2x + 165/4 = 0\n(x - 11/5)(x - 15/4)(x - -5) = 0\nx - 11/5 = 0\nx - 15/4 = 0\nx - -5 = 0\nx = 11/5\nx = 15/4\nx = -5"} {"input": "Find x in 1x - 10 = 0", "output": "1x - 10 = 0\n1x = 10\nx = 10 / 1\nx = 10"} {"input": "Determine x in 7x + 77/3 = 0", "output": "7x + 77/3 = 0\n7x = -77/3\nx = -77/3 / 7\nx = -11/3"} {"input": "Find the solution to x^3 - 57/28x^2 - 5/56x + 75/56 = 0", "output": "x^3 - 57/28x^2 - 5/56x + 75/56 = 0\n(x - 5/4)(x - 3/2)(x - -5/7) = 0\nx - 5/4 = 0\nx - 3/2 = 0\nx - -5/7 = 0\nx = 5/4\nx = 3/2\nx = -5/7"} {"input": "Determine x in x^3 - 3/4x^2 - 31/4x + 21/2 = 0", "output": "x^3 - 3/4x^2 - 31/4x + 21/2 = 0\n(x - 2)(x - 7/4)(x - -3) = 0\nx - 2 = 0\nx - 7/4 = 0\nx - -3 = 0\nx = 2\nx = 7/4\nx = -3"} {"input": "Find x in 4x + 40/3 = 0", "output": "4x + 40/3 = 0\n4x = -40/3\nx = -40/3 / 4\nx = -10/3"} {"input": "Find the solution to x^3 + 25/18x^2 - 181/18x - 28/3 = 0", "output": "x^3 + 25/18x^2 - 181/18x - 28/3 = 0\n(x - -8/9)(x - -7/2)(x - 3) = 0\nx - -8/9 = 0\nx - -7/2 = 0\nx - 3 = 0\nx = -8/9\nx = -7/2\nx = 3"} {"input": "Solve the equation x^2 + 187/10x - 26 = 0", "output": "x^2 + 187/10x - 26 = 0\n(x - 13/10)(x - -20) = 0\nx - 13/10 = 0 or x - -20 = 0\nx = 13/10\nx = -20"} {"input": "Find the solution to x^2 - 11/3x - 14 = 0", "output": "x^2 - 11/3x - 14 = 0\n(x - -7/3)(x - 6) = 0\nx - -7/3 = 0 or x - 6 = 0\nx = -7/3\nx = 6"} {"input": "Compute the solution of 8x + 104 = 0", "output": "8x + 104 = 0\n8x = -104\nx = -104 / 8\nx = -13"} {"input": "Find x in 1x + 7/8 = 0", "output": "1x + 7/8 = 0\n1x = -7/8\nx = -7/8 / 1\nx = -7/8"} {"input": "Determine x in x^3 + 77/20x^2 + 57/25x - 297/100 = 0", "output": "x^3 + 77/20x^2 + 57/25x - 297/100 = 0\n(x - -11/5)(x - -9/4)(x - 3/5) = 0\nx - -11/5 = 0\nx - -9/4 = 0\nx - 3/5 = 0\nx = -11/5\nx = -9/4\nx = 3/5"} {"input": "Find x in x^2 - 10/3x + 221/81 = 0", "output": "x^2 - 10/3x + 221/81 = 0\n(x - 17/9)(x - 13/9) = 0\nx - 17/9 = 0 or x - 13/9 = 0\nx = 17/9\nx = 13/9"} {"input": "Solve the equation x^3 + 49/20x^2 - 3/100x - 27/25 = 0", "output": "x^3 + 49/20x^2 - 3/100x - 27/25 = 0\n(x - -9/4)(x - 3/5)(x - -4/5) = 0\nx - -9/4 = 0\nx - 3/5 = 0\nx - -4/5 = 0\nx = -9/4\nx = 3/5\nx = -4/5"} {"input": "Find x in 1x + 17/2 = 0", "output": "1x + 17/2 = 0\n1x = -17/2\nx = -17/2 / 1\nx = -17/2"} {"input": "Compute the solution of x^3 + 26/7x^2 + 95/28x + 25/28 = 0", "output": "x^3 + 26/7x^2 + 95/28x + 25/28 = 0\n(x - -1/2)(x - -5/7)(x - -5/2) = 0\nx - -1/2 = 0\nx - -5/7 = 0\nx - -5/2 = 0\nx = -1/2\nx = -5/7\nx = -5/2"} {"input": "Determine x in x^2 + 18/5x + 56/25 = 0", "output": "x^2 + 18/5x + 56/25 = 0\n(x - -4/5)(x - -14/5) = 0\nx - -4/5 = 0 or x - -14/5 = 0\nx = -4/5\nx = -14/5"} {"input": "Find x for 9x + 153 = 0", "output": "9x + 153 = 0\n9x = -153\nx = -153 / 9\nx = -17"} {"input": "Find x and y such that\n6x + 1y = 21/2\n4x + 4y = 2", "output": "6x + 1y = 21/2\n4x + 4y = 2\n\nUsing elimination\n4*(6x + 1y = 21/2)\n6*(4x + 4y = 2)\n24x + 4y = 42\n24x + 24y = 12\nSubtract equations\n-20y = 30\ny = 30/-20\ny = -3/2\n\nSubstitute y\n6x + 1(-3/2) = 21/2\n6x = 12\nx = 12/6\nx = 2"} {"input": "Determine x in 1x + 3/2 = 0", "output": "1x + 3/2 = 0\n1x = -3/2\nx = -3/2 / 1\nx = -3/2"} {"input": "Solve simultaneously:\n9x + 8y = 306/35\n2x + 3y = -9/35", "output": "9x + 8y = 306/35\n2x + 3y = -9/35\n\nUsing elimination\n2*(9x + 8y = 306/35)\n9*(2x + 3y = -9/35)\n18x + 16y = 612/35\n18x + 27y = -81/35\nSubtract equations\n-11y = 99/5\ny = 99/5/-11\ny = -9/5\n\nSubstitute y\n9x + 8(-9/5) = 306/35\n9x = 162/7\nx = 162/7/9\nx = 18/7"} {"input": "What value of x satisfies x^3 - 303/20x^2 + 89/40x + 3/8 = 0", "output": "x^3 - 303/20x^2 + 89/40x + 3/8 = 0\n(x - -1/10)(x - 15)(x - 1/4) = 0\nx - -1/10 = 0\nx - 15 = 0\nx - 1/4 = 0\nx = -1/10\nx = 15\nx = 1/4"} {"input": "Solve the system:\n7x + 6y = -24\n1x + 10y = -56/3", "output": "7x + 6y = -24\n1x + 10y = -56/3\n\nUsing elimination\n1*(7x + 6y = -24)\n7*(1x + 10y = -56/3)\n7x + 6y = -24\n7x + 70y = -392/3\nSubtract equations\n-64y = 320/3\ny = 320/3/-64\ny = -5/3\n\nSubstitute y\n7x + 6(-5/3) = -24\n7x = -14\nx = -14/7\nx = -2"} {"input": "Compute the solution of x^3 + 58/5x^2 + 72/5x - 576/5 = 0", "output": "x^3 + 58/5x^2 + 72/5x - 576/5 = 0\n(x - -8)(x - 12/5)(x - -6) = 0\nx - -8 = 0\nx - 12/5 = 0\nx - -6 = 0\nx = -8\nx = 12/5\nx = -6"} {"input": "What value of x satisfies x^3 + 659/280x^2 - 71/280x - 9/4 = 0", "output": "x^3 + 659/280x^2 - 71/280x - 9/4 = 0\n(x - 7/8)(x - -10/7)(x - -9/5) = 0\nx - 7/8 = 0\nx - -10/7 = 0\nx - -9/5 = 0\nx = 7/8\nx = -10/7\nx = -9/5"} {"input": "Determine x in 5x - 15 = 0", "output": "5x - 15 = 0\n5x = 15\nx = 15 / 5\nx = 3"} {"input": "Solve quickly: x^3 - 141/14x^2 - 341/14x + 102/7 = 0", "output": "x^3 - 141/14x^2 - 341/14x + 102/7 = 0\n(x - -17/7)(x - 12)(x - 1/2) = 0\nx - -17/7 = 0\nx - 12 = 0\nx - 1/2 = 0\nx = -17/7\nx = 12\nx = 1/2"} {"input": "Solve simultaneously:\n1x + 7y = 346/5\n8x + 8y = 368/5", "output": "1x + 7y = 346/5\n8x + 8y = 368/5\n\nUsing elimination\n8*(1x + 7y = 346/5)\n1*(8x + 8y = 368/5)\n8x + 56y = 2768/5\n8x + 8y = 368/5\nSubtract equations\n48y = 480\ny = 480/48\ny = 10\n\nSubstitute y\n1x + 7(10) = 346/5\n1x = -4/5\nx = -4/5/1\nx = -4/5"} {"input": "Solve the equation 6x - 6 = 0", "output": "6x - 6 = 0\n6x = 6\nx = 6 / 6\nx = 1"} {"input": "Solve quickly: x^2 - 9x + 17/4 = 0", "output": "x^2 - 9x + 17/4 = 0\n(x - 1/2)(x - 17/2) = 0\nx - 1/2 = 0 or x - 17/2 = 0\nx = 1/2\nx = 17/2"} {"input": "Solve quickly: x^3 - 17/12x^2 + 1/2x = 0", "output": "x^3 - 17/12x^2 + 1/2x = 0\n(x - 3/4)(x - 2/3)(x - 0) = 0\nx - 3/4 = 0\nx - 2/3 = 0\nx - 0 = 0\nx = 3/4\nx = 2/3\nx = 0"} {"input": "Solve simultaneously:\n8x + 3y = -11\n1x + 4y = -5", "output": "8x + 3y = -11\n1x + 4y = -5\n\nUsing elimination\n1*(8x + 3y = -11)\n8*(1x + 4y = -5)\n8x + 3y = -11\n8x + 32y = -40\nSubtract equations\n-29y = 29\ny = 29/-29\ny = -1\n\nSubstitute y\n8x + 3(-1) = -11\n8x = -8\nx = -8/8\nx = -1"} {"input": "Solve x^3 - 9/20x^2 - 71/8x - 63/10 = 0", "output": "x^3 - 9/20x^2 - 71/8x - 63/10 = 0\n(x - 7/2)(x - -4/5)(x - -9/4) = 0\nx - 7/2 = 0\nx - -4/5 = 0\nx - -9/4 = 0\nx = 7/2\nx = -4/5\nx = -9/4"} {"input": "Determine x in 3x + 21/4 = 0", "output": "3x + 21/4 = 0\n3x = -21/4\nx = -21/4 / 3\nx = -7/4"} {"input": "Find x for x^2 + 53/9x - 140/27 = 0", "output": "x^2 + 53/9x - 140/27 = 0\n(x - -20/3)(x - 7/9) = 0\nx - -20/3 = 0 or x - 7/9 = 0\nx = -20/3\nx = 7/9"} {"input": "Find x in 8x - 44/3 = 0", "output": "8x - 44/3 = 0\n8x = 44/3\nx = 44/3 / 8\nx = 11/6"} {"input": "Find the solution to x^2 - 107/28x - 51/28 = 0", "output": "x^2 - 107/28x - 51/28 = 0\n(x - -3/7)(x - 17/4) = 0\nx - -3/7 = 0 or x - 17/4 = 0\nx = -3/7\nx = 17/4"} {"input": "Solve the equations:\n5x + 2y = 64/9\n7x + 10y = -40/9", "output": "5x + 2y = 64/9\n7x + 10y = -40/9\n\nUsing elimination\n7*(5x + 2y = 64/9)\n5*(7x + 10y = -40/9)\n35x + 14y = 448/9\n35x + 50y = -200/9\nSubtract equations\n-36y = 72\ny = 72/-36\ny = -2\n\nSubstitute y\n5x + 2(-2) = 64/9\n5x = 100/9\nx = 100/9/5\nx = 20/9"} {"input": "Solve simultaneously:\n3x + 3y = -150/7\n8x + 3y = -155/7", "output": "3x + 3y = -150/7\n8x + 3y = -155/7\n\nUsing elimination\n8*(3x + 3y = -150/7)\n3*(8x + 3y = -155/7)\n24x + 24y = -1200/7\n24x + 9y = -465/7\nSubtract equations\n15y = -105\ny = -105/15\ny = -7\n\nSubstitute y\n3x + 3(-7) = -150/7\n3x = -3/7\nx = -3/7/3\nx = -1/7"} {"input": "Solve simultaneously:\n3x + 3y = 9/2\n3x + 5y = 27/10", "output": "3x + 3y = 9/2\n3x + 5y = 27/10\n\nUsing elimination\n3*(3x + 3y = 9/2)\n3*(3x + 5y = 27/10)\n9x + 9y = 27/2\n9x + 15y = 81/10\nSubtract equations\n-6y = 27/5\ny = 27/5/-6\ny = -9/10\n\nSubstitute y\n3x + 3(-9/10) = 9/2\n3x = 36/5\nx = 36/5/3\nx = 12/5"} {"input": "Solve simultaneously:\n4x + 6y = 16\n6x + 6y = 19", "output": "4x + 6y = 16\n6x + 6y = 19\n\nUsing elimination\n6*(4x + 6y = 16)\n4*(6x + 6y = 19)\n24x + 36y = 96\n24x + 24y = 76\nSubtract equations\n12y = 20\ny = 20/12\ny = 5/3\n\nSubstitute y\n4x + 6(5/3) = 16\n4x = 6\nx = 6/4\nx = 3/2"} {"input": "Solve the equation x^2 - 115/56x + 25/28 = 0", "output": "x^2 - 115/56x + 25/28 = 0\n(x - 5/8)(x - 10/7) = 0\nx - 5/8 = 0 or x - 10/7 = 0\nx = 5/8\nx = 10/7"} {"input": "Find x in 3x + 9 = 0", "output": "3x + 9 = 0\n3x = -9\nx = -9 / 3\nx = -3"} {"input": "Solve simultaneously:\n7x + 2y = -89/12\n10x + 4y = -73/6", "output": "7x + 2y = -89/12\n10x + 4y = -73/6\n\nUsing elimination\n10*(7x + 2y = -89/12)\n7*(10x + 4y = -73/6)\n70x + 20y = -445/6\n70x + 28y = -511/6\nSubtract equations\n-8y = 11\ny = 11/-8\ny = -11/8\n\nSubstitute y\n7x + 2(-11/8) = -89/12\n7x = -14/3\nx = -14/3/7\nx = -2/3"} {"input": "Find x in 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Find x and y such that\n7x + 9y = -9\n3x + 1y = -1", "output": "7x + 9y = -9\n3x + 1y = -1\n\nUsing elimination\n3*(7x + 9y = -9)\n7*(3x + 1y = -1)\n21x + 27y = -27\n21x + 7y = -7\nSubtract equations\n20y = -20\ny = -20/20\ny = -1\n\nSubstitute y\n7x + 9(-1) = -9\n7x = 0\nx = 0/7\nx = 0"} {"input": "Find x and y such that\n1x + 6y = -5/6\n3x + 8y = -65/18", "output": "1x + 6y = -5/6\n3x + 8y = -65/18\n\nUsing elimination\n3*(1x + 6y = -5/6)\n1*(3x + 8y = -65/18)\n3x + 18y = -5/2\n3x + 8y = -65/18\nSubtract equations\n10y = 10/9\ny = 10/9/10\ny = 1/9\n\nSubstitute y\n1x + 6(1/9) = -5/6\n1x = -3/2\nx = -3/2/1\nx = -3/2"} {"input": "Solve the equation 7x - 28 = 0", "output": "7x - 28 = 0\n7x = 28\nx = 28 / 7\nx = 4"} {"input": "Solve the equations:\n9x + 5y = 167/3\n2x + 3y = 13", "output": "9x + 5y = 167/3\n2x + 3y = 13\n\nUsing elimination\n2*(9x + 5y = 167/3)\n9*(2x + 3y = 13)\n18x + 10y = 334/3\n18x + 27y = 117\nSubtract equations\n-17y = -17/3\ny = -17/3/-17\ny = 1/3\n\nSubstitute y\n9x + 5(1/3) = 167/3\n9x = 54\nx = 54/9\nx = 6"} {"input": "Solve the equation 4x - 9/2 = 0", "output": "4x - 9/2 = 0\n4x = 9/2\nx = 9/2 / 4\nx = 9/8"} {"input": "Find x and y such that\n3x + 9y = 80/3\n2x + 8y = 220/9", "output": "3x + 9y = 80/3\n2x + 8y = 220/9\n\nUsing elimination\n2*(3x + 9y = 80/3)\n3*(2x + 8y = 220/9)\n6x + 18y = 160/3\n6x + 24y = 220/3\nSubtract equations\n-6y = -20\ny = -20/-6\ny = 10/3\n\nSubstitute y\n3x + 9(10/3) = 80/3\n3x = -10/3\nx = -10/3/3\nx = -10/9"} {"input": "Determine x in x^2 + 13x - 68 = 0", "output": "x^2 + 13x - 68 = 0\n(x - -17)(x - 4) = 0\nx - -17 = 0 or x - 4 = 0\nx = -17\nx = 4"} {"input": "Find the solution to x^2 + 12/5x - 13 = 0", "output": "x^2 + 12/5x - 13 = 0\n(x - 13/5)(x - -5) = 0\nx - 13/5 = 0 or x - -5 = 0\nx = 13/5\nx = -5"} {"input": "Find x and y such that\n7x + 8y = 53/5\n3x + 8y = -7/5", "output": "7x + 8y = 53/5\n3x + 8y = -7/5\n\nUsing elimination\n3*(7x + 8y = 53/5)\n7*(3x + 8y = -7/5)\n21x + 24y = 159/5\n21x + 56y = -49/5\nSubtract equations\n-32y = 208/5\ny = 208/5/-32\ny = -13/10\n\nSubstitute y\n7x + 8(-13/10) = 53/5\n7x = 21\nx = 21/7\nx = 3"} {"input": "Compute the solution of x^2 + 10x + 9 = 0", "output": "x^2 + 10x + 9 = 0\n(x - -9)(x - -1) = 0\nx - -9 = 0 or x - -1 = 0\nx = -9\nx = -1"} {"input": "Find the solution to 8x + 18 = 0", "output": "8x + 18 = 0\n8x = -18\nx = -18 / 8\nx = -9/4"} {"input": "Find x in x^3 - 249/40x^2 + 507/40x - 169/20 = 0", "output": "x^3 - 249/40x^2 + 507/40x - 169/20 = 0\n(x - 13/8)(x - 13/5)(x - 2) = 0\nx - 13/8 = 0\nx - 13/5 = 0\nx - 2 = 0\nx = 13/8\nx = 13/5\nx = 2"} {"input": "Solve the equation 7x + 5 = 0", "output": "7x + 5 = 0\n7x = -5\nx = -5 / 7\nx = -5/7"} {"input": "Solve the system:\n10x + 5y = -565/63\n8x + 5y = -425/63", "output": "10x + 5y = -565/63\n8x + 5y = -425/63\n\nUsing elimination\n8*(10x + 5y = -565/63)\n10*(8x + 5y = -425/63)\n80x + 40y = -4520/63\n80x + 50y = -4250/63\nSubtract equations\n-10y = -30/7\ny = -30/7/-10\ny = 3/7\n\nSubstitute y\n10x + 5(3/7) = -565/63\n10x = -100/9\nx = -100/9/10\nx = -10/9"} {"input": "Find the solution to x^3 - 289/42x^2 - 30/7x + 800/21 = 0", "output": "x^3 - 289/42x^2 - 30/7x + 800/21 = 0\n(x - 5/2)(x - 20/3)(x - -16/7) = 0\nx - 5/2 = 0\nx - 20/3 = 0\nx - -16/7 = 0\nx = 5/2\nx = 20/3\nx = -16/7"} {"input": "What value of x satisfies x^3 - 3/2x^2 - 253/64x + 195/32 = 0", "output": "x^3 - 3/2x^2 - 253/64x + 195/32 = 0\n(x - -2)(x - 13/8)(x - 15/8) = 0\nx - -2 = 0\nx - 13/8 = 0\nx - 15/8 = 0\nx = -2\nx = 13/8\nx = 15/8"} {"input": "Find x for x^3 + 114/7x^2 + 1532/49x - 72/7 = 0", "output": "x^3 + 114/7x^2 + 1532/49x - 72/7 = 0\n(x - 2/7)(x - -18/7)(x - -14) = 0\nx - 2/7 = 0\nx - -18/7 = 0\nx - -14 = 0\nx = 2/7\nx = -18/7\nx = -14"} {"input": "Solve x^3 - 141/28x^2 + 155/28x + 12/7 = 0", "output": "x^3 - 141/28x^2 + 155/28x + 12/7 = 0\n(x - 16/7)(x - 3)(x - -1/4) = 0\nx - 16/7 = 0\nx - 3 = 0\nx - -1/4 = 0\nx = 16/7\nx = 3\nx = -1/4"} {"input": "Find x for x^3 - 17/24x^2 - 1325/36x + 3553/72 = 0", "output": "x^3 - 17/24x^2 - 1325/36x + 3553/72 = 0\n(x - 17/3)(x - -19/3)(x - 11/8) = 0\nx - 17/3 = 0\nx - -19/3 = 0\nx - 11/8 = 0\nx = 17/3\nx = -19/3\nx = 11/8"} {"input": "What value of x satisfies x^2 + 8/3x - 11/3 = 0", "output": "x^2 + 8/3x - 11/3 = 0\n(x - -11/3)(x - 1) = 0\nx - -11/3 = 0 or x - 1 = 0\nx = -11/3\nx = 1"} {"input": "Solve quickly: x^2 - 13/6x - 19/6 = 0", "output": "x^2 - 13/6x - 19/6 = 0\n(x - -1)(x - 19/6) = 0\nx - -1 = 0 or x - 19/6 = 0\nx = -1\nx = 19/6"} {"input": "Determine x in x^3 - 563/35x^2 - 556/35x + 204/35 = 0", "output": "x^3 - 563/35x^2 - 556/35x + 204/35 = 0\n(x - -6/5)(x - 2/7)(x - 17) = 0\nx - -6/5 = 0\nx - 2/7 = 0\nx - 17 = 0\nx = -6/5\nx = 2/7\nx = 17"} {"input": "Solve the system:\n10x + 3y = -31\n9x + 2y = -53/2", "output": "10x + 3y = -31\n9x + 2y = -53/2\n\nUsing elimination\n9*(10x + 3y = -31)\n10*(9x + 2y = -53/2)\n90x + 27y = -279\n90x + 20y = -265\nSubtract equations\n7y = -14\ny = -14/7\ny = -2\n\nSubstitute y\n10x + 3(-2) = -31\n10x = -25\nx = -25/10\nx = -5/2"} {"input": "Solve x^3 + 67/10x^2 + 103/10x + 9/5 = 0", "output": "x^3 + 67/10x^2 + 103/10x + 9/5 = 0\n(x - -1/5)(x - -9/2)(x - -2) = 0\nx - -1/5 = 0\nx - -9/2 = 0\nx - -2 = 0\nx = -1/5\nx = -9/2\nx = -2"} {"input": "Determine x in 5x + 15 = 0", "output": "5x + 15 = 0\n5x = -15\nx = -15 / 5\nx = -3"} {"input": "Solve the equation x^3 + 7/2x^2 - 84x + 216 = 0", "output": "x^3 + 7/2x^2 - 84x + 216 = 0\n(x - -12)(x - 9/2)(x - 4) = 0\nx - -12 = 0\nx - 9/2 = 0\nx - 4 = 0\nx = -12\nx = 9/2\nx = 4"} {"input": "Find x and y such that\n5x + 4y = -185/3\n5x + 5y = -205/3", "output": "5x + 4y = -185/3\n5x + 5y = -205/3\n\nUsing elimination\n5*(5x + 4y = -185/3)\n5*(5x + 5y = -205/3)\n25x + 20y = -925/3\n25x + 25y = -1025/3\nSubtract equations\n-5y = 100/3\ny = 100/3/-5\ny = -20/3\n\nSubstitute y\n5x + 4(-20/3) = -185/3\n5x = -35\nx = -35/5\nx = -7"} {"input": "Find x and y such that\n9x + 8y = -493/40\n10x + 10y = -61/4", "output": "9x + 8y = -493/40\n10x + 10y = -61/4\n\nUsing elimination\n10*(9x + 8y = -493/40)\n9*(10x + 10y = -61/4)\n90x + 80y = -493/4\n90x + 90y = -549/4\nSubtract equations\n-10y = 14\ny = 14/-10\ny = -7/5\n\nSubstitute y\n9x + 8(-7/5) = -493/40\n9x = -9/8\nx = -9/8/9\nx = -1/8"} {"input": "Find the solution to x^3 + 29/6x^2 - 167/16x - 1235/24 = 0", "output": "x^3 + 29/6x^2 - 167/16x - 1235/24 = 0\n(x - -10/3)(x - -19/4)(x - 13/4) = 0\nx - -10/3 = 0\nx - -19/4 = 0\nx - 13/4 = 0\nx = -10/3\nx = -19/4\nx = 13/4"} {"input": "Solve the equation x^3 + 19/8x^2 - 57/32x + 9/32 = 0", "output": "x^3 + 19/8x^2 - 57/32x + 9/32 = 0\n(x - 1/4)(x - -3)(x - 3/8) = 0\nx - 1/4 = 0\nx - -3 = 0\nx - 3/8 = 0\nx = 1/4\nx = -3\nx = 3/8"} {"input": "Solve the system:\n6x + 4y = -5\n6x + 7y = -11", "output": "6x + 4y = -5\n6x + 7y = -11\n\nUsing elimination\n6*(6x + 4y = -5)\n6*(6x + 7y = -11)\n36x + 24y = -30\n36x + 42y = -66\nSubtract equations\n-18y = 36\ny = 36/-18\ny = -2\n\nSubstitute y\n6x + 4(-2) = -5\n6x = 3\nx = 3/6\nx = 1/2"} {"input": "Solve quickly: 1x + 18 = 0", "output": "1x + 18 = 0\n1x = -18\nx = -18 / 1\nx = -18"} {"input": "Solve simultaneously:\n2x + 5y = 13/5\n1x + 8y = 23/5", "output": "2x + 5y = 13/5\n1x + 8y = 23/5\n\nUsing elimination\n1*(2x + 5y = 13/5)\n2*(1x + 8y = 23/5)\n2x + 5y = 13/5\n2x + 16y = 46/5\nSubtract equations\n-11y = -33/5\ny = -33/5/-11\ny = 3/5\n\nSubstitute y\n2x + 5(3/5) = 13/5\n2x = -2/5\nx = -2/5/2\nx = -1/5"} {"input": "Solve x^2 - 7x - 60 = 0", "output": "x^2 - 7x - 60 = 0\n(x - 12)(x - -5) = 0\nx - 12 = 0 or x - -5 = 0\nx = 12\nx = -5"} {"input": "Solve the equation x^3 + 100/3x^2 + 281x + 90 = 0", "output": "x^3 + 100/3x^2 + 281x + 90 = 0\n(x - -1/3)(x - -18)(x - -15) = 0\nx - -1/3 = 0\nx - -18 = 0\nx - -15 = 0\nx = -1/3\nx = -18\nx = -15"} {"input": "Find x for x^2 - 41/10x + 4 = 0", "output": "x^2 - 41/10x + 4 = 0\n(x - 5/2)(x - 8/5) = 0\nx - 5/2 = 0 or x - 8/5 = 0\nx = 5/2\nx = 8/5"} {"input": "Compute the solution of x^3 + 11/5x^2 - 144/25x - 324/125 = 0", "output": "x^3 + 11/5x^2 - 144/25x - 324/125 = 0\n(x - -18/5)(x - -2/5)(x - 9/5) = 0\nx - -18/5 = 0\nx - -2/5 = 0\nx - 9/5 = 0\nx = -18/5\nx = -2/5\nx = 9/5"} {"input": "Find x and y such that\n3x + 5y = -15/8\n8x + 5y = -5", "output": "3x + 5y = -15/8\n8x + 5y = -5\n\nUsing elimination\n8*(3x + 5y = -15/8)\n3*(8x + 5y = -5)\n24x + 40y = -15\n24x + 15y = -15\nSubtract equations\n25y = 0\ny = 0/25\ny = 0\n\nSubstitute y\n3x + 5(0) = -15/8\n3x = -15/8\nx = -15/8/3\nx = -5/8"} {"input": "Find x in x^2 - 2/9x - 11/9 = 0", "output": "x^2 - 2/9x - 11/9 = 0\n(x - 11/9)(x - -1) = 0\nx - 11/9 = 0 or x - -1 = 0\nx = 11/9\nx = -1"} {"input": "Solve 7x - 7/8 = 0", "output": "7x - 7/8 = 0\n7x = 7/8\nx = 7/8 / 7\nx = 1/8"} {"input": "Compute the solution of 3x - 27/7 = 0", "output": "3x - 27/7 = 0\n3x = 27/7\nx = 27/7 / 3\nx = 9/7"} {"input": "Find x in x^2 + 7/2x - 2 = 0", "output": "x^2 + 7/2x - 2 = 0\n(x - -4)(x - 1/2) = 0\nx - -4 = 0 or x - 1/2 = 0\nx = -4\nx = 1/2"} {"input": "Solve simultaneously:\n3x + 1y = 85/14\n3x + 10y = -115/7", "output": "3x + 1y = 85/14\n3x + 10y = -115/7\n\nUsing elimination\n3*(3x + 1y = 85/14)\n3*(3x + 10y = -115/7)\n9x + 3y = 255/14\n9x + 30y = -345/7\nSubtract equations\n-27y = 135/2\ny = 135/2/-27\ny = -5/2\n\nSubstitute y\n3x + 1(-5/2) = 85/14\n3x = 60/7\nx = 60/7/3\nx = 20/7"} {"input": "Determine x in x^2 + 65/3x + 66 = 0", "output": "x^2 + 65/3x + 66 = 0\n(x - -11/3)(x - -18) = 0\nx - -11/3 = 0 or x - -18 = 0\nx = -11/3\nx = -18"} {"input": "Solve simultaneously:\n3x + 5y = -32\n5x + 2y = -157/9", "output": "3x + 5y = -32\n5x + 2y = -157/9\n\nUsing elimination\n5*(3x + 5y = -32)\n3*(5x + 2y = -157/9)\n15x + 25y = -160\n15x + 6y = -157/3\nSubtract equations\n19y = -323/3\ny = -323/3/19\ny = -17/3\n\nSubstitute y\n3x + 5(-17/3) = -32\n3x = -11/3\nx = -11/3/3\nx = -11/9"} {"input": "Compute the solution of 7x - 14 = 0", "output": "7x - 14 = 0\n7x = 14\nx = 14 / 7\nx = 2"} {"input": "Determine x in x^3 + 5/9x^2 - 314/225x + 56/225 = 0", "output": "x^3 + 5/9x^2 - 314/225x + 56/225 = 0\n(x - 4/5)(x - 1/5)(x - -14/9) = 0\nx - 4/5 = 0\nx - 1/5 = 0\nx - -14/9 = 0\nx = 4/5\nx = 1/5\nx = -14/9"} {"input": "Find x for 5x - 35 = 0", "output": "5x - 35 = 0\n5x = 35\nx = 35 / 5\nx = 7"} {"input": "Solve simultaneously:\n10x + 6y = -666/5\n4x + 9y = -174/5", "output": "10x + 6y = -666/5\n4x + 9y = -174/5\n\nUsing elimination\n4*(10x + 6y = -666/5)\n10*(4x + 9y = -174/5)\n40x + 24y = -2664/5\n40x + 90y = -348\nSubtract equations\n-66y = -924/5\ny = -924/5/-66\ny = 14/5\n\nSubstitute y\n10x + 6(14/5) = -666/5\n10x = -150\nx = -150/10\nx = -15"} {"input": "Find the solution to x^2 + 10x - 11 = 0", "output": "x^2 + 10x - 11 = 0\n(x - 1)(x - -11) = 0\nx - 1 = 0 or x - -11 = 0\nx = 1\nx = -11"} {"input": "Find x for x^2 + 26/35x - 48/35 = 0", "output": "x^2 + 26/35x - 48/35 = 0\n(x - 6/7)(x - -8/5) = 0\nx - 6/7 = 0 or x - -8/5 = 0\nx = 6/7\nx = -8/5"} {"input": "What value of x satisfies x^2 + 18/7x - 9/7 = 0", "output": "x^2 + 18/7x - 9/7 = 0\n(x - 3/7)(x - -3) = 0\nx - 3/7 = 0 or x - -3 = 0\nx = 3/7\nx = -3"} {"input": "Solve the equation x^3 + 529/56x^2 + 1019/56x + 15/2 = 0", "output": "x^3 + 529/56x^2 + 1019/56x + 15/2 = 0\n(x - -7)(x - -15/8)(x - -4/7) = 0\nx - -7 = 0\nx - -15/8 = 0\nx - -4/7 = 0\nx = -7\nx = -15/8\nx = -4/7"} {"input": "Compute the solution of x^2 - 91/20x + 99/20 = 0", "output": "x^2 - 91/20x + 99/20 = 0\n(x - 9/5)(x - 11/4) = 0\nx - 9/5 = 0 or x - 11/4 = 0\nx = 9/5\nx = 11/4"} {"input": "Solve the system:\n5x + 10y = -925/7\n6x + 9y = -816/7", "output": "5x + 10y = -925/7\n6x + 9y = -816/7\n\nUsing elimination\n6*(5x + 10y = -925/7)\n5*(6x + 9y = -816/7)\n30x + 60y = -5550/7\n30x + 45y = -4080/7\nSubtract equations\n15y = -210\ny = -210/15\ny = -14\n\nSubstitute y\n5x + 10(-14) = -925/7\n5x = 55/7\nx = 55/7/5\nx = 11/7"} {"input": "Solve simultaneously:\n7x + 1y = -93/4\n9x + 9y = -351/4", "output": "7x + 1y = -93/4\n9x + 9y = -351/4\n\nUsing elimination\n9*(7x + 1y = -93/4)\n7*(9x + 9y = -351/4)\n63x + 9y = -837/4\n63x + 63y = -2457/4\nSubtract equations\n-54y = 405\ny = 405/-54\ny = -15/2\n\nSubstitute y\n7x + 1(-15/2) = -93/4\n7x = -63/4\nx = -63/4/7\nx = -9/4"} {"input": "Solve the equations:\n4x + 8y = -16/5\n5x + 8y = -24/5", "output": "4x + 8y = -16/5\n5x + 8y = -24/5\n\nUsing elimination\n5*(4x + 8y = -16/5)\n4*(5x + 8y = -24/5)\n20x + 40y = -16\n20x + 32y = -96/5\nSubtract equations\n8y = 16/5\ny = 16/5/8\ny = 2/5\n\nSubstitute y\n4x + 8(2/5) = -16/5\n4x = -32/5\nx = -32/5/4\nx = -8/5"} {"input": "What value of x satisfies x^3 + 19/4x^2 - 9x - 9 = 0", "output": "x^3 + 19/4x^2 - 9x - 9 = 0\n(x - -3/4)(x - -6)(x - 2) = 0\nx - -3/4 = 0\nx - -6 = 0\nx - 2 = 0\nx = -3/4\nx = -6\nx = 2"} {"input": "What value of x satisfies 4x - 16/3 = 0", "output": "4x - 16/3 = 0\n4x = 16/3\nx = 16/3 / 4\nx = 4/3"} {"input": "Solve simultaneously:\n4x + 10y = 164/7\n2x + 2y = 242/35", "output": "4x + 10y = 164/7\n2x + 2y = 242/35\n\nUsing elimination\n2*(4x + 10y = 164/7)\n4*(2x + 2y = 242/35)\n8x + 20y = 328/7\n8x + 8y = 968/35\nSubtract equations\n12y = 96/5\ny = 96/5/12\ny = 8/5\n\nSubstitute y\n4x + 10(8/5) = 164/7\n4x = 52/7\nx = 52/7/4\nx = 13/7"} {"input": "Find x for x^3 - 171/35x^2 - 342/35x + 648/35 = 0", "output": "x^3 - 171/35x^2 - 342/35x + 648/35 = 0\n(x - 6)(x - -12/5)(x - 9/7) = 0\nx - 6 = 0\nx - -12/5 = 0\nx - 9/7 = 0\nx = 6\nx = -12/5\nx = 9/7"} {"input": "Find x for 8x + 26 = 0", "output": "8x + 26 = 0\n8x = -26\nx = -26 / 8\nx = -13/4"} {"input": "Solve the system:\n1x + 3y = -31/18\n1x + 5y = -49/18", "output": "1x + 3y = -31/18\n1x + 5y = -49/18\n\nUsing elimination\n1*(1x + 3y = -31/18)\n1*(1x + 5y = -49/18)\n1x + 3y = -31/18\n1x + 5y = -49/18\nSubtract equations\n-2y = 1\ny = 1/-2\ny = -1/2\n\nSubstitute y\n1x + 3(-1/2) = -31/18\n1x = -2/9\nx = -2/9/1\nx = -2/9"} {"input": "Solve the equation x^2 + 43/5x - 14 = 0", "output": "x^2 + 43/5x - 14 = 0\n(x - -10)(x - 7/5) = 0\nx - -10 = 0 or x - 7/5 = 0\nx = -10\nx = 7/5"} {"input": "Find the solution to 4x - 2 = 0", "output": "4x - 2 = 0\n4x = 2\nx = 2 / 4\nx = 1/2"} {"input": "Determine x in x^2 + 4/5x - 9/5 = 0", "output": "x^2 + 4/5x - 9/5 = 0\n(x - -9/5)(x - 1) = 0\nx - -9/5 = 0 or x - 1 = 0\nx = -9/5\nx = 1"} {"input": "Determine x in x^3 + 3/4x^2 - 69/4x - 17 = 0", "output": "x^3 + 3/4x^2 - 69/4x - 17 = 0\n(x - -1)(x - -4)(x - 17/4) = 0\nx - -1 = 0\nx - -4 = 0\nx - 17/4 = 0\nx = -1\nx = -4\nx = 17/4"} {"input": "Find x for x^3 - 23/7x^2 + 8/7x + 20/7 = 0", "output": "x^3 - 23/7x^2 + 8/7x + 20/7 = 0\n(x - 2)(x - 2)(x - -5/7) = 0\nx - 2 = 0\nx - 2 = 0\nx - -5/7 = 0\nx = 2\nx = 2\nx = -5/7"} {"input": "Find x in x^3 + 49/9x^2 - 374/81x - 208/27 = 0", "output": "x^3 + 49/9x^2 - 374/81x - 208/27 = 0\n(x - -6)(x - -8/9)(x - 13/9) = 0\nx - -6 = 0\nx - -8/9 = 0\nx - 13/9 = 0\nx = -6\nx = -8/9\nx = 13/9"} {"input": "What value of x satisfies x^3 + 103/30x^2 - 79/10x - 52/3 = 0", "output": "x^3 + 103/30x^2 - 79/10x - 52/3 = 0\n(x - 5/2)(x - -13/3)(x - -8/5) = 0\nx - 5/2 = 0\nx - -13/3 = 0\nx - -8/5 = 0\nx = 5/2\nx = -13/3\nx = -8/5"} {"input": "Solve the system:\n5x + 9y = -193/2\n10x + 9y = -323/2", "output": "5x + 9y = -193/2\n10x + 9y = -323/2\n\nUsing elimination\n10*(5x + 9y = -193/2)\n5*(10x + 9y = -323/2)\n50x + 90y = -965\n50x + 45y = -1615/2\nSubtract equations\n45y = -315/2\ny = -315/2/45\ny = -7/2\n\nSubstitute y\n5x + 9(-7/2) = -193/2\n5x = -65\nx = -65/5\nx = -13"} {"input": "What value of x satisfies x^3 + 107/21x^2 + 10/7x - 8/3 = 0", "output": "x^3 + 107/21x^2 + 10/7x - 8/3 = 0\n(x - -1)(x - 4/7)(x - -14/3) = 0\nx - -1 = 0\nx - 4/7 = 0\nx - -14/3 = 0\nx = -1\nx = 4/7\nx = -14/3"} {"input": "Find x in 6x + 22 = 0", "output": "6x + 22 = 0\n6x = -22\nx = -22 / 6\nx = -11/3"} {"input": "Find the solution to x^3 + 15/8x^2 + 11/16x = 0", "output": "x^3 + 15/8x^2 + 11/16x = 0\n(x - -1/2)(x - 0)(x - -11/8) = 0\nx - -1/2 = 0\nx - 0 = 0\nx - -11/8 = 0\nx = -1/2\nx = 0\nx = -11/8"} {"input": "Solve the system:\n5x + 7y = 56/9\n2x + 10y = 80/9", "output": "5x + 7y = 56/9\n2x + 10y = 80/9\n\nUsing elimination\n2*(5x + 7y = 56/9)\n5*(2x + 10y = 80/9)\n10x + 14y = 112/9\n10x + 50y = 400/9\nSubtract equations\n-36y = -32\ny = -32/-36\ny = 8/9\n\nSubstitute y\n5x + 7(8/9) = 56/9\n5x = 0\nx = 0/5\nx = 0"} {"input": "Find x and y such that\n2x + 2y = -67/9\n2x + 10y = -247/9", "output": "2x + 2y = -67/9\n2x + 10y = -247/9\n\nUsing elimination\n2*(2x + 2y = -67/9)\n2*(2x + 10y = -247/9)\n4x + 4y = -134/9\n4x + 20y = -494/9\nSubtract equations\n-16y = 40\ny = 40/-16\ny = -5/2\n\nSubstitute y\n2x + 2(-5/2) = -67/9\n2x = -22/9\nx = -22/9/2\nx = -11/9"} {"input": "Determine x in x^2 - 87/35x + 54/35 = 0", "output": "x^2 - 87/35x + 54/35 = 0\n(x - 6/5)(x - 9/7) = 0\nx - 6/5 = 0 or x - 9/7 = 0\nx = 6/5\nx = 9/7"} {"input": "What value of x satisfies x^3 - 24/5x^2 + 16/5x = 0", "output": "x^3 - 24/5x^2 + 16/5x = 0\n(x - 0)(x - 4)(x - 4/5) = 0\nx - 0 = 0\nx - 4 = 0\nx - 4/5 = 0\nx = 0\nx = 4\nx = 4/5"} {"input": "Find the solution to x^3 - 40/21x^2 - 199/21x + 110/7 = 0", "output": "x^3 - 40/21x^2 - 199/21x + 110/7 = 0\n(x - 10/3)(x - -3)(x - 11/7) = 0\nx - 10/3 = 0\nx - -3 = 0\nx - 11/7 = 0\nx = 10/3\nx = -3\nx = 11/7"} {"input": "Find the solution to 5x - 25/2 = 0", "output": "5x - 25/2 = 0\n5x = 25/2\nx = 25/2 / 5\nx = 5/2"} {"input": "Find x in x^2 + 77/15x - 38/5 = 0", "output": "x^2 + 77/15x - 38/5 = 0\n(x - -19/3)(x - 6/5) = 0\nx - -19/3 = 0 or x - 6/5 = 0\nx = -19/3\nx = 6/5"} {"input": "Find x for x^3 + 1151/360x^2 - 209/120x - 21/20 = 0", "output": "x^3 + 1151/360x^2 - 209/120x - 21/20 = 0\n(x - -3/8)(x - 7/9)(x - -18/5) = 0\nx - -3/8 = 0\nx - 7/9 = 0\nx - -18/5 = 0\nx = -3/8\nx = 7/9\nx = -18/5"} {"input": "Solve the equation x^2 - 81/14x - 90/7 = 0", "output": "x^2 - 81/14x - 90/7 = 0\n(x - 15/2)(x - -12/7) = 0\nx - 15/2 = 0 or x - -12/7 = 0\nx = 15/2\nx = -12/7"} {"input": "Solve the system:\n4x + 2y = 90/7\n6x + 9y = 153/7", "output": "4x + 2y = 90/7\n6x + 9y = 153/7\n\nUsing elimination\n6*(4x + 2y = 90/7)\n4*(6x + 9y = 153/7)\n24x + 12y = 540/7\n24x + 36y = 612/7\nSubtract equations\n-24y = -72/7\ny = -72/7/-24\ny = 3/7\n\nSubstitute y\n4x + 2(3/7) = 90/7\n4x = 12\nx = 12/4\nx = 3"} {"input": "What value of x satisfies x^2 - 2x + 1 = 0", "output": "x^2 - 2x + 1 = 0\n(x - 1)(x - 1) = 0\nx - 1 = 0 or x - 1 = 0\nx = 1\nx = 1"} {"input": "Find x for x^2 - 26/15x + 8/15 = 0", "output": "x^2 - 26/15x + 8/15 = 0\n(x - 2/5)(x - 4/3) = 0\nx - 2/5 = 0 or x - 4/3 = 0\nx = 2/5\nx = 4/3"} {"input": "Compute the solution of x^2 - 13/5x + 22/25 = 0", "output": "x^2 - 13/5x + 22/25 = 0\n(x - 11/5)(x - 2/5) = 0\nx - 11/5 = 0 or x - 2/5 = 0\nx = 11/5\nx = 2/5"} {"input": "What value of x satisfies 6x - 54/5 = 0", "output": "6x - 54/5 = 0\n6x = 54/5\nx = 54/5 / 6\nx = 9/5"} {"input": "Determine x in x^3 - 4x^2 - 185/4x - 57 = 0", "output": "x^3 - 4x^2 - 185/4x - 57 = 0\n(x - 19/2)(x - -3/2)(x - -4) = 0\nx - 19/2 = 0\nx - -3/2 = 0\nx - -4 = 0\nx = 19/2\nx = -3/2\nx = -4"} {"input": "Find the solution to x^2 - 4/3x - 11/12 = 0", "output": "x^2 - 4/3x - 11/12 = 0\n(x - 11/6)(x - -1/2) = 0\nx - 11/6 = 0 or x - -1/2 = 0\nx = 11/6\nx = -1/2"} {"input": "Find x for 6x + 102/7 = 0", "output": "6x + 102/7 = 0\n6x = -102/7\nx = -102/7 / 6\nx = -17/7"} {"input": "Compute the solution of x^3 - 26/5x^2 + 12/5x + 1512/125 = 0", "output": "x^3 - 26/5x^2 + 12/5x + 1512/125 = 0\n(x - -6/5)(x - 14/5)(x - 18/5) = 0\nx - -6/5 = 0\nx - 14/5 = 0\nx - 18/5 = 0\nx = -6/5\nx = 14/5\nx = 18/5"} {"input": "Find the solution to x^3 + 113/24x^2 + 2x - 10/3 = 0", "output": "x^3 + 113/24x^2 + 2x - 10/3 = 0\n(x - 5/8)(x - -4)(x - -4/3) = 0\nx - 5/8 = 0\nx - -4 = 0\nx - -4/3 = 0\nx = 5/8\nx = -4\nx = -4/3"} {"input": "What value of x satisfies 7x + 21/4 = 0", "output": "7x + 21/4 = 0\n7x = -21/4\nx = -21/4 / 7\nx = -3/4"} {"input": "Find x for x^3 + 203/9x^2 + 1420/27x + 800/27 = 0", "output": "x^3 + 203/9x^2 + 1420/27x + 800/27 = 0\n(x - -8/9)(x - -5/3)(x - -20) = 0\nx - -8/9 = 0\nx - -5/3 = 0\nx - -20 = 0\nx = -8/9\nx = -5/3\nx = -20"} {"input": "Solve x^3 + 21/2x^2 + 1739/64x + 1197/64 = 0", "output": "x^3 + 21/2x^2 + 1739/64x + 1197/64 = 0\n(x - -19/8)(x - -7)(x - -9/8) = 0\nx - -19/8 = 0\nx - -7 = 0\nx - -9/8 = 0\nx = -19/8\nx = -7\nx = -9/8"} {"input": "What value of x satisfies x^2 + 23/7x + 16/7 = 0", "output": "x^2 + 23/7x + 16/7 = 0\n(x - -16/7)(x - -1) = 0\nx - -16/7 = 0 or x - -1 = 0\nx = -16/7\nx = -1"} {"input": "Solve quickly: x^3 + 13/3x^2 - 10/3x = 0", "output": "x^3 + 13/3x^2 - 10/3x = 0\n(x - 0)(x - 2/3)(x - -5) = 0\nx - 0 = 0\nx - 2/3 = 0\nx - -5 = 0\nx = 0\nx = 2/3\nx = -5"} {"input": "Find x for x^3 + 15/8x^2 - 225/16x + 125/16 = 0", "output": "x^3 + 15/8x^2 - 225/16x + 125/16 = 0\n(x - -5)(x - 5/8)(x - 5/2) = 0\nx - -5 = 0\nx - 5/8 = 0\nx - 5/2 = 0\nx = -5\nx = 5/8\nx = 5/2"} {"input": "Solve the equations:\n5x + 5y = 155/8\n8x + 9y = 34", "output": "5x + 5y = 155/8\n8x + 9y = 34\n\nUsing elimination\n8*(5x + 5y = 155/8)\n5*(8x + 9y = 34)\n40x + 40y = 155\n40x + 45y = 170\nSubtract equations\n-5y = -15\ny = -15/-5\ny = 3\n\nSubstitute y\n5x + 5(3) = 155/8\n5x = 35/8\nx = 35/8/5\nx = 7/8"} {"input": "Solve the system:\n5x + 7y = -19/2\n3x + 9y = -21/2", "output": "5x + 7y = -19/2\n3x + 9y = -21/2\n\nUsing elimination\n3*(5x + 7y = -19/2)\n5*(3x + 9y = -21/2)\n15x + 21y = -57/2\n15x + 45y = -105/2\nSubtract equations\n-24y = 24\ny = 24/-24\ny = -1\n\nSubstitute y\n5x + 7(-1) = -19/2\n5x = -5/2\nx = -5/2/5\nx = -1/2"} {"input": "Solve 8x + 72/5 = 0", "output": "8x + 72/5 = 0\n8x = -72/5\nx = -72/5 / 8\nx = -9/5"} {"input": "What value of x satisfies x^3 - 17/2x^2 + 19x - 15/2 = 0", "output": "x^3 - 17/2x^2 + 19x - 15/2 = 0\n(x - 1/2)(x - 3)(x - 5) = 0\nx - 1/2 = 0\nx - 3 = 0\nx - 5 = 0\nx = 1/2\nx = 3\nx = 5"} {"input": "Find x and y such that\n3x + 2y = 17/4\n5x + 7y = 181/24", "output": "3x + 2y = 17/4\n5x + 7y = 181/24\n\nUsing elimination\n5*(3x + 2y = 17/4)\n3*(5x + 7y = 181/24)\n15x + 10y = 85/4\n15x + 21y = 181/8\nSubtract equations\n-11y = -11/8\ny = -11/8/-11\ny = 1/8\n\nSubstitute y\n3x + 2(1/8) = 17/4\n3x = 4\nx = 4/3\nx = 4/3"} {"input": "Determine x in 6x - 57/4 = 0", "output": "6x - 57/4 = 0\n6x = 57/4\nx = 57/4 / 6\nx = 19/8"} {"input": "Solve simultaneously:\n1x + 10y = 0\n6x + 3y = 57/2", "output": "1x + 10y = 0\n6x + 3y = 57/2\n\nUsing elimination\n6*(1x + 10y = 0)\n1*(6x + 3y = 57/2)\n6x + 60y = 0\n6x + 3y = 57/2\nSubtract equations\n57y = -57/2\ny = -57/2/57\ny = -1/2\n\nSubstitute y\n1x + 10(-1/2) = 0\n1x = 5\nx = 5/1\nx = 5"} {"input": "Determine x in x^2 + 157/70x + 44/35 = 0", "output": "x^2 + 157/70x + 44/35 = 0\n(x - -11/10)(x - -8/7) = 0\nx - -11/10 = 0 or x - -8/7 = 0\nx = -11/10\nx = -8/7"} {"input": "What value of x satisfies x^3 - 5/7x^2 - 554/49x - 360/49 = 0", "output": "x^3 - 5/7x^2 - 554/49x - 360/49 = 0\n(x - 4)(x - -18/7)(x - -5/7) = 0\nx - 4 = 0\nx - -18/7 = 0\nx - -5/7 = 0\nx = 4\nx = -18/7\nx = -5/7"} {"input": "Find x for x^3 + 137/24x^2 + 1039/96x + 1309/192 = 0", "output": "x^3 + 137/24x^2 + 1039/96x + 1309/192 = 0\n(x - -11/6)(x - -17/8)(x - -7/4) = 0\nx - -11/6 = 0\nx - -17/8 = 0\nx - -7/4 = 0\nx = -11/6\nx = -17/8\nx = -7/4"} {"input": "Find x for x^3 + 95/6x^2 + 109/3x - 13/2 = 0", "output": "x^3 + 95/6x^2 + 109/3x - 13/2 = 0\n(x - -3)(x - -13)(x - 1/6) = 0\nx - -3 = 0\nx - -13 = 0\nx - 1/6 = 0\nx = -3\nx = -13\nx = 1/6"} {"input": "Determine x in x^3 + 134/15x^2 - 843/5x + 1292/3 = 0", "output": "x^3 + 134/15x^2 - 843/5x + 1292/3 = 0\n(x - -19)(x - 20/3)(x - 17/5) = 0\nx - -19 = 0\nx - 20/3 = 0\nx - 17/5 = 0\nx = -19\nx = 20/3\nx = 17/5"} {"input": "Solve the equation 3x + 57/2 = 0", "output": "3x + 57/2 = 0\n3x = -57/2\nx = -57/2 / 3\nx = -19/2"} {"input": "Solve the equation x^2 + 1x - 6 = 0", "output": "x^2 + 1x - 6 = 0\n(x - 2)(x - -3) = 0\nx - 2 = 0 or x - -3 = 0\nx = 2\nx = -3"} {"input": "Solve x^3 + 29/30x^2 - 1061/75x + 364/25 = 0", "output": "x^3 + 29/30x^2 - 1061/75x + 364/25 = 0\n(x - 13/10)(x - 12/5)(x - -14/3) = 0\nx - 13/10 = 0\nx - 12/5 = 0\nx - -14/3 = 0\nx = 13/10\nx = 12/5\nx = -14/3"} {"input": "Find x for 8x + 76/5 = 0", "output": "8x + 76/5 = 0\n8x = -76/5\nx = -76/5 / 8\nx = -19/10"} {"input": "Solve x^3 - 241/28x^2 - 815/28x + 429/14 = 0", "output": "x^3 - 241/28x^2 - 815/28x + 429/14 = 0\n(x - -13/4)(x - 11)(x - 6/7) = 0\nx - -13/4 = 0\nx - 11 = 0\nx - 6/7 = 0\nx = -13/4\nx = 11\nx = 6/7"} {"input": "Solve x^3 - 47/5x^2 + 343/20x + 221/20 = 0", "output": "x^3 - 47/5x^2 + 343/20x + 221/20 = 0\n(x - 17/5)(x - 13/2)(x - -1/2) = 0\nx - 17/5 = 0\nx - 13/2 = 0\nx - -1/2 = 0\nx = 17/5\nx = 13/2\nx = -1/2"} {"input": "Compute the solution of 2x - 18/7 = 0", "output": "2x - 18/7 = 0\n2x = 18/7\nx = 18/7 / 2\nx = 9/7"} {"input": "Find x for x^2 + 3x + 2 = 0", "output": "x^2 + 3x + 2 = 0\n(x - -1)(x - -2) = 0\nx - -1 = 0 or x - -2 = 0\nx = -1\nx = -2"} {"input": "Compute the solution of 6x - 39 = 0", "output": "6x - 39 = 0\n6x = 39\nx = 39 / 6\nx = 13/2"} {"input": "Solve the system:\n9x + 7y = 157/4\n2x + 8y = 2/3", "output": "9x + 7y = 157/4\n2x + 8y = 2/3\n\nUsing elimination\n2*(9x + 7y = 157/4)\n9*(2x + 8y = 2/3)\n18x + 14y = 157/2\n18x + 72y = 6\nSubtract equations\n-58y = 145/2\ny = 145/2/-58\ny = -5/4\n\nSubstitute y\n9x + 7(-5/4) = 157/4\n9x = 48\nx = 48/9\nx = 16/3"} {"input": "Solve simultaneously:\n6x + 3y = 231/4\n6x + 4y = 307/4", "output": "6x + 3y = 231/4\n6x + 4y = 307/4\n\nUsing elimination\n6*(6x + 3y = 231/4)\n6*(6x + 4y = 307/4)\n36x + 18y = 693/2\n36x + 24y = 921/2\nSubtract equations\n-6y = -114\ny = -114/-6\ny = 19\n\nSubstitute y\n6x + 3(19) = 231/4\n6x = 3/4\nx = 3/4/6\nx = 1/8"} {"input": "Find the solution to x^2 - 9 = 0", "output": "x^2 - 9 = 0\n(x - 3)(x - -3) = 0\nx - 3 = 0 or x - -3 = 0\nx = 3\nx = -3"} {"input": "Find x in x^3 + 13/70x^2 - 157/350x - 3/25 = 0", "output": "x^3 + 13/70x^2 - 157/350x - 3/25 = 0\n(x - -3/5)(x - 7/10)(x - -2/7) = 0\nx - -3/5 = 0\nx - 7/10 = 0\nx - -2/7 = 0\nx = -3/5\nx = 7/10\nx = -2/7"} {"input": "Solve simultaneously:\n8x + 2y = 179/6\n4x + 4y = 83/3", "output": "8x + 2y = 179/6\n4x + 4y = 83/3\n\nUsing elimination\n4*(8x + 2y = 179/6)\n8*(4x + 4y = 83/3)\n32x + 8y = 358/3\n32x + 32y = 664/3\nSubtract equations\n-24y = -102\ny = -102/-24\ny = 17/4\n\nSubstitute y\n8x + 2(17/4) = 179/6\n8x = 64/3\nx = 64/3/8\nx = 8/3"} {"input": "Solve quickly: x^2 - 29/10x - 63/25 = 0", "output": "x^2 - 29/10x - 63/25 = 0\n(x - 18/5)(x - -7/10) = 0\nx - 18/5 = 0 or x - -7/10 = 0\nx = 18/5\nx = -7/10"} {"input": "What value of x satisfies 8x + 16 = 0", "output": "8x + 16 = 0\n8x = -16\nx = -16 / 8\nx = -2"} {"input": "Solve simultaneously:\n4x + 2y = 9/4\n1x + 6y = 5/4", "output": "4x + 2y = 9/4\n1x + 6y = 5/4\n\nUsing elimination\n1*(4x + 2y = 9/4)\n4*(1x + 6y = 5/4)\n4x + 2y = 9/4\n4x + 24y = 5\nSubtract equations\n-22y = -11/4\ny = -11/4/-22\ny = 1/8\n\nSubstitute y\n4x + 2(1/8) = 9/4\n4x = 2\nx = 2/4\nx = 1/2"} {"input": "Solve the system:\n5x + 7y = 23/2\n7x + 4y = 8/5", "output": "5x + 7y = 23/2\n7x + 4y = 8/5\n\nUsing elimination\n7*(5x + 7y = 23/2)\n5*(7x + 4y = 8/5)\n35x + 49y = 161/2\n35x + 20y = 8\nSubtract equations\n29y = 145/2\ny = 145/2/29\ny = 5/2\n\nSubstitute y\n5x + 7(5/2) = 23/2\n5x = -6\nx = -6/5\nx = -6/5"} {"input": "Solve the equation x^2 - 17/6x + 5/6 = 0", "output": "x^2 - 17/6x + 5/6 = 0\n(x - 1/3)(x - 5/2) = 0\nx - 1/3 = 0 or x - 5/2 = 0\nx = 1/3\nx = 5/2"} {"input": "Solve the equation 6x + 120/7 = 0", "output": "6x + 120/7 = 0\n6x = -120/7\nx = -120/7 / 6\nx = -20/7"} {"input": "Find x for x^2 - 13/3x + 10/3 = 0", "output": "x^2 - 13/3x + 10/3 = 0\n(x - 1)(x - 10/3) = 0\nx - 1 = 0 or x - 10/3 = 0\nx = 1\nx = 10/3"} {"input": "Find the solution to x^2 + 35/12x - 19/24 = 0", "output": "x^2 + 35/12x - 19/24 = 0\n(x - -19/6)(x - 1/4) = 0\nx - -19/6 = 0 or x - 1/4 = 0\nx = -19/6\nx = 1/4"} {"input": "Solve simultaneously:\n6x + 2y = 102\n6x + 3y = 99", "output": "6x + 2y = 102\n6x + 3y = 99\n\nUsing elimination\n6*(6x + 2y = 102)\n6*(6x + 3y = 99)\n36x + 12y = 612\n36x + 18y = 594\nSubtract equations\n-6y = 18\ny = 18/-6\ny = -3\n\nSubstitute y\n6x + 2(-3) = 102\n6x = 108\nx = 108/6\nx = 18"} {"input": "Determine x in 10x - 5 = 0", "output": "10x - 5 = 0\n10x = 5\nx = 5 / 10\nx = 1/2"} {"input": "Find x for x^2 - 13/20x - 21/20 = 0", "output": "x^2 - 13/20x - 21/20 = 0\n(x - 7/5)(x - -3/4) = 0\nx - 7/5 = 0 or x - -3/4 = 0\nx = 7/5\nx = -3/4"} {"input": "Determine x in x^3 - 35/4x^2 + 109/8x + 187/8 = 0", "output": "x^3 - 35/4x^2 + 109/8x + 187/8 = 0\n(x - 11/2)(x - 17/4)(x - -1) = 0\nx - 11/2 = 0\nx - 17/4 = 0\nx - -1 = 0\nx = 11/2\nx = 17/4\nx = -1"} {"input": "Solve x^2 - 17/10x + 13/25 = 0", "output": "x^2 - 17/10x + 13/25 = 0\n(x - 13/10)(x - 2/5) = 0\nx - 13/10 = 0 or x - 2/5 = 0\nx = 13/10\nx = 2/5"} {"input": "Solve simultaneously:\n1x + 5y = 187/5\n10x + 5y = 59", "output": "1x + 5y = 187/5\n10x + 5y = 59\n\nUsing elimination\n10*(1x + 5y = 187/5)\n1*(10x + 5y = 59)\n10x + 50y = 374\n10x + 5y = 59\nSubtract equations\n45y = 315\ny = 315/45\ny = 7\n\nSubstitute y\n1x + 5(7) = 187/5\n1x = 12/5\nx = 12/5/1\nx = 12/5"} {"input": "Solve the system:\n6x + 8y = -22\n1x + 3y = -88/9", "output": "6x + 8y = -22\n1x + 3y = -88/9\n\nUsing elimination\n1*(6x + 8y = -22)\n6*(1x + 3y = -88/9)\n6x + 8y = -22\n6x + 18y = -176/3\nSubtract equations\n-10y = 110/3\ny = 110/3/-10\ny = -11/3\n\nSubstitute y\n6x + 8(-11/3) = -22\n6x = 22/3\nx = 22/3/6\nx = 11/9"} {"input": "Solve simultaneously:\n2x + 1y = 5\n4x + 9y = 10", "output": "2x + 1y = 5\n4x + 9y = 10\n\nUsing elimination\n4*(2x + 1y = 5)\n2*(4x + 9y = 10)\n8x + 4y = 20\n8x + 18y = 20\nSubtract equations\n-14y = 0\ny = 0/-14\ny = 0\n\nSubstitute y\n2x + 1(0) = 5\n2x = 5\nx = 5/2\nx = 5/2"} {"input": "Find x for x^3 + 6x^2 + 17/4x - 15/4 = 0", "output": "x^3 + 6x^2 + 17/4x - 15/4 = 0\n(x - -3/2)(x - -5)(x - 1/2) = 0\nx - -3/2 = 0\nx - -5 = 0\nx - 1/2 = 0\nx = -3/2\nx = -5\nx = 1/2"} {"input": "Determine x in 10x - 32 = 0", "output": "10x - 32 = 0\n10x = 32\nx = 32 / 10\nx = 16/5"} {"input": "What value of x satisfies x^3 - 141/20x^2 + 127/20x + 39/2 = 0", "output": "x^3 - 141/20x^2 + 127/20x + 39/2 = 0\n(x - 13/4)(x - -6/5)(x - 5) = 0\nx - 13/4 = 0\nx - -6/5 = 0\nx - 5 = 0\nx = 13/4\nx = -6/5\nx = 5"} {"input": "Solve simultaneously:\n4x + 5y = -99/2\n6x + 2y = -33", "output": "4x + 5y = -99/2\n6x + 2y = -33\n\nUsing elimination\n6*(4x + 5y = -99/2)\n4*(6x + 2y = -33)\n24x + 30y = -297\n24x + 8y = -132\nSubtract equations\n22y = -165\ny = -165/22\ny = -15/2\n\nSubstitute y\n4x + 5(-15/2) = -99/2\n4x = -12\nx = -12/4\nx = -3"} {"input": "What value of x satisfies x^3 + 115/12x^2 + 359/12x + 91/3 = 0", "output": "x^3 + 115/12x^2 + 359/12x + 91/3 = 0\n(x - -4)(x - -13/4)(x - -7/3) = 0\nx - -4 = 0\nx - -13/4 = 0\nx - -7/3 = 0\nx = -4\nx = -13/4\nx = -7/3"} {"input": "Solve simultaneously:\n9x + 6y = 234/5\n3x + 7y = 123/5", "output": "9x + 6y = 234/5\n3x + 7y = 123/5\n\nUsing elimination\n3*(9x + 6y = 234/5)\n9*(3x + 7y = 123/5)\n27x + 18y = 702/5\n27x + 63y = 1107/5\nSubtract equations\n-45y = -81\ny = -81/-45\ny = 9/5\n\nSubstitute y\n9x + 6(9/5) = 234/5\n9x = 36\nx = 36/9\nx = 4"} {"input": "Solve simultaneously:\n7x + 2y = 438/5\n3x + 7y = 243/5", "output": "7x + 2y = 438/5\n3x + 7y = 243/5\n\nUsing elimination\n3*(7x + 2y = 438/5)\n7*(3x + 7y = 243/5)\n21x + 6y = 1314/5\n21x + 49y = 1701/5\nSubtract equations\n-43y = -387/5\ny = -387/5/-43\ny = 9/5\n\nSubstitute y\n7x + 2(9/5) = 438/5\n7x = 84\nx = 84/7\nx = 12"} {"input": "Solve quickly: x^2 - 3/2x - 1 = 0", "output": "x^2 - 3/2x - 1 = 0\n(x - -1/2)(x - 2) = 0\nx - -1/2 = 0 or x - 2 = 0\nx = -1/2\nx = 2"} {"input": "Solve simultaneously:\n3x + 7y = -311/30\n3x + 3y = -77/10", "output": "3x + 7y = -311/30\n3x + 3y = -77/10\n\nUsing elimination\n3*(3x + 7y = -311/30)\n3*(3x + 3y = -77/10)\n9x + 21y = -311/10\n9x + 9y = -231/10\nSubtract equations\n12y = -8\ny = -8/12\ny = -2/3\n\nSubstitute y\n3x + 7(-2/3) = -311/30\n3x = -57/10\nx = -57/10/3\nx = -19/10"} {"input": "Solve the equations:\n8x + 3y = -26\n5x + 8y = 37/3", "output": "8x + 3y = -26\n5x + 8y = 37/3\n\nUsing elimination\n5*(8x + 3y = -26)\n8*(5x + 8y = 37/3)\n40x + 15y = -130\n40x + 64y = 296/3\nSubtract equations\n-49y = -686/3\ny = -686/3/-49\ny = 14/3\n\nSubstitute y\n8x + 3(14/3) = -26\n8x = -40\nx = -40/8\nx = -5"} {"input": "What value of x satisfies 10x = 0", "output": "10x = 0\n10x = 0\nx = 0 / 10\nx = 0"} {"input": "Find the solution to 6x - 30/7 = 0", "output": "6x - 30/7 = 0\n6x = 30/7\nx = 30/7 / 6\nx = 5/7"} {"input": "Compute the solution of x^3 + 5/7x^2 = 0", "output": "x^3 + 5/7x^2 = 0\n(x - -5/7)(x - 0)(x - 0) = 0\nx - -5/7 = 0\nx - 0 = 0\nx - 0 = 0\nx = -5/7\nx = 0\nx = 0"} {"input": "Determine x in x^3 - 7/9x^2 - 100/27x + 100/27 = 0", "output": "x^3 - 7/9x^2 - 100/27x + 100/27 = 0\n(x - 5/3)(x - 10/9)(x - -2) = 0\nx - 5/3 = 0\nx - 10/9 = 0\nx - -2 = 0\nx = 5/3\nx = 10/9\nx = -2"} {"input": "Compute the solution of x^2 + 101/18x - 52/9 = 0", "output": "x^2 + 101/18x - 52/9 = 0\n(x - -13/2)(x - 8/9) = 0\nx - -13/2 = 0 or x - 8/9 = 0\nx = -13/2\nx = 8/9"} {"input": "Determine x in x^2 - 25/2x + 77/2 = 0", "output": "x^2 - 25/2x + 77/2 = 0\n(x - 11/2)(x - 7) = 0\nx - 11/2 = 0 or x - 7 = 0\nx = 11/2\nx = 7"} {"input": "What value of x satisfies x^3 + 1/8x^2 - 61/32x + 15/64 = 0", "output": "x^3 + 1/8x^2 - 61/32x + 15/64 = 0\n(x - 5/4)(x - -3/2)(x - 1/8) = 0\nx - 5/4 = 0\nx - -3/2 = 0\nx - 1/8 = 0\nx = 5/4\nx = -3/2\nx = 1/8"} {"input": "Solve x^3 - 31/18x^2 - 181/225x + 133/150 = 0", "output": "x^3 - 31/18x^2 - 181/225x + 133/150 = 0\n(x - -7/9)(x - 19/10)(x - 3/5) = 0\nx - -7/9 = 0\nx - 19/10 = 0\nx - 3/5 = 0\nx = -7/9\nx = 19/10\nx = 3/5"} {"input": "Find x and y such that\n3x + 3y = 72/7\n5x + 9y = 160/7", "output": "3x + 3y = 72/7\n5x + 9y = 160/7\n\nUsing elimination\n5*(3x + 3y = 72/7)\n3*(5x + 9y = 160/7)\n15x + 15y = 360/7\n15x + 27y = 480/7\nSubtract equations\n-12y = -120/7\ny = -120/7/-12\ny = 10/7\n\nSubstitute y\n3x + 3(10/7) = 72/7\n3x = 6\nx = 6/3\nx = 2"} {"input": "Find x for x^2 - 47/9x - 14/3 = 0", "output": "x^2 - 47/9x - 14/3 = 0\n(x - -7/9)(x - 6) = 0\nx - -7/9 = 0 or x - 6 = 0\nx = -7/9\nx = 6"} {"input": "Solve 2x + 13/5 = 0", "output": "2x + 13/5 = 0\n2x = -13/5\nx = -13/5 / 2\nx = -13/10"} {"input": "Solve the equations:\n6x + 7y = 43/6\n2x + 8y = 10/3", "output": "6x + 7y = 43/6\n2x + 8y = 10/3\n\nUsing elimination\n2*(6x + 7y = 43/6)\n6*(2x + 8y = 10/3)\n12x + 14y = 43/3\n12x + 48y = 20\nSubtract equations\n-34y = -17/3\ny = -17/3/-34\ny = 1/6\n\nSubstitute y\n6x + 7(1/6) = 43/6\n6x = 6\nx = 6/6\nx = 1"} {"input": "Solve the system:\n2x + 10y = -1\n1x + 2y = 10", "output": "2x + 10y = -1\n1x + 2y = 10\n\nUsing elimination\n1*(2x + 10y = -1)\n2*(1x + 2y = 10)\n2x + 10y = -1\n2x + 4y = 20\nSubtract equations\n6y = -21\ny = -21/6\ny = -7/2\n\nSubstitute y\n2x + 10(-7/2) = -1\n2x = 34\nx = 34/2\nx = 17"} {"input": "Solve 1x + 13/9 = 0", "output": "1x + 13/9 = 0\n1x = -13/9\nx = -13/9 / 1\nx = -13/9"} {"input": "Solve simultaneously:\n10x + 9y = 23/8\n9x + 9y = 27/8", "output": "10x + 9y = 23/8\n9x + 9y = 27/8\n\nUsing elimination\n9*(10x + 9y = 23/8)\n10*(9x + 9y = 27/8)\n90x + 81y = 207/8\n90x + 90y = 135/4\nSubtract equations\n-9y = -63/8\ny = -63/8/-9\ny = 7/8\n\nSubstitute y\n10x + 9(7/8) = 23/8\n10x = -5\nx = -5/10\nx = -1/2"} {"input": "Find x in x^3 - 881/210x^2 - 1/7x + 323/30 = 0", "output": "x^3 - 881/210x^2 - 1/7x + 323/30 = 0\n(x - -7/5)(x - 17/7)(x - 19/6) = 0\nx - -7/5 = 0\nx - 17/7 = 0\nx - 19/6 = 0\nx = -7/5\nx = 17/7\nx = 19/6"} {"input": "Solve the system:\n1x + 1y = 29/7\n10x + 5y = 150/7", "output": "1x + 1y = 29/7\n10x + 5y = 150/7\n\nUsing elimination\n10*(1x + 1y = 29/7)\n1*(10x + 5y = 150/7)\n10x + 10y = 290/7\n10x + 5y = 150/7\nSubtract equations\n5y = 20\ny = 20/5\ny = 4\n\nSubstitute y\n1x + 1(4) = 29/7\n1x = 1/7\nx = 1/7/1\nx = 1/7"} {"input": "Solve the equation 1x - 5/4 = 0", "output": "1x - 5/4 = 0\n1x = 5/4\nx = 5/4 / 1\nx = 5/4"} {"input": "Solve 6x + 9 = 0", "output": "6x + 9 = 0\n6x = -9\nx = -9 / 6\nx = -3/2"} {"input": "What value of x satisfies x^2 - 13/20x - 18/5 = 0", "output": "x^2 - 13/20x - 18/5 = 0\n(x - 9/4)(x - -8/5) = 0\nx - 9/4 = 0 or x - -8/5 = 0\nx = 9/4\nx = -8/5"} {"input": "Solve simultaneously:\n7x + 3y = 170\n5x + 1y = 110", "output": "7x + 3y = 170\n5x + 1y = 110\n\nUsing elimination\n5*(7x + 3y = 170)\n7*(5x + 1y = 110)\n35x + 15y = 850\n35x + 7y = 770\nSubtract equations\n8y = 80\ny = 80/8\ny = 10\n\nSubstitute y\n7x + 3(10) = 170\n7x = 140\nx = 140/7\nx = 20"} {"input": "Find the solution to x^2 + 43/7x + 6/7 = 0", "output": "x^2 + 43/7x + 6/7 = 0\n(x - -6)(x - -1/7) = 0\nx - -6 = 0 or x - -1/7 = 0\nx = -6\nx = -1/7"} {"input": "Determine x in 8x - 16/7 = 0", "output": "8x - 16/7 = 0\n8x = 16/7\nx = 16/7 / 8\nx = 2/7"} {"input": "Find x in x^2 - 46/21x - 80/21 = 0", "output": "x^2 - 46/21x - 80/21 = 0\n(x - 10/3)(x - -8/7) = 0\nx - 10/3 = 0 or x - -8/7 = 0\nx = 10/3\nx = -8/7"} {"input": "Solve the system:\n3x + 6y = 19\n5x + 4y = 29/3", "output": "3x + 6y = 19\n5x + 4y = 29/3\n\nUsing elimination\n5*(3x + 6y = 19)\n3*(5x + 4y = 29/3)\n15x + 30y = 95\n15x + 12y = 29\nSubtract equations\n18y = 66\ny = 66/18\ny = 11/3\n\nSubstitute y\n3x + 6(11/3) = 19\n3x = -3\nx = -3/3\nx = -1"} {"input": "Find x for x^2 + 46/5x + 96/5 = 0", "output": "x^2 + 46/5x + 96/5 = 0\n(x - -16/5)(x - -6) = 0\nx - -16/5 = 0 or x - -6 = 0\nx = -16/5\nx = -6"} {"input": "Compute the solution of x^3 - 23/3x^2 - 41x + 143/3 = 0", "output": "x^3 - 23/3x^2 - 41x + 143/3 = 0\n(x - 1)(x - 11)(x - -13/3) = 0\nx - 1 = 0\nx - 11 = 0\nx - -13/3 = 0\nx = 1\nx = 11\nx = -13/3"} {"input": "Solve the equations:\n1x + 7y = -149/12\n5x + 7y = -157/12", "output": "1x + 7y = -149/12\n5x + 7y = -157/12\n\nUsing elimination\n5*(1x + 7y = -149/12)\n1*(5x + 7y = -157/12)\n5x + 35y = -745/12\n5x + 7y = -157/12\nSubtract equations\n28y = -49\ny = -49/28\ny = -7/4\n\nSubstitute y\n1x + 7(-7/4) = -149/12\n1x = -1/6\nx = -1/6/1\nx = -1/6"} {"input": "Find x and y such that\n2x + 6y = 198/7\n6x + 4y = 410/21", "output": "2x + 6y = 198/7\n6x + 4y = 410/21\n\nUsing elimination\n6*(2x + 6y = 198/7)\n2*(6x + 4y = 410/21)\n12x + 36y = 1188/7\n12x + 8y = 820/21\nSubtract equations\n28y = 392/3\ny = 392/3/28\ny = 14/3\n\nSubstitute y\n2x + 6(14/3) = 198/7\n2x = 2/7\nx = 2/7/2\nx = 1/7"} {"input": "Solve the equation x^3 + 3x^2 - 9/16x - 55/16 = 0", "output": "x^3 + 3x^2 - 9/16x - 55/16 = 0\n(x - -5/4)(x - -11/4)(x - 1) = 0\nx - -5/4 = 0\nx - -11/4 = 0\nx - 1 = 0\nx = -5/4\nx = -11/4\nx = 1"} {"input": "Solve x^3 + 119/24x^2 - 1535/144x + 175/36 = 0", "output": "x^3 + 119/24x^2 - 1535/144x + 175/36 = 0\n(x - 5/6)(x - -20/3)(x - 7/8) = 0\nx - 5/6 = 0\nx - -20/3 = 0\nx - 7/8 = 0\nx = 5/6\nx = -20/3\nx = 7/8"} {"input": "Find x for 2x + 2/5 = 0", "output": "2x + 2/5 = 0\n2x = -2/5\nx = -2/5 / 2\nx = -1/5"} {"input": "Solve quickly: x^2 - 41/8x - 21/4 = 0", "output": "x^2 - 41/8x - 21/4 = 0\n(x - -7/8)(x - 6) = 0\nx - -7/8 = 0 or x - 6 = 0\nx = -7/8\nx = 6"} {"input": "Solve the system:\n6x + 7y = -105\n10x + 8y = -1258/7", "output": "6x + 7y = -105\n10x + 8y = -1258/7\n\nUsing elimination\n10*(6x + 7y = -105)\n6*(10x + 8y = -1258/7)\n60x + 70y = -1050\n60x + 48y = -7548/7\nSubtract equations\n22y = 198/7\ny = 198/7/22\ny = 9/7\n\nSubstitute y\n6x + 7(9/7) = -105\n6x = -114\nx = -114/6\nx = -19"} {"input": "Compute the solution of x^2 + 39/20x + 9/10 = 0", "output": "x^2 + 39/20x + 9/10 = 0\n(x - -3/4)(x - -6/5) = 0\nx - -3/4 = 0 or x - -6/5 = 0\nx = -3/4\nx = -6/5"} {"input": "Solve quickly: 6x - 11 = 0", "output": "6x - 11 = 0\n6x = 11\nx = 11 / 6\nx = 11/6"} {"input": "Find x for x^2 - 46/5x - 8 = 0", "output": "x^2 - 46/5x - 8 = 0\n(x - -4/5)(x - 10) = 0\nx - -4/5 = 0 or x - 10 = 0\nx = -4/5\nx = 10"} {"input": "Solve quickly: x^2 + 1/2x - 3/2 = 0", "output": "x^2 + 1/2x - 3/2 = 0\n(x - -3/2)(x - 1) = 0\nx - -3/2 = 0 or x - 1 = 0\nx = -3/2\nx = 1"} {"input": "Find the solution to 4x - 16/3 = 0", "output": "4x - 16/3 = 0\n4x = 16/3\nx = 16/3 / 4\nx = 4/3"} {"input": "Solve the equations:\n4x + 3y = -1/5\n10x + 2y = -8/5", "output": "4x + 3y = -1/5\n10x + 2y = -8/5\n\nUsing elimination\n10*(4x + 3y = -1/5)\n4*(10x + 2y = -8/5)\n40x + 30y = -2\n40x + 8y = -32/5\nSubtract equations\n22y = 22/5\ny = 22/5/22\ny = 1/5\n\nSubstitute y\n4x + 3(1/5) = -1/5\n4x = -4/5\nx = -4/5/4\nx = -1/5"} {"input": "Find x and y such that\n3x + 8y = -18\n1x + 9y = -169/6", "output": "3x + 8y = -18\n1x + 9y = -169/6\n\nUsing elimination\n1*(3x + 8y = -18)\n3*(1x + 9y = -169/6)\n3x + 8y = -18\n3x + 27y = -169/2\nSubtract equations\n-19y = 133/2\ny = 133/2/-19\ny = -7/2\n\nSubstitute y\n3x + 8(-7/2) = -18\n3x = 10\nx = 10/3\nx = 10/3"} {"input": "Find x for 2x - 5/4 = 0", "output": "2x - 5/4 = 0\n2x = 5/4\nx = 5/4 / 2\nx = 5/8"} {"input": "Solve 5x - 35 = 0", "output": "5x - 35 = 0\n5x = 35\nx = 35 / 5\nx = 7"} {"input": "Solve the system:\n4x + 7y = -70/3\n6x + 3y = -5", "output": "4x + 7y = -70/3\n6x + 3y = -5\n\nUsing elimination\n6*(4x + 7y = -70/3)\n4*(6x + 3y = -5)\n24x + 42y = -140\n24x + 12y = -20\nSubtract equations\n30y = -120\ny = -120/30\ny = -4\n\nSubstitute y\n4x + 7(-4) = -70/3\n4x = 14/3\nx = 14/3/4\nx = 7/6"} {"input": "Solve x^3 - 31/3x^2 + 535/36x + 221/36 = 0", "output": "x^3 - 31/3x^2 + 535/36x + 221/36 = 0\n(x - -1/3)(x - 13/6)(x - 17/2) = 0\nx - -1/3 = 0\nx - 13/6 = 0\nx - 17/2 = 0\nx = -1/3\nx = 13/6\nx = 17/2"} {"input": "What value of x satisfies x^3 - 77/20x^2 - 49/10x + 68/5 = 0", "output": "x^3 - 77/20x^2 - 49/10x + 68/5 = 0\n(x - 8/5)(x - 17/4)(x - -2) = 0\nx - 8/5 = 0\nx - 17/4 = 0\nx - -2 = 0\nx = 8/5\nx = 17/4\nx = -2"} {"input": "Solve simultaneously:\n7x + 4y = -72/5\n7x + 10y = -21", "output": "7x + 4y = -72/5\n7x + 10y = -21\n\nUsing elimination\n7*(7x + 4y = -72/5)\n7*(7x + 10y = -21)\n49x + 28y = -504/5\n49x + 70y = -147\nSubtract equations\n-42y = 231/5\ny = 231/5/-42\ny = -11/10\n\nSubstitute y\n7x + 4(-11/10) = -72/5\n7x = -10\nx = -10/7\nx = -10/7"} {"input": "What value of x satisfies 1x - 16/7 = 0", "output": "1x - 16/7 = 0\n1x = 16/7\nx = 16/7 / 1\nx = 16/7"} {"input": "Find x for 5x - 25/3 = 0", "output": "5x - 25/3 = 0\n5x = 25/3\nx = 25/3 / 5\nx = 5/3"} {"input": "What value of x satisfies x^3 + 55/18x^2 - 137/18x - 5 = 0", "output": "x^3 + 55/18x^2 - 137/18x - 5 = 0\n(x - 2)(x - -5/9)(x - -9/2) = 0\nx - 2 = 0\nx - -5/9 = 0\nx - -9/2 = 0\nx = 2\nx = -5/9\nx = -9/2"} {"input": "Compute the solution of x^2 + 57/20x - 27/8 = 0", "output": "x^2 + 57/20x - 27/8 = 0\n(x - -15/4)(x - 9/10) = 0\nx - -15/4 = 0 or x - 9/10 = 0\nx = -15/4\nx = 9/10"} {"input": "Solve the equation 5x - 45/8 = 0", "output": "5x - 45/8 = 0\n5x = 45/8\nx = 45/8 / 5\nx = 9/8"} {"input": "Find x for 5x - 60/7 = 0", "output": "5x - 60/7 = 0\n5x = 60/7\nx = 60/7 / 5\nx = 12/7"} {"input": "Find x and y such that\n9x + 6y = -99/4\n7x + 8y = -18", "output": "9x + 6y = -99/4\n7x + 8y = -18\n\nUsing elimination\n7*(9x + 6y = -99/4)\n9*(7x + 8y = -18)\n63x + 42y = -693/4\n63x + 72y = -162\nSubtract equations\n-30y = -45/4\ny = -45/4/-30\ny = 3/8\n\nSubstitute y\n9x + 6(3/8) = -99/4\n9x = -27\nx = -27/9\nx = -3"} {"input": "Solve quickly: 1x + 2/3 = 0", "output": "1x + 2/3 = 0\n1x = -2/3\nx = -2/3 / 1\nx = -2/3"} {"input": "Find x in x^3 - 259/20x^2 + 601/20x - 11/2 = 0", "output": "x^3 - 259/20x^2 + 601/20x - 11/2 = 0\n(x - 1/5)(x - 11/4)(x - 10) = 0\nx - 1/5 = 0\nx - 11/4 = 0\nx - 10 = 0\nx = 1/5\nx = 11/4\nx = 10"} {"input": "Find x in x^3 + 109/30x^2 - 38/15x - 21/2 = 0", "output": "x^3 + 109/30x^2 - 38/15x - 21/2 = 0\n(x - 5/3)(x - -7/2)(x - -9/5) = 0\nx - 5/3 = 0\nx - -7/2 = 0\nx - -9/5 = 0\nx = 5/3\nx = -7/2\nx = -9/5"} {"input": "What value of x satisfies x^3 + 41/40x^2 - 179/200x + 13/100 = 0", "output": "x^3 + 41/40x^2 - 179/200x + 13/100 = 0\n(x - 2/5)(x - 1/5)(x - -13/8) = 0\nx - 2/5 = 0\nx - 1/5 = 0\nx - -13/8 = 0\nx = 2/5\nx = 1/5\nx = -13/8"} {"input": "Find the solution to x^2 + 163/21x + 272/21 = 0", "output": "x^2 + 163/21x + 272/21 = 0\n(x - -16/3)(x - -17/7) = 0\nx - -16/3 = 0 or x - -17/7 = 0\nx = -16/3\nx = -17/7"} {"input": "Solve quickly: x^3 + 23/10x^2 - 2x + 3/10 = 0", "output": "x^3 + 23/10x^2 - 2x + 3/10 = 0\n(x - 1/5)(x - -3)(x - 1/2) = 0\nx - 1/5 = 0\nx - -3 = 0\nx - 1/2 = 0\nx = 1/5\nx = -3\nx = 1/2"} {"input": "Find the solution to 9x + 135/7 = 0", "output": "9x + 135/7 = 0\n9x = -135/7\nx = -135/7 / 9\nx = -15/7"} {"input": "Solve quickly: x^3 - 233/60x^2 + 521/120x - 3/2 = 0", "output": "x^3 - 233/60x^2 + 521/120x - 3/2 = 0\n(x - 4/5)(x - 9/4)(x - 5/6) = 0\nx - 4/5 = 0\nx - 9/4 = 0\nx - 5/6 = 0\nx = 4/5\nx = 9/4\nx = 5/6"} {"input": "Solve quickly: x^2 - 11/10x - 7/2 = 0", "output": "x^2 - 11/10x - 7/2 = 0\n(x - 5/2)(x - -7/5) = 0\nx - 5/2 = 0 or x - -7/5 = 0\nx = 5/2\nx = -7/5"} {"input": "Determine x in 6x + 66 = 0", "output": "6x + 66 = 0\n6x = -66\nx = -66 / 6\nx = -11"} {"input": "Solve the system:\n4x + 3y = -22/3\n5x + 10y = -65/3", "output": "4x + 3y = -22/3\n5x + 10y = -65/3\n\nUsing elimination\n5*(4x + 3y = -22/3)\n4*(5x + 10y = -65/3)\n20x + 15y = -110/3\n20x + 40y = -260/3\nSubtract equations\n-25y = 50\ny = 50/-25\ny = -2\n\nSubstitute y\n4x + 3(-2) = -22/3\n4x = -4/3\nx = -4/3/4\nx = -1/3"} {"input": "Solve the system:\n8x + 4y = -74/7\n1x + 5y = -113/14", "output": "8x + 4y = -74/7\n1x + 5y = -113/14\n\nUsing elimination\n1*(8x + 4y = -74/7)\n8*(1x + 5y = -113/14)\n8x + 4y = -74/7\n8x + 40y = -452/7\nSubtract equations\n-36y = 54\ny = 54/-36\ny = -3/2\n\nSubstitute y\n8x + 4(-3/2) = -74/7\n8x = -32/7\nx = -32/7/8\nx = -4/7"} {"input": "Find x and y such that\n8x + 8y = -4/5\n7x + 9y = 29/10", "output": "8x + 8y = -4/5\n7x + 9y = 29/10\n\nUsing elimination\n7*(8x + 8y = -4/5)\n8*(7x + 9y = 29/10)\n56x + 56y = -28/5\n56x + 72y = 116/5\nSubtract equations\n-16y = -144/5\ny = -144/5/-16\ny = 9/5\n\nSubstitute y\n8x + 8(9/5) = -4/5\n8x = -76/5\nx = -76/5/8\nx = -19/10"} {"input": "Solve the equation x^2 - 28/15x - 32/15 = 0", "output": "x^2 - 28/15x - 32/15 = 0\n(x - 8/3)(x - -4/5) = 0\nx - 8/3 = 0 or x - -4/5 = 0\nx = 8/3\nx = -4/5"} {"input": "What value of x satisfies x^2 - 8x - 9 = 0", "output": "x^2 - 8x - 9 = 0\n(x - 9)(x - -1) = 0\nx - 9 = 0 or x - -1 = 0\nx = 9\nx = -1"} {"input": "Solve quickly: 8x - 128 = 0", "output": "8x - 128 = 0\n8x = 128\nx = 128 / 8\nx = 16"} {"input": "Solve simultaneously:\n7x + 4y = -80/7\n3x + 3y = -51/7", "output": "7x + 4y = -80/7\n3x + 3y = -51/7\n\nUsing elimination\n3*(7x + 4y = -80/7)\n7*(3x + 3y = -51/7)\n21x + 12y = -240/7\n21x + 21y = -51\nSubtract equations\n-9y = 117/7\ny = 117/7/-9\ny = -13/7\n\nSubstitute y\n7x + 4(-13/7) = -80/7\n7x = -4\nx = -4/7\nx = -4/7"} {"input": "Find x for x^3 + 4x^2 - 135/4x - 225/4 = 0", "output": "x^3 + 4x^2 - 135/4x - 225/4 = 0\n(x - -15/2)(x - -3/2)(x - 5) = 0\nx - -15/2 = 0\nx - -3/2 = 0\nx - 5 = 0\nx = -15/2\nx = -3/2\nx = 5"} {"input": "Solve quickly: 3x + 6 = 0", "output": "3x + 6 = 0\n3x = -6\nx = -6 / 3\nx = -2"} {"input": "Determine x in x^2 - 17/5x - 99/20 = 0", "output": "x^2 - 17/5x - 99/20 = 0\n(x - -11/10)(x - 9/2) = 0\nx - -11/10 = 0 or x - 9/2 = 0\nx = -11/10\nx = 9/2"} {"input": "Solve simultaneously:\n8x + 4y = -200/7\n2x + 4y = -86/7", "output": "8x + 4y = -200/7\n2x + 4y = -86/7\n\nUsing elimination\n2*(8x + 4y = -200/7)\n8*(2x + 4y = -86/7)\n16x + 8y = -400/7\n16x + 32y = -688/7\nSubtract equations\n-24y = 288/7\ny = 288/7/-24\ny = -12/7\n\nSubstitute y\n8x + 4(-12/7) = -200/7\n8x = -152/7\nx = -152/7/8\nx = -19/7"} {"input": "Find x and y such that\n9x + 1y = -157/15\n2x + 3y = -7/5", "output": "9x + 1y = -157/15\n2x + 3y = -7/5\n\nUsing elimination\n2*(9x + 1y = -157/15)\n9*(2x + 3y = -7/5)\n18x + 2y = -314/15\n18x + 27y = -63/5\nSubtract equations\n-25y = -25/3\ny = -25/3/-25\ny = 1/3\n\nSubstitute y\n9x + 1(1/3) = -157/15\n9x = -54/5\nx = -54/5/9\nx = -6/5"} {"input": "Solve 3x - 9/2 = 0", "output": "3x - 9/2 = 0\n3x = 9/2\nx = 9/2 / 3\nx = 3/2"} {"input": "Solve the equation 10x + 20/7 = 0", "output": "10x + 20/7 = 0\n10x = -20/7\nx = -20/7 / 10\nx = -2/7"} {"input": "Find x for x^2 - 37/9x + 38/9 = 0", "output": "x^2 - 37/9x + 38/9 = 0\n(x - 19/9)(x - 2) = 0\nx - 19/9 = 0 or x - 2 = 0\nx = 19/9\nx = 2"} {"input": "Find the solution to x^3 + 487/140x^2 - 379/56x - 969/280 = 0", "output": "x^3 + 487/140x^2 - 379/56x - 969/280 = 0\n(x - 17/10)(x - -19/4)(x - -3/7) = 0\nx - 17/10 = 0\nx - -19/4 = 0\nx - -3/7 = 0\nx = 17/10\nx = -19/4\nx = -3/7"} {"input": "Find x in 2x + 3/2 = 0", "output": "2x + 3/2 = 0\n2x = -3/2\nx = -3/2 / 2\nx = -3/4"} {"input": "Solve the system:\n9x + 10y = 123/4\n5x + 5y = 1135/72", "output": "9x + 10y = 123/4\n5x + 5y = 1135/72\n\nUsing elimination\n5*(9x + 10y = 123/4)\n9*(5x + 5y = 1135/72)\n45x + 50y = 615/4\n45x + 45y = 1135/8\nSubtract equations\n5y = 95/8\ny = 95/8/5\ny = 19/8\n\nSubstitute y\n9x + 10(19/8) = 123/4\n9x = 7\nx = 7/9\nx = 7/9"} {"input": "Solve quickly: x^2 + 11/2x + 68/9 = 0", "output": "x^2 + 11/2x + 68/9 = 0\n(x - -17/6)(x - -8/3) = 0\nx - -17/6 = 0 or x - -8/3 = 0\nx = -17/6\nx = -8/3"} {"input": "Solve the equations:\n1x + 3y = 4\n9x + 6y = 36", "output": "1x + 3y = 4\n9x + 6y = 36\n\nUsing elimination\n9*(1x + 3y = 4)\n1*(9x + 6y = 36)\n9x + 27y = 36\n9x + 6y = 36\nSubtract equations\n21y = 0\ny = 0/21\ny = 0\n\nSubstitute y\n1x + 3(0) = 4\n1x = 4\nx = 4/1\nx = 4"} {"input": "Find x and y such that\n9x + 2y = 141\n10x + 9y = 177", "output": "9x + 2y = 141\n10x + 9y = 177\n\nUsing elimination\n10*(9x + 2y = 141)\n9*(10x + 9y = 177)\n90x + 20y = 1410\n90x + 81y = 1593\nSubtract equations\n-61y = -183\ny = -183/-61\ny = 3\n\nSubstitute y\n9x + 2(3) = 141\n9x = 135\nx = 135/9\nx = 15"} {"input": "Solve 2x - 3 = 0", "output": "2x - 3 = 0\n2x = 3\nx = 3 / 2\nx = 3/2"} {"input": "Solve 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Find x and y such that\n3x + 3y = 57/8\n2x + 9y = 143/8", "output": "3x + 3y = 57/8\n2x + 9y = 143/8\n\nUsing elimination\n2*(3x + 3y = 57/8)\n3*(2x + 9y = 143/8)\n6x + 6y = 57/4\n6x + 27y = 429/8\nSubtract equations\n-21y = -315/8\ny = -315/8/-21\ny = 15/8\n\nSubstitute y\n3x + 3(15/8) = 57/8\n3x = 3/2\nx = 3/2/3\nx = 1/2"} {"input": "Solve simultaneously:\n9x + 8y = 286/35\n5x + 4y = 30/7", "output": "9x + 8y = 286/35\n5x + 4y = 30/7\n\nUsing elimination\n5*(9x + 8y = 286/35)\n9*(5x + 4y = 30/7)\n45x + 40y = 286/7\n45x + 36y = 270/7\nSubtract equations\n4y = 16/7\ny = 16/7/4\ny = 4/7\n\nSubstitute y\n9x + 8(4/7) = 286/35\n9x = 18/5\nx = 18/5/9\nx = 2/5"} {"input": "Solve simultaneously:\n7x + 3y = 1/3\n3x + 4y = 11", "output": "7x + 3y = 1/3\n3x + 4y = 11\n\nUsing elimination\n3*(7x + 3y = 1/3)\n7*(3x + 4y = 11)\n21x + 9y = 1\n21x + 28y = 77\nSubtract equations\n-19y = -76\ny = -76/-19\ny = 4\n\nSubstitute y\n7x + 3(4) = 1/3\n7x = -35/3\nx = -35/3/7\nx = -5/3"} {"input": "Solve simultaneously:\n9x + 10y = -311/8\n7x + 7y = -231/8", "output": "9x + 10y = -311/8\n7x + 7y = -231/8\n\nUsing elimination\n7*(9x + 10y = -311/8)\n9*(7x + 7y = -231/8)\n63x + 70y = -2177/8\n63x + 63y = -2079/8\nSubtract equations\n7y = -49/4\ny = -49/4/7\ny = -7/4\n\nSubstitute y\n9x + 10(-7/4) = -311/8\n9x = -171/8\nx = -171/8/9\nx = -19/8"} {"input": "Solve x^2 - 4/5x - 28/5 = 0", "output": "x^2 - 4/5x - 28/5 = 0\n(x - -2)(x - 14/5) = 0\nx - -2 = 0 or x - 14/5 = 0\nx = -2\nx = 14/5"} {"input": "Find the solution to x^3 - 281/30x^2 + 43/3x - 5/2 = 0", "output": "x^3 - 281/30x^2 + 43/3x - 5/2 = 0\n(x - 15/2)(x - 5/3)(x - 1/5) = 0\nx - 15/2 = 0\nx - 5/3 = 0\nx - 1/5 = 0\nx = 15/2\nx = 5/3\nx = 1/5"} {"input": "Find the solution to x^3 - 19/35x^2 - 99/35x - 9/7 = 0", "output": "x^3 - 19/35x^2 - 99/35x - 9/7 = 0\n(x - 15/7)(x - -1)(x - -3/5) = 0\nx - 15/7 = 0\nx - -1 = 0\nx - -3/5 = 0\nx = 15/7\nx = -1\nx = -3/5"} {"input": "Compute the solution of x^2 - 1 = 0", "output": "x^2 - 1 = 0\n(x - 1)(x - -1) = 0\nx - 1 = 0 or x - -1 = 0\nx = 1\nx = -1"} {"input": "Find x in x^2 + 200/63x + 128/63 = 0", "output": "x^2 + 200/63x + 128/63 = 0\n(x - -8/9)(x - -16/7) = 0\nx - -8/9 = 0 or x - -16/7 = 0\nx = -8/9\nx = -16/7"} {"input": "Solve the equation x^3 - 849/40x^2 + 199/8x - 15/2 = 0", "output": "x^3 - 849/40x^2 + 199/8x - 15/2 = 0\n(x - 3/5)(x - 5/8)(x - 20) = 0\nx - 3/5 = 0\nx - 5/8 = 0\nx - 20 = 0\nx = 3/5\nx = 5/8\nx = 20"} {"input": "What value of x satisfies 8x + 80/3 = 0", "output": "8x + 80/3 = 0\n8x = -80/3\nx = -80/3 / 8\nx = -10/3"} {"input": "Solve the system:\n5x + 2y = -1175/72\n1x + 10y = -1771/72", "output": "5x + 2y = -1175/72\n1x + 10y = -1771/72\n\nUsing elimination\n1*(5x + 2y = -1175/72)\n5*(1x + 10y = -1771/72)\n5x + 2y = -1175/72\n5x + 50y = -8855/72\nSubtract equations\n-48y = 320/3\ny = 320/3/-48\ny = -20/9\n\nSubstitute y\n5x + 2(-20/9) = -1175/72\n5x = -95/8\nx = -95/8/5\nx = -19/8"} {"input": "What value of x satisfies x^3 + 335/72x^2 + 1121/288x - 13/6 = 0", "output": "x^3 + 335/72x^2 + 1121/288x - 13/6 = 0\n(x - -13/4)(x - 3/8)(x - -16/9) = 0\nx - -13/4 = 0\nx - 3/8 = 0\nx - -16/9 = 0\nx = -13/4\nx = 3/8\nx = -16/9"} {"input": "Find x and y such that\n2x + 7y = 97/45\n10x + 3y = 773/45", "output": "2x + 7y = 97/45\n10x + 3y = 773/45\n\nUsing elimination\n10*(2x + 7y = 97/45)\n2*(10x + 3y = 773/45)\n20x + 70y = 194/9\n20x + 6y = 1546/45\nSubtract equations\n64y = -64/5\ny = -64/5/64\ny = -1/5\n\nSubstitute y\n2x + 7(-1/5) = 97/45\n2x = 32/9\nx = 32/9/2\nx = 16/9"} {"input": "What value of x satisfies x^3 - 263/60x^2 + 44/15x + 21/5 = 0", "output": "x^3 - 263/60x^2 + 44/15x + 21/5 = 0\n(x - -2/3)(x - 9/4)(x - 14/5) = 0\nx - -2/3 = 0\nx - 9/4 = 0\nx - 14/5 = 0\nx = -2/3\nx = 9/4\nx = 14/5"} {"input": "Find x for x^3 - 71/8x^2 + 2891/144x - 19/3 = 0", "output": "x^3 - 71/8x^2 + 2891/144x - 19/3 = 0\n(x - 16/3)(x - 19/6)(x - 3/8) = 0\nx - 16/3 = 0\nx - 19/6 = 0\nx - 3/8 = 0\nx = 16/3\nx = 19/6\nx = 3/8"} {"input": "Solve the equations:\n4x + 10y = 19\n7x + 6y = 57/5", "output": "4x + 10y = 19\n7x + 6y = 57/5\n\nUsing elimination\n7*(4x + 10y = 19)\n4*(7x + 6y = 57/5)\n28x + 70y = 133\n28x + 24y = 228/5\nSubtract equations\n46y = 437/5\ny = 437/5/46\ny = 19/10\n\nSubstitute y\n4x + 10(19/10) = 19\n4x = 0\nx = 0/4\nx = 0"} {"input": "Find x in 8x + 40 = 0", "output": "8x + 40 = 0\n8x = -40\nx = -40 / 8\nx = -5"} {"input": "Find x for 10x - 45 = 0", "output": "10x - 45 = 0\n10x = 45\nx = 45 / 10\nx = 9/2"} {"input": "Find the solution to 1x + 4 = 0", "output": "1x + 4 = 0\n1x = -4\nx = -4 / 1\nx = -4"} {"input": "Solve quickly: x^3 + 1/2x^2 - 71/16x - 9/8 = 0", "output": "x^3 + 1/2x^2 - 71/16x - 9/8 = 0\n(x - -1/4)(x - 2)(x - -9/4) = 0\nx - -1/4 = 0\nx - 2 = 0\nx - -9/4 = 0\nx = -1/4\nx = 2\nx = -9/4"} {"input": "Find x for 4x + 76/3 = 0", "output": "4x + 76/3 = 0\n4x = -76/3\nx = -76/3 / 4\nx = -19/3"} {"input": "Find x for x^2 - 23/63x - 22/21 = 0", "output": "x^2 - 23/63x - 22/21 = 0\n(x - -6/7)(x - 11/9) = 0\nx - -6/7 = 0 or x - 11/9 = 0\nx = -6/7\nx = 11/9"} {"input": "Solve simultaneously:\n8x + 9y = -157/10\n10x + 5y = -33/2", "output": "8x + 9y = -157/10\n10x + 5y = -33/2\n\nUsing elimination\n10*(8x + 9y = -157/10)\n8*(10x + 5y = -33/2)\n80x + 90y = -157\n80x + 40y = -132\nSubtract equations\n50y = -25\ny = -25/50\ny = -1/2\n\nSubstitute y\n8x + 9(-1/2) = -157/10\n8x = -56/5\nx = -56/5/8\nx = -7/5"} {"input": "Solve quickly: x^3 - 271/72x^2 - 535/54x - 119/24 = 0", "output": "x^3 - 271/72x^2 - 535/54x - 119/24 = 0\n(x - 17/3)(x - -7/9)(x - -9/8) = 0\nx - 17/3 = 0\nx - -7/9 = 0\nx - -9/8 = 0\nx = 17/3\nx = -7/9\nx = -9/8"} {"input": "Solve the equations:\n1x + 3y = -9\n6x + 3y = 31", "output": "1x + 3y = -9\n6x + 3y = 31\n\nUsing elimination\n6*(1x + 3y = -9)\n1*(6x + 3y = 31)\n6x + 18y = -54\n6x + 3y = 31\nSubtract equations\n15y = -85\ny = -85/15\ny = -17/3\n\nSubstitute y\n1x + 3(-17/3) = -9\n1x = 8\nx = 8/1\nx = 8"} {"input": "What value of x satisfies x^2 + 26/3x + 40/3 = 0", "output": "x^2 + 26/3x + 40/3 = 0\n(x - -20/3)(x - -2) = 0\nx - -20/3 = 0 or x - -2 = 0\nx = -20/3\nx = -2"} {"input": "Determine x in x^2 + 15/4x - 25/4 = 0", "output": "x^2 + 15/4x - 25/4 = 0\n(x - -5)(x - 5/4) = 0\nx - -5 = 0 or x - 5/4 = 0\nx = -5\nx = 5/4"} {"input": "What value of x satisfies x^2 + 10/3x + 1 = 0", "output": "x^2 + 10/3x + 1 = 0\n(x - -3)(x - -1/3) = 0\nx - -3 = 0 or x - -1/3 = 0\nx = -3\nx = -1/3"} {"input": "Find x and y such that\n9x + 9y = -9/8\n10x + 8y = -21/4", "output": "9x + 9y = -9/8\n10x + 8y = -21/4\n\nUsing elimination\n10*(9x + 9y = -9/8)\n9*(10x + 8y = -21/4)\n90x + 90y = -45/4\n90x + 72y = -189/4\nSubtract equations\n18y = 36\ny = 36/18\ny = 2\n\nSubstitute y\n9x + 9(2) = -9/8\n9x = -153/8\nx = -153/8/9\nx = -17/8"} {"input": "What value of x satisfies x^3 + 7/4x^2 - 69/8x - 135/8 = 0", "output": "x^3 + 7/4x^2 - 69/8x - 135/8 = 0\n(x - -9/4)(x - 3)(x - -5/2) = 0\nx - -9/4 = 0\nx - 3 = 0\nx - -5/2 = 0\nx = -9/4\nx = 3\nx = -5/2"} {"input": "Solve x^2 - 3/10x - 17/5 = 0", "output": "x^2 - 3/10x - 17/5 = 0\n(x - -17/10)(x - 2) = 0\nx - -17/10 = 0 or x - 2 = 0\nx = -17/10\nx = 2"} {"input": "Find x for 2x + 8/5 = 0", "output": "2x + 8/5 = 0\n2x = -8/5\nx = -8/5 / 2\nx = -4/5"} {"input": "Find the solution to x^2 + 117/10x - 18/5 = 0", "output": "x^2 + 117/10x - 18/5 = 0\n(x - -12)(x - 3/10) = 0\nx - -12 = 0 or x - 3/10 = 0\nx = -12\nx = 3/10"} {"input": "Determine x in x^3 - 29/9x^2 + 85/27x - 25/27 = 0", "output": "x^3 - 29/9x^2 + 85/27x - 25/27 = 0\n(x - 5/3)(x - 1)(x - 5/9) = 0\nx - 5/3 = 0\nx - 1 = 0\nx - 5/9 = 0\nx = 5/3\nx = 1\nx = 5/9"} {"input": "Find x and y such that\n10x + 1y = 801/35\n2x + 7y = -173/35", "output": "10x + 1y = 801/35\n2x + 7y = -173/35\n\nUsing elimination\n2*(10x + 1y = 801/35)\n10*(2x + 7y = -173/35)\n20x + 2y = 1602/35\n20x + 70y = -346/7\nSubtract equations\n-68y = 476/5\ny = 476/5/-68\ny = -7/5\n\nSubstitute y\n10x + 1(-7/5) = 801/35\n10x = 170/7\nx = 170/7/10\nx = 17/7"} {"input": "Solve simultaneously:\n4x + 6y = -116/21\n4x + 1y = -628/63", "output": "4x + 6y = -116/21\n4x + 1y = -628/63\n\nUsing elimination\n4*(4x + 6y = -116/21)\n4*(4x + 1y = -628/63)\n16x + 24y = -464/21\n16x + 4y = -2512/63\nSubtract equations\n20y = 160/9\ny = 160/9/20\ny = 8/9\n\nSubstitute y\n4x + 6(8/9) = -116/21\n4x = -76/7\nx = -76/7/4\nx = -19/7"} {"input": "Find the solution to 6x + 12 = 0", "output": "6x + 12 = 0\n6x = -12\nx = -12 / 6\nx = -2"} {"input": "Solve the equations:\n5x + 6y = 23\n3x + 9y = 96/5", "output": "5x + 6y = 23\n3x + 9y = 96/5\n\nUsing elimination\n3*(5x + 6y = 23)\n5*(3x + 9y = 96/5)\n15x + 18y = 69\n15x + 45y = 96\nSubtract equations\n-27y = -27\ny = -27/-27\ny = 1\n\nSubstitute y\n5x + 6(1) = 23\n5x = 17\nx = 17/5\nx = 17/5"} {"input": "Find x and y such that\n3x + 5y = -79/2\n4x + 3y = -16", "output": "3x + 5y = -79/2\n4x + 3y = -16\n\nUsing elimination\n4*(3x + 5y = -79/2)\n3*(4x + 3y = -16)\n12x + 20y = -158\n12x + 9y = -48\nSubtract equations\n11y = -110\ny = -110/11\ny = -10\n\nSubstitute y\n3x + 5(-10) = -79/2\n3x = 21/2\nx = 21/2/3\nx = 7/2"} {"input": "Find the solution to 10x - 70/9 = 0", "output": "10x - 70/9 = 0\n10x = 70/9\nx = 70/9 / 10\nx = 7/9"} {"input": "Solve the system:\n6x + 1y = -67/2\n6x + 8y = -179/2", "output": "6x + 1y = -67/2\n6x + 8y = -179/2\n\nUsing elimination\n6*(6x + 1y = -67/2)\n6*(6x + 8y = -179/2)\n36x + 6y = -201\n36x + 48y = -537\nSubtract equations\n-42y = 336\ny = 336/-42\ny = -8\n\nSubstitute y\n6x + 1(-8) = -67/2\n6x = -51/2\nx = -51/2/6\nx = -17/4"} {"input": "Solve the equation x^3 - 43/5x^2 - 771/20x - 27 = 0", "output": "x^3 - 43/5x^2 - 771/20x - 27 = 0\n(x - -5/2)(x - -9/10)(x - 12) = 0\nx - -5/2 = 0\nx - -9/10 = 0\nx - 12 = 0\nx = -5/2\nx = -9/10\nx = 12"} {"input": "Find x in x^2 + 37/8x + 165/32 = 0", "output": "x^2 + 37/8x + 165/32 = 0\n(x - -15/8)(x - -11/4) = 0\nx - -15/8 = 0 or x - -11/4 = 0\nx = -15/8\nx = -11/4"} {"input": "Solve the equation 10x + 50 = 0", "output": "10x + 50 = 0\n10x = -50\nx = -50 / 10\nx = -5"} {"input": "Solve the equation x^3 - 50/9x^2 - 997/9x + 182 = 0", "output": "x^3 - 50/9x^2 - 997/9x + 182 = 0\n(x - 14/9)(x - 13)(x - -9) = 0\nx - 14/9 = 0\nx - 13 = 0\nx - -9 = 0\nx = 14/9\nx = 13\nx = -9"} {"input": "Compute the solution of 2x + 8/9 = 0", "output": "2x + 8/9 = 0\n2x = -8/9\nx = -8/9 / 2\nx = -4/9"} {"input": "What value of x satisfies x^2 + 29/8x + 51/16 = 0", "output": "x^2 + 29/8x + 51/16 = 0\n(x - -17/8)(x - -3/2) = 0\nx - -17/8 = 0 or x - -3/2 = 0\nx = -17/8\nx = -3/2"} {"input": "Solve 5x - 5/7 = 0", "output": "5x - 5/7 = 0\n5x = 5/7\nx = 5/7 / 5\nx = 1/7"} {"input": "Find x for x^2 - 11/15x - 4/5 = 0", "output": "x^2 - 11/15x - 4/5 = 0\n(x - -3/5)(x - 4/3) = 0\nx - -3/5 = 0 or x - 4/3 = 0\nx = -3/5\nx = 4/3"} {"input": "Determine x in 1x - 7/4 = 0", "output": "1x - 7/4 = 0\n1x = 7/4\nx = 7/4 / 1\nx = 7/4"} {"input": "Solve the system:\n1x + 7y = 59/3\n1x + 1y = 11/3", "output": "1x + 7y = 59/3\n1x + 1y = 11/3\n\nUsing elimination\n1*(1x + 7y = 59/3)\n1*(1x + 1y = 11/3)\n1x + 7y = 59/3\n1x + 1y = 11/3\nSubtract equations\n6y = 16\ny = 16/6\ny = 8/3\n\nSubstitute y\n1x + 7(8/3) = 59/3\n1x = 1\nx = 1/1\nx = 1"} {"input": "What value of x satisfies 2x - 16/9 = 0", "output": "2x - 16/9 = 0\n2x = 16/9\nx = 16/9 / 2\nx = 8/9"} {"input": "Solve x^3 + 5/2x^2 - 2x - 3/2 = 0", "output": "x^3 + 5/2x^2 - 2x - 3/2 = 0\n(x - -1/2)(x - 1)(x - -3) = 0\nx - -1/2 = 0\nx - 1 = 0\nx - -3 = 0\nx = -1/2\nx = 1\nx = -3"} {"input": "Solve quickly: x^2 - 37/12x - 95/12 = 0", "output": "x^2 - 37/12x - 95/12 = 0\n(x - -5/3)(x - 19/4) = 0\nx - -5/3 = 0 or x - 19/4 = 0\nx = -5/3\nx = 19/4"} {"input": "Solve simultaneously:\n10x + 2y = -28\n8x + 2y = -25", "output": "10x + 2y = -28\n8x + 2y = -25\n\nUsing elimination\n8*(10x + 2y = -28)\n10*(8x + 2y = -25)\n80x + 16y = -224\n80x + 20y = -250\nSubtract equations\n-4y = 26\ny = 26/-4\ny = -13/2\n\nSubstitute y\n10x + 2(-13/2) = -28\n10x = -15\nx = -15/10\nx = -3/2"} {"input": "Determine x in x^2 - 121/18x - 35/6 = 0", "output": "x^2 - 121/18x - 35/6 = 0\n(x - 15/2)(x - -7/9) = 0\nx - 15/2 = 0 or x - -7/9 = 0\nx = 15/2\nx = -7/9"} {"input": "Determine x in x^2 + 7/5x + 2/5 = 0", "output": "x^2 + 7/5x + 2/5 = 0\n(x - -2/5)(x - -1) = 0\nx - -2/5 = 0 or x - -1 = 0\nx = -2/5\nx = -1"} {"input": "Find x for 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Compute the solution of x^3 + 49/18x^2 + 7/6x + 10/81 = 0", "output": "x^3 + 49/18x^2 + 7/6x + 10/81 = 0\n(x - -1/6)(x - -20/9)(x - -1/3) = 0\nx - -1/6 = 0\nx - -20/9 = 0\nx - -1/3 = 0\nx = -1/6\nx = -20/9\nx = -1/3"} {"input": "Solve 10x - 45/2 = 0", "output": "10x - 45/2 = 0\n10x = 45/2\nx = 45/2 / 10\nx = 9/4"} {"input": "Solve x^2 - 2x + 1 = 0", "output": "x^2 - 2x + 1 = 0\n(x - 1)(x - 1) = 0\nx - 1 = 0 or x - 1 = 0\nx = 1\nx = 1"} {"input": "Find x in x^2 - 25/6x + 19/6 = 0", "output": "x^2 - 25/6x + 19/6 = 0\n(x - 1)(x - 19/6) = 0\nx - 1 = 0 or x - 19/6 = 0\nx = 1\nx = 19/6"} {"input": "Solve the equations:\n6x + 2y = -62/3\n4x + 8y = -16", "output": "6x + 2y = -62/3\n4x + 8y = -16\n\nUsing elimination\n4*(6x + 2y = -62/3)\n6*(4x + 8y = -16)\n24x + 8y = -248/3\n24x + 48y = -96\nSubtract equations\n-40y = 40/3\ny = 40/3/-40\ny = -1/3\n\nSubstitute y\n6x + 2(-1/3) = -62/3\n6x = -20\nx = -20/6\nx = -10/3"} {"input": "Solve the equation x^3 + 134/15x^2 + 347/15x + 52/3 = 0", "output": "x^3 + 134/15x^2 + 347/15x + 52/3 = 0\n(x - -5)(x - -4/3)(x - -13/5) = 0\nx - -5 = 0\nx - -4/3 = 0\nx - -13/5 = 0\nx = -5\nx = -4/3\nx = -13/5"} {"input": "Solve the system:\n1x + 10y = 37/2\n4x + 8y = 10", "output": "1x + 10y = 37/2\n4x + 8y = 10\n\nUsing elimination\n4*(1x + 10y = 37/2)\n1*(4x + 8y = 10)\n4x + 40y = 74\n4x + 8y = 10\nSubtract equations\n32y = 64\ny = 64/32\ny = 2\n\nSubstitute y\n1x + 10(2) = 37/2\n1x = -3/2\nx = -3/2/1\nx = -3/2"} {"input": "Solve x^2 + 13x = 0", "output": "x^2 + 13x = 0\n(x - 0)(x - -13) = 0\nx - 0 = 0 or x - -13 = 0\nx = 0\nx = -13"} {"input": "Solve simultaneously:\n1x + 8y = -104/15\n9x + 4y = -256/15", "output": "1x + 8y = -104/15\n9x + 4y = -256/15\n\nUsing elimination\n9*(1x + 8y = -104/15)\n1*(9x + 4y = -256/15)\n9x + 72y = -312/5\n9x + 4y = -256/15\nSubtract equations\n68y = -136/3\ny = -136/3/68\ny = -2/3\n\nSubstitute y\n1x + 8(-2/3) = -104/15\n1x = -8/5\nx = -8/5/1\nx = -8/5"} {"input": "What value of x satisfies x^3 + 129/8x^2 + 993/16x + 1001/16 = 0", "output": "x^3 + 129/8x^2 + 993/16x + 1001/16 = 0\n(x - -13/8)(x - -7/2)(x - -11) = 0\nx - -13/8 = 0\nx - -7/2 = 0\nx - -11 = 0\nx = -13/8\nx = -7/2\nx = -11"} {"input": "Solve simultaneously:\n9x + 5y = -117/4\n2x + 3y = -13/2", "output": "9x + 5y = -117/4\n2x + 3y = -13/2\n\nUsing elimination\n2*(9x + 5y = -117/4)\n9*(2x + 3y = -13/2)\n18x + 10y = -117/2\n18x + 27y = -117/2\nSubtract equations\n-17y = 0\ny = 0/-17\ny = 0\n\nSubstitute y\n9x + 5(0) = -117/4\n9x = -117/4\nx = -117/4/9\nx = -13/4"} {"input": "Solve quickly: 1x + 11/5 = 0", "output": "1x + 11/5 = 0\n1x = -11/5\nx = -11/5 / 1\nx = -11/5"} {"input": "Solve quickly: x^2 - 47/28x + 5/14 = 0", "output": "x^2 - 47/28x + 5/14 = 0\n(x - 10/7)(x - 1/4) = 0\nx - 10/7 = 0 or x - 1/4 = 0\nx = 10/7\nx = 1/4"} {"input": "Solve the equations:\n1x + 7y = -107/12\n10x + 4y = -271/6", "output": "1x + 7y = -107/12\n10x + 4y = -271/6\n\nUsing elimination\n10*(1x + 7y = -107/12)\n1*(10x + 4y = -271/6)\n10x + 70y = -535/6\n10x + 4y = -271/6\nSubtract equations\n66y = -44\ny = -44/66\ny = -2/3\n\nSubstitute y\n1x + 7(-2/3) = -107/12\n1x = -17/4\nx = -17/4/1\nx = -17/4"} {"input": "Find x for 6x + 24 = 0", "output": "6x + 24 = 0\n6x = -24\nx = -24 / 6\nx = -4"} {"input": "What value of x satisfies 5x + 25/4 = 0", "output": "5x + 25/4 = 0\n5x = -25/4\nx = -25/4 / 5\nx = -5/4"} {"input": "Find the solution to x^2 + 32/3x - 91/3 = 0", "output": "x^2 + 32/3x - 91/3 = 0\n(x - -13)(x - 7/3) = 0\nx - -13 = 0 or x - 7/3 = 0\nx = -13\nx = 7/3"} {"input": "What value of x satisfies 7x - 126/5 = 0", "output": "7x - 126/5 = 0\n7x = 126/5\nx = 126/5 / 7\nx = 18/5"} {"input": "Determine x in x^3 - 1x^2 - 16x + 16 = 0", "output": "x^3 - 1x^2 - 16x + 16 = 0\n(x - -4)(x - 4)(x - 1) = 0\nx - -4 = 0\nx - 4 = 0\nx - 1 = 0\nx = -4\nx = 4\nx = 1"} {"input": "Solve the equation x^3 + 113/35x^2 - 16/35x - 204/35 = 0", "output": "x^3 + 113/35x^2 - 16/35x - 204/35 = 0\n(x - -17/7)(x - 6/5)(x - -2) = 0\nx - -17/7 = 0\nx - 6/5 = 0\nx - -2 = 0\nx = -17/7\nx = 6/5\nx = -2"} {"input": "Solve the equation x^2 - 99/5x + 162/5 = 0", "output": "x^2 - 99/5x + 162/5 = 0\n(x - 9/5)(x - 18) = 0\nx - 9/5 = 0 or x - 18 = 0\nx = 9/5\nx = 18"} {"input": "Find x for 7x + 70/9 = 0", "output": "7x + 70/9 = 0\n7x = -70/9\nx = -70/9 / 7\nx = -10/9"} {"input": "Solve x^2 + 123/40x + 9/4 = 0", "output": "x^2 + 123/40x + 9/4 = 0\n(x - -6/5)(x - -15/8) = 0\nx - -6/5 = 0 or x - -15/8 = 0\nx = -6/5\nx = -15/8"} {"input": "Find x in 5x - 25/7 = 0", "output": "5x - 25/7 = 0\n5x = 25/7\nx = 25/7 / 5\nx = 5/7"} {"input": "Find x in x^3 - 67/6x^2 + 27x - 40/3 = 0", "output": "x^3 - 67/6x^2 + 27x - 40/3 = 0\n(x - 8)(x - 5/2)(x - 2/3) = 0\nx - 8 = 0\nx - 5/2 = 0\nx - 2/3 = 0\nx = 8\nx = 5/2\nx = 2/3"} {"input": "Solve the system:\n1x + 2y = 48/5\n6x + 8y = 322/5", "output": "1x + 2y = 48/5\n6x + 8y = 322/5\n\nUsing elimination\n6*(1x + 2y = 48/5)\n1*(6x + 8y = 322/5)\n6x + 12y = 288/5\n6x + 8y = 322/5\nSubtract equations\n4y = -34/5\ny = -34/5/4\ny = -17/10\n\nSubstitute y\n1x + 2(-17/10) = 48/5\n1x = 13\nx = 13/1\nx = 13"} {"input": "Solve quickly: 10x + 11 = 0", "output": "10x + 11 = 0\n10x = -11\nx = -11 / 10\nx = -11/10"} {"input": "What value of x satisfies 6x + 3 = 0", "output": "6x + 3 = 0\n6x = -3\nx = -3 / 6\nx = -1/2"} {"input": "Find x in 8x + 13 = 0", "output": "8x + 13 = 0\n8x = -13\nx = -13 / 8\nx = -13/8"} {"input": "Find x in x^2 + 35/24x - 25/4 = 0", "output": "x^2 + 35/24x - 25/4 = 0\n(x - -10/3)(x - 15/8) = 0\nx - -10/3 = 0 or x - 15/8 = 0\nx = -10/3\nx = 15/8"} {"input": "Find the solution to 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "Determine x in 10x - 110/7 = 0", "output": "10x - 110/7 = 0\n10x = 110/7\nx = 110/7 / 10\nx = 11/7"} {"input": "Determine x in x^2 + 8/3x - 35/3 = 0", "output": "x^2 + 8/3x - 35/3 = 0\n(x - 7/3)(x - -5) = 0\nx - 7/3 = 0 or x - -5 = 0\nx = 7/3\nx = -5"} {"input": "Solve the equation x^2 + 29/8x + 13/4 = 0", "output": "x^2 + 29/8x + 13/4 = 0\n(x - -2)(x - -13/8) = 0\nx - -2 = 0 or x - -13/8 = 0\nx = -2\nx = -13/8"} {"input": "Solve 10x - 5 = 0", "output": "10x - 5 = 0\n10x = 5\nx = 5 / 10\nx = 1/2"} {"input": "Solve the equation x^3 - 16/15x^2 - 289/45x + 364/45 = 0", "output": "x^3 - 16/15x^2 - 289/45x + 364/45 = 0\n(x - -13/5)(x - 4/3)(x - 7/3) = 0\nx - -13/5 = 0\nx - 4/3 = 0\nx - 7/3 = 0\nx = -13/5\nx = 4/3\nx = 7/3"} {"input": "Find x in 7x - 91 = 0", "output": "7x - 91 = 0\n7x = 91\nx = 91 / 7\nx = 13"} {"input": "Solve the equations:\n3x + 3y = 18\n9x + 4y = 122/3", "output": "3x + 3y = 18\n9x + 4y = 122/3\n\nUsing elimination\n9*(3x + 3y = 18)\n3*(9x + 4y = 122/3)\n27x + 27y = 162\n27x + 12y = 122\nSubtract equations\n15y = 40\ny = 40/15\ny = 8/3\n\nSubstitute y\n3x + 3(8/3) = 18\n3x = 10\nx = 10/3\nx = 10/3"} {"input": "Solve simultaneously:\n8x + 1y = 133/6\n3x + 2y = 14", "output": "8x + 1y = 133/6\n3x + 2y = 14\n\nUsing elimination\n3*(8x + 1y = 133/6)\n8*(3x + 2y = 14)\n24x + 3y = 133/2\n24x + 16y = 112\nSubtract equations\n-13y = -91/2\ny = -91/2/-13\ny = 7/2\n\nSubstitute y\n8x + 1(7/2) = 133/6\n8x = 56/3\nx = 56/3/8\nx = 7/3"} {"input": "What value of x satisfies x^2 + 13x + 12 = 0", "output": "x^2 + 13x + 12 = 0\n(x - -12)(x - -1) = 0\nx - -12 = 0 or x - -1 = 0\nx = -12\nx = -1"} {"input": "Find x in x^3 + 11/10x^2 - 587/80x - 143/16 = 0", "output": "x^3 + 11/10x^2 - 587/80x - 143/16 = 0\n(x - -13/5)(x - 11/4)(x - -5/4) = 0\nx - -13/5 = 0\nx - 11/4 = 0\nx - -5/4 = 0\nx = -13/5\nx = 11/4\nx = -5/4"} {"input": "Find the solution to x^3 - 1147/504x^2 + 181/504x + 143/126 = 0", "output": "x^3 - 1147/504x^2 + 181/504x + 143/126 = 0\n(x - 13/8)(x - 11/9)(x - -4/7) = 0\nx - 13/8 = 0\nx - 11/9 = 0\nx - -4/7 = 0\nx = 13/8\nx = 11/9\nx = -4/7"} {"input": "Determine x in x^2 - 7/6x = 0", "output": "x^2 - 7/6x = 0\n(x - 0)(x - 7/6) = 0\nx - 0 = 0 or x - 7/6 = 0\nx = 0\nx = 7/6"} {"input": "Solve the equations:\n3x + 7y = -25/2\n5x + 5y = -25/6", "output": "3x + 7y = -25/2\n5x + 5y = -25/6\n\nUsing elimination\n5*(3x + 7y = -25/2)\n3*(5x + 5y = -25/6)\n15x + 35y = -125/2\n15x + 15y = -25/2\nSubtract equations\n20y = -50\ny = -50/20\ny = -5/2\n\nSubstitute y\n3x + 7(-5/2) = -25/2\n3x = 5\nx = 5/3\nx = 5/3"} {"input": "Solve quickly: x^3 + 19x^2 + 86x + 104 = 0", "output": "x^3 + 19x^2 + 86x + 104 = 0\n(x - -2)(x - -13)(x - -4) = 0\nx - -2 = 0\nx - -13 = 0\nx - -4 = 0\nx = -2\nx = -13\nx = -4"} {"input": "Solve the system:\n2x + 7y = 365/21\n4x + 4y = 380/21", "output": "2x + 7y = 365/21\n4x + 4y = 380/21\n\nUsing elimination\n4*(2x + 7y = 365/21)\n2*(4x + 4y = 380/21)\n8x + 28y = 1460/21\n8x + 8y = 760/21\nSubtract equations\n20y = 100/3\ny = 100/3/20\ny = 5/3\n\nSubstitute y\n2x + 7(5/3) = 365/21\n2x = 40/7\nx = 40/7/2\nx = 20/7"} {"input": "Solve the equation x^2 - 8/5x - 153/25 = 0", "output": "x^2 - 8/5x - 153/25 = 0\n(x - 17/5)(x - -9/5) = 0\nx - 17/5 = 0 or x - -9/5 = 0\nx = 17/5\nx = -9/5"} {"input": "What value of x satisfies x^3 - 173/42x^2 - 344/21x + 247/42 = 0", "output": "x^3 - 173/42x^2 - 344/21x + 247/42 = 0\n(x - 1/3)(x - 13/2)(x - -19/7) = 0\nx - 1/3 = 0\nx - 13/2 = 0\nx - -19/7 = 0\nx = 1/3\nx = 13/2\nx = -19/7"} {"input": "Find x and y such that\n7x + 5y = -43/3\n8x + 1y = -46/3", "output": "7x + 5y = -43/3\n8x + 1y = -46/3\n\nUsing elimination\n8*(7x + 5y = -43/3)\n7*(8x + 1y = -46/3)\n56x + 40y = -344/3\n56x + 7y = -322/3\nSubtract equations\n33y = -22/3\ny = -22/3/33\ny = -2/9\n\nSubstitute y\n7x + 5(-2/9) = -43/3\n7x = -119/9\nx = -119/9/7\nx = -17/9"} {"input": "Compute the solution of x^3 - 1x^2 - 5x - 3 = 0", "output": "x^3 - 1x^2 - 5x - 3 = 0\n(x - -1)(x - -1)(x - 3) = 0\nx - -1 = 0\nx - -1 = 0\nx - 3 = 0\nx = -1\nx = -1\nx = 3"} {"input": "Compute the solution of x^3 + 25/8x^2 - 17/2x + 35/8 = 0", "output": "x^3 + 25/8x^2 - 17/2x + 35/8 = 0\n(x - -5)(x - 1)(x - 7/8) = 0\nx - -5 = 0\nx - 1 = 0\nx - 7/8 = 0\nx = -5\nx = 1\nx = 7/8"} {"input": "Find x and y such that\n4x + 7y = -248/9\n3x + 8y = -241/9", "output": "4x + 7y = -248/9\n3x + 8y = -241/9\n\nUsing elimination\n3*(4x + 7y = -248/9)\n4*(3x + 8y = -241/9)\n12x + 21y = -248/3\n12x + 32y = -964/9\nSubtract equations\n-11y = 220/9\ny = 220/9/-11\ny = -20/9\n\nSubstitute y\n4x + 7(-20/9) = -248/9\n4x = -12\nx = -12/4\nx = -3"} {"input": "Solve the system:\n9x + 1y = -143/70\n6x + 7y = -43/5", "output": "9x + 1y = -143/70\n6x + 7y = -43/5\n\nUsing elimination\n6*(9x + 1y = -143/70)\n9*(6x + 7y = -43/5)\n54x + 6y = -429/35\n54x + 63y = -387/5\nSubtract equations\n-57y = 456/7\ny = 456/7/-57\ny = -8/7\n\nSubstitute y\n9x + 1(-8/7) = -143/70\n9x = -9/10\nx = -9/10/9\nx = -1/10"} {"input": "Solve x^3 + 71/8x^2 - 253/32x - 1197/64 = 0", "output": "x^3 + 71/8x^2 - 253/32x - 1197/64 = 0\n(x - 7/4)(x - -19/2)(x - -9/8) = 0\nx - 7/4 = 0\nx - -19/2 = 0\nx - -9/8 = 0\nx = 7/4\nx = -19/2\nx = -9/8"} {"input": "Find the solution to x^2 + 89/20x - 57/40 = 0", "output": "x^2 + 89/20x - 57/40 = 0\n(x - 3/10)(x - -19/4) = 0\nx - 3/10 = 0 or x - -19/4 = 0\nx = 3/10\nx = -19/4"} {"input": "Solve quickly: x^3 + 3/8x^2 - 35/32x - 9/32 = 0", "output": "x^3 + 3/8x^2 - 35/32x - 9/32 = 0\n(x - -1/4)(x - 1)(x - -9/8) = 0\nx - -1/4 = 0\nx - 1 = 0\nx - -9/8 = 0\nx = -1/4\nx = 1\nx = -9/8"} {"input": "Solve the equation x^3 - 31/8x^2 - 29/8x + 1105/128 = 0", "output": "x^3 - 31/8x^2 - 29/8x + 1105/128 = 0\n(x - 17/4)(x - -13/8)(x - 5/4) = 0\nx - 17/4 = 0\nx - -13/8 = 0\nx - 5/4 = 0\nx = 17/4\nx = -13/8\nx = 5/4"} {"input": "What value of x satisfies 9x - 54/7 = 0", "output": "9x - 54/7 = 0\n9x = 54/7\nx = 54/7 / 9\nx = 6/7"} {"input": "Solve x^2 - 29/4x - 171/8 = 0", "output": "x^2 - 29/4x - 171/8 = 0\n(x - -9/4)(x - 19/2) = 0\nx - -9/4 = 0 or x - 19/2 = 0\nx = -9/4\nx = 19/2"} {"input": "Find x in 7x + 21/10 = 0", "output": "7x + 21/10 = 0\n7x = -21/10\nx = -21/10 / 7\nx = -3/10"} {"input": "Solve quickly: x^2 + 13/3x + 14/3 = 0", "output": "x^2 + 13/3x + 14/3 = 0\n(x - -7/3)(x - -2) = 0\nx - -7/3 = 0 or x - -2 = 0\nx = -7/3\nx = -2"} {"input": "Solve the system:\n9x + 10y = -43\n6x + 9y = -69/2", "output": "9x + 10y = -43\n6x + 9y = -69/2\n\nUsing elimination\n6*(9x + 10y = -43)\n9*(6x + 9y = -69/2)\n54x + 60y = -258\n54x + 81y = -621/2\nSubtract equations\n-21y = 105/2\ny = 105/2/-21\ny = -5/2\n\nSubstitute y\n9x + 10(-5/2) = -43\n9x = -18\nx = -18/9\nx = -2"} {"input": "Solve x^3 + 313/35x^2 + 165/7x + 135/7 = 0", "output": "x^3 + 313/35x^2 + 165/7x + 135/7 = 0\n(x - -15/7)(x - -5)(x - -9/5) = 0\nx - -15/7 = 0\nx - -5 = 0\nx - -9/5 = 0\nx = -15/7\nx = -5\nx = -9/5"} {"input": "Find x for x^2 + 55/6x + 50/3 = 0", "output": "x^2 + 55/6x + 50/3 = 0\n(x - -20/3)(x - -5/2) = 0\nx - -20/3 = 0 or x - -5/2 = 0\nx = -20/3\nx = -5/2"} {"input": "Find x for x^2 - 3/4x - 7/4 = 0", "output": "x^2 - 3/4x - 7/4 = 0\n(x - 7/4)(x - -1) = 0\nx - 7/4 = 0 or x - -1 = 0\nx = 7/4\nx = -1"} {"input": "Solve the system:\n2x + 7y = 64/9\n9x + 9y = 17", "output": "2x + 7y = 64/9\n9x + 9y = 17\n\nUsing elimination\n9*(2x + 7y = 64/9)\n2*(9x + 9y = 17)\n18x + 63y = 64\n18x + 18y = 34\nSubtract equations\n45y = 30\ny = 30/45\ny = 2/3\n\nSubstitute y\n2x + 7(2/3) = 64/9\n2x = 22/9\nx = 22/9/2\nx = 11/9"} {"input": "Solve quickly: x^3 - 32/5x^2 + 29/5x + 6 = 0", "output": "x^3 - 32/5x^2 + 29/5x + 6 = 0\n(x - -3/5)(x - 2)(x - 5) = 0\nx - -3/5 = 0\nx - 2 = 0\nx - 5 = 0\nx = -3/5\nx = 2\nx = 5"} {"input": "Find x for x^2 + 1/45x - 28/45 = 0", "output": "x^2 + 1/45x - 28/45 = 0\n(x - 7/9)(x - -4/5) = 0\nx - 7/9 = 0 or x - -4/5 = 0\nx = 7/9\nx = -4/5"} {"input": "Solve the system:\n5x + 8y = 26\n8x + 5y = 26", "output": "5x + 8y = 26\n8x + 5y = 26\n\nUsing elimination\n8*(5x + 8y = 26)\n5*(8x + 5y = 26)\n40x + 64y = 208\n40x + 25y = 130\nSubtract equations\n39y = 78\ny = 78/39\ny = 2\n\nSubstitute y\n5x + 8(2) = 26\n5x = 10\nx = 10/5\nx = 2"} {"input": "Solve the system:\n10x + 1y = -348/5\n8x + 1y = -278/5", "output": "10x + 1y = -348/5\n8x + 1y = -278/5\n\nUsing elimination\n8*(10x + 1y = -348/5)\n10*(8x + 1y = -278/5)\n80x + 8y = -2784/5\n80x + 10y = -556\nSubtract equations\n-2y = -4/5\ny = -4/5/-2\ny = 2/5\n\nSubstitute y\n10x + 1(2/5) = -348/5\n10x = -70\nx = -70/10\nx = -7"} {"input": "Determine x in 10x - 7 = 0", "output": "10x - 7 = 0\n10x = 7\nx = 7 / 10\nx = 7/10"} {"input": "Solve quickly: 10x - 10 = 0", "output": "10x - 10 = 0\n10x = 10\nx = 10 / 10\nx = 1"} {"input": "Compute the solution of x^3 + 41/3x^2 + 52/3x - 32 = 0", "output": "x^3 + 41/3x^2 + 52/3x - 32 = 0\n(x - -12)(x - -8/3)(x - 1) = 0\nx - -12 = 0\nx - -8/3 = 0\nx - 1 = 0\nx = -12\nx = -8/3\nx = 1"} {"input": "Find the solution to x^2 - 43/63x - 88/63 = 0", "output": "x^2 - 43/63x - 88/63 = 0\n(x - 11/7)(x - -8/9) = 0\nx - 11/7 = 0 or x - -8/9 = 0\nx = 11/7\nx = -8/9"} {"input": "Find x in x^2 - 4x + 3 = 0", "output": "x^2 - 4x + 3 = 0\n(x - 1)(x - 3) = 0\nx - 1 = 0 or x - 3 = 0\nx = 1\nx = 3"} {"input": "Solve the system:\n1x + 4y = -77\n7x + 10y = -197", "output": "1x + 4y = -77\n7x + 10y = -197\n\nUsing elimination\n7*(1x + 4y = -77)\n1*(7x + 10y = -197)\n7x + 28y = -539\n7x + 10y = -197\nSubtract equations\n18y = -342\ny = -342/18\ny = -19\n\nSubstitute y\n1x + 4(-19) = -77\n1x = -1\nx = -1/1\nx = -1"} {"input": "Find the solution to x^2 + 4/3x + 5/12 = 0", "output": "x^2 + 4/3x + 5/12 = 0\n(x - -5/6)(x - -1/2) = 0\nx - -5/6 = 0 or x - -1/2 = 0\nx = -5/6\nx = -1/2"} {"input": "Find x for 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve quickly: 7x + 14 = 0", "output": "7x + 14 = 0\n7x = -14\nx = -14 / 7\nx = -2"} {"input": "Find x for 1x - 16 = 0", "output": "1x - 16 = 0\n1x = 16\nx = 16 / 1\nx = 16"} {"input": "Find the solution to 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Solve quickly: 9x - 72/5 = 0", "output": "9x - 72/5 = 0\n9x = 72/5\nx = 72/5 / 9\nx = 8/5"} {"input": "Solve simultaneously:\n5x + 1y = -339/56\n8x + 6y = -81/7", "output": "5x + 1y = -339/56\n8x + 6y = -81/7\n\nUsing elimination\n8*(5x + 1y = -339/56)\n5*(8x + 6y = -81/7)\n40x + 8y = -339/7\n40x + 30y = -405/7\nSubtract equations\n-22y = 66/7\ny = 66/7/-22\ny = -3/7\n\nSubstitute y\n5x + 1(-3/7) = -339/56\n5x = -45/8\nx = -45/8/5\nx = -9/8"} {"input": "Compute the solution of 6x + 10/3 = 0", "output": "6x + 10/3 = 0\n6x = -10/3\nx = -10/3 / 6\nx = -5/9"} {"input": "Solve the system:\n10x + 10y = -6\n7x + 10y = -81/5", "output": "10x + 10y = -6\n7x + 10y = -81/5\n\nUsing elimination\n7*(10x + 10y = -6)\n10*(7x + 10y = -81/5)\n70x + 70y = -42\n70x + 100y = -162\nSubtract equations\n-30y = 120\ny = 120/-30\ny = -4\n\nSubstitute y\n10x + 10(-4) = -6\n10x = 34\nx = 34/10\nx = 17/5"} {"input": "Solve simultaneously:\n1x + 3y = -58/5\n7x + 3y = -46/5", "output": "1x + 3y = -58/5\n7x + 3y = -46/5\n\nUsing elimination\n7*(1x + 3y = -58/5)\n1*(7x + 3y = -46/5)\n7x + 21y = -406/5\n7x + 3y = -46/5\nSubtract equations\n18y = -72\ny = -72/18\ny = -4\n\nSubstitute y\n1x + 3(-4) = -58/5\n1x = 2/5\nx = 2/5/1\nx = 2/5"} {"input": "Find x in 10x - 5/2 = 0", "output": "10x - 5/2 = 0\n10x = 5/2\nx = 5/2 / 10\nx = 1/4"} {"input": "Solve the equation x^2 - 5/3x + 2/3 = 0", "output": "x^2 - 5/3x + 2/3 = 0\n(x - 2/3)(x - 1) = 0\nx - 2/3 = 0 or x - 1 = 0\nx = 2/3\nx = 1"} {"input": "Solve the equation x^2 + 27/10x + 7/5 = 0", "output": "x^2 + 27/10x + 7/5 = 0\n(x - -7/10)(x - -2) = 0\nx - -7/10 = 0 or x - -2 = 0\nx = -7/10\nx = -2"} {"input": "Determine x in x^3 + 15/2x^2 - 19x - 315/2 = 0", "output": "x^3 + 15/2x^2 - 19x - 315/2 = 0\n(x - -5)(x - -7)(x - 9/2) = 0\nx - -5 = 0\nx - -7 = 0\nx - 9/2 = 0\nx = -5\nx = -7\nx = 9/2"} {"input": "Solve x^2 - 13/9x - 10/9 = 0", "output": "x^2 - 13/9x - 10/9 = 0\n(x - -5/9)(x - 2) = 0\nx - -5/9 = 0 or x - 2 = 0\nx = -5/9\nx = 2"} {"input": "Find x in x^2 - 93/20x + 91/20 = 0", "output": "x^2 - 93/20x + 91/20 = 0\n(x - 13/4)(x - 7/5) = 0\nx - 13/4 = 0 or x - 7/5 = 0\nx = 13/4\nx = 7/5"} {"input": "Determine x in x^2 - 35/3x - 52/3 = 0", "output": "x^2 - 35/3x - 52/3 = 0\n(x - 13)(x - -4/3) = 0\nx - 13 = 0 or x - -4/3 = 0\nx = 13\nx = -4/3"} {"input": "What value of x satisfies 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Determine x in x^3 - 167/280x^2 - 99/70x - 117/280 = 0", "output": "x^3 - 167/280x^2 - 99/70x - 117/280 = 0\n(x - 13/8)(x - -3/5)(x - -3/7) = 0\nx - 13/8 = 0\nx - -3/5 = 0\nx - -3/7 = 0\nx = 13/8\nx = -3/5\nx = -3/7"} {"input": "What value of x satisfies x^3 - 655/72x^2 - 93/8x + 935/36 = 0", "output": "x^3 - 655/72x^2 - 93/8x + 935/36 = 0\n(x - 10)(x - -17/8)(x - 11/9) = 0\nx - 10 = 0\nx - -17/8 = 0\nx - 11/9 = 0\nx = 10\nx = -17/8\nx = 11/9"} {"input": "Find the solution to x^3 - 16/9x^2 - 31/9x - 2/3 = 0", "output": "x^3 - 16/9x^2 - 31/9x - 2/3 = 0\n(x - -2/9)(x - -1)(x - 3) = 0\nx - -2/9 = 0\nx - -1 = 0\nx - 3 = 0\nx = -2/9\nx = -1\nx = 3"} {"input": "Solve simultaneously:\n3x + 7y = -25/2\n5x + 3y = 19/2", "output": "3x + 7y = -25/2\n5x + 3y = 19/2\n\nUsing elimination\n5*(3x + 7y = -25/2)\n3*(5x + 3y = 19/2)\n15x + 35y = -125/2\n15x + 9y = 57/2\nSubtract equations\n26y = -91\ny = -91/26\ny = -7/2\n\nSubstitute y\n3x + 7(-7/2) = -25/2\n3x = 12\nx = 12/3\nx = 4"} {"input": "Find the solution to x^2 + 23/5x - 84/5 = 0", "output": "x^2 + 23/5x - 84/5 = 0\n(x - 12/5)(x - -7) = 0\nx - 12/5 = 0 or x - -7 = 0\nx = 12/5\nx = -7"} {"input": "Solve simultaneously:\n3x + 9y = -221/3\n4x + 9y = -668/9", "output": "3x + 9y = -221/3\n4x + 9y = -668/9\n\nUsing elimination\n4*(3x + 9y = -221/3)\n3*(4x + 9y = -668/9)\n12x + 36y = -884/3\n12x + 27y = -668/3\nSubtract equations\n9y = -72\ny = -72/9\ny = -8\n\nSubstitute y\n3x + 9(-8) = -221/3\n3x = -5/3\nx = -5/3/3\nx = -5/9"} {"input": "Solve the system:\n3x + 9y = 23/5\n2x + 9y = 64/15", "output": "3x + 9y = 23/5\n2x + 9y = 64/15\n\nUsing elimination\n2*(3x + 9y = 23/5)\n3*(2x + 9y = 64/15)\n6x + 18y = 46/5\n6x + 27y = 64/5\nSubtract equations\n-9y = -18/5\ny = -18/5/-9\ny = 2/5\n\nSubstitute y\n3x + 9(2/5) = 23/5\n3x = 1\nx = 1/3\nx = 1/3"} {"input": "Solve the system:\n5x + 6y = -37\n4x + 5y = -63/2", "output": "5x + 6y = -37\n4x + 5y = -63/2\n\nUsing elimination\n4*(5x + 6y = -37)\n5*(4x + 5y = -63/2)\n20x + 24y = -148\n20x + 25y = -315/2\nSubtract equations\n-1y = 19/2\ny = 19/2/-1\ny = -19/2\n\nSubstitute y\n5x + 6(-19/2) = -37\n5x = 20\nx = 20/5\nx = 4"} {"input": "Solve x^2 - 41/5x + 8/5 = 0", "output": "x^2 - 41/5x + 8/5 = 0\n(x - 8)(x - 1/5) = 0\nx - 8 = 0 or x - 1/5 = 0\nx = 8\nx = 1/5"} {"input": "Solve x^3 - 59/45x^2 + 2/9x = 0", "output": "x^3 - 59/45x^2 + 2/9x = 0\n(x - 10/9)(x - 1/5)(x - 0) = 0\nx - 10/9 = 0\nx - 1/5 = 0\nx - 0 = 0\nx = 10/9\nx = 1/5\nx = 0"} {"input": "Solve the system:\n5x + 5y = 9/2\n7x + 2y = -37/10", "output": "5x + 5y = 9/2\n7x + 2y = -37/10\n\nUsing elimination\n7*(5x + 5y = 9/2)\n5*(7x + 2y = -37/10)\n35x + 35y = 63/2\n35x + 10y = -37/2\nSubtract equations\n25y = 50\ny = 50/25\ny = 2\n\nSubstitute y\n5x + 5(2) = 9/2\n5x = -11/2\nx = -11/2/5\nx = -11/10"} {"input": "Solve the equation x^2 - 16x + 28 = 0", "output": "x^2 - 16x + 28 = 0\n(x - 2)(x - 14) = 0\nx - 2 = 0 or x - 14 = 0\nx = 2\nx = 14"} {"input": "Determine x in x^3 - 4/3x^2 - 79/81x + 110/81 = 0", "output": "x^3 - 4/3x^2 - 79/81x + 110/81 = 0\n(x - 11/9)(x - 10/9)(x - -1) = 0\nx - 11/9 = 0\nx - 10/9 = 0\nx - -1 = 0\nx = 11/9\nx = 10/9\nx = -1"} {"input": "Find x in x^3 - 149/14x^2 - 425/7x - 975/14 = 0", "output": "x^3 - 149/14x^2 - 425/7x - 975/14 = 0\n(x - -5/2)(x - -13/7)(x - 15) = 0\nx - -5/2 = 0\nx - -13/7 = 0\nx - 15 = 0\nx = -5/2\nx = -13/7\nx = 15"} {"input": "Solve quickly: x^2 - 23/10x + 13/10 = 0", "output": "x^2 - 23/10x + 13/10 = 0\n(x - 13/10)(x - 1) = 0\nx - 13/10 = 0 or x - 1 = 0\nx = 13/10\nx = 1"} {"input": "Find x in x^2 + 31/3x + 10/3 = 0", "output": "x^2 + 31/3x + 10/3 = 0\n(x - -10)(x - -1/3) = 0\nx - -10 = 0 or x - -1/3 = 0\nx = -10\nx = -1/3"} {"input": "Find x and y such that\n6x + 7y = -80/3\n1x + 10y = -28", "output": "6x + 7y = -80/3\n1x + 10y = -28\n\nUsing elimination\n1*(6x + 7y = -80/3)\n6*(1x + 10y = -28)\n6x + 7y = -80/3\n6x + 60y = -168\nSubtract equations\n-53y = 424/3\ny = 424/3/-53\ny = -8/3\n\nSubstitute y\n6x + 7(-8/3) = -80/3\n6x = -8\nx = -8/6\nx = -4/3"} {"input": "Find x in 10x - 55/2 = 0", "output": "10x - 55/2 = 0\n10x = 55/2\nx = 55/2 / 10\nx = 11/4"} {"input": "Solve the system:\n3x + 5y = 25/4\n10x + 9y = 17", "output": "3x + 5y = 25/4\n10x + 9y = 17\n\nUsing elimination\n10*(3x + 5y = 25/4)\n3*(10x + 9y = 17)\n30x + 50y = 125/2\n30x + 27y = 51\nSubtract equations\n23y = 23/2\ny = 23/2/23\ny = 1/2\n\nSubstitute y\n3x + 5(1/2) = 25/4\n3x = 15/4\nx = 15/4/3\nx = 5/4"} {"input": "Find x in 9x - 18/7 = 0", "output": "9x - 18/7 = 0\n9x = 18/7\nx = 18/7 / 9\nx = 2/7"} {"input": "Solve quickly: x^3 - 37/6x^2 - 85/6x - 4 = 0", "output": "x^3 - 37/6x^2 - 85/6x - 4 = 0\n(x - 8)(x - -3/2)(x - -1/3) = 0\nx - 8 = 0\nx - -3/2 = 0\nx - -1/3 = 0\nx = 8\nx = -3/2\nx = -1/3"} {"input": "Compute the solution of 7x - 28/3 = 0", "output": "7x - 28/3 = 0\n7x = 28/3\nx = 28/3 / 7\nx = 4/3"} {"input": "Solve quickly: x^3 - 221/36x^2 - 703/24x - 1805/72 = 0", "output": "x^3 - 221/36x^2 - 703/24x - 1805/72 = 0\n(x - -5/4)(x - 19/2)(x - -19/9) = 0\nx - -5/4 = 0\nx - 19/2 = 0\nx - -19/9 = 0\nx = -5/4\nx = 19/2\nx = -19/9"} {"input": "Solve simultaneously:\n9x + 4y = 18\n8x + 1y = 265/18", "output": "9x + 4y = 18\n8x + 1y = 265/18\n\nUsing elimination\n8*(9x + 4y = 18)\n9*(8x + 1y = 265/18)\n72x + 32y = 144\n72x + 9y = 265/2\nSubtract equations\n23y = 23/2\ny = 23/2/23\ny = 1/2\n\nSubstitute y\n9x + 4(1/2) = 18\n9x = 16\nx = 16/9\nx = 16/9"} {"input": "Determine x in 6x - 2 = 0", "output": "6x - 2 = 0\n6x = 2\nx = 2 / 6\nx = 1/3"} {"input": "Determine x in x^2 + 35/12x + 3/2 = 0", "output": "x^2 + 35/12x + 3/2 = 0\n(x - -9/4)(x - -2/3) = 0\nx - -9/4 = 0 or x - -2/3 = 0\nx = -9/4\nx = -2/3"} {"input": "What value of x satisfies x^2 + 116/45x - 209/45 = 0", "output": "x^2 + 116/45x - 209/45 = 0\n(x - -19/5)(x - 11/9) = 0\nx - -19/5 = 0 or x - 11/9 = 0\nx = -19/5\nx = 11/9"} {"input": "Solve x^2 + 34/15x - 13/15 = 0", "output": "x^2 + 34/15x - 13/15 = 0\n(x - -13/5)(x - 1/3) = 0\nx - -13/5 = 0 or x - 1/3 = 0\nx = -13/5\nx = 1/3"} {"input": "Solve the equations:\n10x + 8y = 163/9\n3x + 2y = 421/90", "output": "10x + 8y = 163/9\n3x + 2y = 421/90\n\nUsing elimination\n3*(10x + 8y = 163/9)\n10*(3x + 2y = 421/90)\n30x + 24y = 163/3\n30x + 20y = 421/9\nSubtract equations\n4y = 68/9\ny = 68/9/4\ny = 17/9\n\nSubstitute y\n10x + 8(17/9) = 163/9\n10x = 3\nx = 3/10\nx = 3/10"} {"input": "Solve the equation 1x + 5/2 = 0", "output": "1x + 5/2 = 0\n1x = -5/2\nx = -5/2 / 1\nx = -5/2"} {"input": "Determine x in x^3 - 71/5x^2 - 238/5x = 0", "output": "x^3 - 71/5x^2 - 238/5x = 0\n(x - -14/5)(x - 17)(x - 0) = 0\nx - -14/5 = 0\nx - 17 = 0\nx - 0 = 0\nx = -14/5\nx = 17\nx = 0"} {"input": "Find x in x^2 + 8/7x - 80/7 = 0", "output": "x^2 + 8/7x - 80/7 = 0\n(x - -4)(x - 20/7) = 0\nx - -4 = 0 or x - 20/7 = 0\nx = -4\nx = 20/7"} {"input": "Find the solution to x^2 - 81/5x + 16/5 = 0", "output": "x^2 - 81/5x + 16/5 = 0\n(x - 1/5)(x - 16) = 0\nx - 1/5 = 0 or x - 16 = 0\nx = 1/5\nx = 16"} {"input": "Solve the equation x^3 - 17/12x^2 - 155/12x - 21/2 = 0", "output": "x^3 - 17/12x^2 - 155/12x - 21/2 = 0\n(x - -9/4)(x - 14/3)(x - -1) = 0\nx - -9/4 = 0\nx - 14/3 = 0\nx - -1 = 0\nx = -9/4\nx = 14/3\nx = -1"} {"input": "Find x and y such that\n7x + 9y = 1084/9\n4x + 2y = 280/9", "output": "7x + 9y = 1084/9\n4x + 2y = 280/9\n\nUsing elimination\n4*(7x + 9y = 1084/9)\n7*(4x + 2y = 280/9)\n28x + 36y = 4336/9\n28x + 14y = 1960/9\nSubtract equations\n22y = 264\ny = 264/22\ny = 12\n\nSubstitute y\n7x + 9(12) = 1084/9\n7x = 112/9\nx = 112/9/7\nx = 16/9"} {"input": "Determine x in x^2 + 19/3x + 16/3 = 0", "output": "x^2 + 19/3x + 16/3 = 0\n(x - -16/3)(x - -1) = 0\nx - -16/3 = 0 or x - -1 = 0\nx = -16/3\nx = -1"} {"input": "Find x and y such that\n9x + 4y = -191/5\n6x + 10y = -13", "output": "9x + 4y = -191/5\n6x + 10y = -13\n\nUsing elimination\n6*(9x + 4y = -191/5)\n9*(6x + 10y = -13)\n54x + 24y = -1146/5\n54x + 90y = -117\nSubtract equations\n-66y = -561/5\ny = -561/5/-66\ny = 17/10\n\nSubstitute y\n9x + 4(17/10) = -191/5\n9x = -45\nx = -45/9\nx = -5"} {"input": "Find x for x^2 + 91/72x + 1/3 = 0", "output": "x^2 + 91/72x + 1/3 = 0\n(x - -8/9)(x - -3/8) = 0\nx - -8/9 = 0 or x - -3/8 = 0\nx = -8/9\nx = -3/8"} {"input": "Solve the equation x^3 + 307/40x^2 + 2279/160x + 133/80 = 0", "output": "x^3 + 307/40x^2 + 2279/160x + 133/80 = 0\n(x - -19/4)(x - -1/8)(x - -14/5) = 0\nx - -19/4 = 0\nx - -1/8 = 0\nx - -14/5 = 0\nx = -19/4\nx = -1/8\nx = -14/5"} {"input": "Solve the equations:\n5x + 9y = -40/7\n4x + 7y = -32/7", "output": "5x + 9y = -40/7\n4x + 7y = -32/7\n\nUsing elimination\n4*(5x + 9y = -40/7)\n5*(4x + 7y = -32/7)\n20x + 36y = -160/7\n20x + 35y = -160/7\nSubtract equations\n1y = 0\ny = 0/1\ny = 0\n\nSubstitute y\n5x + 9(0) = -40/7\n5x = -40/7\nx = -40/7/5\nx = -8/7"} {"input": "Find the solution to x^3 + 415/42x^2 + 1558/63x + 1805/126 = 0", "output": "x^3 + 415/42x^2 + 1558/63x + 1805/126 = 0\n(x - -19/3)(x - -19/7)(x - -5/6) = 0\nx - -19/3 = 0\nx - -19/7 = 0\nx - -5/6 = 0\nx = -19/3\nx = -19/7\nx = -5/6"} {"input": "Solve simultaneously:\n6x + 2y = -230/7\n9x + 4y = -415/7", "output": "6x + 2y = -230/7\n9x + 4y = -415/7\n\nUsing elimination\n9*(6x + 2y = -230/7)\n6*(9x + 4y = -415/7)\n54x + 18y = -2070/7\n54x + 24y = -2490/7\nSubtract equations\n-6y = 60\ny = 60/-6\ny = -10\n\nSubstitute y\n6x + 2(-10) = -230/7\n6x = -90/7\nx = -90/7/6\nx = -15/7"} {"input": "Compute the solution of 8x - 56/3 = 0", "output": "8x - 56/3 = 0\n8x = 56/3\nx = 56/3 / 8\nx = 7/3"} {"input": "Compute the solution of x^2 + 13x + 22 = 0", "output": "x^2 + 13x + 22 = 0\n(x - -2)(x - -11) = 0\nx - -2 = 0 or x - -11 = 0\nx = -2\nx = -11"} {"input": "What value of x satisfies x^2 - 117/70x - 81/35 = 0", "output": "x^2 - 117/70x - 81/35 = 0\n(x - 18/7)(x - -9/10) = 0\nx - 18/7 = 0 or x - -9/10 = 0\nx = 18/7\nx = -9/10"} {"input": "Find x in x^2 - 1/24x - 1/8 = 0", "output": "x^2 - 1/24x - 1/8 = 0\n(x - -1/3)(x - 3/8) = 0\nx - -1/3 = 0 or x - 3/8 = 0\nx = -1/3\nx = 3/8"} {"input": "Solve the equations:\n3x + 6y = -450/7\n2x + 5y = -377/7", "output": "3x + 6y = -450/7\n2x + 5y = -377/7\n\nUsing elimination\n2*(3x + 6y = -450/7)\n3*(2x + 5y = -377/7)\n6x + 12y = -900/7\n6x + 15y = -1131/7\nSubtract equations\n-3y = 33\ny = 33/-3\ny = -11\n\nSubstitute y\n3x + 6(-11) = -450/7\n3x = 12/7\nx = 12/7/3\nx = 4/7"} {"input": "Solve the equation 4x + 36/5 = 0", "output": "4x + 36/5 = 0\n4x = -36/5\nx = -36/5 / 4\nx = -9/5"} {"input": "Find x for x^3 - 25/24x^2 - 313/48x + 35/6 = 0", "output": "x^3 - 25/24x^2 - 313/48x + 35/6 = 0\n(x - -5/2)(x - 8/3)(x - 7/8) = 0\nx - -5/2 = 0\nx - 8/3 = 0\nx - 7/8 = 0\nx = -5/2\nx = 8/3\nx = 7/8"} {"input": "Compute the solution of x^3 - 117/35x^2 + 26/7x - 48/35 = 0", "output": "x^3 - 117/35x^2 + 26/7x - 48/35 = 0\n(x - 6/5)(x - 1)(x - 8/7) = 0\nx - 6/5 = 0\nx - 1 = 0\nx - 8/7 = 0\nx = 6/5\nx = 1\nx = 8/7"} {"input": "Find x for x^3 + 52/5x^2 + 25x + 42/5 = 0", "output": "x^3 + 52/5x^2 + 25x + 42/5 = 0\n(x - -7)(x - -2/5)(x - -3) = 0\nx - -7 = 0\nx - -2/5 = 0\nx - -3 = 0\nx = -7\nx = -2/5\nx = -3"} {"input": "Solve simultaneously:\n8x + 3y = 67/8\n10x + 4y = 43/4", "output": "8x + 3y = 67/8\n10x + 4y = 43/4\n\nUsing elimination\n10*(8x + 3y = 67/8)\n8*(10x + 4y = 43/4)\n80x + 30y = 335/4\n80x + 32y = 86\nSubtract equations\n-2y = -9/4\ny = -9/4/-2\ny = 9/8\n\nSubstitute y\n8x + 3(9/8) = 67/8\n8x = 5\nx = 5/8\nx = 5/8"} {"input": "Find x for x^2 - 2x = 0", "output": "x^2 - 2x = 0\n(x - 2)(x - 0) = 0\nx - 2 = 0 or x - 0 = 0\nx = 2\nx = 0"} {"input": "Solve quickly: 7x + 10 = 0", "output": "7x + 10 = 0\n7x = -10\nx = -10 / 7\nx = -10/7"} {"input": "Solve the equations:\n9x + 7y = -2\n9x + 5y = 0", "output": "9x + 7y = -2\n9x + 5y = 0\n\nUsing elimination\n9*(9x + 7y = -2)\n9*(9x + 5y = 0)\n81x + 63y = -18\n81x + 45y = 0\nSubtract equations\n18y = -18\ny = -18/18\ny = -1\n\nSubstitute y\n9x + 7(-1) = -2\n9x = 5\nx = 5/9\nx = 5/9"} {"input": "Find the solution to x^2 - 29/40x - 9/20 = 0", "output": "x^2 - 29/40x - 9/20 = 0\n(x - 9/8)(x - -2/5) = 0\nx - 9/8 = 0 or x - -2/5 = 0\nx = 9/8\nx = -2/5"} {"input": "Determine x in x^2 + 71/30x + 17/15 = 0", "output": "x^2 + 71/30x + 17/15 = 0\n(x - -2/3)(x - -17/10) = 0\nx - -2/3 = 0 or x - -17/10 = 0\nx = -2/3\nx = -17/10"} {"input": "Solve the equation x^3 + 33/40x^2 - 2907/400x + 2023/400 = 0", "output": "x^3 + 33/40x^2 - 2907/400x + 2023/400 = 0\n(x - 7/8)(x - 17/10)(x - -17/5) = 0\nx - 7/8 = 0\nx - 17/10 = 0\nx - -17/5 = 0\nx = 7/8\nx = 17/10\nx = -17/5"} {"input": "What value of x satisfies 9x - 27/2 = 0", "output": "9x - 27/2 = 0\n9x = 27/2\nx = 27/2 / 9\nx = 3/2"} {"input": "Solve 1x + 11/5 = 0", "output": "1x + 11/5 = 0\n1x = -11/5\nx = -11/5 / 1\nx = -11/5"} {"input": "Compute the solution of x^2 - 8x + 7 = 0", "output": "x^2 - 8x + 7 = 0\n(x - 7)(x - 1) = 0\nx - 7 = 0 or x - 1 = 0\nx = 7\nx = 1"} {"input": "Solve x^3 + 1x^2 - 6x = 0", "output": "x^3 + 1x^2 - 6x = 0\n(x - 0)(x - 2)(x - -3) = 0\nx - 0 = 0\nx - 2 = 0\nx - -3 = 0\nx = 0\nx = 2\nx = -3"} {"input": "What value of x satisfies 5x - 95 = 0", "output": "5x - 95 = 0\n5x = 95\nx = 95 / 5\nx = 19"} {"input": "Compute the solution of x^3 + 97/40x^2 - 89/50x - 1001/200 = 0", "output": "x^3 + 97/40x^2 - 89/50x - 1001/200 = 0\n(x - -11/5)(x - 7/5)(x - -13/8) = 0\nx - -11/5 = 0\nx - 7/5 = 0\nx - -13/8 = 0\nx = -11/5\nx = 7/5\nx = -13/8"} {"input": "Find x in x^3 - 101/42x^2 - 3/7x = 0", "output": "x^3 - 101/42x^2 - 3/7x = 0\n(x - -1/6)(x - 18/7)(x - 0) = 0\nx - -1/6 = 0\nx - 18/7 = 0\nx - 0 = 0\nx = -1/6\nx = 18/7\nx = 0"} {"input": "Solve quickly: 7x - 6 = 0", "output": "7x - 6 = 0\n7x = 6\nx = 6 / 7\nx = 6/7"} {"input": "Solve simultaneously:\n2x + 4y = 22/5\n8x + 8y = 164/5", "output": "2x + 4y = 22/5\n8x + 8y = 164/5\n\nUsing elimination\n8*(2x + 4y = 22/5)\n2*(8x + 8y = 164/5)\n16x + 32y = 176/5\n16x + 16y = 328/5\nSubtract equations\n16y = -152/5\ny = -152/5/16\ny = -19/10\n\nSubstitute y\n2x + 4(-19/10) = 22/5\n2x = 12\nx = 12/2\nx = 6"} {"input": "Find x for 5x - 25/7 = 0", "output": "5x - 25/7 = 0\n5x = 25/7\nx = 25/7 / 5\nx = 5/7"} {"input": "What value of x satisfies 2x + 16/3 = 0", "output": "2x + 16/3 = 0\n2x = -16/3\nx = -16/3 / 2\nx = -8/3"} {"input": "Determine x in x^2 - 1 = 0", "output": "x^2 - 1 = 0\n(x - -1)(x - 1) = 0\nx - -1 = 0 or x - 1 = 0\nx = -1\nx = 1"} {"input": "Find x in 3x - 1 = 0", "output": "3x - 1 = 0\n3x = 1\nx = 1 / 3\nx = 1/3"} {"input": "What value of x satisfies 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Find the solution to 7x - 133/4 = 0", "output": "7x - 133/4 = 0\n7x = 133/4\nx = 133/4 / 7\nx = 19/4"} {"input": "Find x in 3x + 6 = 0", "output": "3x + 6 = 0\n3x = -6\nx = -6 / 3\nx = -2"} {"input": "Solve x^2 + 73/45x + 22/45 = 0", "output": "x^2 + 73/45x + 22/45 = 0\n(x - -2/5)(x - -11/9) = 0\nx - -2/5 = 0 or x - -11/9 = 0\nx = -2/5\nx = -11/9"} {"input": "Solve x^2 - 43/7x + 6/7 = 0", "output": "x^2 - 43/7x + 6/7 = 0\n(x - 6)(x - 1/7) = 0\nx - 6 = 0 or x - 1/7 = 0\nx = 6\nx = 1/7"} {"input": "Solve the system:\n3x + 6y = -30\n1x + 4y = -15", "output": "3x + 6y = -30\n1x + 4y = -15\n\nUsing elimination\n1*(3x + 6y = -30)\n3*(1x + 4y = -15)\n3x + 6y = -30\n3x + 12y = -45\nSubtract equations\n-6y = 15\ny = 15/-6\ny = -5/2\n\nSubstitute y\n3x + 6(-5/2) = -30\n3x = -15\nx = -15/3\nx = -5"} {"input": "Determine x in x^3 - 89/35x^2 - 391/35x - 39/7 = 0", "output": "x^3 - 89/35x^2 - 391/35x - 39/7 = 0\n(x - 5)(x - -13/7)(x - -3/5) = 0\nx - 5 = 0\nx - -13/7 = 0\nx - -3/5 = 0\nx = 5\nx = -13/7\nx = -3/5"} {"input": "Compute the solution of x^2 + 77/5x + 156/5 = 0", "output": "x^2 + 77/5x + 156/5 = 0\n(x - -12/5)(x - -13) = 0\nx - -12/5 = 0 or x - -13 = 0\nx = -12/5\nx = -13"} {"input": "Solve the equation x^3 - 25/2x^2 - 92x - 126 = 0", "output": "x^3 - 25/2x^2 - 92x - 126 = 0\n(x - 18)(x - -2)(x - -7/2) = 0\nx - 18 = 0\nx - -2 = 0\nx - -7/2 = 0\nx = 18\nx = -2\nx = -7/2"} {"input": "Find x in x^3 - 1/3x^2 - 158/9x + 104/9 = 0", "output": "x^3 - 1/3x^2 - 158/9x + 104/9 = 0\n(x - 2/3)(x - 4)(x - -13/3) = 0\nx - 2/3 = 0\nx - 4 = 0\nx - -13/3 = 0\nx = 2/3\nx = 4\nx = -13/3"} {"input": "Find the solution to 1x + 1 = 0", "output": "1x + 1 = 0\n1x = -1\nx = -1 / 1\nx = -1"} {"input": "Solve quickly: x^2 + 23/8x + 15/8 = 0", "output": "x^2 + 23/8x + 15/8 = 0\n(x - -15/8)(x - -1) = 0\nx - -15/8 = 0 or x - -1 = 0\nx = -15/8\nx = -1"} {"input": "Determine x in 4x + 4/7 = 0", "output": "4x + 4/7 = 0\n4x = -4/7\nx = -4/7 / 4\nx = -1/7"} {"input": "Find x for x^2 + 19/4x - 26 = 0", "output": "x^2 + 19/4x - 26 = 0\n(x - -8)(x - 13/4) = 0\nx - -8 = 0 or x - 13/4 = 0\nx = -8\nx = 13/4"} {"input": "Solve the system:\n2x + 6y = -8\n7x + 3y = -4", "output": "2x + 6y = -8\n7x + 3y = -4\n\nUsing elimination\n7*(2x + 6y = -8)\n2*(7x + 3y = -4)\n14x + 42y = -56\n14x + 6y = -8\nSubtract equations\n36y = -48\ny = -48/36\ny = -4/3\n\nSubstitute y\n2x + 6(-4/3) = -8\n2x = 0\nx = 0/2\nx = 0"} {"input": "Solve the system:\n4x + 6y = 12\n5x + 8y = 15", "output": "4x + 6y = 12\n5x + 8y = 15\n\nUsing elimination\n5*(4x + 6y = 12)\n4*(5x + 8y = 15)\n20x + 30y = 60\n20x + 32y = 60\nSubtract equations\n-2y = 0\ny = 0/-2\ny = 0\n\nSubstitute y\n4x + 6(0) = 12\n4x = 12\nx = 12/4\nx = 3"} {"input": "Find x in x^3 - 16/3x^2 - 125/3x - 50 = 0", "output": "x^3 - 16/3x^2 - 125/3x - 50 = 0\n(x - -5/3)(x - 10)(x - -3) = 0\nx - -5/3 = 0\nx - 10 = 0\nx - -3 = 0\nx = -5/3\nx = 10\nx = -3"} {"input": "Find x in 4x + 28/3 = 0", "output": "4x + 28/3 = 0\n4x = -28/3\nx = -28/3 / 4\nx = -7/3"} {"input": "Find x for x^3 - 23/15x^2 - 4/15x + 4/5 = 0", "output": "x^3 - 23/15x^2 - 4/15x + 4/5 = 0\n(x - 6/5)(x - -2/3)(x - 1) = 0\nx - 6/5 = 0\nx - -2/3 = 0\nx - 1 = 0\nx = 6/5\nx = -2/3\nx = 1"} {"input": "Solve quickly: 5x - 5 = 0", "output": "5x - 5 = 0\n5x = 5\nx = 5 / 5\nx = 1"} {"input": "Find x for x^3 - 29/42x^2 - 8/3x + 13/14 = 0", "output": "x^3 - 29/42x^2 - 8/3x + 13/14 = 0\n(x - -3/2)(x - 1/3)(x - 13/7) = 0\nx - -3/2 = 0\nx - 1/3 = 0\nx - 13/7 = 0\nx = -3/2\nx = 1/3\nx = 13/7"} {"input": "Find the solution to x^3 + 664/105x^2 + 4559/420x + 19/7 = 0", "output": "x^3 + 664/105x^2 + 4559/420x + 19/7 = 0\n(x - -20/7)(x - -3/10)(x - -19/6) = 0\nx - -20/7 = 0\nx - -3/10 = 0\nx - -19/6 = 0\nx = -20/7\nx = -3/10\nx = -19/6"} {"input": "Solve the equation x^3 + 23/3x^2 + 52/3x + 32/3 = 0", "output": "x^3 + 23/3x^2 + 52/3x + 32/3 = 0\n(x - -8/3)(x - -4)(x - -1) = 0\nx - -8/3 = 0\nx - -4 = 0\nx - -1 = 0\nx = -8/3\nx = -4\nx = -1"} {"input": "Find x for x^2 - 1/15x - 28/5 = 0", "output": "x^2 - 1/15x - 28/5 = 0\n(x - -7/3)(x - 12/5) = 0\nx - -7/3 = 0 or x - 12/5 = 0\nx = -7/3\nx = 12/5"} {"input": "Solve the equation x^3 + 23/4x^2 - 5/4x - 231/16 = 0", "output": "x^3 + 23/4x^2 - 5/4x - 231/16 = 0\n(x - -7/4)(x - 3/2)(x - -11/2) = 0\nx - -7/4 = 0\nx - 3/2 = 0\nx - -11/2 = 0\nx = -7/4\nx = 3/2\nx = -11/2"} {"input": "Solve the equations:\n5x + 6y = -97/2\n9x + 8y = -493/6", "output": "5x + 6y = -97/2\n9x + 8y = -493/6\n\nUsing elimination\n9*(5x + 6y = -97/2)\n5*(9x + 8y = -493/6)\n45x + 54y = -873/2\n45x + 40y = -2465/6\nSubtract equations\n14y = -77/3\ny = -77/3/14\ny = -11/6\n\nSubstitute y\n5x + 6(-11/6) = -97/2\n5x = -75/2\nx = -75/2/5\nx = -15/2"} {"input": "Determine x in 5x - 9/2 = 0", "output": "5x - 9/2 = 0\n5x = 9/2\nx = 9/2 / 5\nx = 9/10"} {"input": "Solve 7x + 28 = 0", "output": "7x + 28 = 0\n7x = -28\nx = -28 / 7\nx = -4"} {"input": "Find x and y such that\n10x + 8y = -1246/9\n2x + 10y = -140/9", "output": "10x + 8y = -1246/9\n2x + 10y = -140/9\n\nUsing elimination\n2*(10x + 8y = -1246/9)\n10*(2x + 10y = -140/9)\n20x + 16y = -2492/9\n20x + 100y = -1400/9\nSubtract equations\n-84y = -364/3\ny = -364/3/-84\ny = 13/9\n\nSubstitute y\n10x + 8(13/9) = -1246/9\n10x = -150\nx = -150/10\nx = -15"} {"input": "Solve the system:\n2x + 5y = -4\n8x + 3y = -46/5", "output": "2x + 5y = -4\n8x + 3y = -46/5\n\nUsing elimination\n8*(2x + 5y = -4)\n2*(8x + 3y = -46/5)\n16x + 40y = -32\n16x + 6y = -92/5\nSubtract equations\n34y = -68/5\ny = -68/5/34\ny = -2/5\n\nSubstitute y\n2x + 5(-2/5) = -4\n2x = -2\nx = -2/2\nx = -1"} {"input": "Find x for x^3 - 73/4x^2 + 173/8x - 51/8 = 0", "output": "x^3 - 73/4x^2 + 173/8x - 51/8 = 0\n(x - 1/2)(x - 3/4)(x - 17) = 0\nx - 1/2 = 0\nx - 3/4 = 0\nx - 17 = 0\nx = 1/2\nx = 3/4\nx = 17"} {"input": "Determine x in x^2 - 138/7x - 40/7 = 0", "output": "x^2 - 138/7x - 40/7 = 0\n(x - -2/7)(x - 20) = 0\nx - -2/7 = 0 or x - 20 = 0\nx = -2/7\nx = 20"} {"input": "Solve the equation x^3 - 67/12x^2 + 67/9x - 55/36 = 0", "output": "x^3 - 67/12x^2 + 67/9x - 55/36 = 0\n(x - 5/3)(x - 11/3)(x - 1/4) = 0\nx - 5/3 = 0\nx - 11/3 = 0\nx - 1/4 = 0\nx = 5/3\nx = 11/3\nx = 1/4"} {"input": "Solve the equation 6x - 15/2 = 0", "output": "6x - 15/2 = 0\n6x = 15/2\nx = 15/2 / 6\nx = 5/4"} {"input": "Determine x in x^3 - 21/10x^2 - 21/5x + 8 = 0", "output": "x^3 - 21/10x^2 - 21/5x + 8 = 0\n(x - 8/5)(x - 5/2)(x - -2) = 0\nx - 8/5 = 0\nx - 5/2 = 0\nx - -2 = 0\nx = 8/5\nx = 5/2\nx = -2"} {"input": "Determine x in x^2 + 63/10x - 187/10 = 0", "output": "x^2 + 63/10x - 187/10 = 0\n(x - -17/2)(x - 11/5) = 0\nx - -17/2 = 0 or x - 11/5 = 0\nx = -17/2\nx = 11/5"} {"input": "What value of x satisfies 5x = 0", "output": "5x = 0\n5x = 0\nx = 0 / 5\nx = 0"} {"input": "Solve quickly: x^3 - 443/63x^2 + 704/63x - 320/63 = 0", "output": "x^3 - 443/63x^2 + 704/63x - 320/63 = 0\n(x - 8/9)(x - 8/7)(x - 5) = 0\nx - 8/9 = 0\nx - 8/7 = 0\nx - 5 = 0\nx = 8/9\nx = 8/7\nx = 5"} {"input": "Compute the solution of x^3 + 2x^2 + 99/100x = 0", "output": "x^3 + 2x^2 + 99/100x = 0\n(x - -9/10)(x - -11/10)(x - 0) = 0\nx - -9/10 = 0\nx - -11/10 = 0\nx - 0 = 0\nx = -9/10\nx = -11/10\nx = 0"} {"input": "Find the solution to 2x - 4 = 0", "output": "2x - 4 = 0\n2x = 4\nx = 4 / 2\nx = 2"} {"input": "Solve the system:\n4x + 5y = 61/6\n10x + 2y = 271/15", "output": "4x + 5y = 61/6\n10x + 2y = 271/15\n\nUsing elimination\n10*(4x + 5y = 61/6)\n4*(10x + 2y = 271/15)\n40x + 50y = 305/3\n40x + 8y = 1084/15\nSubtract equations\n42y = 147/5\ny = 147/5/42\ny = 7/10\n\nSubstitute y\n4x + 5(7/10) = 61/6\n4x = 20/3\nx = 20/3/4\nx = 5/3"} {"input": "What value of x satisfies x^3 - 181/12x^2 - 29/2x - 8/3 = 0", "output": "x^3 - 181/12x^2 - 29/2x - 8/3 = 0\n(x - 16)(x - -2/3)(x - -1/4) = 0\nx - 16 = 0\nx - -2/3 = 0\nx - -1/4 = 0\nx = 16\nx = -2/3\nx = -1/4"} {"input": "Find x and y such that\n1x + 8y = -331/8\n2x + 6y = -131/4", "output": "1x + 8y = -331/8\n2x + 6y = -131/4\n\nUsing elimination\n2*(1x + 8y = -331/8)\n1*(2x + 6y = -131/4)\n2x + 16y = -331/4\n2x + 6y = -131/4\nSubtract equations\n10y = -50\ny = -50/10\ny = -5\n\nSubstitute y\n1x + 8(-5) = -331/8\n1x = -11/8\nx = -11/8/1\nx = -11/8"} {"input": "Find x in 6x + 12 = 0", "output": "6x + 12 = 0\n6x = -12\nx = -12 / 6\nx = -2"} {"input": "Compute the solution of x^3 - 1579/315x^2 + 526/63x - 208/45 = 0", "output": "x^3 - 1579/315x^2 + 526/63x - 208/45 = 0\n(x - 8/5)(x - 14/9)(x - 13/7) = 0\nx - 8/5 = 0\nx - 14/9 = 0\nx - 13/7 = 0\nx = 8/5\nx = 14/9\nx = 13/7"} {"input": "What value of x satisfies 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Find x in 3x - 27/5 = 0", "output": "3x - 27/5 = 0\n3x = 27/5\nx = 27/5 / 3\nx = 9/5"} {"input": "Solve 5x - 75/7 = 0", "output": "5x - 75/7 = 0\n5x = 75/7\nx = 75/7 / 5\nx = 15/7"} {"input": "Determine x in 4x - 2 = 0", "output": "4x - 2 = 0\n4x = 2\nx = 2 / 4\nx = 1/2"} {"input": "Compute the solution of 4x + 1 = 0", "output": "4x + 1 = 0\n4x = -1\nx = -1 / 4\nx = -1/4"} {"input": "What value of x satisfies x^2 - 71/18x + 65/18 = 0", "output": "x^2 - 71/18x + 65/18 = 0\n(x - 5/2)(x - 13/9) = 0\nx - 5/2 = 0 or x - 13/9 = 0\nx = 5/2\nx = 13/9"} {"input": "Find x in 5x + 5 = 0", "output": "5x + 5 = 0\n5x = -5\nx = -5 / 5\nx = -1"} {"input": "Find x in x^2 - 9/5x + 4/5 = 0", "output": "x^2 - 9/5x + 4/5 = 0\n(x - 1)(x - 4/5) = 0\nx - 1 = 0 or x - 4/5 = 0\nx = 1\nx = 4/5"} {"input": "Solve x^2 - 21/8x + 19/32 = 0", "output": "x^2 - 21/8x + 19/32 = 0\n(x - 19/8)(x - 1/4) = 0\nx - 19/8 = 0 or x - 1/4 = 0\nx = 19/8\nx = 1/4"} {"input": "Determine x in x^3 + 49/5x^2 + 132/5x + 108/5 = 0", "output": "x^3 + 49/5x^2 + 132/5x + 108/5 = 0\n(x - -2)(x - -6)(x - -9/5) = 0\nx - -2 = 0\nx - -6 = 0\nx - -9/5 = 0\nx = -2\nx = -6\nx = -9/5"} {"input": "Solve quickly: 9x + 27 = 0", "output": "9x + 27 = 0\n9x = -27\nx = -27 / 9\nx = -3"} {"input": "Solve the equations:\n4x + 7y = 117/8\n2x + 5y = 63/8", "output": "4x + 7y = 117/8\n2x + 5y = 63/8\n\nUsing elimination\n2*(4x + 7y = 117/8)\n4*(2x + 5y = 63/8)\n8x + 14y = 117/4\n8x + 20y = 63/2\nSubtract equations\n-6y = -9/4\ny = -9/4/-6\ny = 3/8\n\nSubstitute y\n4x + 7(3/8) = 117/8\n4x = 12\nx = 12/4\nx = 3"} {"input": "Find x in x^2 - 50/3x + 200/3 = 0", "output": "x^2 - 50/3x + 200/3 = 0\n(x - 20/3)(x - 10) = 0\nx - 20/3 = 0 or x - 10 = 0\nx = 20/3\nx = 10"} {"input": "Compute the solution of x^2 + 73/15x + 22/5 = 0", "output": "x^2 + 73/15x + 22/5 = 0\n(x - -6/5)(x - -11/3) = 0\nx - -6/5 = 0 or x - -11/3 = 0\nx = -6/5\nx = -11/3"} {"input": "Solve the equations:\n9x + 6y = -145/7\n2x + 8y = -830/63", "output": "9x + 6y = -145/7\n2x + 8y = -830/63\n\nUsing elimination\n2*(9x + 6y = -145/7)\n9*(2x + 8y = -830/63)\n18x + 12y = -290/7\n18x + 72y = -830/7\nSubtract equations\n-60y = 540/7\ny = 540/7/-60\ny = -9/7\n\nSubstitute y\n9x + 6(-9/7) = -145/7\n9x = -13\nx = -13/9\nx = -13/9"} {"input": "Find the solution to x^2 - 23/6x - 55/6 = 0", "output": "x^2 - 23/6x - 55/6 = 0\n(x - 11/2)(x - -5/3) = 0\nx - 11/2 = 0 or x - -5/3 = 0\nx = 11/2\nx = -5/3"} {"input": "Find the solution to 3x + 51/7 = 0", "output": "3x + 51/7 = 0\n3x = -51/7\nx = -51/7 / 3\nx = -17/7"} {"input": "What value of x satisfies x^3 + 253/40x^2 - 109/8x - 9/5 = 0", "output": "x^3 + 253/40x^2 - 109/8x - 9/5 = 0\n(x - -8)(x - -1/8)(x - 9/5) = 0\nx - -8 = 0\nx - -1/8 = 0\nx - 9/5 = 0\nx = -8\nx = -1/8\nx = 9/5"} {"input": "What value of x satisfies 6x - 48 = 0", "output": "6x - 48 = 0\n6x = 48\nx = 48 / 6\nx = 8"} {"input": "Solve simultaneously:\n10x + 6y = -262/3\n3x + 10y = -59", "output": "10x + 6y = -262/3\n3x + 10y = -59\n\nUsing elimination\n3*(10x + 6y = -262/3)\n10*(3x + 10y = -59)\n30x + 18y = -262\n30x + 100y = -590\nSubtract equations\n-82y = 328\ny = 328/-82\ny = -4\n\nSubstitute y\n10x + 6(-4) = -262/3\n10x = -190/3\nx = -190/3/10\nx = -19/3"} {"input": "Find x for x^3 + 89/30x^2 - 68/15x - 8/5 = 0", "output": "x^3 + 89/30x^2 - 68/15x - 8/5 = 0\n(x - -3/10)(x - 4/3)(x - -4) = 0\nx - -3/10 = 0\nx - 4/3 = 0\nx - -4 = 0\nx = -3/10\nx = 4/3\nx = -4"} {"input": "Compute the solution of x^3 - 169/12x^2 + 205/6x + 200/3 = 0", "output": "x^3 - 169/12x^2 + 205/6x + 200/3 = 0\n(x - 10)(x - -5/4)(x - 16/3) = 0\nx - 10 = 0\nx - -5/4 = 0\nx - 16/3 = 0\nx = 10\nx = -5/4\nx = 16/3"} {"input": "Solve the equations:\n6x + 3y = -27/10\n5x + 3y = -49/20", "output": "6x + 3y = -27/10\n5x + 3y = -49/20\n\nUsing elimination\n5*(6x + 3y = -27/10)\n6*(5x + 3y = -49/20)\n30x + 15y = -27/2\n30x + 18y = -147/10\nSubtract equations\n-3y = 6/5\ny = 6/5/-3\ny = -2/5\n\nSubstitute y\n6x + 3(-2/5) = -27/10\n6x = -3/2\nx = -3/2/6\nx = -1/4"} {"input": "Solve simultaneously:\n1x + 9y = 576/7\n7x + 6y = 63", "output": "1x + 9y = 576/7\n7x + 6y = 63\n\nUsing elimination\n7*(1x + 9y = 576/7)\n1*(7x + 6y = 63)\n7x + 63y = 576\n7x + 6y = 63\nSubtract equations\n57y = 513\ny = 513/57\ny = 9\n\nSubstitute y\n1x + 9(9) = 576/7\n1x = 9/7\nx = 9/7/1\nx = 9/7"} {"input": "Compute the solution of x^3 - 155/18x^2 + 233/27x - 20/9 = 0", "output": "x^3 - 155/18x^2 + 233/27x - 20/9 = 0\n(x - 2/3)(x - 15/2)(x - 4/9) = 0\nx - 2/3 = 0\nx - 15/2 = 0\nx - 4/9 = 0\nx = 2/3\nx = 15/2\nx = 4/9"} {"input": "Determine x in x^3 + 167/30x^2 - 31x - 1547/30 = 0", "output": "x^3 + 167/30x^2 - 31x - 1547/30 = 0\n(x - 13/3)(x - -7/5)(x - -17/2) = 0\nx - 13/3 = 0\nx - -7/5 = 0\nx - -17/2 = 0\nx = 13/3\nx = -7/5\nx = -17/2"} {"input": "Solve 10x - 65 = 0", "output": "10x - 65 = 0\n10x = 65\nx = 65 / 10\nx = 13/2"} {"input": "Solve the equation x^2 - 49/4x + 55/4 = 0", "output": "x^2 - 49/4x + 55/4 = 0\n(x - 11)(x - 5/4) = 0\nx - 11 = 0 or x - 5/4 = 0\nx = 11\nx = 5/4"} {"input": "Solve x^2 + 25/8x + 57/32 = 0", "output": "x^2 + 25/8x + 57/32 = 0\n(x - -19/8)(x - -3/4) = 0\nx - -19/8 = 0 or x - -3/4 = 0\nx = -19/8\nx = -3/4"} {"input": "Find x in x^2 + 5/2x + 3/2 = 0", "output": "x^2 + 5/2x + 3/2 = 0\n(x - -3/2)(x - -1) = 0\nx - -3/2 = 0 or x - -1 = 0\nx = -3/2\nx = -1"} {"input": "Solve x^3 - 19/3x^2 - 170/3x + 200 = 0", "output": "x^3 - 19/3x^2 - 170/3x + 200 = 0\n(x - 3)(x - 10)(x - -20/3) = 0\nx - 3 = 0\nx - 10 = 0\nx - -20/3 = 0\nx = 3\nx = 10\nx = -20/3"} {"input": "Solve quickly: x^2 - 35/2x + 153/2 = 0", "output": "x^2 - 35/2x + 153/2 = 0\n(x - 17/2)(x - 9) = 0\nx - 17/2 = 0 or x - 9 = 0\nx = 17/2\nx = 9"} {"input": "What value of x satisfies 1x + 1/3 = 0", "output": "1x + 1/3 = 0\n1x = -1/3\nx = -1/3 / 1\nx = -1/3"} {"input": "Find the solution to 1x + 1 = 0", "output": "1x + 1 = 0\n1x = -1\nx = -1 / 1\nx = -1"} {"input": "Solve the equations:\n4x + 2y = -1\n8x + 3y = 1/2", "output": "4x + 2y = -1\n8x + 3y = 1/2\n\nUsing elimination\n8*(4x + 2y = -1)\n4*(8x + 3y = 1/2)\n32x + 16y = -8\n32x + 12y = 2\nSubtract equations\n4y = -10\ny = -10/4\ny = -5/2\n\nSubstitute y\n4x + 2(-5/2) = -1\n4x = 4\nx = 4/4\nx = 1"} {"input": "Solve quickly: x^2 - 99/20x + 28/5 = 0", "output": "x^2 - 99/20x + 28/5 = 0\n(x - 16/5)(x - 7/4) = 0\nx - 16/5 = 0 or x - 7/4 = 0\nx = 16/5\nx = 7/4"} {"input": "Solve x^3 - 4/5x^2 - 367/80x + 819/160 = 0", "output": "x^3 - 4/5x^2 - 367/80x + 819/160 = 0\n(x - -9/4)(x - 7/4)(x - 13/10) = 0\nx - -9/4 = 0\nx - 7/4 = 0\nx - 13/10 = 0\nx = -9/4\nx = 7/4\nx = 13/10"} {"input": "Determine x in 5x + 5/3 = 0", "output": "5x + 5/3 = 0\n5x = -5/3\nx = -5/3 / 5\nx = -1/3"} {"input": "Find the solution to x^2 - 28/15x + 1/3 = 0", "output": "x^2 - 28/15x + 1/3 = 0\n(x - 5/3)(x - 1/5) = 0\nx - 5/3 = 0 or x - 1/5 = 0\nx = 5/3\nx = 1/5"} {"input": "Solve quickly: 3x + 2 = 0", "output": "3x + 2 = 0\n3x = -2\nx = -2 / 3\nx = -2/3"} {"input": "Solve the equation x^3 + 73/21x^2 + 67/21x + 5/7 = 0", "output": "x^3 + 73/21x^2 + 67/21x + 5/7 = 0\n(x - -1/3)(x - -15/7)(x - -1) = 0\nx - -1/3 = 0\nx - -15/7 = 0\nx - -1 = 0\nx = -1/3\nx = -15/7\nx = -1"} {"input": "What value of x satisfies x^3 + 257/210x^2 - 898/105x - 38/5 = 0", "output": "x^3 + 257/210x^2 - 898/105x - 38/5 = 0\n(x - 14/5)(x - -6/7)(x - -19/6) = 0\nx - 14/5 = 0\nx - -6/7 = 0\nx - -19/6 = 0\nx = 14/5\nx = -6/7\nx = -19/6"} {"input": "Solve x^3 + 75/14x^2 + 103/14x + 3 = 0", "output": "x^3 + 75/14x^2 + 103/14x + 3 = 0\n(x - -7/2)(x - -6/7)(x - -1) = 0\nx - -7/2 = 0\nx - -6/7 = 0\nx - -1 = 0\nx = -7/2\nx = -6/7\nx = -1"} {"input": "Solve x^2 - 104/5x + 171/5 = 0", "output": "x^2 - 104/5x + 171/5 = 0\n(x - 9/5)(x - 19) = 0\nx - 9/5 = 0 or x - 19 = 0\nx = 9/5\nx = 19"} {"input": "Solve the equations:\n8x + 7y = -21/10\n4x + 7y = -21/10", "output": "8x + 7y = -21/10\n4x + 7y = -21/10\n\nUsing elimination\n4*(8x + 7y = -21/10)\n8*(4x + 7y = -21/10)\n32x + 28y = -42/5\n32x + 56y = -84/5\nSubtract equations\n-28y = 42/5\ny = 42/5/-28\ny = -3/10\n\nSubstitute y\n8x + 7(-3/10) = -21/10\n8x = 0\nx = 0/8\nx = 0"} {"input": "Compute the solution of x^2 - 14/3x = 0", "output": "x^2 - 14/3x = 0\n(x - 14/3)(x - 0) = 0\nx - 14/3 = 0 or x - 0 = 0\nx = 14/3\nx = 0"} {"input": "Find x in x^2 + 19/5x + 13/4 = 0", "output": "x^2 + 19/5x + 13/4 = 0\n(x - -5/2)(x - -13/10) = 0\nx - -5/2 = 0 or x - -13/10 = 0\nx = -5/2\nx = -13/10"} {"input": "Solve the equation x^2 + 83/20x + 117/40 = 0", "output": "x^2 + 83/20x + 117/40 = 0\n(x - -9/10)(x - -13/4) = 0\nx - -9/10 = 0 or x - -13/4 = 0\nx = -9/10\nx = -13/4"} {"input": "Solve the system:\n8x + 4y = 328/15\n6x + 10y = 43", "output": "8x + 4y = 328/15\n6x + 10y = 43\n\nUsing elimination\n6*(8x + 4y = 328/15)\n8*(6x + 10y = 43)\n48x + 24y = 656/5\n48x + 80y = 344\nSubtract equations\n-56y = -1064/5\ny = -1064/5/-56\ny = 19/5\n\nSubstitute y\n8x + 4(19/5) = 328/15\n8x = 20/3\nx = 20/3/8\nx = 5/6"} {"input": "Find the solution to x^2 - 97/56x + 3/4 = 0", "output": "x^2 - 97/56x + 3/4 = 0\n(x - 7/8)(x - 6/7) = 0\nx - 7/8 = 0 or x - 6/7 = 0\nx = 7/8\nx = 6/7"} {"input": "Solve simultaneously:\n4x + 4y = -7/2\n4x + 5y = -43/8", "output": "4x + 4y = -7/2\n4x + 5y = -43/8\n\nUsing elimination\n4*(4x + 4y = -7/2)\n4*(4x + 5y = -43/8)\n16x + 16y = -14\n16x + 20y = -43/2\nSubtract equations\n-4y = 15/2\ny = 15/2/-4\ny = -15/8\n\nSubstitute y\n4x + 4(-15/8) = -7/2\n4x = 4\nx = 4/4\nx = 1"} {"input": "Compute the solution of x^3 + 17/3x^2 + 4x - 32/3 = 0", "output": "x^3 + 17/3x^2 + 4x - 32/3 = 0\n(x - 1)(x - -4)(x - -8/3) = 0\nx - 1 = 0\nx - -4 = 0\nx - -8/3 = 0\nx = 1\nx = -4\nx = -8/3"} {"input": "Solve quickly: x^3 + 77/4x^2 + 109/2x + 40 = 0", "output": "x^3 + 77/4x^2 + 109/2x + 40 = 0\n(x - -5/4)(x - -16)(x - -2) = 0\nx - -5/4 = 0\nx - -16 = 0\nx - -2 = 0\nx = -5/4\nx = -16\nx = -2"} {"input": "Determine x in x^2 - 11/30x - 1/5 = 0", "output": "x^2 - 11/30x - 1/5 = 0\n(x - -3/10)(x - 2/3) = 0\nx - -3/10 = 0 or x - 2/3 = 0\nx = -3/10\nx = 2/3"} {"input": "Solve the system:\n9x + 10y = 521/7\n1x + 3y = 124/7", "output": "9x + 10y = 521/7\n1x + 3y = 124/7\n\nUsing elimination\n1*(9x + 10y = 521/7)\n9*(1x + 3y = 124/7)\n9x + 10y = 521/7\n9x + 27y = 1116/7\nSubtract equations\n-17y = -85\ny = -85/-17\ny = 5\n\nSubstitute y\n9x + 10(5) = 521/7\n9x = 171/7\nx = 171/7/9\nx = 19/7"} {"input": "Solve the system:\n3x + 7y = -597/7\n2x + 1y = -90/7", "output": "3x + 7y = -597/7\n2x + 1y = -90/7\n\nUsing elimination\n2*(3x + 7y = -597/7)\n3*(2x + 1y = -90/7)\n6x + 14y = -1194/7\n6x + 3y = -270/7\nSubtract equations\n11y = -132\ny = -132/11\ny = -12\n\nSubstitute y\n3x + 7(-12) = -597/7\n3x = -9/7\nx = -9/7/3\nx = -3/7"} {"input": "Solve the equations:\n4x + 10y = 66/7\n4x + 8y = 40/7", "output": "4x + 10y = 66/7\n4x + 8y = 40/7\n\nUsing elimination\n4*(4x + 10y = 66/7)\n4*(4x + 8y = 40/7)\n16x + 40y = 264/7\n16x + 32y = 160/7\nSubtract equations\n8y = 104/7\ny = 104/7/8\ny = 13/7\n\nSubstitute y\n4x + 10(13/7) = 66/7\n4x = -64/7\nx = -64/7/4\nx = -16/7"} {"input": "Solve the equations:\n5x + 5y = 5/3\n3x + 1y = 3", "output": "5x + 5y = 5/3\n3x + 1y = 3\n\nUsing elimination\n3*(5x + 5y = 5/3)\n5*(3x + 1y = 3)\n15x + 15y = 5\n15x + 5y = 15\nSubtract equations\n10y = -10\ny = -10/10\ny = -1\n\nSubstitute y\n5x + 5(-1) = 5/3\n5x = 20/3\nx = 20/3/5\nx = 4/3"} {"input": "Find the solution to x^2 + 3/5x + 1/20 = 0", "output": "x^2 + 3/5x + 1/20 = 0\n(x - -1/10)(x - -1/2) = 0\nx - -1/10 = 0 or x - -1/2 = 0\nx = -1/10\nx = -1/2"} {"input": "Solve simultaneously:\n5x + 6y = -283/12\n2x + 7y = -323/24", "output": "5x + 6y = -283/12\n2x + 7y = -323/24\n\nUsing elimination\n2*(5x + 6y = -283/12)\n5*(2x + 7y = -323/24)\n10x + 12y = -283/6\n10x + 35y = -1615/24\nSubtract equations\n-23y = 161/8\ny = 161/8/-23\ny = -7/8\n\nSubstitute y\n5x + 6(-7/8) = -283/12\n5x = -55/3\nx = -55/3/5\nx = -11/3"} {"input": "Solve the equation x^2 - 25/3x + 28/3 = 0", "output": "x^2 - 25/3x + 28/3 = 0\n(x - 7)(x - 4/3) = 0\nx - 7 = 0 or x - 4/3 = 0\nx = 7\nx = 4/3"} {"input": "Solve the equation 7x + 7/3 = 0", "output": "7x + 7/3 = 0\n7x = -7/3\nx = -7/3 / 7\nx = -1/3"} {"input": "What value of x satisfies x^3 - 123/10x^2 + 593/25x + 684/25 = 0", "output": "x^3 - 123/10x^2 + 593/25x + 684/25 = 0\n(x - -4/5)(x - 19/2)(x - 18/5) = 0\nx - -4/5 = 0\nx - 19/2 = 0\nx - 18/5 = 0\nx = -4/5\nx = 19/2\nx = 18/5"} {"input": "Find x in x^3 + 79/84x^2 - 233/168x - 5/4 = 0", "output": "x^3 + 79/84x^2 - 233/168x - 5/4 = 0\n(x - -5/4)(x - -6/7)(x - 7/6) = 0\nx - -5/4 = 0\nx - -6/7 = 0\nx - 7/6 = 0\nx = -5/4\nx = -6/7\nx = 7/6"} {"input": "Solve the equation x^3 - 67/20x^2 - 117/10x + 153/4 = 0", "output": "x^3 - 67/20x^2 - 117/10x + 153/4 = 0\n(x - -17/5)(x - 15/4)(x - 3) = 0\nx - -17/5 = 0\nx - 15/4 = 0\nx - 3 = 0\nx = -17/5\nx = 15/4\nx = 3"} {"input": "Compute the solution of 4x + 28/9 = 0", "output": "4x + 28/9 = 0\n4x = -28/9\nx = -28/9 / 4\nx = -7/9"} {"input": "Solve simultaneously:\n2x + 2y = -3/10\n8x + 5y = -99/20", "output": "2x + 2y = -3/10\n8x + 5y = -99/20\n\nUsing elimination\n8*(2x + 2y = -3/10)\n2*(8x + 5y = -99/20)\n16x + 16y = -12/5\n16x + 10y = -99/10\nSubtract equations\n6y = 15/2\ny = 15/2/6\ny = 5/4\n\nSubstitute y\n2x + 2(5/4) = -3/10\n2x = -14/5\nx = -14/5/2\nx = -7/5"} {"input": "Solve the equations:\n1x + 9y = -193/12\n10x + 2y = -41/6", "output": "1x + 9y = -193/12\n10x + 2y = -41/6\n\nUsing elimination\n10*(1x + 9y = -193/12)\n1*(10x + 2y = -41/6)\n10x + 90y = -965/6\n10x + 2y = -41/6\nSubtract equations\n88y = -154\ny = -154/88\ny = -7/4\n\nSubstitute y\n1x + 9(-7/4) = -193/12\n1x = -1/3\nx = -1/3/1\nx = -1/3"} {"input": "Determine x in x^3 + 39/2x^2 + 205/2x + 150 = 0", "output": "x^3 + 39/2x^2 + 205/2x + 150 = 0\n(x - -5/2)(x - -12)(x - -5) = 0\nx - -5/2 = 0\nx - -12 = 0\nx - -5 = 0\nx = -5/2\nx = -12\nx = -5"} {"input": "Find x for x^3 - 153/35x^2 + 148/35x + 36/35 = 0", "output": "x^3 - 153/35x^2 + 148/35x + 36/35 = 0\n(x - 2)(x - 18/7)(x - -1/5) = 0\nx - 2 = 0\nx - 18/7 = 0\nx - -1/5 = 0\nx = 2\nx = 18/7\nx = -1/5"} {"input": "Solve simultaneously:\n6x + 3y = 27\n7x + 5y = 27", "output": "6x + 3y = 27\n7x + 5y = 27\n\nUsing elimination\n7*(6x + 3y = 27)\n6*(7x + 5y = 27)\n42x + 21y = 189\n42x + 30y = 162\nSubtract equations\n-9y = 27\ny = 27/-9\ny = -3\n\nSubstitute y\n6x + 3(-3) = 27\n6x = 36\nx = 36/6\nx = 6"} {"input": "Solve the equation x^2 + 127/35x + 22/7 = 0", "output": "x^2 + 127/35x + 22/7 = 0\n(x - -11/5)(x - -10/7) = 0\nx - -11/5 = 0 or x - -10/7 = 0\nx = -11/5\nx = -10/7"} {"input": "Solve the equations:\n4x + 4y = 128/9\n3x + 4y = 41/3", "output": "4x + 4y = 128/9\n3x + 4y = 41/3\n\nUsing elimination\n3*(4x + 4y = 128/9)\n4*(3x + 4y = 41/3)\n12x + 12y = 128/3\n12x + 16y = 164/3\nSubtract equations\n-4y = -12\ny = -12/-4\ny = 3\n\nSubstitute y\n4x + 4(3) = 128/9\n4x = 20/9\nx = 20/9/4\nx = 5/9"} {"input": "Find the solution to 4x - 52/9 = 0", "output": "4x - 52/9 = 0\n4x = 52/9\nx = 52/9 / 4\nx = 13/9"} {"input": "Compute the solution of 8x + 80/9 = 0", "output": "8x + 80/9 = 0\n8x = -80/9\nx = -80/9 / 8\nx = -10/9"} {"input": "What value of x satisfies x^3 + 91/9x^2 + 18x + 80/9 = 0", "output": "x^3 + 91/9x^2 + 18x + 80/9 = 0\n(x - -8)(x - -10/9)(x - -1) = 0\nx - -8 = 0\nx - -10/9 = 0\nx - -1 = 0\nx = -8\nx = -10/9\nx = -1"} {"input": "Compute the solution of x^2 + 53/42x - 22/21 = 0", "output": "x^2 + 53/42x - 22/21 = 0\n(x - 4/7)(x - -11/6) = 0\nx - 4/7 = 0 or x - -11/6 = 0\nx = 4/7\nx = -11/6"} {"input": "Solve simultaneously:\n9x + 9y = -18\n3x + 8y = -23/3", "output": "9x + 9y = -18\n3x + 8y = -23/3\n\nUsing elimination\n3*(9x + 9y = -18)\n9*(3x + 8y = -23/3)\n27x + 27y = -54\n27x + 72y = -69\nSubtract equations\n-45y = 15\ny = 15/-45\ny = -1/3\n\nSubstitute y\n9x + 9(-1/3) = -18\n9x = -15\nx = -15/9\nx = -5/3"} {"input": "Find the solution to x^2 - 181/28x + 285/28 = 0", "output": "x^2 - 181/28x + 285/28 = 0\n(x - 15/4)(x - 19/7) = 0\nx - 15/4 = 0 or x - 19/7 = 0\nx = 15/4\nx = 19/7"} {"input": "Solve the equations:\n3x + 10y = -19/3\n8x + 1y = -25/3", "output": "3x + 10y = -19/3\n8x + 1y = -25/3\n\nUsing elimination\n8*(3x + 10y = -19/3)\n3*(8x + 1y = -25/3)\n24x + 80y = -152/3\n24x + 3y = -25\nSubtract equations\n77y = -77/3\ny = -77/3/77\ny = -1/3\n\nSubstitute y\n3x + 10(-1/3) = -19/3\n3x = -3\nx = -3/3\nx = -1"} {"input": "Solve x^3 + 4/5x^2 - 1473/20x + 171/2 = 0", "output": "x^3 + 4/5x^2 - 1473/20x + 171/2 = 0\n(x - -19/2)(x - 6/5)(x - 15/2) = 0\nx - -19/2 = 0\nx - 6/5 = 0\nx - 15/2 = 0\nx = -19/2\nx = 6/5\nx = 15/2"} {"input": "Solve quickly: x^2 + 1/3x - 10/3 = 0", "output": "x^2 + 1/3x - 10/3 = 0\n(x - -2)(x - 5/3) = 0\nx - -2 = 0 or x - 5/3 = 0\nx = -2\nx = 5/3"} {"input": "Find x in x^2 - 17/8x - 15/2 = 0", "output": "x^2 - 17/8x - 15/2 = 0\n(x - -15/8)(x - 4) = 0\nx - -15/8 = 0 or x - 4 = 0\nx = -15/8\nx = 4"} {"input": "What value of x satisfies 1x + 5/2 = 0", "output": "1x + 5/2 = 0\n1x = -5/2\nx = -5/2 / 1\nx = -5/2"} {"input": "Find x in x^3 - 23/2x^2 + 611/16x - 1183/32 = 0", "output": "x^3 - 23/2x^2 + 611/16x - 1183/32 = 0\n(x - 7/4)(x - 13/4)(x - 13/2) = 0\nx - 7/4 = 0\nx - 13/4 = 0\nx - 13/2 = 0\nx = 7/4\nx = 13/4\nx = 13/2"} {"input": "Solve the system:\n2x + 2y = 62/3\n4x + 10y = 304/3", "output": "2x + 2y = 62/3\n4x + 10y = 304/3\n\nUsing elimination\n4*(2x + 2y = 62/3)\n2*(4x + 10y = 304/3)\n8x + 8y = 248/3\n8x + 20y = 608/3\nSubtract equations\n-12y = -120\ny = -120/-12\ny = 10\n\nSubstitute y\n2x + 2(10) = 62/3\n2x = 2/3\nx = 2/3/2\nx = 1/3"} {"input": "Find x and y such that\n5x + 3y = -57/20\n2x + 4y = -3/10", "output": "5x + 3y = -57/20\n2x + 4y = -3/10\n\nUsing elimination\n2*(5x + 3y = -57/20)\n5*(2x + 4y = -3/10)\n10x + 6y = -57/10\n10x + 20y = -3/2\nSubtract equations\n-14y = -21/5\ny = -21/5/-14\ny = 3/10\n\nSubstitute y\n5x + 3(3/10) = -57/20\n5x = -15/4\nx = -15/4/5\nx = -3/4"} {"input": "Compute the solution of 6x + 28 = 0", "output": "6x + 28 = 0\n6x = -28\nx = -28 / 6\nx = -14/3"} {"input": "Determine x in x^2 + 86/45x + 8/9 = 0", "output": "x^2 + 86/45x + 8/9 = 0\n(x - -4/5)(x - -10/9) = 0\nx - -4/5 = 0 or x - -10/9 = 0\nx = -4/5\nx = -10/9"} {"input": "Solve x^3 + 29/45x^2 - 91/15x + 3 = 0", "output": "x^3 + 29/45x^2 - 91/15x + 3 = 0\n(x - 9/5)(x - 5/9)(x - -3) = 0\nx - 9/5 = 0\nx - 5/9 = 0\nx - -3 = 0\nx = 9/5\nx = 5/9\nx = -3"} {"input": "Find x for 10x + 34 = 0", "output": "10x + 34 = 0\n10x = -34\nx = -34 / 10\nx = -17/5"} {"input": "Solve the equations:\n5x + 7y = 31/2\n5x + 8y = 20", "output": "5x + 7y = 31/2\n5x + 8y = 20\n\nUsing elimination\n5*(5x + 7y = 31/2)\n5*(5x + 8y = 20)\n25x + 35y = 155/2\n25x + 40y = 100\nSubtract equations\n-5y = -45/2\ny = -45/2/-5\ny = 9/2\n\nSubstitute y\n5x + 7(9/2) = 31/2\n5x = -16\nx = -16/5\nx = -16/5"} {"input": "Find x and y such that\n5x + 10y = 0\n6x + 1y = 110/3", "output": "5x + 10y = 0\n6x + 1y = 110/3\n\nUsing elimination\n6*(5x + 10y = 0)\n5*(6x + 1y = 110/3)\n30x + 60y = 0\n30x + 5y = 550/3\nSubtract equations\n55y = -550/3\ny = -550/3/55\ny = -10/3\n\nSubstitute y\n5x + 10(-10/3) = 0\n5x = 100/3\nx = 100/3/5\nx = 20/3"} {"input": "Find x and y such that\n4x + 7y = -5/3\n10x + 1y = -29/3", "output": "4x + 7y = -5/3\n10x + 1y = -29/3\n\nUsing elimination\n10*(4x + 7y = -5/3)\n4*(10x + 1y = -29/3)\n40x + 70y = -50/3\n40x + 4y = -116/3\nSubtract equations\n66y = 22\ny = 22/66\ny = 1/3\n\nSubstitute y\n4x + 7(1/3) = -5/3\n4x = -4\nx = -4/4\nx = -1"} {"input": "Solve simultaneously:\n3x + 7y = 259/4\n10x + 8y = 166", "output": "3x + 7y = 259/4\n10x + 8y = 166\n\nUsing elimination\n10*(3x + 7y = 259/4)\n3*(10x + 8y = 166)\n30x + 70y = 1295/2\n30x + 24y = 498\nSubtract equations\n46y = 299/2\ny = 299/2/46\ny = 13/4\n\nSubstitute y\n3x + 7(13/4) = 259/4\n3x = 42\nx = 42/3\nx = 14"} {"input": "Compute the solution of 5x - 16 = 0", "output": "5x - 16 = 0\n5x = 16\nx = 16 / 5\nx = 16/5"} {"input": "Solve the equations:\n2x + 3y = 1\n7x + 1y = 45/2", "output": "2x + 3y = 1\n7x + 1y = 45/2\n\nUsing elimination\n7*(2x + 3y = 1)\n2*(7x + 1y = 45/2)\n14x + 21y = 7\n14x + 2y = 45\nSubtract equations\n19y = -38\ny = -38/19\ny = -2\n\nSubstitute y\n2x + 3(-2) = 1\n2x = 7\nx = 7/2\nx = 7/2"} {"input": "Solve the system:\n3x + 10y = -17/4\n7x + 6y = -5/4", "output": "3x + 10y = -17/4\n7x + 6y = -5/4\n\nUsing elimination\n7*(3x + 10y = -17/4)\n3*(7x + 6y = -5/4)\n21x + 70y = -119/4\n21x + 18y = -15/4\nSubtract equations\n52y = -26\ny = -26/52\ny = -1/2\n\nSubstitute y\n3x + 10(-1/2) = -17/4\n3x = 3/4\nx = 3/4/3\nx = 1/4"} {"input": "Solve the system:\n4x + 3y = -313/5\n6x + 9y = -429/5", "output": "4x + 3y = -313/5\n6x + 9y = -429/5\n\nUsing elimination\n6*(4x + 3y = -313/5)\n4*(6x + 9y = -429/5)\n24x + 18y = -1878/5\n24x + 36y = -1716/5\nSubtract equations\n-18y = -162/5\ny = -162/5/-18\ny = 9/5\n\nSubstitute y\n4x + 3(9/5) = -313/5\n4x = -68\nx = -68/4\nx = -17"} {"input": "Find x and y such that\n5x + 7y = 389/12\n7x + 10y = 275/6", "output": "5x + 7y = 389/12\n7x + 10y = 275/6\n\nUsing elimination\n7*(5x + 7y = 389/12)\n5*(7x + 10y = 275/6)\n35x + 49y = 2723/12\n35x + 50y = 1375/6\nSubtract equations\n-1y = -9/4\ny = -9/4/-1\ny = 9/4\n\nSubstitute y\n5x + 7(9/4) = 389/12\n5x = 50/3\nx = 50/3/5\nx = 10/3"} {"input": "Find the solution to x^3 - 31/10x^2 + 3/2x = 0", "output": "x^3 - 31/10x^2 + 3/2x = 0\n(x - 3/5)(x - 0)(x - 5/2) = 0\nx - 3/5 = 0\nx - 0 = 0\nx - 5/2 = 0\nx = 3/5\nx = 0\nx = 5/2"} {"input": "Find the solution to 9x - 9/4 = 0", "output": "9x - 9/4 = 0\n9x = 9/4\nx = 9/4 / 9\nx = 1/4"} {"input": "Determine x in 6x - 17 = 0", "output": "6x - 17 = 0\n6x = 17\nx = 17 / 6\nx = 17/6"} {"input": "Find x and y such that\n5x + 1y = 48\n10x + 7y = 197/2", "output": "5x + 1y = 48\n10x + 7y = 197/2\n\nUsing elimination\n10*(5x + 1y = 48)\n5*(10x + 7y = 197/2)\n50x + 10y = 480\n50x + 35y = 985/2\nSubtract equations\n-25y = -25/2\ny = -25/2/-25\ny = 1/2\n\nSubstitute y\n5x + 1(1/2) = 48\n5x = 95/2\nx = 95/2/5\nx = 19/2"} {"input": "Solve quickly: x^3 + 20/3x^2 + 13/3x - 20 = 0", "output": "x^3 + 20/3x^2 + 13/3x - 20 = 0\n(x - -3)(x - 4/3)(x - -5) = 0\nx - -3 = 0\nx - 4/3 = 0\nx - -5 = 0\nx = -3\nx = 4/3\nx = -5"} {"input": "Find x and y such that\n8x + 2y = -19/15\n8x + 7y = -13/30", "output": "8x + 2y = -19/15\n8x + 7y = -13/30\n\nUsing elimination\n8*(8x + 2y = -19/15)\n8*(8x + 7y = -13/30)\n64x + 16y = -152/15\n64x + 56y = -52/15\nSubtract equations\n-40y = -20/3\ny = -20/3/-40\ny = 1/6\n\nSubstitute y\n8x + 2(1/6) = -19/15\n8x = -8/5\nx = -8/5/8\nx = -1/5"} {"input": "Find x for x^3 - 5/6x^2 - 8/3x + 5/2 = 0", "output": "x^3 - 5/6x^2 - 8/3x + 5/2 = 0\n(x - 3/2)(x - -5/3)(x - 1) = 0\nx - 3/2 = 0\nx - -5/3 = 0\nx - 1 = 0\nx = 3/2\nx = -5/3\nx = 1"} {"input": "Find x and y such that\n9x + 10y = -34/9\n5x + 6y = -2", "output": "9x + 10y = -34/9\n5x + 6y = -2\n\nUsing elimination\n5*(9x + 10y = -34/9)\n9*(5x + 6y = -2)\n45x + 50y = -170/9\n45x + 54y = -18\nSubtract equations\n-4y = -8/9\ny = -8/9/-4\ny = 2/9\n\nSubstitute y\n9x + 10(2/9) = -34/9\n9x = -6\nx = -6/9\nx = -2/3"} {"input": "Solve x^2 + 26/3x + 16/3 = 0", "output": "x^2 + 26/3x + 16/3 = 0\n(x - -8)(x - -2/3) = 0\nx - -8 = 0 or x - -2/3 = 0\nx = -8\nx = -2/3"} {"input": "Solve simultaneously:\n2x + 6y = -266/15\n7x + 6y = -616/15", "output": "2x + 6y = -266/15\n7x + 6y = -616/15\n\nUsing elimination\n7*(2x + 6y = -266/15)\n2*(7x + 6y = -616/15)\n14x + 42y = -1862/15\n14x + 12y = -1232/15\nSubtract equations\n30y = -42\ny = -42/30\ny = -7/5\n\nSubstitute y\n2x + 6(-7/5) = -266/15\n2x = -28/3\nx = -28/3/2\nx = -14/3"} {"input": "Solve x^2 + 10x + 16 = 0", "output": "x^2 + 10x + 16 = 0\n(x - -2)(x - -8) = 0\nx - -2 = 0 or x - -8 = 0\nx = -2\nx = -8"} {"input": "Find x and y such that\n2x + 5y = -75/7\n3x + 4y = -88/7", "output": "2x + 5y = -75/7\n3x + 4y = -88/7\n\nUsing elimination\n3*(2x + 5y = -75/7)\n2*(3x + 4y = -88/7)\n6x + 15y = -225/7\n6x + 8y = -176/7\nSubtract equations\n7y = -7\ny = -7/7\ny = -1\n\nSubstitute y\n2x + 5(-1) = -75/7\n2x = -40/7\nx = -40/7/2\nx = -20/7"} {"input": "Solve quickly: x^3 - 93/10x^2 + 1367/100x - 51/40 = 0", "output": "x^3 - 93/10x^2 + 1367/100x - 51/40 = 0\n(x - 15/2)(x - 17/10)(x - 1/10) = 0\nx - 15/2 = 0\nx - 17/10 = 0\nx - 1/10 = 0\nx = 15/2\nx = 17/10\nx = 1/10"} {"input": "Solve the equation 7x + 56/5 = 0", "output": "7x + 56/5 = 0\n7x = -56/5\nx = -56/5 / 7\nx = -8/5"} {"input": "Solve the equation 10x - 10/3 = 0", "output": "10x - 10/3 = 0\n10x = 10/3\nx = 10/3 / 10\nx = 1/3"} {"input": "Find x and y such that\n8x + 3y = -127/7\n7x + 8y = -52/7", "output": "8x + 3y = -127/7\n7x + 8y = -52/7\n\nUsing elimination\n7*(8x + 3y = -127/7)\n8*(7x + 8y = -52/7)\n56x + 21y = -127\n56x + 64y = -416/7\nSubtract equations\n-43y = -473/7\ny = -473/7/-43\ny = 11/7\n\nSubstitute y\n8x + 3(11/7) = -127/7\n8x = -160/7\nx = -160/7/8\nx = -20/7"} {"input": "Solve x^2 + 13/4x - 35/4 = 0", "output": "x^2 + 13/4x - 35/4 = 0\n(x - -5)(x - 7/4) = 0\nx - -5 = 0 or x - 7/4 = 0\nx = -5\nx = 7/4"} {"input": "Solve simultaneously:\n9x + 8y = -66\n10x + 1y = -97", "output": "9x + 8y = -66\n10x + 1y = -97\n\nUsing elimination\n10*(9x + 8y = -66)\n9*(10x + 1y = -97)\n90x + 80y = -660\n90x + 9y = -873\nSubtract equations\n71y = 213\ny = 213/71\ny = 3\n\nSubstitute y\n9x + 8(3) = -66\n9x = -90\nx = -90/9\nx = -10"} {"input": "Find the solution to x^3 - 1229/56x^2 + 4187/56x - 1881/28 = 0", "output": "x^3 - 1229/56x^2 + 4187/56x - 1881/28 = 0\n(x - 18)(x - 11/7)(x - 19/8) = 0\nx - 18 = 0\nx - 11/7 = 0\nx - 19/8 = 0\nx = 18\nx = 11/7\nx = 19/8"} {"input": "Find x and y such that\n5x + 10y = -13/3\n3x + 5y = -2", "output": "5x + 10y = -13/3\n3x + 5y = -2\n\nUsing elimination\n3*(5x + 10y = -13/3)\n5*(3x + 5y = -2)\n15x + 30y = -13\n15x + 25y = -10\nSubtract equations\n5y = -3\ny = -3/5\ny = -3/5\n\nSubstitute y\n5x + 10(-3/5) = -13/3\n5x = 5/3\nx = 5/3/5\nx = 1/3"} {"input": "Solve x^3 - 29/14x^2 - 9/7x = 0", "output": "x^3 - 29/14x^2 - 9/7x = 0\n(x - 18/7)(x - 0)(x - -1/2) = 0\nx - 18/7 = 0\nx - 0 = 0\nx - -1/2 = 0\nx = 18/7\nx = 0\nx = -1/2"} {"input": "Solve the system:\n7x + 7y = -119/4\n1x + 5y = -21/4", "output": "7x + 7y = -119/4\n1x + 5y = -21/4\n\nUsing elimination\n1*(7x + 7y = -119/4)\n7*(1x + 5y = -21/4)\n7x + 7y = -119/4\n7x + 35y = -147/4\nSubtract equations\n-28y = 7\ny = 7/-28\ny = -1/4\n\nSubstitute y\n7x + 7(-1/4) = -119/4\n7x = -28\nx = -28/7\nx = -4"} {"input": "Solve the equation x^2 + 19/5x - 6 = 0", "output": "x^2 + 19/5x - 6 = 0\n(x - 6/5)(x - -5) = 0\nx - 6/5 = 0 or x - -5 = 0\nx = 6/5\nx = -5"} {"input": "Find x in x^2 - 4x - 5 = 0", "output": "x^2 - 4x - 5 = 0\n(x - -1)(x - 5) = 0\nx - -1 = 0 or x - 5 = 0\nx = -1\nx = 5"} {"input": "Compute the solution of x^2 + 3/5x - 8/5 = 0", "output": "x^2 + 3/5x - 8/5 = 0\n(x - 1)(x - -8/5) = 0\nx - 1 = 0 or x - -8/5 = 0\nx = 1\nx = -8/5"} {"input": "Find x for x^3 + 11/2x^2 - 6x - 18 = 0", "output": "x^3 + 11/2x^2 - 6x - 18 = 0\n(x - 2)(x - -3/2)(x - -6) = 0\nx - 2 = 0\nx - -3/2 = 0\nx - -6 = 0\nx = 2\nx = -3/2\nx = -6"} {"input": "Solve 4x + 11 = 0", "output": "4x + 11 = 0\n4x = -11\nx = -11 / 4\nx = -11/4"} {"input": "Find x and y such that\n6x + 7y = -29/10\n6x + 10y = -7/2", "output": "6x + 7y = -29/10\n6x + 10y = -7/2\n\nUsing elimination\n6*(6x + 7y = -29/10)\n6*(6x + 10y = -7/2)\n36x + 42y = -87/5\n36x + 60y = -21\nSubtract equations\n-18y = 18/5\ny = 18/5/-18\ny = -1/5\n\nSubstitute y\n6x + 7(-1/5) = -29/10\n6x = -3/2\nx = -3/2/6\nx = -1/4"} {"input": "Find the solution to 5x + 20 = 0", "output": "5x + 20 = 0\n5x = -20\nx = -20 / 5\nx = -4"} {"input": "Solve simultaneously:\n7x + 1y = 15\n1x + 3y = -85/7", "output": "7x + 1y = 15\n1x + 3y = -85/7\n\nUsing elimination\n1*(7x + 1y = 15)\n7*(1x + 3y = -85/7)\n7x + 1y = 15\n7x + 21y = -85\nSubtract equations\n-20y = 100\ny = 100/-20\ny = -5\n\nSubstitute y\n7x + 1(-5) = 15\n7x = 20\nx = 20/7\nx = 20/7"} {"input": "Find x and y such that\n8x + 10y = -72\n5x + 3y = -199/5", "output": "8x + 10y = -72\n5x + 3y = -199/5\n\nUsing elimination\n5*(8x + 10y = -72)\n8*(5x + 3y = -199/5)\n40x + 50y = -360\n40x + 24y = -1592/5\nSubtract equations\n26y = -208/5\ny = -208/5/26\ny = -8/5\n\nSubstitute y\n8x + 10(-8/5) = -72\n8x = -56\nx = -56/8\nx = -7"} {"input": "Solve simultaneously:\n8x + 9y = 33\n3x + 6y = 95/4", "output": "8x + 9y = 33\n3x + 6y = 95/4\n\nUsing elimination\n3*(8x + 9y = 33)\n8*(3x + 6y = 95/4)\n24x + 27y = 99\n24x + 48y = 190\nSubtract equations\n-21y = -91\ny = -91/-21\ny = 13/3\n\nSubstitute y\n8x + 9(13/3) = 33\n8x = -6\nx = -6/8\nx = -3/4"} {"input": "What value of x satisfies x^3 - 16/3x^2 - 121/12x + 95/4 = 0", "output": "x^3 - 16/3x^2 - 121/12x + 95/4 = 0\n(x - -5/2)(x - 19/3)(x - 3/2) = 0\nx - -5/2 = 0\nx - 19/3 = 0\nx - 3/2 = 0\nx = -5/2\nx = 19/3\nx = 3/2"} {"input": "Find x in x^2 - 31/8x - 45/8 = 0", "output": "x^2 - 31/8x - 45/8 = 0\n(x - -9/8)(x - 5) = 0\nx - -9/8 = 0 or x - 5 = 0\nx = -9/8\nx = 5"} {"input": "Determine x in 10x - 90 = 0", "output": "10x - 90 = 0\n10x = 90\nx = 90 / 10\nx = 9"} {"input": "What value of x satisfies x^3 - 397/42x^2 + 313/21x + 95/6 = 0", "output": "x^3 - 397/42x^2 + 313/21x + 95/6 = 0\n(x - -5/7)(x - 19/6)(x - 7) = 0\nx - -5/7 = 0\nx - 19/6 = 0\nx - 7 = 0\nx = -5/7\nx = 19/6\nx = 7"} {"input": "Determine x in x^3 + 13/6x^2 - 3/2x - 5/3 = 0", "output": "x^3 + 13/6x^2 - 3/2x - 5/3 = 0\n(x - 1)(x - -2/3)(x - -5/2) = 0\nx - 1 = 0\nx - -2/3 = 0\nx - -5/2 = 0\nx = 1\nx = -2/3\nx = -5/2"} {"input": "Find x and y such that\n2x + 5y = -1\n6x + 9y = -27/5", "output": "2x + 5y = -1\n6x + 9y = -27/5\n\nUsing elimination\n6*(2x + 5y = -1)\n2*(6x + 9y = -27/5)\n12x + 30y = -6\n12x + 18y = -54/5\nSubtract equations\n12y = 24/5\ny = 24/5/12\ny = 2/5\n\nSubstitute y\n2x + 5(2/5) = -1\n2x = -3\nx = -3/2\nx = -3/2"} {"input": "Find the solution to x^3 - 37/40x^2 - 31/40x + 7/10 = 0", "output": "x^3 - 37/40x^2 - 31/40x + 7/10 = 0\n(x - 1)(x - -7/8)(x - 4/5) = 0\nx - 1 = 0\nx - -7/8 = 0\nx - 4/5 = 0\nx = 1\nx = -7/8\nx = 4/5"} {"input": "Solve quickly: 6x - 54/5 = 0", "output": "6x - 54/5 = 0\n6x = 54/5\nx = 54/5 / 6\nx = 9/5"} {"input": "Solve the equation x^3 - 53/28x^2 - 95/7x = 0", "output": "x^3 - 53/28x^2 - 95/7x = 0\n(x - 0)(x - -20/7)(x - 19/4) = 0\nx - 0 = 0\nx - -20/7 = 0\nx - 19/4 = 0\nx = 0\nx = -20/7\nx = 19/4"} {"input": "Compute the solution of x^3 - 23/10x^2 - 427/80x + 441/40 = 0", "output": "x^3 - 23/10x^2 - 427/80x + 441/40 = 0\n(x - 14/5)(x - -9/4)(x - 7/4) = 0\nx - 14/5 = 0\nx - -9/4 = 0\nx - 7/4 = 0\nx = 14/5\nx = -9/4\nx = 7/4"} {"input": "Solve the equations:\n3x + 4y = 97/7\n9x + 1y = 163/28", "output": "3x + 4y = 97/7\n9x + 1y = 163/28\n\nUsing elimination\n9*(3x + 4y = 97/7)\n3*(9x + 1y = 163/28)\n27x + 36y = 873/7\n27x + 3y = 489/28\nSubtract equations\n33y = 429/4\ny = 429/4/33\ny = 13/4\n\nSubstitute y\n3x + 4(13/4) = 97/7\n3x = 6/7\nx = 6/7/3\nx = 2/7"} {"input": "Solve x^2 - 3x - 10 = 0", "output": "x^2 - 3x - 10 = 0\n(x - 5)(x - -2) = 0\nx - 5 = 0 or x - -2 = 0\nx = 5\nx = -2"} {"input": "Solve the equations:\n7x + 7y = 47\n10x + 3y = 127/7", "output": "7x + 7y = 47\n10x + 3y = 127/7\n\nUsing elimination\n10*(7x + 7y = 47)\n7*(10x + 3y = 127/7)\n70x + 70y = 470\n70x + 21y = 127\nSubtract equations\n49y = 343\ny = 343/49\ny = 7\n\nSubstitute y\n7x + 7(7) = 47\n7x = -2\nx = -2/7\nx = -2/7"} {"input": "Find the solution to 7x + 21/2 = 0", "output": "7x + 21/2 = 0\n7x = -21/2\nx = -21/2 / 7\nx = -3/2"} {"input": "Solve simultaneously:\n2x + 8y = 8/3\n7x + 9y = 22", "output": "2x + 8y = 8/3\n7x + 9y = 22\n\nUsing elimination\n7*(2x + 8y = 8/3)\n2*(7x + 9y = 22)\n14x + 56y = 56/3\n14x + 18y = 44\nSubtract equations\n38y = -76/3\ny = -76/3/38\ny = -2/3\n\nSubstitute y\n2x + 8(-2/3) = 8/3\n2x = 8\nx = 8/2\nx = 4"} {"input": "Solve 5x - 25/8 = 0", "output": "5x - 25/8 = 0\n5x = 25/8\nx = 25/8 / 5\nx = 5/8"} {"input": "Find x for 1x - 5/2 = 0", "output": "1x - 5/2 = 0\n1x = 5/2\nx = 5/2 / 1\nx = 5/2"} {"input": "Solve the equations:\n7x + 9y = -101/6\n6x + 3y = -5", "output": "7x + 9y = -101/6\n6x + 3y = -5\n\nUsing elimination\n6*(7x + 9y = -101/6)\n7*(6x + 3y = -5)\n42x + 54y = -101\n42x + 21y = -35\nSubtract equations\n33y = -66\ny = -66/33\ny = -2\n\nSubstitute y\n7x + 9(-2) = -101/6\n7x = 7/6\nx = 7/6/7\nx = 1/6"} {"input": "Determine x in x^2 - 7/5x + 2/5 = 0", "output": "x^2 - 7/5x + 2/5 = 0\n(x - 1)(x - 2/5) = 0\nx - 1 = 0 or x - 2/5 = 0\nx = 1\nx = 2/5"} {"input": "Solve 9x - 27/2 = 0", "output": "9x - 27/2 = 0\n9x = 27/2\nx = 27/2 / 9\nx = 3/2"} {"input": "Solve the equation x^2 + 2x = 0", "output": "x^2 + 2x = 0\n(x - 0)(x - -2) = 0\nx - 0 = 0 or x - -2 = 0\nx = 0\nx = -2"} {"input": "Compute the solution of 2x - 12 = 0", "output": "2x - 12 = 0\n2x = 12\nx = 12 / 2\nx = 6"} {"input": "Solve quickly: x^3 - 143/28x^2 + 309/56x - 45/28 = 0", "output": "x^3 - 143/28x^2 + 309/56x - 45/28 = 0\n(x - 1/2)(x - 15/4)(x - 6/7) = 0\nx - 1/2 = 0\nx - 15/4 = 0\nx - 6/7 = 0\nx = 1/2\nx = 15/4\nx = 6/7"} {"input": "What value of x satisfies x^3 + 61/5x^2 + 111/4x - 189/20 = 0", "output": "x^3 + 61/5x^2 + 111/4x - 189/20 = 0\n(x - -7/2)(x - -9)(x - 3/10) = 0\nx - -7/2 = 0\nx - -9 = 0\nx - 3/10 = 0\nx = -7/2\nx = -9\nx = 3/10"} {"input": "Find the solution to x^3 + 53/6x^2 + 24x + 56/3 = 0", "output": "x^3 + 53/6x^2 + 24x + 56/3 = 0\n(x - -4)(x - -4/3)(x - -7/2) = 0\nx - -4 = 0\nx - -4/3 = 0\nx - -7/2 = 0\nx = -4\nx = -4/3\nx = -7/2"} {"input": "Solve simultaneously:\n5x + 7y = 29/6\n4x + 7y = 47/6", "output": "5x + 7y = 29/6\n4x + 7y = 47/6\n\nUsing elimination\n4*(5x + 7y = 29/6)\n5*(4x + 7y = 47/6)\n20x + 28y = 58/3\n20x + 35y = 235/6\nSubtract equations\n-7y = -119/6\ny = -119/6/-7\ny = 17/6\n\nSubstitute y\n5x + 7(17/6) = 29/6\n5x = -15\nx = -15/5\nx = -3"} {"input": "Find the solution to x^3 - 19/30x^2 - 271/25x + 396/25 = 0", "output": "x^3 - 19/30x^2 - 271/25x + 396/25 = 0\n(x - 11/6)(x - -18/5)(x - 12/5) = 0\nx - 11/6 = 0\nx - -18/5 = 0\nx - 12/5 = 0\nx = 11/6\nx = -18/5\nx = 12/5"} {"input": "Solve the equation x^3 - 10/9x^2 - 272/81x + 256/81 = 0", "output": "x^3 - 10/9x^2 - 272/81x + 256/81 = 0\n(x - 8/9)(x - -16/9)(x - 2) = 0\nx - 8/9 = 0\nx - -16/9 = 0\nx - 2 = 0\nx = 8/9\nx = -16/9\nx = 2"} {"input": "Solve the system:\n4x + 2y = 88\n6x + 8y = 162", "output": "4x + 2y = 88\n6x + 8y = 162\n\nUsing elimination\n6*(4x + 2y = 88)\n4*(6x + 8y = 162)\n24x + 12y = 528\n24x + 32y = 648\nSubtract equations\n-20y = -120\ny = -120/-20\ny = 6\n\nSubstitute y\n4x + 2(6) = 88\n4x = 76\nx = 76/4\nx = 19"} {"input": "Solve quickly: x^2 - 4x - 153/4 = 0", "output": "x^2 - 4x - 153/4 = 0\n(x - -9/2)(x - 17/2) = 0\nx - -9/2 = 0 or x - 17/2 = 0\nx = -9/2\nx = 17/2"} {"input": "Solve the equation x^3 + 22/15x^2 - 28/15x - 8/5 = 0", "output": "x^3 + 22/15x^2 - 28/15x - 8/5 = 0\n(x - -2)(x - -2/3)(x - 6/5) = 0\nx - -2 = 0\nx - -2/3 = 0\nx - 6/5 = 0\nx = -2\nx = -2/3\nx = 6/5"} {"input": "Solve quickly: x^2 - 11/24x - 7/6 = 0", "output": "x^2 - 11/24x - 7/6 = 0\n(x - 4/3)(x - -7/8) = 0\nx - 4/3 = 0 or x - -7/8 = 0\nx = 4/3\nx = -7/8"} {"input": "Find x in x^2 - 87/5x + 112/5 = 0", "output": "x^2 - 87/5x + 112/5 = 0\n(x - 16)(x - 7/5) = 0\nx - 16 = 0 or x - 7/5 = 0\nx = 16\nx = 7/5"} {"input": "Compute the solution of 10x + 14 = 0", "output": "10x + 14 = 0\n10x = -14\nx = -14 / 10\nx = -7/5"} {"input": "Find the solution to 6x - 22 = 0", "output": "6x - 22 = 0\n6x = 22\nx = 22 / 6\nx = 11/3"} {"input": "Solve the system:\n9x + 4y = 53\n1x + 6y = 43/4", "output": "9x + 4y = 53\n1x + 6y = 43/4\n\nUsing elimination\n1*(9x + 4y = 53)\n9*(1x + 6y = 43/4)\n9x + 4y = 53\n9x + 54y = 387/4\nSubtract equations\n-50y = -175/4\ny = -175/4/-50\ny = 7/8\n\nSubstitute y\n9x + 4(7/8) = 53\n9x = 99/2\nx = 99/2/9\nx = 11/2"} {"input": "Find x and y such that\n2x + 6y = -4\n4x + 10y = -8", "output": "2x + 6y = -4\n4x + 10y = -8\n\nUsing elimination\n4*(2x + 6y = -4)\n2*(4x + 10y = -8)\n8x + 24y = -16\n8x + 20y = -16\nSubtract equations\n4y = 0\ny = 0/4\ny = 0\n\nSubstitute y\n2x + 6(0) = -4\n2x = -4\nx = -4/2\nx = -2"} {"input": "Solve the equation x^2 - 7x = 0", "output": "x^2 - 7x = 0\n(x - 0)(x - 7) = 0\nx - 0 = 0 or x - 7 = 0\nx = 0\nx = 7"} {"input": "Find x for 4x - 11 = 0", "output": "4x - 11 = 0\n4x = 11\nx = 11 / 4\nx = 11/4"} {"input": "Solve quickly: x^3 + 277/36x^2 + 275/18x + 325/36 = 0", "output": "x^3 + 277/36x^2 + 275/18x + 325/36 = 0\n(x - -5/4)(x - -13/9)(x - -5) = 0\nx - -5/4 = 0\nx - -13/9 = 0\nx - -5 = 0\nx = -5/4\nx = -13/9\nx = -5"} {"input": "Solve simultaneously:\n1x + 4y = 11/3\n4x + 4y = 8/3", "output": "1x + 4y = 11/3\n4x + 4y = 8/3\n\nUsing elimination\n4*(1x + 4y = 11/3)\n1*(4x + 4y = 8/3)\n4x + 16y = 44/3\n4x + 4y = 8/3\nSubtract equations\n12y = 12\ny = 12/12\ny = 1\n\nSubstitute y\n1x + 4(1) = 11/3\n1x = -1/3\nx = -1/3/1\nx = -1/3"} {"input": "What value of x satisfies x^2 - 9/7x + 2/7 = 0", "output": "x^2 - 9/7x + 2/7 = 0\n(x - 1)(x - 2/7) = 0\nx - 1 = 0 or x - 2/7 = 0\nx = 1\nx = 2/7"} {"input": "Find x and y such that\n6x + 1y = 47/14\n3x + 2y = -1/28", "output": "6x + 1y = 47/14\n3x + 2y = -1/28\n\nUsing elimination\n3*(6x + 1y = 47/14)\n6*(3x + 2y = -1/28)\n18x + 3y = 141/14\n18x + 12y = -3/14\nSubtract equations\n-9y = 72/7\ny = 72/7/-9\ny = -8/7\n\nSubstitute y\n6x + 1(-8/7) = 47/14\n6x = 9/2\nx = 9/2/6\nx = 3/4"} {"input": "Determine x in x^2 - 11/6x + 1/2 = 0", "output": "x^2 - 11/6x + 1/2 = 0\n(x - 3/2)(x - 1/3) = 0\nx - 3/2 = 0 or x - 1/3 = 0\nx = 3/2\nx = 1/3"} {"input": "Solve the system:\n8x + 8y = -776/5\n5x + 3y = -451/5", "output": "8x + 8y = -776/5\n5x + 3y = -451/5\n\nUsing elimination\n5*(8x + 8y = -776/5)\n8*(5x + 3y = -451/5)\n40x + 40y = -776\n40x + 24y = -3608/5\nSubtract equations\n16y = -272/5\ny = -272/5/16\ny = -17/5\n\nSubstitute y\n8x + 8(-17/5) = -776/5\n8x = -128\nx = -128/8\nx = -16"} {"input": "Solve quickly: 10x + 70/3 = 0", "output": "10x + 70/3 = 0\n10x = -70/3\nx = -70/3 / 10\nx = -7/3"} {"input": "Find x and y such that\n6x + 5y = -17/4\n5x + 1y = 27/4", "output": "6x + 5y = -17/4\n5x + 1y = 27/4\n\nUsing elimination\n5*(6x + 5y = -17/4)\n6*(5x + 1y = 27/4)\n30x + 25y = -85/4\n30x + 6y = 81/2\nSubtract equations\n19y = -247/4\ny = -247/4/19\ny = -13/4\n\nSubstitute y\n6x + 5(-13/4) = -17/4\n6x = 12\nx = 12/6\nx = 2"} {"input": "Solve quickly: 2x + 12/5 = 0", "output": "2x + 12/5 = 0\n2x = -12/5\nx = -12/5 / 2\nx = -6/5"} {"input": "Solve quickly: x^2 + 19/9x + 10/9 = 0", "output": "x^2 + 19/9x + 10/9 = 0\n(x - -10/9)(x - -1) = 0\nx - -10/9 = 0 or x - -1 = 0\nx = -10/9\nx = -1"} {"input": "Solve the system:\n10x + 3y = 29\n6x + 7y = 20", "output": "10x + 3y = 29\n6x + 7y = 20\n\nUsing elimination\n6*(10x + 3y = 29)\n10*(6x + 7y = 20)\n60x + 18y = 174\n60x + 70y = 200\nSubtract equations\n-52y = -26\ny = -26/-52\ny = 1/2\n\nSubstitute y\n10x + 3(1/2) = 29\n10x = 55/2\nx = 55/2/10\nx = 11/4"} {"input": "Compute the solution of x^3 + 27/20x^2 - 2/5x = 0", "output": "x^3 + 27/20x^2 - 2/5x = 0\n(x - 1/4)(x - -8/5)(x - 0) = 0\nx - 1/4 = 0\nx - -8/5 = 0\nx - 0 = 0\nx = 1/4\nx = -8/5\nx = 0"} {"input": "Find the solution to x^3 - 44/9x^2 + 211/27x - 110/27 = 0", "output": "x^3 - 44/9x^2 + 211/27x - 110/27 = 0\n(x - 2)(x - 5/3)(x - 11/9) = 0\nx - 2 = 0\nx - 5/3 = 0\nx - 11/9 = 0\nx = 2\nx = 5/3\nx = 11/9"} {"input": "Solve 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Solve quickly: x^3 + 13/4x^2 - 81/16x - 1053/64 = 0", "output": "x^3 + 13/4x^2 - 81/16x - 1053/64 = 0\n(x - 9/4)(x - -9/4)(x - -13/4) = 0\nx - 9/4 = 0\nx - -9/4 = 0\nx - -13/4 = 0\nx = 9/4\nx = -9/4\nx = -13/4"} {"input": "Solve 6x + 36 = 0", "output": "6x + 36 = 0\n6x = -36\nx = -36 / 6\nx = -6"} {"input": "Solve simultaneously:\n9x + 7y = 133/8\n9x + 8y = 18", "output": "9x + 7y = 133/8\n9x + 8y = 18\n\nUsing elimination\n9*(9x + 7y = 133/8)\n9*(9x + 8y = 18)\n81x + 63y = 1197/8\n81x + 72y = 162\nSubtract equations\n-9y = -99/8\ny = -99/8/-9\ny = 11/8\n\nSubstitute y\n9x + 7(11/8) = 133/8\n9x = 7\nx = 7/9\nx = 7/9"} {"input": "Solve the equations:\n8x + 8y = 512/5\n9x + 6y = 351/5", "output": "8x + 8y = 512/5\n9x + 6y = 351/5\n\nUsing elimination\n9*(8x + 8y = 512/5)\n8*(9x + 6y = 351/5)\n72x + 72y = 4608/5\n72x + 48y = 2808/5\nSubtract equations\n24y = 360\ny = 360/24\ny = 15\n\nSubstitute y\n8x + 8(15) = 512/5\n8x = -88/5\nx = -88/5/8\nx = -11/5"} {"input": "Solve the equation 10x - 180/7 = 0", "output": "10x - 180/7 = 0\n10x = 180/7\nx = 180/7 / 10\nx = 18/7"} {"input": "Solve the equation x^3 + 133/10x^2 - 1982/25x + 2394/25 = 0", "output": "x^3 + 133/10x^2 - 1982/25x + 2394/25 = 0\n(x - 19/10)(x - -18)(x - 14/5) = 0\nx - 19/10 = 0\nx - -18 = 0\nx - 14/5 = 0\nx = 19/10\nx = -18\nx = 14/5"} {"input": "Solve quickly: 5x + 20 = 0", "output": "5x + 20 = 0\n5x = -20\nx = -20 / 5\nx = -4"} {"input": "Find x in 9x - 144 = 0", "output": "9x - 144 = 0\n9x = 144\nx = 144 / 9\nx = 16"} {"input": "Find x in 9x - 171/4 = 0", "output": "9x - 171/4 = 0\n9x = 171/4\nx = 171/4 / 9\nx = 19/4"} {"input": "Solve the equations:\n8x + 5y = 20\n10x + 9y = 136/5", "output": "8x + 5y = 20\n10x + 9y = 136/5\n\nUsing elimination\n10*(8x + 5y = 20)\n8*(10x + 9y = 136/5)\n80x + 50y = 200\n80x + 72y = 1088/5\nSubtract equations\n-22y = -88/5\ny = -88/5/-22\ny = 4/5\n\nSubstitute y\n8x + 5(4/5) = 20\n8x = 16\nx = 16/8\nx = 2"} {"input": "Solve quickly: x^3 + 49/24x^2 - 1/24x - 1/4 = 0", "output": "x^3 + 49/24x^2 - 1/24x - 1/4 = 0\n(x - 1/3)(x - -3/8)(x - -2) = 0\nx - 1/3 = 0\nx - -3/8 = 0\nx - -2 = 0\nx = 1/3\nx = -3/8\nx = -2"} {"input": "Solve quickly: 4x - 10 = 0", "output": "4x - 10 = 0\n4x = 10\nx = 10 / 4\nx = 5/2"} {"input": "Find x for 2x + 1/4 = 0", "output": "2x + 1/4 = 0\n2x = -1/4\nx = -1/4 / 2\nx = -1/8"} {"input": "Find x in 3x + 12 = 0", "output": "3x + 12 = 0\n3x = -12\nx = -12 / 3\nx = -4"} {"input": "Solve 10x - 110/3 = 0", "output": "10x - 110/3 = 0\n10x = 110/3\nx = 110/3 / 10\nx = 11/3"} {"input": "Solve the system:\n9x + 8y = 15\n6x + 6y = 9", "output": "9x + 8y = 15\n6x + 6y = 9\n\nUsing elimination\n6*(9x + 8y = 15)\n9*(6x + 6y = 9)\n54x + 48y = 90\n54x + 54y = 81\nSubtract equations\n-6y = 9\ny = 9/-6\ny = -3/2\n\nSubstitute y\n9x + 8(-3/2) = 15\n9x = 27\nx = 27/9\nx = 3"} {"input": "Find x for 4x - 1/2 = 0", "output": "4x - 1/2 = 0\n4x = 1/2\nx = 1/2 / 4\nx = 1/8"} {"input": "Solve the equation x^3 - 23/21x^2 - 75/7x + 33/7 = 0", "output": "x^3 - 23/21x^2 - 75/7x + 33/7 = 0\n(x - -3)(x - 3/7)(x - 11/3) = 0\nx - -3 = 0\nx - 3/7 = 0\nx - 11/3 = 0\nx = -3\nx = 3/7\nx = 11/3"} {"input": "Solve the equations:\n9x + 3y = -1071/8\n6x + 4y = -177/2", "output": "9x + 3y = -1071/8\n6x + 4y = -177/2\n\nUsing elimination\n6*(9x + 3y = -1071/8)\n9*(6x + 4y = -177/2)\n54x + 18y = -3213/4\n54x + 36y = -1593/2\nSubtract equations\n-18y = -27/4\ny = -27/4/-18\ny = 3/8\n\nSubstitute y\n9x + 3(3/8) = -1071/8\n9x = -135\nx = -135/9\nx = -15"} {"input": "Find x for x^2 - 3/2x - 7 = 0", "output": "x^2 - 3/2x - 7 = 0\n(x - 7/2)(x - -2) = 0\nx - 7/2 = 0 or x - -2 = 0\nx = 7/2\nx = -2"} {"input": "Solve the system:\n10x + 2y = -556/21\n8x + 7y = -974/21", "output": "10x + 2y = -556/21\n8x + 7y = -974/21\n\nUsing elimination\n8*(10x + 2y = -556/21)\n10*(8x + 7y = -974/21)\n80x + 16y = -4448/21\n80x + 70y = -9740/21\nSubtract equations\n-54y = 252\ny = 252/-54\ny = -14/3\n\nSubstitute y\n10x + 2(-14/3) = -556/21\n10x = -120/7\nx = -120/7/10\nx = -12/7"} {"input": "Solve the equations:\n2x + 4y = -31/3\n8x + 8y = -40/3", "output": "2x + 4y = -31/3\n8x + 8y = -40/3\n\nUsing elimination\n8*(2x + 4y = -31/3)\n2*(8x + 8y = -40/3)\n16x + 32y = -248/3\n16x + 16y = -80/3\nSubtract equations\n16y = -56\ny = -56/16\ny = -7/2\n\nSubstitute y\n2x + 4(-7/2) = -31/3\n2x = 11/3\nx = 11/3/2\nx = 11/6"} {"input": "Determine x in 6x + 20 = 0", "output": "6x + 20 = 0\n6x = -20\nx = -20 / 6\nx = -10/3"} {"input": "Find x and y such that\n9x + 6y = -57\n1x + 5y = 63", "output": "9x + 6y = -57\n1x + 5y = 63\n\nUsing elimination\n1*(9x + 6y = -57)\n9*(1x + 5y = 63)\n9x + 6y = -57\n9x + 45y = 567\nSubtract equations\n-39y = -624\ny = -624/-39\ny = 16\n\nSubstitute y\n9x + 6(16) = -57\n9x = -153\nx = -153/9\nx = -17"} {"input": "Solve simultaneously:\n7x + 7y = -427/8\n10x + 7y = -233/4", "output": "7x + 7y = -427/8\n10x + 7y = -233/4\n\nUsing elimination\n10*(7x + 7y = -427/8)\n7*(10x + 7y = -233/4)\n70x + 70y = -2135/4\n70x + 49y = -1631/4\nSubtract equations\n21y = -126\ny = -126/21\ny = -6\n\nSubstitute y\n7x + 7(-6) = -427/8\n7x = -91/8\nx = -91/8/7\nx = -13/8"} {"input": "Find the solution to 8x + 76 = 0", "output": "8x + 76 = 0\n8x = -76\nx = -76 / 8\nx = -19/2"} {"input": "Determine x in x^2 + 35/8x + 3/2 = 0", "output": "x^2 + 35/8x + 3/2 = 0\n(x - -4)(x - -3/8) = 0\nx - -4 = 0 or x - -3/8 = 0\nx = -4\nx = -3/8"} {"input": "Solve x^2 - 32/3x + 80/3 = 0", "output": "x^2 - 32/3x + 80/3 = 0\n(x - 4)(x - 20/3) = 0\nx - 4 = 0 or x - 20/3 = 0\nx = 4\nx = 20/3"} {"input": "Solve simultaneously:\n10x + 3y = -52/5\n8x + 5y = -52/5", "output": "10x + 3y = -52/5\n8x + 5y = -52/5\n\nUsing elimination\n8*(10x + 3y = -52/5)\n10*(8x + 5y = -52/5)\n80x + 24y = -416/5\n80x + 50y = -104\nSubtract equations\n-26y = 104/5\ny = 104/5/-26\ny = -4/5\n\nSubstitute y\n10x + 3(-4/5) = -52/5\n10x = -8\nx = -8/10\nx = -4/5"} {"input": "Find the solution to x^3 + 43/8x^2 - 7/36x - 20/9 = 0", "output": "x^3 + 43/8x^2 - 7/36x - 20/9 = 0\n(x - -2/3)(x - 5/8)(x - -16/3) = 0\nx - -2/3 = 0\nx - 5/8 = 0\nx - -16/3 = 0\nx = -2/3\nx = 5/8\nx = -16/3"} {"input": "Solve simultaneously:\n6x + 5y = 397/6\n4x + 6y = 41", "output": "6x + 5y = 397/6\n4x + 6y = 41\n\nUsing elimination\n4*(6x + 5y = 397/6)\n6*(4x + 6y = 41)\n24x + 20y = 794/3\n24x + 36y = 246\nSubtract equations\n-16y = 56/3\ny = 56/3/-16\ny = -7/6\n\nSubstitute y\n6x + 5(-7/6) = 397/6\n6x = 72\nx = 72/6\nx = 12"} {"input": "Solve the system:\n2x + 2y = 37/9\n1x + 8y = 23/18", "output": "2x + 2y = 37/9\n1x + 8y = 23/18\n\nUsing elimination\n1*(2x + 2y = 37/9)\n2*(1x + 8y = 23/18)\n2x + 2y = 37/9\n2x + 16y = 23/9\nSubtract equations\n-14y = 14/9\ny = 14/9/-14\ny = -1/9\n\nSubstitute y\n2x + 2(-1/9) = 37/9\n2x = 13/3\nx = 13/3/2\nx = 13/6"} {"input": "Find the solution to 4x - 28 = 0", "output": "4x - 28 = 0\n4x = 28\nx = 28 / 4\nx = 7"} {"input": "Solve quickly: x^2 - 7/40x - 33/20 = 0", "output": "x^2 - 7/40x - 33/20 = 0\n(x - -6/5)(x - 11/8) = 0\nx - -6/5 = 0 or x - 11/8 = 0\nx = -6/5\nx = 11/8"} {"input": "Solve the system:\n10x + 8y = 34/5\n8x + 10y = 29/5", "output": "10x + 8y = 34/5\n8x + 10y = 29/5\n\nUsing elimination\n8*(10x + 8y = 34/5)\n10*(8x + 10y = 29/5)\n80x + 64y = 272/5\n80x + 100y = 58\nSubtract equations\n-36y = -18/5\ny = -18/5/-36\ny = 1/10\n\nSubstitute y\n10x + 8(1/10) = 34/5\n10x = 6\nx = 6/10\nx = 3/5"} {"input": "Find x for x^3 + 6/5x^2 - 1x - 6/5 = 0", "output": "x^3 + 6/5x^2 - 1x - 6/5 = 0\n(x - 1)(x - -1)(x - -6/5) = 0\nx - 1 = 0\nx - -1 = 0\nx - -6/5 = 0\nx = 1\nx = -1\nx = -6/5"} {"input": "Compute the solution of x^3 - 459/140x^2 + 213/70x - 4/7 = 0", "output": "x^3 - 459/140x^2 + 213/70x - 4/7 = 0\n(x - 1/4)(x - 8/5)(x - 10/7) = 0\nx - 1/4 = 0\nx - 8/5 = 0\nx - 10/7 = 0\nx = 1/4\nx = 8/5\nx = 10/7"} {"input": "Determine x in x^2 + 24/35x - 128/35 = 0", "output": "x^2 + 24/35x - 128/35 = 0\n(x - 8/5)(x - -16/7) = 0\nx - 8/5 = 0 or x - -16/7 = 0\nx = 8/5\nx = -16/7"} {"input": "Compute the solution of 2x - 34/7 = 0", "output": "2x - 34/7 = 0\n2x = 34/7\nx = 34/7 / 2\nx = 17/7"} {"input": "Solve the equations:\n10x + 1y = 10\n6x + 9y = 6", "output": "10x + 1y = 10\n6x + 9y = 6\n\nUsing elimination\n6*(10x + 1y = 10)\n10*(6x + 9y = 6)\n60x + 6y = 60\n60x + 90y = 60\nSubtract equations\n-84y = 0\ny = 0/-84\ny = 0\n\nSubstitute y\n10x + 1(0) = 10\n10x = 10\nx = 10/10\nx = 1"} {"input": "Solve x^3 - 15/2x^2 - 22x + 144 = 0", "output": "x^3 - 15/2x^2 - 22x + 144 = 0\n(x - 8)(x - 4)(x - -9/2) = 0\nx - 8 = 0\nx - 4 = 0\nx - -9/2 = 0\nx = 8\nx = 4\nx = -9/2"} {"input": "Determine x in x^3 + 7/10x^2 - 81/25x - 567/250 = 0", "output": "x^3 + 7/10x^2 - 81/25x - 567/250 = 0\n(x - -9/5)(x - -7/10)(x - 9/5) = 0\nx - -9/5 = 0\nx - -7/10 = 0\nx - 9/5 = 0\nx = -9/5\nx = -7/10\nx = 9/5"} {"input": "Find x in x^2 + 9/5x + 4/5 = 0", "output": "x^2 + 9/5x + 4/5 = 0\n(x - -4/5)(x - -1) = 0\nx - -4/5 = 0 or x - -1 = 0\nx = -4/5\nx = -1"} {"input": "Solve 8x + 28/5 = 0", "output": "8x + 28/5 = 0\n8x = -28/5\nx = -28/5 / 8\nx = -7/10"} {"input": "Solve quickly: x^2 - 19/6x - 10/3 = 0", "output": "x^2 - 19/6x - 10/3 = 0\n(x - -5/6)(x - 4) = 0\nx - -5/6 = 0 or x - 4 = 0\nx = -5/6\nx = 4"} {"input": "Find x and y such that\n3x + 7y = 5\n10x + 2y = 38", "output": "3x + 7y = 5\n10x + 2y = 38\n\nUsing elimination\n10*(3x + 7y = 5)\n3*(10x + 2y = 38)\n30x + 70y = 50\n30x + 6y = 114\nSubtract equations\n64y = -64\ny = -64/64\ny = -1\n\nSubstitute y\n3x + 7(-1) = 5\n3x = 12\nx = 12/3\nx = 4"} {"input": "Find x in x^2 - 17/4x + 15/4 = 0", "output": "x^2 - 17/4x + 15/4 = 0\n(x - 5/4)(x - 3) = 0\nx - 5/4 = 0 or x - 3 = 0\nx = 5/4\nx = 3"} {"input": "Find x for 6x + 9/2 = 0", "output": "6x + 9/2 = 0\n6x = -9/2\nx = -9/2 / 6\nx = -3/4"} {"input": "What value of x satisfies x^3 - 86/9x^2 + 595/27x + 208/81 = 0", "output": "x^3 - 86/9x^2 + 595/27x + 208/81 = 0\n(x - -1/9)(x - 13/3)(x - 16/3) = 0\nx - -1/9 = 0\nx - 13/3 = 0\nx - 16/3 = 0\nx = -1/9\nx = 13/3\nx = 16/3"} {"input": "Solve 7x + 49/3 = 0", "output": "7x + 49/3 = 0\n7x = -49/3\nx = -49/3 / 7\nx = -7/3"} {"input": "Solve x^2 + 31/36x - 95/36 = 0", "output": "x^2 + 31/36x - 95/36 = 0\n(x - 5/4)(x - -19/9) = 0\nx - 5/4 = 0 or x - -19/9 = 0\nx = 5/4\nx = -19/9"} {"input": "Solve the system:\n1x + 4y = 10\n5x + 1y = 43/2", "output": "1x + 4y = 10\n5x + 1y = 43/2\n\nUsing elimination\n5*(1x + 4y = 10)\n1*(5x + 1y = 43/2)\n5x + 20y = 50\n5x + 1y = 43/2\nSubtract equations\n19y = 57/2\ny = 57/2/19\ny = 3/2\n\nSubstitute y\n1x + 4(3/2) = 10\n1x = 4\nx = 4/1\nx = 4"} {"input": "What value of x satisfies x^3 + 33/8x^2 + 27/8x - 243/128 = 0", "output": "x^3 + 33/8x^2 + 27/8x - 243/128 = 0\n(x - 3/8)(x - -9/4)(x - -9/4) = 0\nx - 3/8 = 0\nx - -9/4 = 0\nx - -9/4 = 0\nx = 3/8\nx = -9/4\nx = -9/4"} {"input": "Solve the equations:\n4x + 10y = 11/2\n1x + 3y = 49/40", "output": "4x + 10y = 11/2\n1x + 3y = 49/40\n\nUsing elimination\n1*(4x + 10y = 11/2)\n4*(1x + 3y = 49/40)\n4x + 10y = 11/2\n4x + 12y = 49/10\nSubtract equations\n-2y = 3/5\ny = 3/5/-2\ny = -3/10\n\nSubstitute y\n4x + 10(-3/10) = 11/2\n4x = 17/2\nx = 17/2/4\nx = 17/8"} {"input": "Find x in 1x + 5/3 = 0", "output": "1x + 5/3 = 0\n1x = -5/3\nx = -5/3 / 1\nx = -5/3"} {"input": "What value of x satisfies x^3 - 193/140x^2 - 233/140x - 11/35 = 0", "output": "x^3 - 193/140x^2 - 233/140x - 11/35 = 0\n(x - -1/4)(x - 11/5)(x - -4/7) = 0\nx - -1/4 = 0\nx - 11/5 = 0\nx - -4/7 = 0\nx = -1/4\nx = 11/5\nx = -4/7"} {"input": "Find x and y such that\n9x + 5y = 3\n9x + 10y = 3", "output": "9x + 5y = 3\n9x + 10y = 3\n\nUsing elimination\n9*(9x + 5y = 3)\n9*(9x + 10y = 3)\n81x + 45y = 27\n81x + 90y = 27\nSubtract equations\n-45y = 0\ny = 0/-45\ny = 0\n\nSubstitute y\n9x + 5(0) = 3\n9x = 3\nx = 3/9\nx = 1/3"} {"input": "Solve the equation 3x - 24/7 = 0", "output": "3x - 24/7 = 0\n3x = 24/7\nx = 24/7 / 3\nx = 8/7"} {"input": "Find x for x^2 + 53/30x + 7/10 = 0", "output": "x^2 + 53/30x + 7/10 = 0\n(x - -3/5)(x - -7/6) = 0\nx - -3/5 = 0 or x - -7/6 = 0\nx = -3/5\nx = -7/6"} {"input": "Compute the solution of x^3 + 113/20x^2 + 127/20x + 17/10 = 0", "output": "x^3 + 113/20x^2 + 127/20x + 17/10 = 0\n(x - -2/5)(x - -1)(x - -17/4) = 0\nx - -2/5 = 0\nx - -1 = 0\nx - -17/4 = 0\nx = -2/5\nx = -1\nx = -17/4"} {"input": "Determine x in 3x + 9/8 = 0", "output": "3x + 9/8 = 0\n3x = -9/8\nx = -9/8 / 3\nx = -3/8"} {"input": "Solve the equation 2x + 36/7 = 0", "output": "2x + 36/7 = 0\n2x = -36/7\nx = -36/7 / 2\nx = -18/7"} {"input": "Find x in 3x + 36/7 = 0", "output": "3x + 36/7 = 0\n3x = -36/7\nx = -36/7 / 3\nx = -12/7"} {"input": "Find x for x^2 + 14/5x + 9/5 = 0", "output": "x^2 + 14/5x + 9/5 = 0\n(x - -9/5)(x - -1) = 0\nx - -9/5 = 0 or x - -1 = 0\nx = -9/5\nx = -1"} {"input": "Solve the equation x^2 - 2x = 0", "output": "x^2 - 2x = 0\n(x - 0)(x - 2) = 0\nx - 0 = 0 or x - 2 = 0\nx = 0\nx = 2"} {"input": "Find x in x^3 + 128/35x^2 + 117/35x = 0", "output": "x^3 + 128/35x^2 + 117/35x = 0\n(x - -13/7)(x - 0)(x - -9/5) = 0\nx - -13/7 = 0\nx - 0 = 0\nx - -9/5 = 0\nx = -13/7\nx = 0\nx = -9/5"} {"input": "Solve the equations:\n6x + 7y = 161/3\n3x + 1y = 113/3", "output": "6x + 7y = 161/3\n3x + 1y = 113/3\n\nUsing elimination\n3*(6x + 7y = 161/3)\n6*(3x + 1y = 113/3)\n18x + 21y = 161\n18x + 6y = 226\nSubtract equations\n15y = -65\ny = -65/15\ny = -13/3\n\nSubstitute y\n6x + 7(-13/3) = 161/3\n6x = 84\nx = 84/6\nx = 14"} {"input": "Determine x in x^2 + 15/4x - 27/2 = 0", "output": "x^2 + 15/4x - 27/2 = 0\n(x - 9/4)(x - -6) = 0\nx - 9/4 = 0 or x - -6 = 0\nx = 9/4\nx = -6"} {"input": "Find x and y such that\n1x + 6y = 9/2\n8x + 7y = 113/2", "output": "1x + 6y = 9/2\n8x + 7y = 113/2\n\nUsing elimination\n8*(1x + 6y = 9/2)\n1*(8x + 7y = 113/2)\n8x + 48y = 36\n8x + 7y = 113/2\nSubtract equations\n41y = -41/2\ny = -41/2/41\ny = -1/2\n\nSubstitute y\n1x + 6(-1/2) = 9/2\n1x = 15/2\nx = 15/2/1\nx = 15/2"} {"input": "Solve the equation x^2 - 34/15x - 16/15 = 0", "output": "x^2 - 34/15x - 16/15 = 0\n(x - -2/5)(x - 8/3) = 0\nx - -2/5 = 0 or x - 8/3 = 0\nx = -2/5\nx = 8/3"} {"input": "What value of x satisfies 1x - 4 = 0", "output": "1x - 4 = 0\n1x = 4\nx = 4 / 1\nx = 4"} {"input": "Determine x in 10x + 9 = 0", "output": "10x + 9 = 0\n10x = -9\nx = -9 / 10\nx = -9/10"} {"input": "Find x for x^3 - 307/120x^2 + 419/240x - 3/20 = 0", "output": "x^3 - 307/120x^2 + 419/240x - 3/20 = 0\n(x - 1/10)(x - 9/8)(x - 4/3) = 0\nx - 1/10 = 0\nx - 9/8 = 0\nx - 4/3 = 0\nx = 1/10\nx = 9/8\nx = 4/3"} {"input": "Solve x^3 - 35/6x^2 + 643/75x - 4/5 = 0", "output": "x^3 - 35/6x^2 + 643/75x - 4/5 = 0\n(x - 10/3)(x - 12/5)(x - 1/10) = 0\nx - 10/3 = 0\nx - 12/5 = 0\nx - 1/10 = 0\nx = 10/3\nx = 12/5\nx = 1/10"} {"input": "Solve x^2 + 23/7x + 60/49 = 0", "output": "x^2 + 23/7x + 60/49 = 0\n(x - -20/7)(x - -3/7) = 0\nx - -20/7 = 0 or x - -3/7 = 0\nx = -20/7\nx = -3/7"} {"input": "Solve the equations:\n2x + 6y = 91/6\n7x + 1y = 1111/36", "output": "2x + 6y = 91/6\n7x + 1y = 1111/36\n\nUsing elimination\n7*(2x + 6y = 91/6)\n2*(7x + 1y = 1111/36)\n14x + 42y = 637/6\n14x + 2y = 1111/18\nSubtract equations\n40y = 400/9\ny = 400/9/40\ny = 10/9\n\nSubstitute y\n2x + 6(10/9) = 91/6\n2x = 17/2\nx = 17/2/2\nx = 17/4"} {"input": "Compute the solution of x^3 - 198/35x^2 + 373/35x - 234/35 = 0", "output": "x^3 - 198/35x^2 + 373/35x - 234/35 = 0\n(x - 2)(x - 9/5)(x - 13/7) = 0\nx - 2 = 0\nx - 9/5 = 0\nx - 13/7 = 0\nx = 2\nx = 9/5\nx = 13/7"} {"input": "Compute the solution of x^2 + 31/3x + 12 = 0", "output": "x^2 + 31/3x + 12 = 0\n(x - -9)(x - -4/3) = 0\nx - -9 = 0 or x - -4/3 = 0\nx = -9\nx = -4/3"} {"input": "Find x in x^3 + 83/12x^2 - 167/8x - 153/8 = 0", "output": "x^3 + 83/12x^2 - 167/8x - 153/8 = 0\n(x - -9)(x - -3/4)(x - 17/6) = 0\nx - -9 = 0\nx - -3/4 = 0\nx - 17/6 = 0\nx = -9\nx = -3/4\nx = 17/6"} {"input": "Solve the equations:\n6x + 4y = -20\n4x + 5y = -47/3", "output": "6x + 4y = -20\n4x + 5y = -47/3\n\nUsing elimination\n4*(6x + 4y = -20)\n6*(4x + 5y = -47/3)\n24x + 16y = -80\n24x + 30y = -94\nSubtract equations\n-14y = 14\ny = 14/-14\ny = -1\n\nSubstitute y\n6x + 4(-1) = -20\n6x = -16\nx = -16/6\nx = -8/3"} {"input": "Solve quickly: 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Solve the equation x^3 - 29/10x^2 - 1/2x + 3/5 = 0", "output": "x^3 - 29/10x^2 - 1/2x + 3/5 = 0\n(x - 2/5)(x - -1/2)(x - 3) = 0\nx - 2/5 = 0\nx - -1/2 = 0\nx - 3 = 0\nx = 2/5\nx = -1/2\nx = 3"} {"input": "Solve the equations:\n10x + 2y = -361/12\n2x + 6y = -95/4", "output": "10x + 2y = -361/12\n2x + 6y = -95/4\n\nUsing elimination\n2*(10x + 2y = -361/12)\n10*(2x + 6y = -95/4)\n20x + 4y = -361/6\n20x + 60y = -475/2\nSubtract equations\n-56y = 532/3\ny = 532/3/-56\ny = -19/6\n\nSubstitute y\n10x + 2(-19/6) = -361/12\n10x = -95/4\nx = -95/4/10\nx = -19/8"} {"input": "Solve the system:\n2x + 9y = 35\n10x + 6y = 19", "output": "2x + 9y = 35\n10x + 6y = 19\n\nUsing elimination\n10*(2x + 9y = 35)\n2*(10x + 6y = 19)\n20x + 90y = 350\n20x + 12y = 38\nSubtract equations\n78y = 312\ny = 312/78\ny = 4\n\nSubstitute y\n2x + 9(4) = 35\n2x = -1\nx = -1/2\nx = -1/2"} {"input": "Find x and y such that\n1x + 2y = 29/12\n2x + 3y = 89/24", "output": "1x + 2y = 29/12\n2x + 3y = 89/24\n\nUsing elimination\n2*(1x + 2y = 29/12)\n1*(2x + 3y = 89/24)\n2x + 4y = 29/6\n2x + 3y = 89/24\nSubtract equations\n1y = 9/8\ny = 9/8/1\ny = 9/8\n\nSubstitute y\n1x + 2(9/8) = 29/12\n1x = 1/6\nx = 1/6/1\nx = 1/6"} {"input": "Determine x in x^2 + 39/5x + 54/5 = 0", "output": "x^2 + 39/5x + 54/5 = 0\n(x - -9/5)(x - -6) = 0\nx - -9/5 = 0 or x - -6 = 0\nx = -9/5\nx = -6"} {"input": "Solve x^2 + 38/7x + 40/7 = 0", "output": "x^2 + 38/7x + 40/7 = 0\n(x - -10/7)(x - -4) = 0\nx - -10/7 = 0 or x - -4 = 0\nx = -10/7\nx = -4"} {"input": "Solve the system:\n1x + 2y = 164/45\n3x + 4y = 292/45", "output": "1x + 2y = 164/45\n3x + 4y = 292/45\n\nUsing elimination\n3*(1x + 2y = 164/45)\n1*(3x + 4y = 292/45)\n3x + 6y = 164/15\n3x + 4y = 292/45\nSubtract equations\n2y = 40/9\ny = 40/9/2\ny = 20/9\n\nSubstitute y\n1x + 2(20/9) = 164/45\n1x = -4/5\nx = -4/5/1\nx = -4/5"} {"input": "Find x for x^3 + 71/210x^2 - 111/14x + 114/35 = 0", "output": "x^3 + 71/210x^2 - 111/14x + 114/35 = 0\n(x - 12/5)(x - -19/6)(x - 3/7) = 0\nx - 12/5 = 0\nx - -19/6 = 0\nx - 3/7 = 0\nx = 12/5\nx = -19/6\nx = 3/7"} {"input": "Find x in 7x - 14 = 0", "output": "7x - 14 = 0\n7x = 14\nx = 14 / 7\nx = 2"} {"input": "Solve quickly: x^2 - 127/8x - 153/8 = 0", "output": "x^2 - 127/8x - 153/8 = 0\n(x - -9/8)(x - 17) = 0\nx - -9/8 = 0 or x - 17 = 0\nx = -9/8\nx = 17"} {"input": "Solve quickly: x^2 + 11x + 10 = 0", "output": "x^2 + 11x + 10 = 0\n(x - -10)(x - -1) = 0\nx - -10 = 0 or x - -1 = 0\nx = -10\nx = -1"} {"input": "Find x and y such that\n1x + 7y = -5\n7x + 7y = -17", "output": "1x + 7y = -5\n7x + 7y = -17\n\nUsing elimination\n7*(1x + 7y = -5)\n1*(7x + 7y = -17)\n7x + 49y = -35\n7x + 7y = -17\nSubtract equations\n42y = -18\ny = -18/42\ny = -3/7\n\nSubstitute y\n1x + 7(-3/7) = -5\n1x = -2\nx = -2/1\nx = -2"} {"input": "Solve simultaneously:\n7x + 10y = 428/9\n3x + 10y = 164/3", "output": "7x + 10y = 428/9\n3x + 10y = 164/3\n\nUsing elimination\n3*(7x + 10y = 428/9)\n7*(3x + 10y = 164/3)\n21x + 30y = 428/3\n21x + 70y = 1148/3\nSubtract equations\n-40y = -240\ny = -240/-40\ny = 6\n\nSubstitute y\n7x + 10(6) = 428/9\n7x = -112/9\nx = -112/9/7\nx = -16/9"} {"input": "Solve quickly: 6x - 7 = 0", "output": "6x - 7 = 0\n6x = 7\nx = 7 / 6\nx = 7/6"} {"input": "Find x in x^3 + 926/35x^2 + 976/7x + 1440/7 = 0", "output": "x^3 + 926/35x^2 + 976/7x + 1440/7 = 0\n(x - -18/5)(x - -20)(x - -20/7) = 0\nx - -18/5 = 0\nx - -20 = 0\nx - -20/7 = 0\nx = -18/5\nx = -20\nx = -20/7"} {"input": "Determine x in 4x + 64/7 = 0", "output": "4x + 64/7 = 0\n4x = -64/7\nx = -64/7 / 4\nx = -16/7"} {"input": "Solve quickly: 4x + 12 = 0", "output": "4x + 12 = 0\n4x = -12\nx = -12 / 4\nx = -3"} {"input": "Solve the system:\n7x + 5y = -1109/42\n5x + 7y = -169/6", "output": "7x + 5y = -1109/42\n5x + 7y = -169/6\n\nUsing elimination\n5*(7x + 5y = -1109/42)\n7*(5x + 7y = -169/6)\n35x + 25y = -5545/42\n35x + 49y = -1183/6\nSubtract equations\n-24y = 456/7\ny = 456/7/-24\ny = -19/7\n\nSubstitute y\n7x + 5(-19/7) = -1109/42\n7x = -77/6\nx = -77/6/7\nx = -11/6"} {"input": "Compute the solution of 10x - 5/2 = 0", "output": "10x - 5/2 = 0\n10x = 5/2\nx = 5/2 / 10\nx = 1/4"} {"input": "What value of x satisfies 2x + 2 = 0", "output": "2x + 2 = 0\n2x = -2\nx = -2 / 2\nx = -1"} {"input": "Solve x^2 - 6/7x - 40/7 = 0", "output": "x^2 - 6/7x - 40/7 = 0\n(x - -2)(x - 20/7) = 0\nx - -2 = 0 or x - 20/7 = 0\nx = -2\nx = 20/7"} {"input": "Find x for x^2 + 1/6x - 17/2 = 0", "output": "x^2 + 1/6x - 17/2 = 0\n(x - 17/6)(x - -3) = 0\nx - 17/6 = 0 or x - -3 = 0\nx = 17/6\nx = -3"} {"input": "Solve x^3 + 73/72x^2 - 139/216x - 7/12 = 0", "output": "x^3 + 73/72x^2 - 139/216x - 7/12 = 0\n(x - -2/3)(x - -9/8)(x - 7/9) = 0\nx - -2/3 = 0\nx - -9/8 = 0\nx - 7/9 = 0\nx = -2/3\nx = -9/8\nx = 7/9"} {"input": "Solve x^3 + 35/8x^2 - 539/32x + 343/32 = 0", "output": "x^3 + 35/8x^2 - 539/32x + 343/32 = 0\n(x - -7)(x - 7/4)(x - 7/8) = 0\nx - -7 = 0\nx - 7/4 = 0\nx - 7/8 = 0\nx = -7\nx = 7/4\nx = 7/8"} {"input": "Determine x in 9x - 27/2 = 0", "output": "9x - 27/2 = 0\n9x = 27/2\nx = 27/2 / 9\nx = 3/2"} {"input": "What value of x satisfies x^2 + 29/5x + 36/5 = 0", "output": "x^2 + 29/5x + 36/5 = 0\n(x - -9/5)(x - -4) = 0\nx - -9/5 = 0 or x - -4 = 0\nx = -9/5\nx = -4"} {"input": "Solve 6x + 12 = 0", "output": "6x + 12 = 0\n6x = -12\nx = -12 / 6\nx = -2"} {"input": "Find the solution to x^3 + 3/8x^2 - 523/144x + 35/16 = 0", "output": "x^3 + 3/8x^2 - 523/144x + 35/16 = 0\n(x - -7/3)(x - 5/6)(x - 9/8) = 0\nx - -7/3 = 0\nx - 5/6 = 0\nx - 9/8 = 0\nx = -7/3\nx = 5/6\nx = 9/8"} {"input": "Solve x^2 - 3/5x - 68/5 = 0", "output": "x^2 - 3/5x - 68/5 = 0\n(x - 4)(x - -17/5) = 0\nx - 4 = 0 or x - -17/5 = 0\nx = 4\nx = -17/5"} {"input": "Find x and y such that\n6x + 2y = -77/20\n5x + 8y = -1091/40", "output": "6x + 2y = -77/20\n5x + 8y = -1091/40\n\nUsing elimination\n5*(6x + 2y = -77/20)\n6*(5x + 8y = -1091/40)\n30x + 10y = -77/4\n30x + 48y = -3273/20\nSubtract equations\n-38y = 722/5\ny = 722/5/-38\ny = -19/5\n\nSubstitute y\n6x + 2(-19/5) = -77/20\n6x = 15/4\nx = 15/4/6\nx = 5/8"} {"input": "Find the solution to x^2 + 17/36x - 35/36 = 0", "output": "x^2 + 17/36x - 35/36 = 0\n(x - 7/9)(x - -5/4) = 0\nx - 7/9 = 0 or x - -5/4 = 0\nx = 7/9\nx = -5/4"} {"input": "Find x and y such that\n9x + 8y = -89/10\n8x + 1y = -9/5", "output": "9x + 8y = -89/10\n8x + 1y = -9/5\n\nUsing elimination\n8*(9x + 8y = -89/10)\n9*(8x + 1y = -9/5)\n72x + 64y = -356/5\n72x + 9y = -81/5\nSubtract equations\n55y = -55\ny = -55/55\ny = -1\n\nSubstitute y\n9x + 8(-1) = -89/10\n9x = -9/10\nx = -9/10/9\nx = -1/10"} {"input": "Determine x in 8x - 72/5 = 0", "output": "8x - 72/5 = 0\n8x = 72/5\nx = 72/5 / 8\nx = 9/5"} {"input": "Find x in x^2 + 59/30x - 28/15 = 0", "output": "x^2 + 59/30x - 28/15 = 0\n(x - -8/3)(x - 7/10) = 0\nx - -8/3 = 0 or x - 7/10 = 0\nx = -8/3\nx = 7/10"} {"input": "Find x in x^3 + 12/7x^2 - 4/7x = 0", "output": "x^3 + 12/7x^2 - 4/7x = 0\n(x - -2)(x - 0)(x - 2/7) = 0\nx - -2 = 0\nx - 0 = 0\nx - 2/7 = 0\nx = -2\nx = 0\nx = 2/7"} {"input": "What value of x satisfies x^3 + 119/72x^2 - 329/144x - 11/3 = 0", "output": "x^3 + 119/72x^2 - 329/144x - 11/3 = 0\n(x - 3/2)(x - -11/8)(x - -16/9) = 0\nx - 3/2 = 0\nx - -11/8 = 0\nx - -16/9 = 0\nx = 3/2\nx = -11/8\nx = -16/9"} {"input": "Find x in 5x + 65/3 = 0", "output": "5x + 65/3 = 0\n5x = -65/3\nx = -65/3 / 5\nx = -13/3"} {"input": "Compute the solution of x^2 + 11/4x - 51/8 = 0", "output": "x^2 + 11/4x - 51/8 = 0\n(x - -17/4)(x - 3/2) = 0\nx - -17/4 = 0 or x - 3/2 = 0\nx = -17/4\nx = 3/2"} {"input": "Solve quickly: 4x + 38 = 0", "output": "4x + 38 = 0\n4x = -38\nx = -38 / 4\nx = -19/2"} {"input": "Find x for x^2 - 5/6x - 7/3 = 0", "output": "x^2 - 5/6x - 7/3 = 0\n(x - 2)(x - -7/6) = 0\nx - 2 = 0 or x - -7/6 = 0\nx = 2\nx = -7/6"} {"input": "Solve quickly: 2x + 13/2 = 0", "output": "2x + 13/2 = 0\n2x = -13/2\nx = -13/2 / 2\nx = -13/4"} {"input": "Solve the equation 4x + 6 = 0", "output": "4x + 6 = 0\n4x = -6\nx = -6 / 4\nx = -3/2"} {"input": "Find the solution to x^3 - 11/24x^2 - 547/48x - 133/12 = 0", "output": "x^3 - 11/24x^2 - 547/48x - 133/12 = 0\n(x - -19/8)(x - 4)(x - -7/6) = 0\nx - -19/8 = 0\nx - 4 = 0\nx - -7/6 = 0\nx = -19/8\nx = 4\nx = -7/6"} {"input": "Find x in 1x - 9/10 = 0", "output": "1x - 9/10 = 0\n1x = 9/10\nx = 9/10 / 1\nx = 9/10"} {"input": "Solve the equations:\n4x + 8y = -280/9\n10x + 1y = -377/9", "output": "4x + 8y = -280/9\n10x + 1y = -377/9\n\nUsing elimination\n10*(4x + 8y = -280/9)\n4*(10x + 1y = -377/9)\n40x + 80y = -2800/9\n40x + 4y = -1508/9\nSubtract equations\n76y = -1292/9\ny = -1292/9/76\ny = -17/9\n\nSubstitute y\n4x + 8(-17/9) = -280/9\n4x = -16\nx = -16/4\nx = -4"} {"input": "Solve the equation 2x - 6/5 = 0", "output": "2x - 6/5 = 0\n2x = 6/5\nx = 6/5 / 2\nx = 3/5"} {"input": "Find x for x^3 - 109/30x^2 - 808/45x - 136/9 = 0", "output": "x^3 - 109/30x^2 - 808/45x - 136/9 = 0\n(x - -17/10)(x - 20/3)(x - -4/3) = 0\nx - -17/10 = 0\nx - 20/3 = 0\nx - -4/3 = 0\nx = -17/10\nx = 20/3\nx = -4/3"} {"input": "Determine x in x^2 + 1x - 2 = 0", "output": "x^2 + 1x - 2 = 0\n(x - 1)(x - -2) = 0\nx - 1 = 0 or x - -2 = 0\nx = 1\nx = -2"} {"input": "Find x and y such that\n4x + 6y = 144/5\n6x + 6y = 156/5", "output": "4x + 6y = 144/5\n6x + 6y = 156/5\n\nUsing elimination\n6*(4x + 6y = 144/5)\n4*(6x + 6y = 156/5)\n24x + 36y = 864/5\n24x + 24y = 624/5\nSubtract equations\n12y = 48\ny = 48/12\ny = 4\n\nSubstitute y\n4x + 6(4) = 144/5\n4x = 24/5\nx = 24/5/4\nx = 6/5"} {"input": "Find x for x^3 - 641/105x^2 + 1262/105x - 264/35 = 0", "output": "x^3 - 641/105x^2 + 1262/105x - 264/35 = 0\n(x - 4/3)(x - 11/5)(x - 18/7) = 0\nx - 4/3 = 0\nx - 11/5 = 0\nx - 18/7 = 0\nx = 4/3\nx = 11/5\nx = 18/7"} {"input": "Determine x in x^2 + 10/3x - 32/3 = 0", "output": "x^2 + 10/3x - 32/3 = 0\n(x - 2)(x - -16/3) = 0\nx - 2 = 0 or x - -16/3 = 0\nx = 2\nx = -16/3"} {"input": "Determine x in 2x + 4/3 = 0", "output": "2x + 4/3 = 0\n2x = -4/3\nx = -4/3 / 2\nx = -2/3"} {"input": "Solve the system:\n2x + 7y = -7\n7x + 10y = -302/7", "output": "2x + 7y = -7\n7x + 10y = -302/7\n\nUsing elimination\n7*(2x + 7y = -7)\n2*(7x + 10y = -302/7)\n14x + 49y = -49\n14x + 20y = -604/7\nSubtract equations\n29y = 261/7\ny = 261/7/29\ny = 9/7\n\nSubstitute y\n2x + 7(9/7) = -7\n2x = -16\nx = -16/2\nx = -8"} {"input": "Find x in x^2 - 18x - 40 = 0", "output": "x^2 - 18x - 40 = 0\n(x - -2)(x - 20) = 0\nx - -2 = 0 or x - 20 = 0\nx = -2\nx = 20"} {"input": "Solve x^3 + 41/12x^2 + 71/24x + 3/4 = 0", "output": "x^3 + 41/12x^2 + 71/24x + 3/4 = 0\n(x - -9/4)(x - -2/3)(x - -1/2) = 0\nx - -9/4 = 0\nx - -2/3 = 0\nx - -1/2 = 0\nx = -9/4\nx = -2/3\nx = -1/2"} {"input": "Solve quickly: 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "What value of x satisfies 5x = 0", "output": "5x = 0\n5x = 0\nx = 0 / 5\nx = 0"} {"input": "Solve quickly: x^2 + 17/6x + 2 = 0", "output": "x^2 + 17/6x + 2 = 0\n(x - -3/2)(x - -4/3) = 0\nx - -3/2 = 0 or x - -4/3 = 0\nx = -3/2\nx = -4/3"} {"input": "Solve simultaneously:\n5x + 3y = 113/4\n10x + 8y = 119/2", "output": "5x + 3y = 113/4\n10x + 8y = 119/2\n\nUsing elimination\n10*(5x + 3y = 113/4)\n5*(10x + 8y = 119/2)\n50x + 30y = 565/2\n50x + 40y = 595/2\nSubtract equations\n-10y = -15\ny = -15/-10\ny = 3/2\n\nSubstitute y\n5x + 3(3/2) = 113/4\n5x = 95/4\nx = 95/4/5\nx = 19/4"} {"input": "Compute the solution of x^2 + 3/2x - 27/2 = 0", "output": "x^2 + 3/2x - 27/2 = 0\n(x - 3)(x - -9/2) = 0\nx - 3 = 0 or x - -9/2 = 0\nx = 3\nx = -9/2"} {"input": "Compute the solution of x^3 + 7/8x^2 - 121/16x + 91/16 = 0", "output": "x^3 + 7/8x^2 - 121/16x + 91/16 = 0\n(x - -7/2)(x - 1)(x - 13/8) = 0\nx - -7/2 = 0\nx - 1 = 0\nx - 13/8 = 0\nx = -7/2\nx = 1\nx = 13/8"} {"input": "Solve the equations:\n1x + 6y = -157/5\n6x + 10y = -746/15", "output": "1x + 6y = -157/5\n6x + 10y = -746/15\n\nUsing elimination\n6*(1x + 6y = -157/5)\n1*(6x + 10y = -746/15)\n6x + 36y = -942/5\n6x + 10y = -746/15\nSubtract equations\n26y = -416/3\ny = -416/3/26\ny = -16/3\n\nSubstitute y\n1x + 6(-16/3) = -157/5\n1x = 3/5\nx = 3/5/1\nx = 3/5"} {"input": "What value of x satisfies x^2 + 29/40x - 39/8 = 0", "output": "x^2 + 29/40x - 39/8 = 0\n(x - -13/5)(x - 15/8) = 0\nx - -13/5 = 0 or x - 15/8 = 0\nx = -13/5\nx = 15/8"} {"input": "Solve the system:\n3x + 8y = -198/5\n4x + 8y = -288/5", "output": "3x + 8y = -198/5\n4x + 8y = -288/5\n\nUsing elimination\n4*(3x + 8y = -198/5)\n3*(4x + 8y = -288/5)\n12x + 32y = -792/5\n12x + 24y = -864/5\nSubtract equations\n8y = 72/5\ny = 72/5/8\ny = 9/5\n\nSubstitute y\n3x + 8(9/5) = -198/5\n3x = -54\nx = -54/3\nx = -18"} {"input": "Find x and y such that\n10x + 6y = -27\n10x + 10y = -35", "output": "10x + 6y = -27\n10x + 10y = -35\n\nUsing elimination\n10*(10x + 6y = -27)\n10*(10x + 10y = -35)\n100x + 60y = -270\n100x + 100y = -350\nSubtract equations\n-40y = 80\ny = 80/-40\ny = -2\n\nSubstitute y\n10x + 6(-2) = -27\n10x = -15\nx = -15/10\nx = -3/2"} {"input": "Find x in x^2 + 47/10x + 51/10 = 0", "output": "x^2 + 47/10x + 51/10 = 0\n(x - -3)(x - -17/10) = 0\nx - -3 = 0 or x - -17/10 = 0\nx = -3\nx = -17/10"} {"input": "Determine x in x^2 - 67/9x + 26/3 = 0", "output": "x^2 - 67/9x + 26/3 = 0\n(x - 6)(x - 13/9) = 0\nx - 6 = 0 or x - 13/9 = 0\nx = 6\nx = 13/9"} {"input": "Determine x in x^3 + 3/2x^2 - 71/18x + 5/3 = 0", "output": "x^3 + 3/2x^2 - 71/18x + 5/3 = 0\n(x - 5/6)(x - 2/3)(x - -3) = 0\nx - 5/6 = 0\nx - 2/3 = 0\nx - -3 = 0\nx = 5/6\nx = 2/3\nx = -3"} {"input": "Compute the solution of x^2 - 12x + 35 = 0", "output": "x^2 - 12x + 35 = 0\n(x - 5)(x - 7) = 0\nx - 5 = 0 or x - 7 = 0\nx = 5\nx = 7"} {"input": "What value of x satisfies x^3 + 14/9x^2 + 29/36x + 5/36 = 0", "output": "x^3 + 14/9x^2 + 29/36x + 5/36 = 0\n(x - -1/2)(x - -5/9)(x - -1/2) = 0\nx - -1/2 = 0\nx - -5/9 = 0\nx - -1/2 = 0\nx = -1/2\nx = -5/9\nx = -1/2"} {"input": "Solve the equations:\n1x + 7y = 392/5\n8x + 1y = 111/5", "output": "1x + 7y = 392/5\n8x + 1y = 111/5\n\nUsing elimination\n8*(1x + 7y = 392/5)\n1*(8x + 1y = 111/5)\n8x + 56y = 3136/5\n8x + 1y = 111/5\nSubtract equations\n55y = 605\ny = 605/55\ny = 11\n\nSubstitute y\n1x + 7(11) = 392/5\n1x = 7/5\nx = 7/5/1\nx = 7/5"} {"input": "Find x in x^3 - 29/5x^2 + 219/20x - 27/4 = 0", "output": "x^3 - 29/5x^2 + 219/20x - 27/4 = 0\n(x - 5/2)(x - 3/2)(x - 9/5) = 0\nx - 5/2 = 0\nx - 3/2 = 0\nx - 9/5 = 0\nx = 5/2\nx = 3/2\nx = 9/5"} {"input": "Solve the equation x^3 - 71/12x^2 + 45/4x - 325/48 = 0", "output": "x^3 - 71/12x^2 + 45/4x - 325/48 = 0\n(x - 13/6)(x - 5/2)(x - 5/4) = 0\nx - 13/6 = 0\nx - 5/2 = 0\nx - 5/4 = 0\nx = 13/6\nx = 5/2\nx = 5/4"} {"input": "Determine x in x^2 - 4/15x - 32/5 = 0", "output": "x^2 - 4/15x - 32/5 = 0\n(x - -12/5)(x - 8/3) = 0\nx - -12/5 = 0 or x - 8/3 = 0\nx = -12/5\nx = 8/3"} {"input": "Compute the solution of 8x - 68 = 0", "output": "8x - 68 = 0\n8x = 68\nx = 68 / 8\nx = 17/2"} {"input": "Find x for x^3 + 41/24x^2 - 131/36x - 26/9 = 0", "output": "x^3 + 41/24x^2 - 131/36x - 26/9 = 0\n(x - -2/3)(x - 13/8)(x - -8/3) = 0\nx - -2/3 = 0\nx - 13/8 = 0\nx - -8/3 = 0\nx = -2/3\nx = 13/8\nx = -8/3"} {"input": "Solve simultaneously:\n7x + 9y = 141/10\n3x + 6y = 69/10", "output": "7x + 9y = 141/10\n3x + 6y = 69/10\n\nUsing elimination\n3*(7x + 9y = 141/10)\n7*(3x + 6y = 69/10)\n21x + 27y = 423/10\n21x + 42y = 483/10\nSubtract equations\n-15y = -6\ny = -6/-15\ny = 2/5\n\nSubstitute y\n7x + 9(2/5) = 141/10\n7x = 21/2\nx = 21/2/7\nx = 3/2"} {"input": "Solve quickly: x^2 - 19/24x - 143/48 = 0", "output": "x^2 - 19/24x - 143/48 = 0\n(x - -11/8)(x - 13/6) = 0\nx - -11/8 = 0 or x - 13/6 = 0\nx = -11/8\nx = 13/6"} {"input": "Solve the system:\n3x + 7y = 199/18\n10x + 1y = -115/9", "output": "3x + 7y = 199/18\n10x + 1y = -115/9\n\nUsing elimination\n10*(3x + 7y = 199/18)\n3*(10x + 1y = -115/9)\n30x + 70y = 995/9\n30x + 3y = -115/3\nSubtract equations\n67y = 1340/9\ny = 1340/9/67\ny = 20/9\n\nSubstitute y\n3x + 7(20/9) = 199/18\n3x = -9/2\nx = -9/2/3\nx = -3/2"} {"input": "Solve the equations:\n3x + 4y = -11/2\n1x + 2y = -5/2", "output": "3x + 4y = -11/2\n1x + 2y = -5/2\n\nUsing elimination\n1*(3x + 4y = -11/2)\n3*(1x + 2y = -5/2)\n3x + 4y = -11/2\n3x + 6y = -15/2\nSubtract equations\n-2y = 2\ny = 2/-2\ny = -1\n\nSubstitute y\n3x + 4(-1) = -11/2\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Find x in x^3 - 119/40x^2 + 21/80x + 27/8 = 0", "output": "x^3 - 119/40x^2 + 21/80x + 27/8 = 0\n(x - 2)(x - 15/8)(x - -9/10) = 0\nx - 2 = 0\nx - 15/8 = 0\nx - -9/10 = 0\nx = 2\nx = 15/8\nx = -9/10"} {"input": "What value of x satisfies x^2 + 71/5x - 342/5 = 0", "output": "x^2 + 71/5x - 342/5 = 0\n(x - 19/5)(x - -18) = 0\nx - 19/5 = 0 or x - -18 = 0\nx = 19/5\nx = -18"} {"input": "Find the solution to 4x - 8/3 = 0", "output": "4x - 8/3 = 0\n4x = 8/3\nx = 8/3 / 4\nx = 2/3"} {"input": "Find x in x^3 + 19/8x^2 - 5/8x - 11/4 = 0", "output": "x^3 + 19/8x^2 - 5/8x - 11/4 = 0\n(x - -2)(x - 1)(x - -11/8) = 0\nx - -2 = 0\nx - 1 = 0\nx - -11/8 = 0\nx = -2\nx = 1\nx = -11/8"} {"input": "Solve quickly: x^2 - 43/12x + 35/12 = 0", "output": "x^2 - 43/12x + 35/12 = 0\n(x - 5/4)(x - 7/3) = 0\nx - 5/4 = 0 or x - 7/3 = 0\nx = 5/4\nx = 7/3"} {"input": "Find x for x^2 + 53/15x + 187/60 = 0", "output": "x^2 + 53/15x + 187/60 = 0\n(x - -17/10)(x - -11/6) = 0\nx - -17/10 = 0 or x - -11/6 = 0\nx = -17/10\nx = -11/6"} {"input": "What value of x satisfies 8x - 160/7 = 0", "output": "8x - 160/7 = 0\n8x = 160/7\nx = 160/7 / 8\nx = 20/7"} {"input": "Find the solution to 10x + 50/3 = 0", "output": "10x + 50/3 = 0\n10x = -50/3\nx = -50/3 / 10\nx = -5/3"} {"input": "What value of x satisfies x^2 - 29/2x + 45 = 0", "output": "x^2 - 29/2x + 45 = 0\n(x - 10)(x - 9/2) = 0\nx - 10 = 0 or x - 9/2 = 0\nx = 10\nx = 9/2"} {"input": "Solve simultaneously:\n4x + 10y = 10\n6x + 2y = 33/10", "output": "4x + 10y = 10\n6x + 2y = 33/10\n\nUsing elimination\n6*(4x + 10y = 10)\n4*(6x + 2y = 33/10)\n24x + 60y = 60\n24x + 8y = 66/5\nSubtract equations\n52y = 234/5\ny = 234/5/52\ny = 9/10\n\nSubstitute y\n4x + 10(9/10) = 10\n4x = 1\nx = 1/4\nx = 1/4"} {"input": "Solve quickly: 2x - 1 = 0", "output": "2x - 1 = 0\n2x = 1\nx = 1 / 2\nx = 1/2"} {"input": "Solve x^2 + 17x + 30 = 0", "output": "x^2 + 17x + 30 = 0\n(x - -2)(x - -15) = 0\nx - -2 = 0 or x - -15 = 0\nx = -2\nx = -15"} {"input": "Solve quickly: x^3 - 19/5x^2 + 48/25x + 36/25 = 0", "output": "x^3 - 19/5x^2 + 48/25x + 36/25 = 0\n(x - -2/5)(x - 3)(x - 6/5) = 0\nx - -2/5 = 0\nx - 3 = 0\nx - 6/5 = 0\nx = -2/5\nx = 3\nx = 6/5"} {"input": "Solve x^2 + 139/36x + 55/18 = 0", "output": "x^2 + 139/36x + 55/18 = 0\n(x - -11/4)(x - -10/9) = 0\nx - -11/4 = 0 or x - -10/9 = 0\nx = -11/4\nx = -10/9"} {"input": "Solve quickly: x^2 + 38/5x - 63/5 = 0", "output": "x^2 + 38/5x - 63/5 = 0\n(x - -9)(x - 7/5) = 0\nx - -9 = 0 or x - 7/5 = 0\nx = -9\nx = 7/5"} {"input": "Solve x^3 + 23/3x^2 - 11/4x - 2/3 = 0", "output": "x^3 + 23/3x^2 - 11/4x - 2/3 = 0\n(x - -1/6)(x - -8)(x - 1/2) = 0\nx - -1/6 = 0\nx - -8 = 0\nx - 1/2 = 0\nx = -1/6\nx = -8\nx = 1/2"} {"input": "Solve quickly: x^3 + 181/20x^2 + 7/2x - 196/5 = 0", "output": "x^3 + 181/20x^2 + 7/2x - 196/5 = 0\n(x - 7/4)(x - -8)(x - -14/5) = 0\nx - 7/4 = 0\nx - -8 = 0\nx - -14/5 = 0\nx = 7/4\nx = -8\nx = -14/5"} {"input": "Compute the solution of x^2 - 13/9x - 10/27 = 0", "output": "x^2 - 13/9x - 10/27 = 0\n(x - -2/9)(x - 5/3) = 0\nx - -2/9 = 0 or x - 5/3 = 0\nx = -2/9\nx = 5/3"} {"input": "What value of x satisfies x^2 - 13/40x + 1/40 = 0", "output": "x^2 - 13/40x + 1/40 = 0\n(x - 1/5)(x - 1/8) = 0\nx - 1/5 = 0 or x - 1/8 = 0\nx = 1/5\nx = 1/8"} {"input": "Compute the solution of x^2 + 9/20x - 77/20 = 0", "output": "x^2 + 9/20x - 77/20 = 0\n(x - -11/5)(x - 7/4) = 0\nx - -11/5 = 0 or x - 7/4 = 0\nx = -11/5\nx = 7/4"} {"input": "Solve the system:\n7x + 6y = 77/10\n5x + 9y = 11/2", "output": "7x + 6y = 77/10\n5x + 9y = 11/2\n\nUsing elimination\n5*(7x + 6y = 77/10)\n7*(5x + 9y = 11/2)\n35x + 30y = 77/2\n35x + 63y = 77/2\nSubtract equations\n-33y = 0\ny = 0/-33\ny = 0\n\nSubstitute y\n7x + 6(0) = 77/10\n7x = 77/10\nx = 77/10/7\nx = 11/10"} {"input": "Find the solution to 5x + 85/9 = 0", "output": "5x + 85/9 = 0\n5x = -85/9\nx = -85/9 / 5\nx = -17/9"} {"input": "Solve the equation x^3 - 58/21x^2 - 5/12x + 17/28 = 0", "output": "x^3 - 58/21x^2 - 5/12x + 17/28 = 0\n(x - 3/7)(x - -1/2)(x - 17/6) = 0\nx - 3/7 = 0\nx - -1/2 = 0\nx - 17/6 = 0\nx = 3/7\nx = -1/2\nx = 17/6"} {"input": "Solve quickly: x^3 + 17/2x^2 + 33/2x + 9 = 0", "output": "x^3 + 17/2x^2 + 33/2x + 9 = 0\n(x - -6)(x - -3/2)(x - -1) = 0\nx - -6 = 0\nx - -3/2 = 0\nx - -1 = 0\nx = -6\nx = -3/2\nx = -1"} {"input": "Find x in 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "Solve the equations:\n8x + 1y = -453/35\n1x + 4y = -572/35", "output": "8x + 1y = -453/35\n1x + 4y = -572/35\n\nUsing elimination\n1*(8x + 1y = -453/35)\n8*(1x + 4y = -572/35)\n8x + 1y = -453/35\n8x + 32y = -4576/35\nSubtract equations\n-31y = 589/5\ny = 589/5/-31\ny = -19/5\n\nSubstitute y\n8x + 1(-19/5) = -453/35\n8x = -64/7\nx = -64/7/8\nx = -8/7"} {"input": "Find the solution to x^3 - 65/3x^2 + 296/3x - 128 = 0", "output": "x^3 - 65/3x^2 + 296/3x - 128 = 0\n(x - 8/3)(x - 16)(x - 3) = 0\nx - 8/3 = 0\nx - 16 = 0\nx - 3 = 0\nx = 8/3\nx = 16\nx = 3"} {"input": "Find x and y such that\n1x + 3y = -146/15\n5x + 10y = -119/3", "output": "1x + 3y = -146/15\n5x + 10y = -119/3\n\nUsing elimination\n5*(1x + 3y = -146/15)\n1*(5x + 10y = -119/3)\n5x + 15y = -146/3\n5x + 10y = -119/3\nSubtract equations\n5y = -9\ny = -9/5\ny = -9/5\n\nSubstitute y\n1x + 3(-9/5) = -146/15\n1x = -13/3\nx = -13/3/1\nx = -13/3"} {"input": "Solve 1x - 8/3 = 0", "output": "1x - 8/3 = 0\n1x = 8/3\nx = 8/3 / 1\nx = 8/3"} {"input": "Solve simultaneously:\n5x + 8y = 216/7\n5x + 5y = 465/28", "output": "5x + 8y = 216/7\n5x + 5y = 465/28\n\nUsing elimination\n5*(5x + 8y = 216/7)\n5*(5x + 5y = 465/28)\n25x + 40y = 1080/7\n25x + 25y = 2325/28\nSubtract equations\n15y = 285/4\ny = 285/4/15\ny = 19/4\n\nSubstitute y\n5x + 8(19/4) = 216/7\n5x = -50/7\nx = -50/7/5\nx = -10/7"} {"input": "Solve quickly: 7x + 13 = 0", "output": "7x + 13 = 0\n7x = -13\nx = -13 / 7\nx = -13/7"} {"input": "What value of x satisfies x^2 - 59/18x + 8/3 = 0", "output": "x^2 - 59/18x + 8/3 = 0\n(x - 3/2)(x - 16/9) = 0\nx - 3/2 = 0 or x - 16/9 = 0\nx = 3/2\nx = 16/9"} {"input": "Solve quickly: x^2 + 3/2x - 7/16 = 0", "output": "x^2 + 3/2x - 7/16 = 0\n(x - 1/4)(x - -7/4) = 0\nx - 1/4 = 0 or x - -7/4 = 0\nx = 1/4\nx = -7/4"} {"input": "Compute the solution of 10x - 100/9 = 0", "output": "10x - 100/9 = 0\n10x = 100/9\nx = 100/9 / 10\nx = 10/9"} {"input": "Solve quickly: x^2 - 109/9x + 4/3 = 0", "output": "x^2 - 109/9x + 4/3 = 0\n(x - 12)(x - 1/9) = 0\nx - 12 = 0 or x - 1/9 = 0\nx = 12\nx = 1/9"} {"input": "Solve the equations:\n8x + 7y = 208/5\n6x + 7y = 191/5", "output": "8x + 7y = 208/5\n6x + 7y = 191/5\n\nUsing elimination\n6*(8x + 7y = 208/5)\n8*(6x + 7y = 191/5)\n48x + 42y = 1248/5\n48x + 56y = 1528/5\nSubtract equations\n-14y = -56\ny = -56/-14\ny = 4\n\nSubstitute y\n8x + 7(4) = 208/5\n8x = 68/5\nx = 68/5/8\nx = 17/10"} {"input": "Solve the equation x^3 + 102/35x^2 - 11/5x - 144/35 = 0", "output": "x^3 + 102/35x^2 - 11/5x - 144/35 = 0\n(x - -1)(x - -16/5)(x - 9/7) = 0\nx - -1 = 0\nx - -16/5 = 0\nx - 9/7 = 0\nx = -1\nx = -16/5\nx = 9/7"} {"input": "Find the solution to x^2 + 27/28x - 5/14 = 0", "output": "x^2 + 27/28x - 5/14 = 0\n(x - 2/7)(x - -5/4) = 0\nx - 2/7 = 0 or x - -5/4 = 0\nx = 2/7\nx = -5/4"} {"input": "Solve the equation 6x + 32/3 = 0", "output": "6x + 32/3 = 0\n6x = -32/3\nx = -32/3 / 6\nx = -16/9"} {"input": "Compute the solution of 2x + 4 = 0", "output": "2x + 4 = 0\n2x = -4\nx = -4 / 2\nx = -2"} {"input": "Find x in 1x + 9 = 0", "output": "1x + 9 = 0\n1x = -9\nx = -9 / 1\nx = -9"} {"input": "Determine x in x^3 + 13x^2 - 106x + 152 = 0", "output": "x^3 + 13x^2 - 106x + 152 = 0\n(x - 2)(x - 4)(x - -19) = 0\nx - 2 = 0\nx - 4 = 0\nx - -19 = 0\nx = 2\nx = 4\nx = -19"} {"input": "Determine x in x^2 + 1/2x - 33/50 = 0", "output": "x^2 + 1/2x - 33/50 = 0\n(x - -11/10)(x - 3/5) = 0\nx - -11/10 = 0 or x - 3/5 = 0\nx = -11/10\nx = 3/5"} {"input": "Find x for x^2 + 9/8x - 9/16 = 0", "output": "x^2 + 9/8x - 9/16 = 0\n(x - -3/2)(x - 3/8) = 0\nx - -3/2 = 0 or x - 3/8 = 0\nx = -3/2\nx = 3/8"} {"input": "Solve simultaneously:\n9x + 7y = -48\n5x + 7y = -164/3", "output": "9x + 7y = -48\n5x + 7y = -164/3\n\nUsing elimination\n5*(9x + 7y = -48)\n9*(5x + 7y = -164/3)\n45x + 35y = -240\n45x + 63y = -492\nSubtract equations\n-28y = 252\ny = 252/-28\ny = -9\n\nSubstitute y\n9x + 7(-9) = -48\n9x = 15\nx = 15/9\nx = 5/3"} {"input": "Solve the system:\n5x + 10y = 5\n7x + 5y = 11/2", "output": "5x + 10y = 5\n7x + 5y = 11/2\n\nUsing elimination\n7*(5x + 10y = 5)\n5*(7x + 5y = 11/2)\n35x + 70y = 35\n35x + 25y = 55/2\nSubtract equations\n45y = 15/2\ny = 15/2/45\ny = 1/6\n\nSubstitute y\n5x + 10(1/6) = 5\n5x = 10/3\nx = 10/3/5\nx = 2/3"} {"input": "Determine x in 9x - 7 = 0", "output": "9x - 7 = 0\n9x = 7\nx = 7 / 9\nx = 7/9"} {"input": "Find x in x^2 + 23/9x + 14/9 = 0", "output": "x^2 + 23/9x + 14/9 = 0\n(x - -14/9)(x - -1) = 0\nx - -14/9 = 0 or x - -1 = 0\nx = -14/9\nx = -1"} {"input": "Solve x^2 + 59/9x - 28/9 = 0", "output": "x^2 + 59/9x - 28/9 = 0\n(x - -7)(x - 4/9) = 0\nx - -7 = 0 or x - 4/9 = 0\nx = -7\nx = 4/9"} {"input": "Find the solution to x^2 - 33/2x + 8 = 0", "output": "x^2 - 33/2x + 8 = 0\n(x - 16)(x - 1/2) = 0\nx - 16 = 0 or x - 1/2 = 0\nx = 16\nx = 1/2"} {"input": "Solve quickly: 9x - 90/7 = 0", "output": "9x - 90/7 = 0\n9x = 90/7\nx = 90/7 / 9\nx = 10/7"} {"input": "Find x in x^2 + 13/5x - 28/5 = 0", "output": "x^2 + 13/5x - 28/5 = 0\n(x - 7/5)(x - -4) = 0\nx - 7/5 = 0 or x - -4 = 0\nx = 7/5\nx = -4"} {"input": "Find x for 10x - 15 = 0", "output": "10x - 15 = 0\n10x = 15\nx = 15 / 10\nx = 3/2"} {"input": "Solve the system:\n2x + 2y = -14/3\n7x + 10y = -79/3", "output": "2x + 2y = -14/3\n7x + 10y = -79/3\n\nUsing elimination\n7*(2x + 2y = -14/3)\n2*(7x + 10y = -79/3)\n14x + 14y = -98/3\n14x + 20y = -158/3\nSubtract equations\n-6y = 20\ny = 20/-6\ny = -10/3\n\nSubstitute y\n2x + 2(-10/3) = -14/3\n2x = 2\nx = 2/2\nx = 1"} {"input": "Compute the solution of x^2 + 67/4x + 12 = 0", "output": "x^2 + 67/4x + 12 = 0\n(x - -3/4)(x - -16) = 0\nx - -3/4 = 0 or x - -16 = 0\nx = -3/4\nx = -16"} {"input": "Solve the system:\n8x + 3y = 31/24\n5x + 3y = 43/24", "output": "8x + 3y = 31/24\n5x + 3y = 43/24\n\nUsing elimination\n5*(8x + 3y = 31/24)\n8*(5x + 3y = 43/24)\n40x + 15y = 155/24\n40x + 24y = 43/3\nSubtract equations\n-9y = -63/8\ny = -63/8/-9\ny = 7/8\n\nSubstitute y\n8x + 3(7/8) = 31/24\n8x = -4/3\nx = -4/3/8\nx = -1/6"} {"input": "Solve simultaneously:\n7x + 9y = 2/15\n1x + 10y = 89/6", "output": "7x + 9y = 2/15\n1x + 10y = 89/6\n\nUsing elimination\n1*(7x + 9y = 2/15)\n7*(1x + 10y = 89/6)\n7x + 9y = 2/15\n7x + 70y = 623/6\nSubtract equations\n-61y = -1037/10\ny = -1037/10/-61\ny = 17/10\n\nSubstitute y\n7x + 9(17/10) = 2/15\n7x = -91/6\nx = -91/6/7\nx = -13/6"} {"input": "Find the solution to x^2 + 35/24x - 49/24 = 0", "output": "x^2 + 35/24x - 49/24 = 0\n(x - -7/3)(x - 7/8) = 0\nx - -7/3 = 0 or x - 7/8 = 0\nx = -7/3\nx = 7/8"} {"input": "Compute the solution of 5x - 25 = 0", "output": "5x - 25 = 0\n5x = 25\nx = 25 / 5\nx = 5"} {"input": "Solve simultaneously:\n6x + 2y = -178/5\n8x + 5y = -40", "output": "6x + 2y = -178/5\n8x + 5y = -40\n\nUsing elimination\n8*(6x + 2y = -178/5)\n6*(8x + 5y = -40)\n48x + 16y = -1424/5\n48x + 30y = -240\nSubtract equations\n-14y = -224/5\ny = -224/5/-14\ny = 16/5\n\nSubstitute y\n6x + 2(16/5) = -178/5\n6x = -42\nx = -42/6\nx = -7"} {"input": "Find x in x^3 - 47/10x^2 + 113/25x - 28/25 = 0", "output": "x^3 - 47/10x^2 + 113/25x - 28/25 = 0\n(x - 7/2)(x - 2/5)(x - 4/5) = 0\nx - 7/2 = 0\nx - 2/5 = 0\nx - 4/5 = 0\nx = 7/2\nx = 2/5\nx = 4/5"} {"input": "Solve the equation 8x + 8/7 = 0", "output": "8x + 8/7 = 0\n8x = -8/7\nx = -8/7 / 8\nx = -1/7"} {"input": "What value of x satisfies x^2 - 196/45x + 19/9 = 0", "output": "x^2 - 196/45x + 19/9 = 0\n(x - 19/5)(x - 5/9) = 0\nx - 19/5 = 0 or x - 5/9 = 0\nx = 19/5\nx = 5/9"} {"input": "Solve the equation x^2 - 10/3x - 16 = 0", "output": "x^2 - 10/3x - 16 = 0\n(x - 6)(x - -8/3) = 0\nx - 6 = 0 or x - -8/3 = 0\nx = 6\nx = -8/3"} {"input": "Find x for x^3 - 33/40x^2 - 26/5x + 57/10 = 0", "output": "x^3 - 33/40x^2 - 26/5x + 57/10 = 0\n(x - 2)(x - -19/8)(x - 6/5) = 0\nx - 2 = 0\nx - -19/8 = 0\nx - 6/5 = 0\nx = 2\nx = -19/8\nx = 6/5"} {"input": "Find the solution to x^2 - 1/10x - 3/50 = 0", "output": "x^2 - 1/10x - 3/50 = 0\n(x - 3/10)(x - -1/5) = 0\nx - 3/10 = 0 or x - -1/5 = 0\nx = 3/10\nx = -1/5"} {"input": "Solve x^3 + 7/2x^2 - 2x = 0", "output": "x^3 + 7/2x^2 - 2x = 0\n(x - -4)(x - 1/2)(x - 0) = 0\nx - -4 = 0\nx - 1/2 = 0\nx - 0 = 0\nx = -4\nx = 1/2\nx = 0"} {"input": "Find the solution to x^3 + 3/4x^2 - 107/8x - 45/2 = 0", "output": "x^3 + 3/4x^2 - 107/8x - 45/2 = 0\n(x - 4)(x - -5/2)(x - -9/4) = 0\nx - 4 = 0\nx - -5/2 = 0\nx - -9/4 = 0\nx = 4\nx = -5/2\nx = -9/4"} {"input": "Find x for x^3 - 235/36x^2 + 493/36x - 28/3 = 0", "output": "x^3 - 235/36x^2 + 493/36x - 28/3 = 0\n(x - 16/9)(x - 7/4)(x - 3) = 0\nx - 16/9 = 0\nx - 7/4 = 0\nx - 3 = 0\nx = 16/9\nx = 7/4\nx = 3"} {"input": "Find x in 10x - 16 = 0", "output": "10x - 16 = 0\n10x = 16\nx = 16 / 10\nx = 8/5"} {"input": "Compute the solution of x^2 - 5/4x - 25/8 = 0", "output": "x^2 - 5/4x - 25/8 = 0\n(x - -5/4)(x - 5/2) = 0\nx - -5/4 = 0 or x - 5/2 = 0\nx = -5/4\nx = 5/2"} {"input": "Solve the equation 1x + 2 = 0", "output": "1x + 2 = 0\n1x = -2\nx = -2 / 1\nx = -2"} {"input": "Solve the system:\n9x + 1y = 43\n10x + 4y = -4/3", "output": "9x + 1y = 43\n10x + 4y = -4/3\n\nUsing elimination\n10*(9x + 1y = 43)\n9*(10x + 4y = -4/3)\n90x + 10y = 430\n90x + 36y = -12\nSubtract equations\n-26y = 442\ny = 442/-26\ny = -17\n\nSubstitute y\n9x + 1(-17) = 43\n9x = 60\nx = 60/9\nx = 20/3"} {"input": "Determine x in x^3 + 59/15x^2 - 14x - 48/5 = 0", "output": "x^3 + 59/15x^2 - 14x - 48/5 = 0\n(x - 8/3)(x - -6)(x - -3/5) = 0\nx - 8/3 = 0\nx - -6 = 0\nx - -3/5 = 0\nx = 8/3\nx = -6\nx = -3/5"} {"input": "Find the solution to x^3 + 67/24x^2 + 23/72x - 7/4 = 0", "output": "x^3 + 67/24x^2 + 23/72x - 7/4 = 0\n(x - 2/3)(x - -9/8)(x - -7/3) = 0\nx - 2/3 = 0\nx - -9/8 = 0\nx - -7/3 = 0\nx = 2/3\nx = -9/8\nx = -7/3"} {"input": "Solve the equation 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve the system:\n3x + 4y = -69/7\n10x + 1y = -505/21", "output": "3x + 4y = -69/7\n10x + 1y = -505/21\n\nUsing elimination\n10*(3x + 4y = -69/7)\n3*(10x + 1y = -505/21)\n30x + 40y = -690/7\n30x + 3y = -505/7\nSubtract equations\n37y = -185/7\ny = -185/7/37\ny = -5/7\n\nSubstitute y\n3x + 4(-5/7) = -69/7\n3x = -7\nx = -7/3\nx = -7/3"} {"input": "What value of x satisfies 1x + 3/4 = 0", "output": "1x + 3/4 = 0\n1x = -3/4\nx = -3/4 / 1\nx = -3/4"} {"input": "Find the solution to 3x - 18 = 0", "output": "3x - 18 = 0\n3x = 18\nx = 18 / 3\nx = 6"} {"input": "Solve quickly: x^3 + 191/84x^2 - 29/14x - 44/21 = 0", "output": "x^3 + 191/84x^2 - 29/14x - 44/21 = 0\n(x - -2/3)(x - 8/7)(x - -11/4) = 0\nx - -2/3 = 0\nx - 8/7 = 0\nx - -11/4 = 0\nx = -2/3\nx = 8/7\nx = -11/4"} {"input": "Find x for 4x - 34 = 0", "output": "4x - 34 = 0\n4x = 34\nx = 34 / 4\nx = 17/2"} {"input": "Solve simultaneously:\n7x + 9y = 6\n2x + 6y = -12", "output": "7x + 9y = 6\n2x + 6y = -12\n\nUsing elimination\n2*(7x + 9y = 6)\n7*(2x + 6y = -12)\n14x + 18y = 12\n14x + 42y = -84\nSubtract equations\n-24y = 96\ny = 96/-24\ny = -4\n\nSubstitute y\n7x + 9(-4) = 6\n7x = 42\nx = 42/7\nx = 6"} {"input": "Find x in x^2 + 31/30x - 91/30 = 0", "output": "x^2 + 31/30x - 91/30 = 0\n(x - 13/10)(x - -7/3) = 0\nx - 13/10 = 0 or x - -7/3 = 0\nx = 13/10\nx = -7/3"} {"input": "Solve simultaneously:\n2x + 6y = 69/7\n1x + 1y = 9/14", "output": "2x + 6y = 69/7\n1x + 1y = 9/14\n\nUsing elimination\n1*(2x + 6y = 69/7)\n2*(1x + 1y = 9/14)\n2x + 6y = 69/7\n2x + 2y = 9/7\nSubtract equations\n4y = 60/7\ny = 60/7/4\ny = 15/7\n\nSubstitute y\n2x + 6(15/7) = 69/7\n2x = -3\nx = -3/2\nx = -3/2"} {"input": "Find x for x^2 - 8/3x + 7/9 = 0", "output": "x^2 - 8/3x + 7/9 = 0\n(x - 1/3)(x - 7/3) = 0\nx - 1/3 = 0 or x - 7/3 = 0\nx = 1/3\nx = 7/3"} {"input": "Find x and y such that\n6x + 9y = 279/7\n2x + 8y = 108/7", "output": "6x + 9y = 279/7\n2x + 8y = 108/7\n\nUsing elimination\n2*(6x + 9y = 279/7)\n6*(2x + 8y = 108/7)\n12x + 18y = 558/7\n12x + 48y = 648/7\nSubtract equations\n-30y = -90/7\ny = -90/7/-30\ny = 3/7\n\nSubstitute y\n6x + 9(3/7) = 279/7\n6x = 36\nx = 36/6\nx = 6"} {"input": "What value of x satisfies x^2 + 13/6x - 119/6 = 0", "output": "x^2 + 13/6x - 119/6 = 0\n(x - 7/2)(x - -17/3) = 0\nx - 7/2 = 0 or x - -17/3 = 0\nx = 7/2\nx = -17/3"} {"input": "Find x for x^3 - 22/5x^2 - 29/5x + 14 = 0", "output": "x^3 - 22/5x^2 - 29/5x + 14 = 0\n(x - 5)(x - -2)(x - 7/5) = 0\nx - 5 = 0\nx - -2 = 0\nx - 7/5 = 0\nx = 5\nx = -2\nx = 7/5"} {"input": "Solve the equation x^3 - 107/8x^2 - 201/8x + 45/4 = 0", "output": "x^3 - 107/8x^2 - 201/8x + 45/4 = 0\n(x - 15)(x - 3/8)(x - -2) = 0\nx - 15 = 0\nx - 3/8 = 0\nx - -2 = 0\nx = 15\nx = 3/8\nx = -2"} {"input": "Solve the equation x^2 + 3/2x - 22 = 0", "output": "x^2 + 3/2x - 22 = 0\n(x - 4)(x - -11/2) = 0\nx - 4 = 0 or x - -11/2 = 0\nx = 4\nx = -11/2"} {"input": "Solve 2x + 3 = 0", "output": "2x + 3 = 0\n2x = -3\nx = -3 / 2\nx = -3/2"} {"input": "Solve x^2 + 31/15x + 14/15 = 0", "output": "x^2 + 31/15x + 14/15 = 0\n(x - -2/3)(x - -7/5) = 0\nx - -2/3 = 0 or x - -7/5 = 0\nx = -2/3\nx = -7/5"} {"input": "Find x for x^3 - 217/24x^2 - 3043/48x - 2023/24 = 0", "output": "x^3 - 217/24x^2 - 3043/48x - 2023/24 = 0\n(x - 14)(x - -17/8)(x - -17/6) = 0\nx - 14 = 0\nx - -17/8 = 0\nx - -17/6 = 0\nx = 14\nx = -17/8\nx = -17/6"} {"input": "Solve the equation x^3 + 229/72x^2 + 65/24x + 25/36 = 0", "output": "x^3 + 229/72x^2 + 65/24x + 25/36 = 0\n(x - -5/9)(x - -2)(x - -5/8) = 0\nx - -5/9 = 0\nx - -2 = 0\nx - -5/8 = 0\nx = -5/9\nx = -2\nx = -5/8"} {"input": "Find the solution to 1x - 5/7 = 0", "output": "1x - 5/7 = 0\n1x = 5/7\nx = 5/7 / 1\nx = 5/7"} {"input": "Solve the system:\n6x + 6y = -35\n7x + 4y = -127/3", "output": "6x + 6y = -35\n7x + 4y = -127/3\n\nUsing elimination\n7*(6x + 6y = -35)\n6*(7x + 4y = -127/3)\n42x + 42y = -245\n42x + 24y = -254\nSubtract equations\n18y = 9\ny = 9/18\ny = 1/2\n\nSubstitute y\n6x + 6(1/2) = -35\n6x = -38\nx = -38/6\nx = -19/3"} {"input": "Find x for x^2 - 28/5x + 36/5 = 0", "output": "x^2 - 28/5x + 36/5 = 0\n(x - 18/5)(x - 2) = 0\nx - 18/5 = 0 or x - 2 = 0\nx = 18/5\nx = 2"} {"input": "Solve quickly: x^2 + 3/2x = 0", "output": "x^2 + 3/2x = 0\n(x - -3/2)(x - 0) = 0\nx - -3/2 = 0 or x - 0 = 0\nx = -3/2\nx = 0"} {"input": "Find x in x^2 - 149/20x + 68/5 = 0", "output": "x^2 - 149/20x + 68/5 = 0\n(x - 16/5)(x - 17/4) = 0\nx - 16/5 = 0 or x - 17/4 = 0\nx = 16/5\nx = 17/4"} {"input": "Solve the equation x^3 + 736/45x^2 + 2033/45x + 182/9 = 0", "output": "x^3 + 736/45x^2 + 2033/45x + 182/9 = 0\n(x - -14/5)(x - -13)(x - -5/9) = 0\nx - -14/5 = 0\nx - -13 = 0\nx - -5/9 = 0\nx = -14/5\nx = -13\nx = -5/9"} {"input": "Determine x in x^3 - 9/5x^2 - 129/100x + 209/100 = 0", "output": "x^3 - 9/5x^2 - 129/100x + 209/100 = 0\n(x - -11/10)(x - 19/10)(x - 1) = 0\nx - -11/10 = 0\nx - 19/10 = 0\nx - 1 = 0\nx = -11/10\nx = 19/10\nx = 1"} {"input": "Solve the equations:\n3x + 4y = 578/21\n2x + 6y = 284/7", "output": "3x + 4y = 578/21\n2x + 6y = 284/7\n\nUsing elimination\n2*(3x + 4y = 578/21)\n3*(2x + 6y = 284/7)\n6x + 8y = 1156/21\n6x + 18y = 852/7\nSubtract equations\n-10y = -200/3\ny = -200/3/-10\ny = 20/3\n\nSubstitute y\n3x + 4(20/3) = 578/21\n3x = 6/7\nx = 6/7/3\nx = 2/7"} {"input": "Find the solution to 8x - 76 = 0", "output": "8x - 76 = 0\n8x = 76\nx = 76 / 8\nx = 19/2"} {"input": "Solve the equations:\n9x + 9y = 111/2\n1x + 6y = 157/6", "output": "9x + 9y = 111/2\n1x + 6y = 157/6\n\nUsing elimination\n1*(9x + 9y = 111/2)\n9*(1x + 6y = 157/6)\n9x + 9y = 111/2\n9x + 54y = 471/2\nSubtract equations\n-45y = -180\ny = -180/-45\ny = 4\n\nSubstitute y\n9x + 9(4) = 111/2\n9x = 39/2\nx = 39/2/9\nx = 13/6"} {"input": "Compute the solution of x^2 + 149/21x + 34/3 = 0", "output": "x^2 + 149/21x + 34/3 = 0\n(x - -14/3)(x - -17/7) = 0\nx - -14/3 = 0 or x - -17/7 = 0\nx = -14/3\nx = -17/7"} {"input": "Find x and y such that\n4x + 6y = -82/5\n1x + 6y = -88/5", "output": "4x + 6y = -82/5\n1x + 6y = -88/5\n\nUsing elimination\n1*(4x + 6y = -82/5)\n4*(1x + 6y = -88/5)\n4x + 6y = -82/5\n4x + 24y = -352/5\nSubtract equations\n-18y = 54\ny = 54/-18\ny = -3\n\nSubstitute y\n4x + 6(-3) = -82/5\n4x = 8/5\nx = 8/5/4\nx = 2/5"} {"input": "Find x for x^2 - 7/12x - 51/8 = 0", "output": "x^2 - 7/12x - 51/8 = 0\n(x - -9/4)(x - 17/6) = 0\nx - -9/4 = 0 or x - 17/6 = 0\nx = -9/4\nx = 17/6"} {"input": "Solve 4x + 16 = 0", "output": "4x + 16 = 0\n4x = -16\nx = -16 / 4\nx = -4"} {"input": "Find x in 7x - 7/9 = 0", "output": "7x - 7/9 = 0\n7x = 7/9\nx = 7/9 / 7\nx = 1/9"} {"input": "Find x and y such that\n6x + 1y = 24/5\n10x + 2y = 8", "output": "6x + 1y = 24/5\n10x + 2y = 8\n\nUsing elimination\n10*(6x + 1y = 24/5)\n6*(10x + 2y = 8)\n60x + 10y = 48\n60x + 12y = 48\nSubtract equations\n-2y = 0\ny = 0/-2\ny = 0\n\nSubstitute y\n6x + 1(0) = 24/5\n6x = 24/5\nx = 24/5/6\nx = 4/5"} {"input": "Solve simultaneously:\n7x + 7y = 259/6\n9x + 7y = 277/6", "output": "7x + 7y = 259/6\n9x + 7y = 277/6\n\nUsing elimination\n9*(7x + 7y = 259/6)\n7*(9x + 7y = 277/6)\n63x + 63y = 777/2\n63x + 49y = 1939/6\nSubtract equations\n14y = 196/3\ny = 196/3/14\ny = 14/3\n\nSubstitute y\n7x + 7(14/3) = 259/6\n7x = 21/2\nx = 21/2/7\nx = 3/2"} {"input": "Determine x in 9x - 162 = 0", "output": "9x - 162 = 0\n9x = 162\nx = 162 / 9\nx = 18"} {"input": "Solve the equation x^2 + 4/5x - 57/5 = 0", "output": "x^2 + 4/5x - 57/5 = 0\n(x - -19/5)(x - 3) = 0\nx - -19/5 = 0 or x - 3 = 0\nx = -19/5\nx = 3"} {"input": "Solve the system:\n2x + 9y = 137\n7x + 6y = 46", "output": "2x + 9y = 137\n7x + 6y = 46\n\nUsing elimination\n7*(2x + 9y = 137)\n2*(7x + 6y = 46)\n14x + 63y = 959\n14x + 12y = 92\nSubtract equations\n51y = 867\ny = 867/51\ny = 17\n\nSubstitute y\n2x + 9(17) = 137\n2x = -16\nx = -16/2\nx = -8"} {"input": "Solve quickly: x^2 + 1/4x = 0", "output": "x^2 + 1/4x = 0\n(x - 0)(x - -1/4) = 0\nx - 0 = 0 or x - -1/4 = 0\nx = 0\nx = -1/4"} {"input": "Solve quickly: x^3 + 54/7x^2 - 156/7x + 40/7 = 0", "output": "x^3 + 54/7x^2 - 156/7x + 40/7 = 0\n(x - 2/7)(x - 2)(x - -10) = 0\nx - 2/7 = 0\nx - 2 = 0\nx - -10 = 0\nx = 2/7\nx = 2\nx = -10"} {"input": "Find x in 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Solve quickly: x^3 + 10/7x^2 = 0", "output": "x^3 + 10/7x^2 = 0\n(x - 0)(x - -10/7)(x - 0) = 0\nx - 0 = 0\nx - -10/7 = 0\nx - 0 = 0\nx = 0\nx = -10/7\nx = 0"} {"input": "Solve the equation x^3 - 47/12x^2 - 5/6x + 2 = 0", "output": "x^3 - 47/12x^2 - 5/6x + 2 = 0\n(x - 4)(x - -3/4)(x - 2/3) = 0\nx - 4 = 0\nx - -3/4 = 0\nx - 2/3 = 0\nx = 4\nx = -3/4\nx = 2/3"} {"input": "What value of x satisfies x^2 + 13/14x - 6/7 = 0", "output": "x^2 + 13/14x - 6/7 = 0\n(x - -3/2)(x - 4/7) = 0\nx - -3/2 = 0 or x - 4/7 = 0\nx = -3/2\nx = 4/7"} {"input": "Solve the equation x^2 - 8x + 143/9 = 0", "output": "x^2 - 8x + 143/9 = 0\n(x - 11/3)(x - 13/3) = 0\nx - 11/3 = 0 or x - 13/3 = 0\nx = 11/3\nx = 13/3"} {"input": "Find x in x^2 + 56/9x + 4/3 = 0", "output": "x^2 + 56/9x + 4/3 = 0\n(x - -2/9)(x - -6) = 0\nx - -2/9 = 0 or x - -6 = 0\nx = -2/9\nx = -6"} {"input": "Solve the equations:\n8x + 9y = -16/5\n6x + 6y = -33/10", "output": "8x + 9y = -16/5\n6x + 6y = -33/10\n\nUsing elimination\n6*(8x + 9y = -16/5)\n8*(6x + 6y = -33/10)\n48x + 54y = -96/5\n48x + 48y = -132/5\nSubtract equations\n6y = 36/5\ny = 36/5/6\ny = 6/5\n\nSubstitute y\n8x + 9(6/5) = -16/5\n8x = -14\nx = -14/8\nx = -7/4"} {"input": "Determine x in x^2 + 17/3x - 30 = 0", "output": "x^2 + 17/3x - 30 = 0\n(x - 10/3)(x - -9) = 0\nx - 10/3 = 0 or x - -9 = 0\nx = 10/3\nx = -9"} {"input": "Compute the solution of x^3 + 286/21x^2 - 167/3x + 646/21 = 0", "output": "x^3 + 286/21x^2 - 167/3x + 646/21 = 0\n(x - 19/7)(x - 2/3)(x - -17) = 0\nx - 19/7 = 0\nx - 2/3 = 0\nx - -17 = 0\nx = 19/7\nx = 2/3\nx = -17"} {"input": "Solve quickly: x^2 + 46/21x + 8/7 = 0", "output": "x^2 + 46/21x + 8/7 = 0\n(x - -4/3)(x - -6/7) = 0\nx - -4/3 = 0 or x - -6/7 = 0\nx = -4/3\nx = -6/7"} {"input": "Solve simultaneously:\n8x + 7y = -493/9\n2x + 10y = -280/9", "output": "8x + 7y = -493/9\n2x + 10y = -280/9\n\nUsing elimination\n2*(8x + 7y = -493/9)\n8*(2x + 10y = -280/9)\n16x + 14y = -986/9\n16x + 80y = -2240/9\nSubtract equations\n-66y = 418/3\ny = 418/3/-66\ny = -19/9\n\nSubstitute y\n8x + 7(-19/9) = -493/9\n8x = -40\nx = -40/8\nx = -5"} {"input": "Find x for 1x - 4 = 0", "output": "1x - 4 = 0\n1x = 4\nx = 4 / 1\nx = 4"} {"input": "Solve the equation x^2 - 37/3x - 40 = 0", "output": "x^2 - 37/3x - 40 = 0\n(x - 15)(x - -8/3) = 0\nx - 15 = 0 or x - -8/3 = 0\nx = 15\nx = -8/3"} {"input": "Solve x^3 - 3/2x^2 + 1/2 = 0", "output": "x^3 - 3/2x^2 + 1/2 = 0\n(x - -1/2)(x - 1)(x - 1) = 0\nx - -1/2 = 0\nx - 1 = 0\nx - 1 = 0\nx = -1/2\nx = 1\nx = 1"} {"input": "Find x and y such that\n4x + 5y = -52/5\n10x + 2y = -26", "output": "4x + 5y = -52/5\n10x + 2y = -26\n\nUsing elimination\n10*(4x + 5y = -52/5)\n4*(10x + 2y = -26)\n40x + 50y = -104\n40x + 8y = -104\nSubtract equations\n42y = 0\ny = 0/42\ny = 0\n\nSubstitute y\n4x + 5(0) = -52/5\n4x = -52/5\nx = -52/5/4\nx = -13/5"} {"input": "Solve the equations:\n5x + 2y = 277/36\n4x + 6y = 479/36", "output": "5x + 2y = 277/36\n4x + 6y = 479/36\n\nUsing elimination\n4*(5x + 2y = 277/36)\n5*(4x + 6y = 479/36)\n20x + 8y = 277/9\n20x + 30y = 2395/36\nSubtract equations\n-22y = -143/4\ny = -143/4/-22\ny = 13/8\n\nSubstitute y\n5x + 2(13/8) = 277/36\n5x = 40/9\nx = 40/9/5\nx = 8/9"} {"input": "Solve simultaneously:\n1x + 6y = 9\n2x + 7y = 21/2", "output": "1x + 6y = 9\n2x + 7y = 21/2\n\nUsing elimination\n2*(1x + 6y = 9)\n1*(2x + 7y = 21/2)\n2x + 12y = 18\n2x + 7y = 21/2\nSubtract equations\n5y = 15/2\ny = 15/2/5\ny = 3/2\n\nSubstitute y\n1x + 6(3/2) = 9\n1x = 0\nx = 0/1\nx = 0"} {"input": "Find x in x^2 + 59/45x - 272/45 = 0", "output": "x^2 + 59/45x - 272/45 = 0\n(x - 17/9)(x - -16/5) = 0\nx - 17/9 = 0 or x - -16/5 = 0\nx = 17/9\nx = -16/5"} {"input": "Solve 8x + 40/7 = 0", "output": "8x + 40/7 = 0\n8x = -40/7\nx = -40/7 / 8\nx = -5/7"} {"input": "Determine x in x^2 - 53/21x - 20/21 = 0", "output": "x^2 - 53/21x - 20/21 = 0\n(x - -1/3)(x - 20/7) = 0\nx - -1/3 = 0 or x - 20/7 = 0\nx = -1/3\nx = 20/7"} {"input": "Find the solution to x^2 - 9/16 = 0", "output": "x^2 - 9/16 = 0\n(x - -3/4)(x - 3/4) = 0\nx - -3/4 = 0 or x - 3/4 = 0\nx = -3/4\nx = 3/4"} {"input": "Find x for 10x + 55/4 = 0", "output": "10x + 55/4 = 0\n10x = -55/4\nx = -55/4 / 10\nx = -11/8"} {"input": "Compute the solution of x^3 + 29/6x^2 + 20/3x + 17/6 = 0", "output": "x^3 + 29/6x^2 + 20/3x + 17/6 = 0\n(x - -1)(x - -1)(x - -17/6) = 0\nx - -1 = 0\nx - -1 = 0\nx - -17/6 = 0\nx = -1\nx = -1\nx = -17/6"} {"input": "Solve the system:\n3x + 6y = 57/2\n8x + 1y = -4", "output": "3x + 6y = 57/2\n8x + 1y = -4\n\nUsing elimination\n8*(3x + 6y = 57/2)\n3*(8x + 1y = -4)\n24x + 48y = 228\n24x + 3y = -12\nSubtract equations\n45y = 240\ny = 240/45\ny = 16/3\n\nSubstitute y\n3x + 6(16/3) = 57/2\n3x = -7/2\nx = -7/2/3\nx = -7/6"} {"input": "Find the solution to x^3 + 59/30x^2 + 37/75x - 21/50 = 0", "output": "x^3 + 59/30x^2 + 37/75x - 21/50 = 0\n(x - -7/5)(x - -9/10)(x - 1/3) = 0\nx - -7/5 = 0\nx - -9/10 = 0\nx - 1/3 = 0\nx = -7/5\nx = -9/10\nx = 1/3"} {"input": "Find x and y such that\n3x + 10y = -309/7\n7x + 2y = -465/7", "output": "3x + 10y = -309/7\n7x + 2y = -465/7\n\nUsing elimination\n7*(3x + 10y = -309/7)\n3*(7x + 2y = -465/7)\n21x + 70y = -309\n21x + 6y = -1395/7\nSubtract equations\n64y = -768/7\ny = -768/7/64\ny = -12/7\n\nSubstitute y\n3x + 10(-12/7) = -309/7\n3x = -27\nx = -27/3\nx = -9"} {"input": "Compute the solution of x^3 + 35/12x^2 - 7/6x - 6 = 0", "output": "x^3 + 35/12x^2 - 7/6x - 6 = 0\n(x - -9/4)(x - 4/3)(x - -2) = 0\nx - -9/4 = 0\nx - 4/3 = 0\nx - -2 = 0\nx = -9/4\nx = 4/3\nx = -2"} {"input": "Determine x in 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Solve quickly: x^2 + 19x + 34 = 0", "output": "x^2 + 19x + 34 = 0\n(x - -17)(x - -2) = 0\nx - -17 = 0 or x - -2 = 0\nx = -17\nx = -2"} {"input": "Solve x^3 + 1/5x^2 - 278/45x - 176/45 = 0", "output": "x^3 + 1/5x^2 - 278/45x - 176/45 = 0\n(x - -2/3)(x - -11/5)(x - 8/3) = 0\nx - -2/3 = 0\nx - -11/5 = 0\nx - 8/3 = 0\nx = -2/3\nx = -11/5\nx = 8/3"} {"input": "Find x for x^2 - 5x - 24 = 0", "output": "x^2 - 5x - 24 = 0\n(x - -3)(x - 8) = 0\nx - -3 = 0 or x - 8 = 0\nx = -3\nx = 8"} {"input": "Find the solution to x^3 + 1088/315x^2 + 947/315x + 38/105 = 0", "output": "x^3 + 1088/315x^2 + 947/315x + 38/105 = 0\n(x - -6/5)(x - -1/7)(x - -19/9) = 0\nx - -6/5 = 0\nx - -1/7 = 0\nx - -19/9 = 0\nx = -6/5\nx = -1/7\nx = -19/9"} {"input": "Determine x in x^3 + 7/4x^2 - 14x + 45/4 = 0", "output": "x^3 + 7/4x^2 - 14x + 45/4 = 0\n(x - -5)(x - 9/4)(x - 1) = 0\nx - -5 = 0\nx - 9/4 = 0\nx - 1 = 0\nx = -5\nx = 9/4\nx = 1"} {"input": "Solve the system:\n5x + 8y = 10/3\n1x + 2y = 4/3", "output": "5x + 8y = 10/3\n1x + 2y = 4/3\n\nUsing elimination\n1*(5x + 8y = 10/3)\n5*(1x + 2y = 4/3)\n5x + 8y = 10/3\n5x + 10y = 20/3\nSubtract equations\n-2y = -10/3\ny = -10/3/-2\ny = 5/3\n\nSubstitute y\n5x + 8(5/3) = 10/3\n5x = -10\nx = -10/5\nx = -2"} {"input": "Find x and y such that\n3x + 8y = 13\n1x + 8y = 25/3", "output": "3x + 8y = 13\n1x + 8y = 25/3\n\nUsing elimination\n1*(3x + 8y = 13)\n3*(1x + 8y = 25/3)\n3x + 8y = 13\n3x + 24y = 25\nSubtract equations\n-16y = -12\ny = -12/-16\ny = 3/4\n\nSubstitute y\n3x + 8(3/4) = 13\n3x = 7\nx = 7/3\nx = 7/3"} {"input": "Find x and y such that\n5x + 10y = -125/3\n8x + 7y = -157/6", "output": "5x + 10y = -125/3\n8x + 7y = -157/6\n\nUsing elimination\n8*(5x + 10y = -125/3)\n5*(8x + 7y = -157/6)\n40x + 80y = -1000/3\n40x + 35y = -785/6\nSubtract equations\n45y = -405/2\ny = -405/2/45\ny = -9/2\n\nSubstitute y\n5x + 10(-9/2) = -125/3\n5x = 10/3\nx = 10/3/5\nx = 2/3"} {"input": "Compute the solution of x^2 - 1x - 6 = 0", "output": "x^2 - 1x - 6 = 0\n(x - -2)(x - 3) = 0\nx - -2 = 0 or x - 3 = 0\nx = -2\nx = 3"} {"input": "Compute the solution of 5x + 25/2 = 0", "output": "5x + 25/2 = 0\n5x = -25/2\nx = -25/2 / 5\nx = -5/2"} {"input": "Determine x in 4x + 8 = 0", "output": "4x + 8 = 0\n4x = -8\nx = -8 / 4\nx = -2"} {"input": "Find x for x^2 + 63/10x + 19/2 = 0", "output": "x^2 + 63/10x + 19/2 = 0\n(x - -5/2)(x - -19/5) = 0\nx - -5/2 = 0 or x - -19/5 = 0\nx = -5/2\nx = -19/5"} {"input": "What value of x satisfies x^3 - 209/15x^2 + 157/3x - 133/5 = 0", "output": "x^3 - 209/15x^2 + 157/3x - 133/5 = 0\n(x - 7)(x - 3/5)(x - 19/3) = 0\nx - 7 = 0\nx - 3/5 = 0\nx - 19/3 = 0\nx = 7\nx = 3/5\nx = 19/3"} {"input": "Determine x in x^2 - 1/3x - 8 = 0", "output": "x^2 - 1/3x - 8 = 0\n(x - 3)(x - -8/3) = 0\nx - 3 = 0 or x - -8/3 = 0\nx = 3\nx = -8/3"} {"input": "Solve simultaneously:\n4x + 5y = 9/2\n1x + 8y = -63/10", "output": "4x + 5y = 9/2\n1x + 8y = -63/10\n\nUsing elimination\n1*(4x + 5y = 9/2)\n4*(1x + 8y = -63/10)\n4x + 5y = 9/2\n4x + 32y = -126/5\nSubtract equations\n-27y = 297/10\ny = 297/10/-27\ny = -11/10\n\nSubstitute y\n4x + 5(-11/10) = 9/2\n4x = 10\nx = 10/4\nx = 5/2"} {"input": "Find x for x^2 - 1 = 0", "output": "x^2 - 1 = 0\n(x - -1)(x - 1) = 0\nx - -1 = 0 or x - 1 = 0\nx = -1\nx = 1"} {"input": "Solve quickly: x^2 - 19/24x + 1/12 = 0", "output": "x^2 - 19/24x + 1/12 = 0\n(x - 2/3)(x - 1/8) = 0\nx - 2/3 = 0 or x - 1/8 = 0\nx = 2/3\nx = 1/8"} {"input": "Solve the equation x^2 + 20/7x + 64/49 = 0", "output": "x^2 + 20/7x + 64/49 = 0\n(x - -4/7)(x - -16/7) = 0\nx - -4/7 = 0 or x - -16/7 = 0\nx = -4/7\nx = -16/7"} {"input": "Solve 10x + 30 = 0", "output": "10x + 30 = 0\n10x = -30\nx = -30 / 10\nx = -3"} {"input": "Solve the system:\n8x + 8y = -376/3\n1x + 2y = -52/3", "output": "8x + 8y = -376/3\n1x + 2y = -52/3\n\nUsing elimination\n1*(8x + 8y = -376/3)\n8*(1x + 2y = -52/3)\n8x + 8y = -376/3\n8x + 16y = -416/3\nSubtract equations\n-8y = 40/3\ny = 40/3/-8\ny = -5/3\n\nSubstitute y\n8x + 8(-5/3) = -376/3\n8x = -112\nx = -112/8\nx = -14"} {"input": "Solve quickly: x^2 + 11x - 26 = 0", "output": "x^2 + 11x - 26 = 0\n(x - -13)(x - 2) = 0\nx - -13 = 0 or x - 2 = 0\nx = -13\nx = 2"} {"input": "Find the solution to x^2 + 25/3x - 50/3 = 0", "output": "x^2 + 25/3x - 50/3 = 0\n(x - 5/3)(x - -10) = 0\nx - 5/3 = 0 or x - -10 = 0\nx = 5/3\nx = -10"} {"input": "Determine x in 7x - 14/3 = 0", "output": "7x - 14/3 = 0\n7x = 14/3\nx = 14/3 / 7\nx = 2/3"} {"input": "Solve quickly: x^2 - 23/5x + 12/5 = 0", "output": "x^2 - 23/5x + 12/5 = 0\n(x - 4)(x - 3/5) = 0\nx - 4 = 0 or x - 3/5 = 0\nx = 4\nx = 3/5"} {"input": "Find x for x^2 + 13x + 42 = 0", "output": "x^2 + 13x + 42 = 0\n(x - -7)(x - -6) = 0\nx - -7 = 0 or x - -6 = 0\nx = -7\nx = -6"} {"input": "Find x for x^2 + 19/9x + 16/27 = 0", "output": "x^2 + 19/9x + 16/27 = 0\n(x - -1/3)(x - -16/9) = 0\nx - -1/3 = 0 or x - -16/9 = 0\nx = -1/3\nx = -16/9"} {"input": "Determine x in 10x + 120 = 0", "output": "10x + 120 = 0\n10x = -120\nx = -120 / 10\nx = -12"} {"input": "Solve simultaneously:\n6x + 2y = 232/7\n4x + 6y = 108/7", "output": "6x + 2y = 232/7\n4x + 6y = 108/7\n\nUsing elimination\n4*(6x + 2y = 232/7)\n6*(4x + 6y = 108/7)\n24x + 8y = 928/7\n24x + 36y = 648/7\nSubtract equations\n-28y = 40\ny = 40/-28\ny = -10/7\n\nSubstitute y\n6x + 2(-10/7) = 232/7\n6x = 36\nx = 36/6\nx = 6"} {"input": "Determine x in x^2 - 17x - 38 = 0", "output": "x^2 - 17x - 38 = 0\n(x - 19)(x - -2) = 0\nx - 19 = 0 or x - -2 = 0\nx = 19\nx = -2"} {"input": "Find x and y such that\n6x + 5y = 50\n1x + 6y = -2", "output": "6x + 5y = 50\n1x + 6y = -2\n\nUsing elimination\n1*(6x + 5y = 50)\n6*(1x + 6y = -2)\n6x + 5y = 50\n6x + 36y = -12\nSubtract equations\n-31y = 62\ny = 62/-31\ny = -2\n\nSubstitute y\n6x + 5(-2) = 50\n6x = 60\nx = 60/6\nx = 10"} {"input": "Compute the solution of x^3 - 730/63x^2 - 736/21x + 160/9 = 0", "output": "x^3 - 730/63x^2 - 736/21x + 160/9 = 0\n(x - 4/9)(x - -20/7)(x - 14) = 0\nx - 4/9 = 0\nx - -20/7 = 0\nx - 14 = 0\nx = 4/9\nx = -20/7\nx = 14"} {"input": "Compute the solution of 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve the equation x^3 + 44/15x^2 - 73/20x - 9/2 = 0", "output": "x^3 + 44/15x^2 - 73/20x - 9/2 = 0\n(x - -18/5)(x - 3/2)(x - -5/6) = 0\nx - -18/5 = 0\nx - 3/2 = 0\nx - -5/6 = 0\nx = -18/5\nx = 3/2\nx = -5/6"} {"input": "Compute the solution of x^2 + 11/30x - 121/30 = 0", "output": "x^2 + 11/30x - 121/30 = 0\n(x - -11/5)(x - 11/6) = 0\nx - -11/5 = 0 or x - 11/6 = 0\nx = -11/5\nx = 11/6"} {"input": "Find x in x^2 - 14/3x - 49/3 = 0", "output": "x^2 - 14/3x - 49/3 = 0\n(x - -7/3)(x - 7) = 0\nx - -7/3 = 0 or x - 7 = 0\nx = -7/3\nx = 7"} {"input": "Solve 7x - 28 = 0", "output": "7x - 28 = 0\n7x = 28\nx = 28 / 7\nx = 4"} {"input": "Find x for 3x + 54/5 = 0", "output": "3x + 54/5 = 0\n3x = -54/5\nx = -54/5 / 3\nx = -18/5"} {"input": "Compute the solution of x^2 - 37/4x + 105/8 = 0", "output": "x^2 - 37/4x + 105/8 = 0\n(x - 15/2)(x - 7/4) = 0\nx - 15/2 = 0 or x - 7/4 = 0\nx = 15/2\nx = 7/4"} {"input": "Find x and y such that\n3x + 10y = -39/4\n9x + 1y = -411/20", "output": "3x + 10y = -39/4\n9x + 1y = -411/20\n\nUsing elimination\n9*(3x + 10y = -39/4)\n3*(9x + 1y = -411/20)\n27x + 90y = -351/4\n27x + 3y = -1233/20\nSubtract equations\n87y = -261/10\ny = -261/10/87\ny = -3/10\n\nSubstitute y\n3x + 10(-3/10) = -39/4\n3x = -27/4\nx = -27/4/3\nx = -9/4"} {"input": "Find the solution to x^3 - 59/42x^2 + 10/21x = 0", "output": "x^3 - 59/42x^2 + 10/21x = 0\n(x - 4/7)(x - 5/6)(x - 0) = 0\nx - 4/7 = 0\nx - 5/6 = 0\nx - 0 = 0\nx = 4/7\nx = 5/6\nx = 0"} {"input": "Determine x in x^3 + 1/9x^2 - 188/27x - 64/9 = 0", "output": "x^3 + 1/9x^2 - 188/27x - 64/9 = 0\n(x - 3)(x - -16/9)(x - -4/3) = 0\nx - 3 = 0\nx - -16/9 = 0\nx - -4/3 = 0\nx = 3\nx = -16/9\nx = -4/3"} {"input": "What value of x satisfies x^2 + 7/3x - 10/3 = 0", "output": "x^2 + 7/3x - 10/3 = 0\n(x - 1)(x - -10/3) = 0\nx - 1 = 0 or x - -10/3 = 0\nx = 1\nx = -10/3"} {"input": "Determine x in x^3 - 23/4x^2 - 1205/72x + 425/6 = 0", "output": "x^3 - 23/4x^2 - 1205/72x + 425/6 = 0\n(x - 20/3)(x - -15/4)(x - 17/6) = 0\nx - 20/3 = 0\nx - -15/4 = 0\nx - 17/6 = 0\nx = 20/3\nx = -15/4\nx = 17/6"} {"input": "Solve the system:\n5x + 7y = -208/3\n3x + 5y = -48", "output": "5x + 7y = -208/3\n3x + 5y = -48\n\nUsing elimination\n3*(5x + 7y = -208/3)\n5*(3x + 5y = -48)\n15x + 21y = -208\n15x + 25y = -240\nSubtract equations\n-4y = 32\ny = 32/-4\ny = -8\n\nSubstitute y\n5x + 7(-8) = -208/3\n5x = -40/3\nx = -40/3/5\nx = -8/3"} {"input": "Solve the equations:\n4x + 2y = -46/5\n6x + 9y = -99/5", "output": "4x + 2y = -46/5\n6x + 9y = -99/5\n\nUsing elimination\n6*(4x + 2y = -46/5)\n4*(6x + 9y = -99/5)\n24x + 12y = -276/5\n24x + 36y = -396/5\nSubtract equations\n-24y = 24\ny = 24/-24\ny = -1\n\nSubstitute y\n4x + 2(-1) = -46/5\n4x = -36/5\nx = -36/5/4\nx = -9/5"} {"input": "Find x and y such that\n2x + 6y = -29/6\n5x + 5y = 5/12", "output": "2x + 6y = -29/6\n5x + 5y = 5/12\n\nUsing elimination\n5*(2x + 6y = -29/6)\n2*(5x + 5y = 5/12)\n10x + 30y = -145/6\n10x + 10y = 5/6\nSubtract equations\n20y = -25\ny = -25/20\ny = -5/4\n\nSubstitute y\n2x + 6(-5/4) = -29/6\n2x = 8/3\nx = 8/3/2\nx = 4/3"} {"input": "Find the solution to x^2 + 1/5x - 18/5 = 0", "output": "x^2 + 1/5x - 18/5 = 0\n(x - -2)(x - 9/5) = 0\nx - -2 = 0 or x - 9/5 = 0\nx = -2\nx = 9/5"} {"input": "Solve quickly: x^3 + 59/9x^2 + 16/9x - 28/3 = 0", "output": "x^3 + 59/9x^2 + 16/9x - 28/3 = 0\n(x - 1)(x - -6)(x - -14/9) = 0\nx - 1 = 0\nx - -6 = 0\nx - -14/9 = 0\nx = 1\nx = -6\nx = -14/9"} {"input": "Solve the equations:\n5x + 1y = -28\n7x + 4y = -378/5", "output": "5x + 1y = -28\n7x + 4y = -378/5\n\nUsing elimination\n7*(5x + 1y = -28)\n5*(7x + 4y = -378/5)\n35x + 7y = -196\n35x + 20y = -378\nSubtract equations\n-13y = 182\ny = 182/-13\ny = -14\n\nSubstitute y\n5x + 1(-14) = -28\n5x = -14\nx = -14/5\nx = -14/5"} {"input": "Find the solution to x^3 + 403/20x^2 + 391/8x - 3179/40 = 0", "output": "x^3 + 403/20x^2 + 391/8x - 3179/40 = 0\n(x - -17/4)(x - -17)(x - 11/10) = 0\nx - -17/4 = 0\nx - -17 = 0\nx - 11/10 = 0\nx = -17/4\nx = -17\nx = 11/10"} {"input": "Solve the system:\n1x + 7y = 27/2\n5x + 4y = 201/14", "output": "1x + 7y = 27/2\n5x + 4y = 201/14\n\nUsing elimination\n5*(1x + 7y = 27/2)\n1*(5x + 4y = 201/14)\n5x + 35y = 135/2\n5x + 4y = 201/14\nSubtract equations\n31y = 372/7\ny = 372/7/31\ny = 12/7\n\nSubstitute y\n1x + 7(12/7) = 27/2\n1x = 3/2\nx = 3/2/1\nx = 3/2"} {"input": "Determine x in x^2 - 55/3x + 68/3 = 0", "output": "x^2 - 55/3x + 68/3 = 0\n(x - 17)(x - 4/3) = 0\nx - 17 = 0 or x - 4/3 = 0\nx = 17\nx = 4/3"} {"input": "Compute the solution of x^3 + 14/3x^2 - 212/9x - 280/3 = 0", "output": "x^3 + 14/3x^2 - 212/9x - 280/3 = 0\n(x - -10/3)(x - -6)(x - 14/3) = 0\nx - -10/3 = 0\nx - -6 = 0\nx - 14/3 = 0\nx = -10/3\nx = -6\nx = 14/3"} {"input": "Solve the equation x^2 - 39/5x + 14 = 0", "output": "x^2 - 39/5x + 14 = 0\n(x - 5)(x - 14/5) = 0\nx - 5 = 0 or x - 14/5 = 0\nx = 5\nx = 14/5"} {"input": "Find x and y such that\n2x + 4y = -16/3\n6x + 2y = -98/3", "output": "2x + 4y = -16/3\n6x + 2y = -98/3\n\nUsing elimination\n6*(2x + 4y = -16/3)\n2*(6x + 2y = -98/3)\n12x + 24y = -32\n12x + 4y = -196/3\nSubtract equations\n20y = 100/3\ny = 100/3/20\ny = 5/3\n\nSubstitute y\n2x + 4(5/3) = -16/3\n2x = -12\nx = -12/2\nx = -6"} {"input": "What value of x satisfies x^2 + 43/6x - 20/3 = 0", "output": "x^2 + 43/6x - 20/3 = 0\n(x - -8)(x - 5/6) = 0\nx - -8 = 0 or x - 5/6 = 0\nx = -8\nx = 5/6"} {"input": "Solve the equation x^2 + 71/24x - 143/24 = 0", "output": "x^2 + 71/24x - 143/24 = 0\n(x - 11/8)(x - -13/3) = 0\nx - 11/8 = 0 or x - -13/3 = 0\nx = 11/8\nx = -13/3"} {"input": "Find the solution to x^3 - 169/10x^2 + 731/10x - 133/5 = 0", "output": "x^3 - 169/10x^2 + 731/10x - 133/5 = 0\n(x - 2/5)(x - 19/2)(x - 7) = 0\nx - 2/5 = 0\nx - 19/2 = 0\nx - 7 = 0\nx = 2/5\nx = 19/2\nx = 7"} {"input": "Solve the equation x^3 - 11/3x^2 + 10/3x = 0", "output": "x^3 - 11/3x^2 + 10/3x = 0\n(x - 0)(x - 2)(x - 5/3) = 0\nx - 0 = 0\nx - 2 = 0\nx - 5/3 = 0\nx = 0\nx = 2\nx = 5/3"} {"input": "Find x in 7x + 140/3 = 0", "output": "7x + 140/3 = 0\n7x = -140/3\nx = -140/3 / 7\nx = -20/3"} {"input": "Solve the system:\n1x + 8y = -79/10\n7x + 3y = -23/10", "output": "1x + 8y = -79/10\n7x + 3y = -23/10\n\nUsing elimination\n7*(1x + 8y = -79/10)\n1*(7x + 3y = -23/10)\n7x + 56y = -553/10\n7x + 3y = -23/10\nSubtract equations\n53y = -53\ny = -53/53\ny = -1\n\nSubstitute y\n1x + 8(-1) = -79/10\n1x = 1/10\nx = 1/10/1\nx = 1/10"} {"input": "Solve 1x + 8/3 = 0", "output": "1x + 8/3 = 0\n1x = -8/3\nx = -8/3 / 1\nx = -8/3"} {"input": "Find x in 2x + 14/5 = 0", "output": "2x + 14/5 = 0\n2x = -14/5\nx = -14/5 / 2\nx = -7/5"} {"input": "Find x in 4x + 4/7 = 0", "output": "4x + 4/7 = 0\n4x = -4/7\nx = -4/7 / 4\nx = -1/7"} {"input": "What value of x satisfies x^3 - 163/28x^2 - 375/14x - 459/28 = 0", "output": "x^3 - 163/28x^2 - 375/14x - 459/28 = 0\n(x - -3/4)(x - 9)(x - -17/7) = 0\nx - -3/4 = 0\nx - 9 = 0\nx - -17/7 = 0\nx = -3/4\nx = 9\nx = -17/7"} {"input": "Solve simultaneously:\n1x + 9y = -593/10\n2x + 10y = -979/15", "output": "1x + 9y = -593/10\n2x + 10y = -979/15\n\nUsing elimination\n2*(1x + 9y = -593/10)\n1*(2x + 10y = -979/15)\n2x + 18y = -593/5\n2x + 10y = -979/15\nSubtract equations\n8y = -160/3\ny = -160/3/8\ny = -20/3\n\nSubstitute y\n1x + 9(-20/3) = -593/10\n1x = 7/10\nx = 7/10/1\nx = 7/10"} {"input": "Solve the equation 10x = 0", "output": "10x = 0\n10x = 0\nx = 0 / 10\nx = 0"} {"input": "Find the solution to 4x + 8/7 = 0", "output": "4x + 8/7 = 0\n4x = -8/7\nx = -8/7 / 4\nx = -2/7"} {"input": "Compute the solution of x^3 - 14/45x^2 - 373/135x + 28/15 = 0", "output": "x^3 - 14/45x^2 - 373/135x + 28/15 = 0\n(x - 4/3)(x - -9/5)(x - 7/9) = 0\nx - 4/3 = 0\nx - -9/5 = 0\nx - 7/9 = 0\nx = 4/3\nx = -9/5\nx = 7/9"} {"input": "Find x for x^2 - 1x - 12 = 0", "output": "x^2 - 1x - 12 = 0\n(x - 4)(x - -3) = 0\nx - 4 = 0 or x - -3 = 0\nx = 4\nx = -3"} {"input": "Solve quickly: x^2 - 3/10x - 11/2 = 0", "output": "x^2 - 3/10x - 11/2 = 0\n(x - 5/2)(x - -11/5) = 0\nx - 5/2 = 0 or x - -11/5 = 0\nx = 5/2\nx = -11/5"} {"input": "Solve simultaneously:\n9x + 9y = -18\n1x + 9y = -22/3", "output": "9x + 9y = -18\n1x + 9y = -22/3\n\nUsing elimination\n1*(9x + 9y = -18)\n9*(1x + 9y = -22/3)\n9x + 9y = -18\n9x + 81y = -66\nSubtract equations\n-72y = 48\ny = 48/-72\ny = -2/3\n\nSubstitute y\n9x + 9(-2/3) = -18\n9x = -12\nx = -12/9\nx = -4/3"} {"input": "Solve 7x + 119/3 = 0", "output": "7x + 119/3 = 0\n7x = -119/3\nx = -119/3 / 7\nx = -17/3"} {"input": "Find x for x^3 - 47/60x^2 - 383/120x + 21/8 = 0", "output": "x^3 - 47/60x^2 - 383/120x + 21/8 = 0\n(x - -9/5)(x - 5/6)(x - 7/4) = 0\nx - -9/5 = 0\nx - 5/6 = 0\nx - 7/4 = 0\nx = -9/5\nx = 5/6\nx = 7/4"} {"input": "Find the solution to x^3 - 23/7x^2 - 163/7x - 19 = 0", "output": "x^3 - 23/7x^2 - 163/7x - 19 = 0\n(x - -19/7)(x - -1)(x - 7) = 0\nx - -19/7 = 0\nx - -1 = 0\nx - 7 = 0\nx = -19/7\nx = -1\nx = 7"} {"input": "Compute the solution of 6x - 36 = 0", "output": "6x - 36 = 0\n6x = 36\nx = 36 / 6\nx = 6"} {"input": "Compute the solution of x^3 + 181/12x^2 - 605/12x + 75/2 = 0", "output": "x^3 + 181/12x^2 - 605/12x + 75/2 = 0\n(x - 5/3)(x - -18)(x - 5/4) = 0\nx - 5/3 = 0\nx - -18 = 0\nx - 5/4 = 0\nx = 5/3\nx = -18\nx = 5/4"} {"input": "Find x and y such that\n6x + 9y = -57/4\n5x + 4y = -39/8", "output": "6x + 9y = -57/4\n5x + 4y = -39/8\n\nUsing elimination\n5*(6x + 9y = -57/4)\n6*(5x + 4y = -39/8)\n30x + 45y = -285/4\n30x + 24y = -117/4\nSubtract equations\n21y = -42\ny = -42/21\ny = -2\n\nSubstitute y\n6x + 9(-2) = -57/4\n6x = 15/4\nx = 15/4/6\nx = 5/8"} {"input": "What value of x satisfies x^2 + 132/35x + 121/35 = 0", "output": "x^2 + 132/35x + 121/35 = 0\n(x - -11/7)(x - -11/5) = 0\nx - -11/7 = 0 or x - -11/5 = 0\nx = -11/7\nx = -11/5"} {"input": "Compute the solution of x^2 + 151/21x + 208/21 = 0", "output": "x^2 + 151/21x + 208/21 = 0\n(x - -13/7)(x - -16/3) = 0\nx - -13/7 = 0 or x - -16/3 = 0\nx = -13/7\nx = -16/3"} {"input": "Solve the equation 9x - 30 = 0", "output": "9x - 30 = 0\n9x = 30\nx = 30 / 9\nx = 10/3"} {"input": "Solve 6x - 60 = 0", "output": "6x - 60 = 0\n6x = 60\nx = 60 / 6\nx = 10"} {"input": "Find x for 8x + 24/7 = 0", "output": "8x + 24/7 = 0\n8x = -24/7\nx = -24/7 / 8\nx = -3/7"} {"input": "Solve x^2 - 17/7x - 38/49 = 0", "output": "x^2 - 17/7x - 38/49 = 0\n(x - -2/7)(x - 19/7) = 0\nx - -2/7 = 0 or x - 19/7 = 0\nx = -2/7\nx = 19/7"} {"input": "Solve quickly: x^3 - 19/6x^2 + 87/50x + 19/15 = 0", "output": "x^3 - 19/6x^2 + 87/50x + 19/15 = 0\n(x - 19/10)(x - -2/5)(x - 5/3) = 0\nx - 19/10 = 0\nx - -2/5 = 0\nx - 5/3 = 0\nx = 19/10\nx = -2/5\nx = 5/3"} {"input": "Find x and y such that\n2x + 8y = -128/21\n8x + 9y = 661/21", "output": "2x + 8y = -128/21\n8x + 9y = 661/21\n\nUsing elimination\n8*(2x + 8y = -128/21)\n2*(8x + 9y = 661/21)\n16x + 64y = -1024/21\n16x + 18y = 1322/21\nSubtract equations\n46y = -782/7\ny = -782/7/46\ny = -17/7\n\nSubstitute y\n2x + 8(-17/7) = -128/21\n2x = 40/3\nx = 40/3/2\nx = 20/3"} {"input": "Solve quickly: 1x - 7/6 = 0", "output": "1x - 7/6 = 0\n1x = 7/6\nx = 7/6 / 1\nx = 7/6"} {"input": "Solve x^2 + 6x - 7 = 0", "output": "x^2 + 6x - 7 = 0\n(x - -7)(x - 1) = 0\nx - -7 = 0 or x - 1 = 0\nx = -7\nx = 1"} {"input": "Solve the system:\n5x + 7y = 283/36\n9x + 6y = 293/12", "output": "5x + 7y = 283/36\n9x + 6y = 293/12\n\nUsing elimination\n9*(5x + 7y = 283/36)\n5*(9x + 6y = 293/12)\n45x + 63y = 283/4\n45x + 30y = 1465/12\nSubtract equations\n33y = -154/3\ny = -154/3/33\ny = -14/9\n\nSubstitute y\n5x + 7(-14/9) = 283/36\n5x = 75/4\nx = 75/4/5\nx = 15/4"} {"input": "Solve quickly: x^3 + 21/2x^2 + 35/64x - 1425/32 = 0", "output": "x^3 + 21/2x^2 + 35/64x - 1425/32 = 0\n(x - 15/8)(x - -19/8)(x - -10) = 0\nx - 15/8 = 0\nx - -19/8 = 0\nx - -10 = 0\nx = 15/8\nx = -19/8\nx = -10"} {"input": "Compute the solution of 2x - 7/2 = 0", "output": "2x - 7/2 = 0\n2x = 7/2\nx = 7/2 / 2\nx = 7/4"} {"input": "What value of x satisfies 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "Find x and y such that\n6x + 10y = 1/7\n3x + 7y = -1/2", "output": "6x + 10y = 1/7\n3x + 7y = -1/2\n\nUsing elimination\n3*(6x + 10y = 1/7)\n6*(3x + 7y = -1/2)\n18x + 30y = 3/7\n18x + 42y = -3\nSubtract equations\n-12y = 24/7\ny = 24/7/-12\ny = -2/7\n\nSubstitute y\n6x + 10(-2/7) = 1/7\n6x = 3\nx = 3/6\nx = 1/2"} {"input": "Determine x in x^3 - 241/30x^2 - 67/5x - 76/15 = 0", "output": "x^3 - 241/30x^2 - 67/5x - 76/15 = 0\n(x - 19/2)(x - -2/3)(x - -4/5) = 0\nx - 19/2 = 0\nx - -2/3 = 0\nx - -4/5 = 0\nx = 19/2\nx = -2/3\nx = -4/5"} {"input": "Find x for 6x + 42 = 0", "output": "6x + 42 = 0\n6x = -42\nx = -42 / 6\nx = -7"} {"input": "What value of x satisfies x^3 - 37/14x^2 - 156/49x + 360/49 = 0", "output": "x^3 - 37/14x^2 - 156/49x + 360/49 = 0\n(x - 3/2)(x - 20/7)(x - -12/7) = 0\nx - 3/2 = 0\nx - 20/7 = 0\nx - -12/7 = 0\nx = 3/2\nx = 20/7\nx = -12/7"} {"input": "Find the solution to 3x + 39 = 0", "output": "3x + 39 = 0\n3x = -39\nx = -39 / 3\nx = -13"} {"input": "Solve the equation x^3 - 11/14x^2 - 30/7x = 0", "output": "x^3 - 11/14x^2 - 30/7x = 0\n(x - 5/2)(x - -12/7)(x - 0) = 0\nx - 5/2 = 0\nx - -12/7 = 0\nx - 0 = 0\nx = 5/2\nx = -12/7\nx = 0"} {"input": "Find x in x^2 - 18/5x - 119/5 = 0", "output": "x^2 - 18/5x - 119/5 = 0\n(x - -17/5)(x - 7) = 0\nx - -17/5 = 0 or x - 7 = 0\nx = -17/5\nx = 7"} {"input": "Determine x in x^3 - 63/4x^2 - 325/4x - 75 = 0", "output": "x^3 - 63/4x^2 - 325/4x - 75 = 0\n(x - -3)(x - -5/4)(x - 20) = 0\nx - -3 = 0\nx - -5/4 = 0\nx - 20 = 0\nx = -3\nx = -5/4\nx = 20"} {"input": "Solve the system:\n2x + 7y = 67/9\n1x + 1y = 11/9", "output": "2x + 7y = 67/9\n1x + 1y = 11/9\n\nUsing elimination\n1*(2x + 7y = 67/9)\n2*(1x + 1y = 11/9)\n2x + 7y = 67/9\n2x + 2y = 22/9\nSubtract equations\n5y = 5\ny = 5/5\ny = 1\n\nSubstitute y\n2x + 7(1) = 67/9\n2x = 4/9\nx = 4/9/2\nx = 2/9"} {"input": "Find the solution to x^3 - 17/2x^2 - 40/9x - 1/2 = 0", "output": "x^3 - 17/2x^2 - 40/9x - 1/2 = 0\n(x - -1/6)(x - -1/3)(x - 9) = 0\nx - -1/6 = 0\nx - -1/3 = 0\nx - 9 = 0\nx = -1/6\nx = -1/3\nx = 9"} {"input": "Determine x in 6x + 27 = 0", "output": "6x + 27 = 0\n6x = -27\nx = -27 / 6\nx = -9/2"} {"input": "Solve quickly: x^2 + 18/7x + 11/7 = 0", "output": "x^2 + 18/7x + 11/7 = 0\n(x - -1)(x - -11/7) = 0\nx - -1 = 0 or x - -11/7 = 0\nx = -1\nx = -11/7"} {"input": "Find x for x^2 - 7/4x - 99/8 = 0", "output": "x^2 - 7/4x - 99/8 = 0\n(x - 9/2)(x - -11/4) = 0\nx - 9/2 = 0 or x - -11/4 = 0\nx = 9/2\nx = -11/4"} {"input": "Find x in x^2 - 78/5x - 119/5 = 0", "output": "x^2 - 78/5x - 119/5 = 0\n(x - 17)(x - -7/5) = 0\nx - 17 = 0 or x - -7/5 = 0\nx = 17\nx = -7/5"} {"input": "Determine x in x^3 + 100/9x^2 - 117x - 2584/9 = 0", "output": "x^3 + 100/9x^2 - 117x - 2584/9 = 0\n(x - 8)(x - -19/9)(x - -17) = 0\nx - 8 = 0\nx - -19/9 = 0\nx - -17 = 0\nx = 8\nx = -19/9\nx = -17"} {"input": "Find the solution to 4x - 2 = 0", "output": "4x - 2 = 0\n4x = 2\nx = 2 / 4\nx = 1/2"} {"input": "Solve simultaneously:\n8x + 1y = -119\n9x + 9y = -126", "output": "8x + 1y = -119\n9x + 9y = -126\n\nUsing elimination\n9*(8x + 1y = -119)\n8*(9x + 9y = -126)\n72x + 9y = -1071\n72x + 72y = -1008\nSubtract equations\n-63y = -63\ny = -63/-63\ny = 1\n\nSubstitute y\n8x + 1(1) = -119\n8x = -120\nx = -120/8\nx = -15"} {"input": "Solve the equations:\n9x + 6y = 324/5\n1x + 8y = -8/5", "output": "9x + 6y = 324/5\n1x + 8y = -8/5\n\nUsing elimination\n1*(9x + 6y = 324/5)\n9*(1x + 8y = -8/5)\n9x + 6y = 324/5\n9x + 72y = -72/5\nSubtract equations\n-66y = 396/5\ny = 396/5/-66\ny = -6/5\n\nSubstitute y\n9x + 6(-6/5) = 324/5\n9x = 72\nx = 72/9\nx = 8"} {"input": "What value of x satisfies x^2 + 33/8x + 27/8 = 0", "output": "x^2 + 33/8x + 27/8 = 0\n(x - -9/8)(x - -3) = 0\nx - -9/8 = 0 or x - -3 = 0\nx = -9/8\nx = -3"} {"input": "Find the solution to x^3 - 1/6x^2 - 173/3x + 136 = 0", "output": "x^3 - 1/6x^2 - 173/3x + 136 = 0\n(x - 8/3)(x - -17/2)(x - 6) = 0\nx - 8/3 = 0\nx - -17/2 = 0\nx - 6 = 0\nx = 8/3\nx = -17/2\nx = 6"} {"input": "Compute the solution of 8x - 88/9 = 0", "output": "8x - 88/9 = 0\n8x = 88/9\nx = 88/9 / 8\nx = 11/9"} {"input": "Determine x in 7x + 21/8 = 0", "output": "7x + 21/8 = 0\n7x = -21/8\nx = -21/8 / 7\nx = -3/8"} {"input": "Solve the equation x^2 - 153/70x + 81/70 = 0", "output": "x^2 - 153/70x + 81/70 = 0\n(x - 9/10)(x - 9/7) = 0\nx - 9/10 = 0 or x - 9/7 = 0\nx = 9/10\nx = 9/7"} {"input": "Solve the equation 7x - 112/9 = 0", "output": "7x - 112/9 = 0\n7x = 112/9\nx = 112/9 / 7\nx = 16/9"} {"input": "Solve the system:\n1x + 6y = 10/3\n4x + 2y = 40/3", "output": "1x + 6y = 10/3\n4x + 2y = 40/3\n\nUsing elimination\n4*(1x + 6y = 10/3)\n1*(4x + 2y = 40/3)\n4x + 24y = 40/3\n4x + 2y = 40/3\nSubtract equations\n22y = 0\ny = 0/22\ny = 0\n\nSubstitute y\n1x + 6(0) = 10/3\n1x = 10/3\nx = 10/3/1\nx = 10/3"} {"input": "Determine x in x^3 + 10/3x^2 + 3x + 2/3 = 0", "output": "x^3 + 10/3x^2 + 3x + 2/3 = 0\n(x - -2)(x - -1/3)(x - -1) = 0\nx - -2 = 0\nx - -1/3 = 0\nx - -1 = 0\nx = -2\nx = -1/3\nx = -1"} {"input": "Solve simultaneously:\n8x + 9y = -12\n4x + 8y = -61/9", "output": "8x + 9y = -12\n4x + 8y = -61/9\n\nUsing elimination\n4*(8x + 9y = -12)\n8*(4x + 8y = -61/9)\n32x + 36y = -48\n32x + 64y = -488/9\nSubtract equations\n-28y = 56/9\ny = 56/9/-28\ny = -2/9\n\nSubstitute y\n8x + 9(-2/9) = -12\n8x = -10\nx = -10/8\nx = -5/4"} {"input": "Solve quickly: x^3 + 15x^2 + 494/9x + 440/9 = 0", "output": "x^3 + 15x^2 + 494/9x + 440/9 = 0\n(x - -10)(x - -11/3)(x - -4/3) = 0\nx - -10 = 0\nx - -11/3 = 0\nx - -4/3 = 0\nx = -10\nx = -11/3\nx = -4/3"} {"input": "Solve the system:\n6x + 2y = -22/7\n2x + 10y = 114/7", "output": "6x + 2y = -22/7\n2x + 10y = 114/7\n\nUsing elimination\n2*(6x + 2y = -22/7)\n6*(2x + 10y = 114/7)\n12x + 4y = -44/7\n12x + 60y = 684/7\nSubtract equations\n-56y = -104\ny = -104/-56\ny = 13/7\n\nSubstitute y\n6x + 2(13/7) = -22/7\n6x = -48/7\nx = -48/7/6\nx = -8/7"} {"input": "Find x in x^2 - 5/3x - 2/3 = 0", "output": "x^2 - 5/3x - 2/3 = 0\n(x - -1/3)(x - 2) = 0\nx - -1/3 = 0 or x - 2 = 0\nx = -1/3\nx = 2"} {"input": "Solve the equation x^3 - 83/15x^2 + 32/5x - 16/15 = 0", "output": "x^3 - 83/15x^2 + 32/5x - 16/15 = 0\n(x - 4/3)(x - 4)(x - 1/5) = 0\nx - 4/3 = 0\nx - 4 = 0\nx - 1/5 = 0\nx = 4/3\nx = 4\nx = 1/5"} {"input": "Find x in 10x + 5 = 0", "output": "10x + 5 = 0\n10x = -5\nx = -5 / 10\nx = -1/2"} {"input": "Find x in x^3 - 11/15x^2 - 86/15x - 16/5 = 0", "output": "x^3 - 11/15x^2 - 86/15x - 16/5 = 0\n(x - -2/3)(x - -8/5)(x - 3) = 0\nx - -2/3 = 0\nx - -8/5 = 0\nx - 3 = 0\nx = -2/3\nx = -8/5\nx = 3"} {"input": "Find the solution to x^2 - 17/3x + 20/3 = 0", "output": "x^2 - 17/3x + 20/3 = 0\n(x - 4)(x - 5/3) = 0\nx - 4 = 0 or x - 5/3 = 0\nx = 4\nx = 5/3"} {"input": "Find the solution to x^3 + 107/20x^2 - 31/40x - 247/10 = 0", "output": "x^3 + 107/20x^2 - 31/40x - 247/10 = 0\n(x - -13/4)(x - -4)(x - 19/10) = 0\nx - -13/4 = 0\nx - -4 = 0\nx - 19/10 = 0\nx = -13/4\nx = -4\nx = 19/10"} {"input": "Find the solution to x^2 + 23/18x + 7/18 = 0", "output": "x^2 + 23/18x + 7/18 = 0\n(x - -1/2)(x - -7/9) = 0\nx - -1/2 = 0 or x - -7/9 = 0\nx = -1/2\nx = -7/9"} {"input": "Determine x in x^2 - 1x - 10/9 = 0", "output": "x^2 - 1x - 10/9 = 0\n(x - -2/3)(x - 5/3) = 0\nx - -2/3 = 0 or x - 5/3 = 0\nx = -2/3\nx = 5/3"} {"input": "Solve the equations:\n10x + 3y = 1/2\n6x + 9y = 159/10", "output": "10x + 3y = 1/2\n6x + 9y = 159/10\n\nUsing elimination\n6*(10x + 3y = 1/2)\n10*(6x + 9y = 159/10)\n60x + 18y = 3\n60x + 90y = 159\nSubtract equations\n-72y = -156\ny = -156/-72\ny = 13/6\n\nSubstitute y\n10x + 3(13/6) = 1/2\n10x = -6\nx = -6/10\nx = -3/5"} {"input": "Find x for x^2 - 27/10x - 8/5 = 0", "output": "x^2 - 27/10x - 8/5 = 0\n(x - -1/2)(x - 16/5) = 0\nx - -1/2 = 0 or x - 16/5 = 0\nx = -1/2\nx = 16/5"} {"input": "Solve quickly: 6x + 30 = 0", "output": "6x + 30 = 0\n6x = -30\nx = -30 / 6\nx = -5"} {"input": "Solve simultaneously:\n10x + 6y = -50\n6x + 10y = -218/3", "output": "10x + 6y = -50\n6x + 10y = -218/3\n\nUsing elimination\n6*(10x + 6y = -50)\n10*(6x + 10y = -218/3)\n60x + 36y = -300\n60x + 100y = -2180/3\nSubtract equations\n-64y = 1280/3\ny = 1280/3/-64\ny = -20/3\n\nSubstitute y\n10x + 6(-20/3) = -50\n10x = -10\nx = -10/10\nx = -1"} {"input": "Solve the equations:\n2x + 7y = 16\n10x + 7y = -4", "output": "2x + 7y = 16\n10x + 7y = -4\n\nUsing elimination\n10*(2x + 7y = 16)\n2*(10x + 7y = -4)\n20x + 70y = 160\n20x + 14y = -8\nSubtract equations\n56y = 168\ny = 168/56\ny = 3\n\nSubstitute y\n2x + 7(3) = 16\n2x = -5\nx = -5/2\nx = -5/2"} {"input": "Find the solution to x^2 + 57/70x - 54/35 = 0", "output": "x^2 + 57/70x - 54/35 = 0\n(x - -12/7)(x - 9/10) = 0\nx - -12/7 = 0 or x - 9/10 = 0\nx = -12/7\nx = 9/10"} {"input": "Solve the equation x^2 + 31/70x - 4/5 = 0", "output": "x^2 + 31/70x - 4/5 = 0\n(x - -8/7)(x - 7/10) = 0\nx - -8/7 = 0 or x - 7/10 = 0\nx = -8/7\nx = 7/10"} {"input": "Find x in 1x + 4 = 0", "output": "1x + 4 = 0\n1x = -4\nx = -4 / 1\nx = -4"} {"input": "Determine x in 2x + 10 = 0", "output": "2x + 10 = 0\n2x = -10\nx = -10 / 2\nx = -5"} {"input": "Solve the system:\n2x + 10y = -30\n4x + 4y = -108/5", "output": "2x + 10y = -30\n4x + 4y = -108/5\n\nUsing elimination\n4*(2x + 10y = -30)\n2*(4x + 4y = -108/5)\n8x + 40y = -120\n8x + 8y = -216/5\nSubtract equations\n32y = -384/5\ny = -384/5/32\ny = -12/5\n\nSubstitute y\n2x + 10(-12/5) = -30\n2x = -6\nx = -6/2\nx = -3"} {"input": "Solve quickly: x^3 + 31/10x^2 - 62/5x + 22/5 = 0", "output": "x^3 + 31/10x^2 - 62/5x + 22/5 = 0\n(x - 2)(x - 2/5)(x - -11/2) = 0\nx - 2 = 0\nx - 2/5 = 0\nx - -11/2 = 0\nx = 2\nx = 2/5\nx = -11/2"} {"input": "Find x for x^3 - 202/15x^2 + 752/15x - 32 = 0", "output": "x^3 - 202/15x^2 + 752/15x - 32 = 0\n(x - 20/3)(x - 6)(x - 4/5) = 0\nx - 20/3 = 0\nx - 6 = 0\nx - 4/5 = 0\nx = 20/3\nx = 6\nx = 4/5"} {"input": "Solve the equation x^2 - 5/6x - 28/3 = 0", "output": "x^2 - 5/6x - 28/3 = 0\n(x - -8/3)(x - 7/2) = 0\nx - -8/3 = 0 or x - 7/2 = 0\nx = -8/3\nx = 7/2"} {"input": "Solve the equation x^3 + 68/15x^2 + 4x = 0", "output": "x^3 + 68/15x^2 + 4x = 0\n(x - -10/3)(x - -6/5)(x - 0) = 0\nx - -10/3 = 0\nx - -6/5 = 0\nx - 0 = 0\nx = -10/3\nx = -6/5\nx = 0"} {"input": "Solve quickly: x^3 + 53/3x^2 + 67/9x - 595/9 = 0", "output": "x^3 + 53/3x^2 + 67/9x - 595/9 = 0\n(x - -7/3)(x - -17)(x - 5/3) = 0\nx - -7/3 = 0\nx - -17 = 0\nx - 5/3 = 0\nx = -7/3\nx = -17\nx = 5/3"} {"input": "Solve simultaneously:\n9x + 3y = 16\n7x + 3y = 136/9", "output": "9x + 3y = 16\n7x + 3y = 136/9\n\nUsing elimination\n7*(9x + 3y = 16)\n9*(7x + 3y = 136/9)\n63x + 21y = 112\n63x + 27y = 136\nSubtract equations\n-6y = -24\ny = -24/-6\ny = 4\n\nSubstitute y\n9x + 3(4) = 16\n9x = 4\nx = 4/9\nx = 4/9"} {"input": "Find the solution to x^2 + 15/4x + 7/2 = 0", "output": "x^2 + 15/4x + 7/2 = 0\n(x - -2)(x - -7/4) = 0\nx - -2 = 0 or x - -7/4 = 0\nx = -2\nx = -7/4"} {"input": "Solve simultaneously:\n4x + 1y = 95/14\n4x + 4y = -26/7", "output": "4x + 1y = 95/14\n4x + 4y = -26/7\n\nUsing elimination\n4*(4x + 1y = 95/14)\n4*(4x + 4y = -26/7)\n16x + 4y = 190/7\n16x + 16y = -104/7\nSubtract equations\n-12y = 42\ny = 42/-12\ny = -7/2\n\nSubstitute y\n4x + 1(-7/2) = 95/14\n4x = 72/7\nx = 72/7/4\nx = 18/7"} {"input": "Solve the system:\n1x + 9y = 44\n2x + 10y = 52", "output": "1x + 9y = 44\n2x + 10y = 52\n\nUsing elimination\n2*(1x + 9y = 44)\n1*(2x + 10y = 52)\n2x + 18y = 88\n2x + 10y = 52\nSubtract equations\n8y = 36\ny = 36/8\ny = 9/2\n\nSubstitute y\n1x + 9(9/2) = 44\n1x = 7/2\nx = 7/2/1\nx = 7/2"} {"input": "Find x for x^3 + 28/15x^2 - 1/3x - 2/15 = 0", "output": "x^3 + 28/15x^2 - 1/3x - 2/15 = 0\n(x - -2)(x - 1/3)(x - -1/5) = 0\nx - -2 = 0\nx - 1/3 = 0\nx - -1/5 = 0\nx = -2\nx = 1/3\nx = -1/5"} {"input": "What value of x satisfies x^2 + 7/5x - 198/25 = 0", "output": "x^2 + 7/5x - 198/25 = 0\n(x - -18/5)(x - 11/5) = 0\nx - -18/5 = 0 or x - 11/5 = 0\nx = -18/5\nx = 11/5"} {"input": "Solve quickly: x^2 - 19/10x - 28/5 = 0", "output": "x^2 - 19/10x - 28/5 = 0\n(x - 7/2)(x - -8/5) = 0\nx - 7/2 = 0 or x - -8/5 = 0\nx = 7/2\nx = -8/5"} {"input": "Solve the system:\n2x + 5y = 71/15\n6x + 5y = -37/15", "output": "2x + 5y = 71/15\n6x + 5y = -37/15\n\nUsing elimination\n6*(2x + 5y = 71/15)\n2*(6x + 5y = -37/15)\n12x + 30y = 142/5\n12x + 10y = -74/15\nSubtract equations\n20y = 100/3\ny = 100/3/20\ny = 5/3\n\nSubstitute y\n2x + 5(5/3) = 71/15\n2x = -18/5\nx = -18/5/2\nx = -9/5"} {"input": "Find x for x^2 - 46/9x + 40/9 = 0", "output": "x^2 - 46/9x + 40/9 = 0\n(x - 4)(x - 10/9) = 0\nx - 4 = 0 or x - 10/9 = 0\nx = 4\nx = 10/9"} {"input": "Solve quickly: x^2 + 17/4x - 15/4 = 0", "output": "x^2 + 17/4x - 15/4 = 0\n(x - 3/4)(x - -5) = 0\nx - 3/4 = 0 or x - -5 = 0\nx = 3/4\nx = -5"} {"input": "Solve 10x - 90 = 0", "output": "10x - 90 = 0\n10x = 90\nx = 90 / 10\nx = 9"} {"input": "Find x and y such that\n1x + 1y = -37/6\n5x + 1y = -109/6", "output": "1x + 1y = -37/6\n5x + 1y = -109/6\n\nUsing elimination\n5*(1x + 1y = -37/6)\n1*(5x + 1y = -109/6)\n5x + 5y = -185/6\n5x + 1y = -109/6\nSubtract equations\n4y = -38/3\ny = -38/3/4\ny = -19/6\n\nSubstitute y\n1x + 1(-19/6) = -37/6\n1x = -3\nx = -3/1\nx = -3"} {"input": "Find the solution to 2x + 14/5 = 0", "output": "2x + 14/5 = 0\n2x = -14/5\nx = -14/5 / 2\nx = -7/5"} {"input": "Determine x in x^2 + 33/7x + 36/7 = 0", "output": "x^2 + 33/7x + 36/7 = 0\n(x - -12/7)(x - -3) = 0\nx - -12/7 = 0 or x - -3 = 0\nx = -12/7\nx = -3"} {"input": "Find the solution to 2x + 6 = 0", "output": "2x + 6 = 0\n2x = -6\nx = -6 / 2\nx = -3"} {"input": "Find the solution to 6x + 6 = 0", "output": "6x + 6 = 0\n6x = -6\nx = -6 / 6\nx = -1"} {"input": "Determine x in x^3 - 241/90x^2 - 371/90x + 196/45 = 0", "output": "x^3 - 241/90x^2 - 371/90x + 196/45 = 0\n(x - 7/9)(x - 7/2)(x - -8/5) = 0\nx - 7/9 = 0\nx - 7/2 = 0\nx - -8/5 = 0\nx = 7/9\nx = 7/2\nx = -8/5"} {"input": "Find x for x^3 + 185/24x^2 + 173/12x + 35/8 = 0", "output": "x^3 + 185/24x^2 + 173/12x + 35/8 = 0\n(x - -3/8)(x - -7/3)(x - -5) = 0\nx - -3/8 = 0\nx - -7/3 = 0\nx - -5 = 0\nx = -3/8\nx = -7/3\nx = -5"} {"input": "Solve x^2 - 86/63x - 5/3 = 0", "output": "x^2 - 86/63x - 5/3 = 0\n(x - -7/9)(x - 15/7) = 0\nx - -7/9 = 0 or x - 15/7 = 0\nx = -7/9\nx = 15/7"} {"input": "Find x for 8x + 8 = 0", "output": "8x + 8 = 0\n8x = -8\nx = -8 / 8\nx = -1"} {"input": "Solve the system:\n7x + 7y = -119/4\n2x + 3y = -25/4", "output": "7x + 7y = -119/4\n2x + 3y = -25/4\n\nUsing elimination\n2*(7x + 7y = -119/4)\n7*(2x + 3y = -25/4)\n14x + 14y = -119/2\n14x + 21y = -175/4\nSubtract equations\n-7y = -63/4\ny = -63/4/-7\ny = 9/4\n\nSubstitute y\n7x + 7(9/4) = -119/4\n7x = -91/2\nx = -91/2/7\nx = -13/2"} {"input": "Determine x in x^3 - 5x^2 - 13x - 7 = 0", "output": "x^3 - 5x^2 - 13x - 7 = 0\n(x - 7)(x - -1)(x - -1) = 0\nx - 7 = 0\nx - -1 = 0\nx - -1 = 0\nx = 7\nx = -1\nx = -1"} {"input": "Solve the equation x^3 - 49/8x^2 + 225/8 = 0", "output": "x^3 - 49/8x^2 + 225/8 = 0\n(x - -15/8)(x - 5)(x - 3) = 0\nx - -15/8 = 0\nx - 5 = 0\nx - 3 = 0\nx = -15/8\nx = 5\nx = 3"} {"input": "Find the solution to 9x - 153/4 = 0", "output": "9x - 153/4 = 0\n9x = 153/4\nx = 153/4 / 9\nx = 17/4"} {"input": "What value of x satisfies x^3 - 7/5x^2 - 58/5x + 24/5 = 0", "output": "x^3 - 7/5x^2 - 58/5x + 24/5 = 0\n(x - -3)(x - 4)(x - 2/5) = 0\nx - -3 = 0\nx - 4 = 0\nx - 2/5 = 0\nx = -3\nx = 4\nx = 2/5"} {"input": "Compute the solution of x^2 + 104/21x + 4/3 = 0", "output": "x^2 + 104/21x + 4/3 = 0\n(x - -2/7)(x - -14/3) = 0\nx - -2/7 = 0 or x - -14/3 = 0\nx = -2/7\nx = -14/3"} {"input": "Solve quickly: x^2 + 5/9x - 4/9 = 0", "output": "x^2 + 5/9x - 4/9 = 0\n(x - -1)(x - 4/9) = 0\nx - -1 = 0 or x - 4/9 = 0\nx = -1\nx = 4/9"} {"input": "Find x for x^2 + 6x - 16 = 0", "output": "x^2 + 6x - 16 = 0\n(x - -8)(x - 2) = 0\nx - -8 = 0 or x - 2 = 0\nx = -8\nx = 2"} {"input": "Find x in x^3 - 3/56x^2 - 243/56x + 95/28 = 0", "output": "x^3 - 3/56x^2 - 243/56x + 95/28 = 0\n(x - -19/8)(x - 1)(x - 10/7) = 0\nx - -19/8 = 0\nx - 1 = 0\nx - 10/7 = 0\nx = -19/8\nx = 1\nx = 10/7"} {"input": "Find x for x^2 + 47/6x + 19/2 = 0", "output": "x^2 + 47/6x + 19/2 = 0\n(x - -19/3)(x - -3/2) = 0\nx - -19/3 = 0 or x - -3/2 = 0\nx = -19/3\nx = -3/2"} {"input": "Solve simultaneously:\n3x + 4y = -73/8\n8x + 5y = -9/2", "output": "3x + 4y = -73/8\n8x + 5y = -9/2\n\nUsing elimination\n8*(3x + 4y = -73/8)\n3*(8x + 5y = -9/2)\n24x + 32y = -73\n24x + 15y = -27/2\nSubtract equations\n17y = -119/2\ny = -119/2/17\ny = -7/2\n\nSubstitute y\n3x + 4(-7/2) = -73/8\n3x = 39/8\nx = 39/8/3\nx = 13/8"} {"input": "Compute the solution of x^2 + 157/8x - 15/2 = 0", "output": "x^2 + 157/8x - 15/2 = 0\n(x - 3/8)(x - -20) = 0\nx - 3/8 = 0 or x - -20 = 0\nx = 3/8\nx = -20"} {"input": "Solve x^2 + 2/45x - 112/45 = 0", "output": "x^2 + 2/45x - 112/45 = 0\n(x - -8/5)(x - 14/9) = 0\nx - -8/5 = 0 or x - 14/9 = 0\nx = -8/5\nx = 14/9"} {"input": "Solve simultaneously:\n4x + 6y = -100/3\n1x + 7y = -139/18", "output": "4x + 6y = -100/3\n1x + 7y = -139/18\n\nUsing elimination\n1*(4x + 6y = -100/3)\n4*(1x + 7y = -139/18)\n4x + 6y = -100/3\n4x + 28y = -278/9\nSubtract equations\n-22y = -22/9\ny = -22/9/-22\ny = 1/9\n\nSubstitute y\n4x + 6(1/9) = -100/3\n4x = -34\nx = -34/4\nx = -17/2"} {"input": "Find x in x^3 + 1/10x^2 - 9/10x = 0", "output": "x^3 + 1/10x^2 - 9/10x = 0\n(x - -1)(x - 0)(x - 9/10) = 0\nx - -1 = 0\nx - 0 = 0\nx - 9/10 = 0\nx = -1\nx = 0\nx = 9/10"} {"input": "What value of x satisfies x^2 + 73/90x - 247/90 = 0", "output": "x^2 + 73/90x - 247/90 = 0\n(x - 13/10)(x - -19/9) = 0\nx - 13/10 = 0 or x - -19/9 = 0\nx = 13/10\nx = -19/9"} {"input": "Solve quickly: 8x + 52 = 0", "output": "8x + 52 = 0\n8x = -52\nx = -52 / 8\nx = -13/2"} {"input": "Solve the equations:\n5x + 5y = -36\n3x + 9y = -114/5", "output": "5x + 5y = -36\n3x + 9y = -114/5\n\nUsing elimination\n3*(5x + 5y = -36)\n5*(3x + 9y = -114/5)\n15x + 15y = -108\n15x + 45y = -114\nSubtract equations\n-30y = 6\ny = 6/-30\ny = -1/5\n\nSubstitute y\n5x + 5(-1/5) = -36\n5x = -35\nx = -35/5\nx = -7"} {"input": "Solve the equation x^3 + 21/2x^2 + 27/2x = 0", "output": "x^3 + 21/2x^2 + 27/2x = 0\n(x - 0)(x - -9)(x - -3/2) = 0\nx - 0 = 0\nx - -9 = 0\nx - -3/2 = 0\nx = 0\nx = -9\nx = -3/2"} {"input": "Solve the equation 7x + 28/3 = 0", "output": "7x + 28/3 = 0\n7x = -28/3\nx = -28/3 / 7\nx = -4/3"} {"input": "Find the solution to x^3 - 89/8x^2 + 81/4x - 81/8 = 0", "output": "x^3 - 89/8x^2 + 81/4x - 81/8 = 0\n(x - 9/8)(x - 1)(x - 9) = 0\nx - 9/8 = 0\nx - 1 = 0\nx - 9 = 0\nx = 9/8\nx = 1\nx = 9"} {"input": "Find x for x^2 + 34/7x + 40/7 = 0", "output": "x^2 + 34/7x + 40/7 = 0\n(x - -20/7)(x - -2) = 0\nx - -20/7 = 0 or x - -2 = 0\nx = -20/7\nx = -2"} {"input": "Solve the system:\n8x + 2y = 12/7\n4x + 8y = 97/7", "output": "8x + 2y = 12/7\n4x + 8y = 97/7\n\nUsing elimination\n4*(8x + 2y = 12/7)\n8*(4x + 8y = 97/7)\n32x + 8y = 48/7\n32x + 64y = 776/7\nSubtract equations\n-56y = -104\ny = -104/-56\ny = 13/7\n\nSubstitute y\n8x + 2(13/7) = 12/7\n8x = -2\nx = -2/8\nx = -1/4"} {"input": "Solve the equations:\n3x + 3y = -39/10\n8x + 7y = -51/5", "output": "3x + 3y = -39/10\n8x + 7y = -51/5\n\nUsing elimination\n8*(3x + 3y = -39/10)\n3*(8x + 7y = -51/5)\n24x + 24y = -156/5\n24x + 21y = -153/5\nSubtract equations\n3y = -3/5\ny = -3/5/3\ny = -1/5\n\nSubstitute y\n3x + 3(-1/5) = -39/10\n3x = -33/10\nx = -33/10/3\nx = -11/10"} {"input": "Solve the system:\n3x + 3y = -3/10\n1x + 3y = -7/10", "output": "3x + 3y = -3/10\n1x + 3y = -7/10\n\nUsing elimination\n1*(3x + 3y = -3/10)\n3*(1x + 3y = -7/10)\n3x + 3y = -3/10\n3x + 9y = -21/10\nSubtract equations\n-6y = 9/5\ny = 9/5/-6\ny = -3/10\n\nSubstitute y\n3x + 3(-3/10) = -3/10\n3x = 3/5\nx = 3/5/3\nx = 1/5"} {"input": "Compute the solution of x^2 - 8x - 153 = 0", "output": "x^2 - 8x - 153 = 0\n(x - 17)(x - -9) = 0\nx - 17 = 0 or x - -9 = 0\nx = 17\nx = -9"} {"input": "Find x in x^3 - 1/30x^2 - 217/150x - 49/75 = 0", "output": "x^3 - 1/30x^2 - 217/150x - 49/75 = 0\n(x - 7/5)(x - -2/3)(x - -7/10) = 0\nx - 7/5 = 0\nx - -2/3 = 0\nx - -7/10 = 0\nx = 7/5\nx = -2/3\nx = -7/10"} {"input": "Find the solution to x^3 + 1/4x^2 - 117/8x + 81/4 = 0", "output": "x^3 + 1/4x^2 - 117/8x + 81/4 = 0\n(x - 9/4)(x - 2)(x - -9/2) = 0\nx - 9/4 = 0\nx - 2 = 0\nx - -9/2 = 0\nx = 9/4\nx = 2\nx = -9/2"} {"input": "Determine x in x^2 + 5/12x - 25/24 = 0", "output": "x^2 + 5/12x - 25/24 = 0\n(x - -5/4)(x - 5/6) = 0\nx - -5/4 = 0 or x - 5/6 = 0\nx = -5/4\nx = 5/6"} {"input": "Solve the equations:\n6x + 1y = 551/35\n5x + 4y = 95/7", "output": "6x + 1y = 551/35\n5x + 4y = 95/7\n\nUsing elimination\n5*(6x + 1y = 551/35)\n6*(5x + 4y = 95/7)\n30x + 5y = 551/7\n30x + 24y = 570/7\nSubtract equations\n-19y = -19/7\ny = -19/7/-19\ny = 1/7\n\nSubstitute y\n6x + 1(1/7) = 551/35\n6x = 78/5\nx = 78/5/6\nx = 13/5"} {"input": "Solve simultaneously:\n5x + 2y = -19/3\n5x + 1y = -22/3", "output": "5x + 2y = -19/3\n5x + 1y = -22/3\n\nUsing elimination\n5*(5x + 2y = -19/3)\n5*(5x + 1y = -22/3)\n25x + 10y = -95/3\n25x + 5y = -110/3\nSubtract equations\n5y = 5\ny = 5/5\ny = 1\n\nSubstitute y\n5x + 2(1) = -19/3\n5x = -25/3\nx = -25/3/5\nx = -5/3"} {"input": "Solve the equation x^3 + 107/5x^2 + 134/5x - 24 = 0", "output": "x^3 + 107/5x^2 + 134/5x - 24 = 0\n(x - -20)(x - -2)(x - 3/5) = 0\nx - -20 = 0\nx - -2 = 0\nx - 3/5 = 0\nx = -20\nx = -2\nx = 3/5"} {"input": "Compute the solution of 5x + 15 = 0", "output": "5x + 15 = 0\n5x = -15\nx = -15 / 5\nx = -3"} {"input": "Compute the solution of 2x - 14/9 = 0", "output": "2x - 14/9 = 0\n2x = 14/9\nx = 14/9 / 2\nx = 7/9"} {"input": "Compute the solution of x^3 + 139/20x^2 + 269/20x + 33/5 = 0", "output": "x^3 + 139/20x^2 + 269/20x + 33/5 = 0\n(x - -11/5)(x - -3/4)(x - -4) = 0\nx - -11/5 = 0\nx - -3/4 = 0\nx - -4 = 0\nx = -11/5\nx = -3/4\nx = -4"} {"input": "Solve simultaneously:\n4x + 9y = -217/10\n1x + 7y = -21/10", "output": "4x + 9y = -217/10\n1x + 7y = -21/10\n\nUsing elimination\n1*(4x + 9y = -217/10)\n4*(1x + 7y = -21/10)\n4x + 9y = -217/10\n4x + 28y = -42/5\nSubtract equations\n-19y = -133/10\ny = -133/10/-19\ny = 7/10\n\nSubstitute y\n4x + 9(7/10) = -217/10\n4x = -28\nx = -28/4\nx = -7"} {"input": "Determine x in 7x + 49 = 0", "output": "7x + 49 = 0\n7x = -49\nx = -49 / 7\nx = -7"} {"input": "Find the solution to 6x + 2 = 0", "output": "6x + 2 = 0\n6x = -2\nx = -2 / 6\nx = -1/3"} {"input": "Find x for x^3 + 8/5x^2 - 23/5x - 26/5 = 0", "output": "x^3 + 8/5x^2 - 23/5x - 26/5 = 0\n(x - 2)(x - -13/5)(x - -1) = 0\nx - 2 = 0\nx - -13/5 = 0\nx - -1 = 0\nx = 2\nx = -13/5\nx = -1"} {"input": "What value of x satisfies x^3 - 277/18x^2 + 277/9x + 65/18 = 0", "output": "x^3 - 277/18x^2 + 277/9x + 65/18 = 0\n(x - -1/9)(x - 5/2)(x - 13) = 0\nx - -1/9 = 0\nx - 5/2 = 0\nx - 13 = 0\nx = -1/9\nx = 5/2\nx = 13"} {"input": "Find the solution to 10x - 18 = 0", "output": "10x - 18 = 0\n10x = 18\nx = 18 / 10\nx = 9/5"} {"input": "Solve x^2 - 35/12x + 25/12 = 0", "output": "x^2 - 35/12x + 25/12 = 0\n(x - 5/4)(x - 5/3) = 0\nx - 5/4 = 0 or x - 5/3 = 0\nx = 5/4\nx = 5/3"} {"input": "Find the solution to 7x + 21/5 = 0", "output": "7x + 21/5 = 0\n7x = -21/5\nx = -21/5 / 7\nx = -3/5"} {"input": "Solve the equation 5x + 95 = 0", "output": "5x + 95 = 0\n5x = -95\nx = -95 / 5\nx = -19"} {"input": "Find the solution to 9x + 54 = 0", "output": "9x + 54 = 0\n9x = -54\nx = -54 / 9\nx = -6"} {"input": "Solve the equation x^2 - 2x + 32/81 = 0", "output": "x^2 - 2x + 32/81 = 0\n(x - 16/9)(x - 2/9) = 0\nx - 16/9 = 0 or x - 2/9 = 0\nx = 16/9\nx = 2/9"} {"input": "Find x and y such that\n7x + 5y = -2/3\n2x + 1y = 2/3", "output": "7x + 5y = -2/3\n2x + 1y = 2/3\n\nUsing elimination\n2*(7x + 5y = -2/3)\n7*(2x + 1y = 2/3)\n14x + 10y = -4/3\n14x + 7y = 14/3\nSubtract equations\n3y = -6\ny = -6/3\ny = -2\n\nSubstitute y\n7x + 5(-2) = -2/3\n7x = 28/3\nx = 28/3/7\nx = 4/3"} {"input": "Solve the equations:\n10x + 1y = -94/3\n4x + 10y = 196/15", "output": "10x + 1y = -94/3\n4x + 10y = 196/15\n\nUsing elimination\n4*(10x + 1y = -94/3)\n10*(4x + 10y = 196/15)\n40x + 4y = -376/3\n40x + 100y = 392/3\nSubtract equations\n-96y = -256\ny = -256/-96\ny = 8/3\n\nSubstitute y\n10x + 1(8/3) = -94/3\n10x = -34\nx = -34/10\nx = -17/5"} {"input": "Solve quickly: x^2 + 33/8x + 17/4 = 0", "output": "x^2 + 33/8x + 17/4 = 0\n(x - -2)(x - -17/8) = 0\nx - -2 = 0 or x - -17/8 = 0\nx = -2\nx = -17/8"} {"input": "Solve 6x + 90 = 0", "output": "6x + 90 = 0\n6x = -90\nx = -90 / 6\nx = -15"} {"input": "What value of x satisfies 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "What value of x satisfies x^3 - 25/18x^2 - 659/144x + 95/16 = 0", "output": "x^3 - 25/18x^2 - 659/144x + 95/16 = 0\n(x - -19/9)(x - 9/4)(x - 5/4) = 0\nx - -19/9 = 0\nx - 9/4 = 0\nx - 5/4 = 0\nx = -19/9\nx = 9/4\nx = 5/4"} {"input": "Solve the system:\n7x + 1y = -13/3\n7x + 9y = -61/3", "output": "7x + 1y = -13/3\n7x + 9y = -61/3\n\nUsing elimination\n7*(7x + 1y = -13/3)\n7*(7x + 9y = -61/3)\n49x + 7y = -91/3\n49x + 63y = -427/3\nSubtract equations\n-56y = 112\ny = 112/-56\ny = -2\n\nSubstitute y\n7x + 1(-2) = -13/3\n7x = -7/3\nx = -7/3/7\nx = -1/3"} {"input": "Determine x in x^2 + 25/9x - 44/9 = 0", "output": "x^2 + 25/9x - 44/9 = 0\n(x - 11/9)(x - -4) = 0\nx - 11/9 = 0 or x - -4 = 0\nx = 11/9\nx = -4"} {"input": "Solve quickly: x^2 - 43/9x - 340/27 = 0", "output": "x^2 - 43/9x - 340/27 = 0\n(x - 20/3)(x - -17/9) = 0\nx - 20/3 = 0 or x - -17/9 = 0\nx = 20/3\nx = -17/9"} {"input": "Solve x^2 - 18/35x - 8/35 = 0", "output": "x^2 - 18/35x - 8/35 = 0\n(x - -2/7)(x - 4/5) = 0\nx - -2/7 = 0 or x - 4/5 = 0\nx = -2/7\nx = 4/5"} {"input": "Find the solution to x^3 - 33/14x^2 + 2/7x + 6/7 = 0", "output": "x^3 - 33/14x^2 + 2/7x + 6/7 = 0\n(x - 2)(x - 6/7)(x - -1/2) = 0\nx - 2 = 0\nx - 6/7 = 0\nx - -1/2 = 0\nx = 2\nx = 6/7\nx = -1/2"} {"input": "Solve the equation x^3 + 64/15x^2 + 1787/300x + 273/100 = 0", "output": "x^3 + 64/15x^2 + 1787/300x + 273/100 = 0\n(x - -7/6)(x - -13/10)(x - -9/5) = 0\nx - -7/6 = 0\nx - -13/10 = 0\nx - -9/5 = 0\nx = -7/6\nx = -13/10\nx = -9/5"} {"input": "What value of x satisfies x^2 - 17/20x - 11/40 = 0", "output": "x^2 - 17/20x - 11/40 = 0\n(x - -1/4)(x - 11/10) = 0\nx - -1/4 = 0 or x - 11/10 = 0\nx = -1/4\nx = 11/10"} {"input": "Find x for 4x - 48 = 0", "output": "4x - 48 = 0\n4x = 48\nx = 48 / 4\nx = 12"} {"input": "Solve the equations:\n5x + 6y = 355/12\n1x + 4y = 67/6", "output": "5x + 6y = 355/12\n1x + 4y = 67/6\n\nUsing elimination\n1*(5x + 6y = 355/12)\n5*(1x + 4y = 67/6)\n5x + 6y = 355/12\n5x + 20y = 335/6\nSubtract equations\n-14y = -105/4\ny = -105/4/-14\ny = 15/8\n\nSubstitute y\n5x + 6(15/8) = 355/12\n5x = 55/3\nx = 55/3/5\nx = 11/3"} {"input": "Solve simultaneously:\n5x + 3y = -57/8\n1x + 3y = -189/40", "output": "5x + 3y = -57/8\n1x + 3y = -189/40\n\nUsing elimination\n1*(5x + 3y = -57/8)\n5*(1x + 3y = -189/40)\n5x + 3y = -57/8\n5x + 15y = -189/8\nSubtract equations\n-12y = 33/2\ny = 33/2/-12\ny = -11/8\n\nSubstitute y\n5x + 3(-11/8) = -57/8\n5x = -3\nx = -3/5\nx = -3/5"} {"input": "Solve simultaneously:\n8x + 2y = -60\n7x + 10y = -36", "output": "8x + 2y = -60\n7x + 10y = -36\n\nUsing elimination\n7*(8x + 2y = -60)\n8*(7x + 10y = -36)\n56x + 14y = -420\n56x + 80y = -288\nSubtract equations\n-66y = -132\ny = -132/-66\ny = 2\n\nSubstitute y\n8x + 2(2) = -60\n8x = -64\nx = -64/8\nx = -8"} {"input": "Solve the system:\n3x + 2y = -46\n2x + 5y = -93", "output": "3x + 2y = -46\n2x + 5y = -93\n\nUsing elimination\n2*(3x + 2y = -46)\n3*(2x + 5y = -93)\n6x + 4y = -92\n6x + 15y = -279\nSubtract equations\n-11y = 187\ny = 187/-11\ny = -17\n\nSubstitute y\n3x + 2(-17) = -46\n3x = -12\nx = -12/3\nx = -4"} {"input": "Solve simultaneously:\n6x + 8y = -49/4\n2x + 5y = -7/2", "output": "6x + 8y = -49/4\n2x + 5y = -7/2\n\nUsing elimination\n2*(6x + 8y = -49/4)\n6*(2x + 5y = -7/2)\n12x + 16y = -49/2\n12x + 30y = -21\nSubtract equations\n-14y = -7/2\ny = -7/2/-14\ny = 1/4\n\nSubstitute y\n6x + 8(1/4) = -49/4\n6x = -57/4\nx = -57/4/6\nx = -19/8"} {"input": "Solve quickly: 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "What value of x satisfies 7x - 35/6 = 0", "output": "7x - 35/6 = 0\n7x = 35/6\nx = 35/6 / 7\nx = 5/6"} {"input": "Solve quickly: x^3 + 2x^2 - 37/9x + 10/9 = 0", "output": "x^3 + 2x^2 - 37/9x + 10/9 = 0\n(x - 1)(x - 1/3)(x - -10/3) = 0\nx - 1 = 0\nx - 1/3 = 0\nx - -10/3 = 0\nx = 1\nx = 1/3\nx = -10/3"} {"input": "Solve the equation x^2 + 3/2x + 1/2 = 0", "output": "x^2 + 3/2x + 1/2 = 0\n(x - -1)(x - -1/2) = 0\nx - -1 = 0 or x - -1/2 = 0\nx = -1\nx = -1/2"} {"input": "Solve quickly: 5x - 15 = 0", "output": "5x - 15 = 0\n5x = 15\nx = 15 / 5\nx = 3"} {"input": "Determine x in x^3 - 61/28x^2 + 1/4x + 3/14 = 0", "output": "x^3 - 61/28x^2 + 1/4x + 3/14 = 0\n(x - 3/7)(x - -1/4)(x - 2) = 0\nx - 3/7 = 0\nx - -1/4 = 0\nx - 2 = 0\nx = 3/7\nx = -1/4\nx = 2"} {"input": "Solve the equations:\n3x + 7y = -5\n7x + 3y = 15", "output": "3x + 7y = -5\n7x + 3y = 15\n\nUsing elimination\n7*(3x + 7y = -5)\n3*(7x + 3y = 15)\n21x + 49y = -35\n21x + 9y = 45\nSubtract equations\n40y = -80\ny = -80/40\ny = -2\n\nSubstitute y\n3x + 7(-2) = -5\n3x = 9\nx = 9/3\nx = 3"} {"input": "Find x and y such that\n3x + 3y = 18/5\n8x + 9y = 63/5", "output": "3x + 3y = 18/5\n8x + 9y = 63/5\n\nUsing elimination\n8*(3x + 3y = 18/5)\n3*(8x + 9y = 63/5)\n24x + 24y = 144/5\n24x + 27y = 189/5\nSubtract equations\n-3y = -9\ny = -9/-3\ny = 3\n\nSubstitute y\n3x + 3(3) = 18/5\n3x = -27/5\nx = -27/5/3\nx = -9/5"} {"input": "Compute the solution of x^3 - 39/7x^2 + 530/63x - 200/63 = 0", "output": "x^3 - 39/7x^2 + 530/63x - 200/63 = 0\n(x - 10/3)(x - 4/7)(x - 5/3) = 0\nx - 10/3 = 0\nx - 4/7 = 0\nx - 5/3 = 0\nx = 10/3\nx = 4/7\nx = 5/3"} {"input": "Solve quickly: x^3 + 7/9x^2 - 91/36x - 4/3 = 0", "output": "x^3 + 7/9x^2 - 91/36x - 4/3 = 0\n(x - -1/2)(x - -16/9)(x - 3/2) = 0\nx - -1/2 = 0\nx - -16/9 = 0\nx - 3/2 = 0\nx = -1/2\nx = -16/9\nx = 3/2"} {"input": "Find x in x^2 + 46/5x + 77/5 = 0", "output": "x^2 + 46/5x + 77/5 = 0\n(x - -11/5)(x - -7) = 0\nx - -11/5 = 0 or x - -7 = 0\nx = -11/5\nx = -7"} {"input": "Compute the solution of 7x + 7/3 = 0", "output": "7x + 7/3 = 0\n7x = -7/3\nx = -7/3 / 7\nx = -1/3"} {"input": "Compute the solution of x^3 + 21/8x^2 - 499/16x - 63/16 = 0", "output": "x^3 + 21/8x^2 - 499/16x - 63/16 = 0\n(x - -7)(x - -1/8)(x - 9/2) = 0\nx - -7 = 0\nx - -1/8 = 0\nx - 9/2 = 0\nx = -7\nx = -1/8\nx = 9/2"} {"input": "Find x and y such that\n10x + 7y = -293/10\n10x + 9y = -291/10", "output": "10x + 7y = -293/10\n10x + 9y = -291/10\n\nUsing elimination\n10*(10x + 7y = -293/10)\n10*(10x + 9y = -291/10)\n100x + 70y = -293\n100x + 90y = -291\nSubtract equations\n-20y = -2\ny = -2/-20\ny = 1/10\n\nSubstitute y\n10x + 7(1/10) = -293/10\n10x = -30\nx = -30/10\nx = -3"} {"input": "Solve simultaneously:\n3x + 7y = 946/63\n5x + 1y = 382/63", "output": "3x + 7y = 946/63\n5x + 1y = 382/63\n\nUsing elimination\n5*(3x + 7y = 946/63)\n3*(5x + 1y = 382/63)\n15x + 35y = 4730/63\n15x + 3y = 382/21\nSubtract equations\n32y = 512/9\ny = 512/9/32\ny = 16/9\n\nSubstitute y\n3x + 7(16/9) = 946/63\n3x = 18/7\nx = 18/7/3\nx = 6/7"} {"input": "Solve the system:\n8x + 3y = 4\n8x + 9y = 24", "output": "8x + 3y = 4\n8x + 9y = 24\n\nUsing elimination\n8*(8x + 3y = 4)\n8*(8x + 9y = 24)\n64x + 24y = 32\n64x + 72y = 192\nSubtract equations\n-48y = -160\ny = -160/-48\ny = 10/3\n\nSubstitute y\n8x + 3(10/3) = 4\n8x = -6\nx = -6/8\nx = -3/4"} {"input": "Compute the solution of x^3 + 7/18x^2 - 161/225x + 11/150 = 0", "output": "x^3 + 7/18x^2 - 161/225x + 11/150 = 0\n(x - -11/10)(x - 1/9)(x - 3/5) = 0\nx - -11/10 = 0\nx - 1/9 = 0\nx - 3/5 = 0\nx = -11/10\nx = 1/9\nx = 3/5"} {"input": "Determine x in x^3 - 148/15x^2 - 13/3x + 30 = 0", "output": "x^3 - 148/15x^2 - 13/3x + 30 = 0\n(x - 5/3)(x - -9/5)(x - 10) = 0\nx - 5/3 = 0\nx - -9/5 = 0\nx - 10 = 0\nx = 5/3\nx = -9/5\nx = 10"} {"input": "Compute the solution of x^3 - 7/2x^2 - 7/2x + 6 = 0", "output": "x^3 - 7/2x^2 - 7/2x + 6 = 0\n(x - -3/2)(x - 1)(x - 4) = 0\nx - -3/2 = 0\nx - 1 = 0\nx - 4 = 0\nx = -3/2\nx = 1\nx = 4"} {"input": "Solve quickly: 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Determine x in 1x - 6 = 0", "output": "1x - 6 = 0\n1x = 6\nx = 6 / 1\nx = 6"} {"input": "Solve quickly: x^2 - 46/7x - 3 = 0", "output": "x^2 - 46/7x - 3 = 0\n(x - 7)(x - -3/7) = 0\nx - 7 = 0 or x - -3/7 = 0\nx = 7\nx = -3/7"} {"input": "Solve quickly: 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Solve x^3 - 37/2x^2 + 629/16x + 11 = 0", "output": "x^3 - 37/2x^2 + 629/16x + 11 = 0\n(x - -1/4)(x - 11/4)(x - 16) = 0\nx - -1/4 = 0\nx - 11/4 = 0\nx - 16 = 0\nx = -1/4\nx = 11/4\nx = 16"} {"input": "Solve the equation x^2 - 87/35x + 22/35 = 0", "output": "x^2 - 87/35x + 22/35 = 0\n(x - 2/7)(x - 11/5) = 0\nx - 2/7 = 0 or x - 11/5 = 0\nx = 2/7\nx = 11/5"} {"input": "Determine x in 7x - 70 = 0", "output": "7x - 70 = 0\n7x = 70\nx = 70 / 7\nx = 10"} {"input": "Find the solution to x^2 - 25/4x + 17/2 = 0", "output": "x^2 - 25/4x + 17/2 = 0\n(x - 17/4)(x - 2) = 0\nx - 17/4 = 0 or x - 2 = 0\nx = 17/4\nx = 2"} {"input": "Find x and y such that\n1x + 5y = -11/10\n7x + 10y = -101/5", "output": "1x + 5y = -11/10\n7x + 10y = -101/5\n\nUsing elimination\n7*(1x + 5y = -11/10)\n1*(7x + 10y = -101/5)\n7x + 35y = -77/10\n7x + 10y = -101/5\nSubtract equations\n25y = 25/2\ny = 25/2/25\ny = 1/2\n\nSubstitute y\n1x + 5(1/2) = -11/10\n1x = -18/5\nx = -18/5/1\nx = -18/5"} {"input": "Solve quickly: x^2 - 11/2x - 63/2 = 0", "output": "x^2 - 11/2x - 63/2 = 0\n(x - 9)(x - -7/2) = 0\nx - 9 = 0 or x - -7/2 = 0\nx = 9\nx = -7/2"} {"input": "Find x for x^3 - 142/21x^2 + 83/7x - 68/21 = 0", "output": "x^3 - 142/21x^2 + 83/7x - 68/21 = 0\n(x - 17/7)(x - 1/3)(x - 4) = 0\nx - 17/7 = 0\nx - 1/3 = 0\nx - 4 = 0\nx = 17/7\nx = 1/3\nx = 4"} {"input": "Solve simultaneously:\n2x + 3y = -9/2\n10x + 9y = -23/2", "output": "2x + 3y = -9/2\n10x + 9y = -23/2\n\nUsing elimination\n10*(2x + 3y = -9/2)\n2*(10x + 9y = -23/2)\n20x + 30y = -45\n20x + 18y = -23\nSubtract equations\n12y = -22\ny = -22/12\ny = -11/6\n\nSubstitute y\n2x + 3(-11/6) = -9/2\n2x = 1\nx = 1/2\nx = 1/2"} {"input": "Solve simultaneously:\n7x + 1y = -40/3\n8x + 9y = -35/9", "output": "7x + 1y = -40/3\n8x + 9y = -35/9\n\nUsing elimination\n8*(7x + 1y = -40/3)\n7*(8x + 9y = -35/9)\n56x + 8y = -320/3\n56x + 63y = -245/9\nSubtract equations\n-55y = -715/9\ny = -715/9/-55\ny = 13/9\n\nSubstitute y\n7x + 1(13/9) = -40/3\n7x = -133/9\nx = -133/9/7\nx = -19/9"} {"input": "Find x for x^2 + 207/56x + 81/28 = 0", "output": "x^2 + 207/56x + 81/28 = 0\n(x - -9/8)(x - -18/7) = 0\nx - -9/8 = 0 or x - -18/7 = 0\nx = -9/8\nx = -18/7"} {"input": "Find x for x^2 + 23/12x - 13/24 = 0", "output": "x^2 + 23/12x - 13/24 = 0\n(x - 1/4)(x - -13/6) = 0\nx - 1/4 = 0 or x - -13/6 = 0\nx = 1/4\nx = -13/6"} {"input": "Find x for x^3 - 121/45x^2 - 436/75x + 228/25 = 0", "output": "x^3 - 121/45x^2 - 436/75x + 228/25 = 0\n(x - -19/9)(x - 18/5)(x - 6/5) = 0\nx - -19/9 = 0\nx - 18/5 = 0\nx - 6/5 = 0\nx = -19/9\nx = 18/5\nx = 6/5"} {"input": "What value of x satisfies 9x + 117/10 = 0", "output": "9x + 117/10 = 0\n9x = -117/10\nx = -117/10 / 9\nx = -13/10"} {"input": "Find x in 9x + 3 = 0", "output": "9x + 3 = 0\n9x = -3\nx = -3 / 9\nx = -1/3"} {"input": "Solve the equations:\n10x + 7y = -191/14\n9x + 1y = -209/14", "output": "10x + 7y = -191/14\n9x + 1y = -209/14\n\nUsing elimination\n9*(10x + 7y = -191/14)\n10*(9x + 1y = -209/14)\n90x + 63y = -1719/14\n90x + 10y = -1045/7\nSubtract equations\n53y = 53/2\ny = 53/2/53\ny = 1/2\n\nSubstitute y\n10x + 7(1/2) = -191/14\n10x = -120/7\nx = -120/7/10\nx = -12/7"} {"input": "Solve the equations:\n10x + 4y = 197/6\n2x + 2y = 13/6", "output": "10x + 4y = 197/6\n2x + 2y = 13/6\n\nUsing elimination\n2*(10x + 4y = 197/6)\n10*(2x + 2y = 13/6)\n20x + 8y = 197/3\n20x + 20y = 65/3\nSubtract equations\n-12y = 44\ny = 44/-12\ny = -11/3\n\nSubstitute y\n10x + 4(-11/3) = 197/6\n10x = 95/2\nx = 95/2/10\nx = 19/4"} {"input": "Solve x^2 - 51/4x - 135/4 = 0", "output": "x^2 - 51/4x - 135/4 = 0\n(x - -9/4)(x - 15) = 0\nx - -9/4 = 0 or x - 15 = 0\nx = -9/4\nx = 15"} {"input": "Solve the system:\n4x + 8y = 1204/45\n3x + 1y = 46/15", "output": "4x + 8y = 1204/45\n3x + 1y = 46/15\n\nUsing elimination\n3*(4x + 8y = 1204/45)\n4*(3x + 1y = 46/15)\n12x + 24y = 1204/15\n12x + 4y = 184/15\nSubtract equations\n20y = 68\ny = 68/20\ny = 17/5\n\nSubstitute y\n4x + 8(17/5) = 1204/45\n4x = -4/9\nx = -4/9/4\nx = -1/9"} {"input": "Solve the equations:\n9x + 6y = -85/2\n6x + 6y = -35", "output": "9x + 6y = -85/2\n6x + 6y = -35\n\nUsing elimination\n6*(9x + 6y = -85/2)\n9*(6x + 6y = -35)\n54x + 36y = -255\n54x + 54y = -315\nSubtract equations\n-18y = 60\ny = 60/-18\ny = -10/3\n\nSubstitute y\n9x + 6(-10/3) = -85/2\n9x = -45/2\nx = -45/2/9\nx = -5/2"} {"input": "Find the solution to x^2 + 13/4x - 99/8 = 0", "output": "x^2 + 13/4x - 99/8 = 0\n(x - -11/2)(x - 9/4) = 0\nx - -11/2 = 0 or x - 9/4 = 0\nx = -11/2\nx = 9/4"} {"input": "Find x for x^2 + 45/4x + 26 = 0", "output": "x^2 + 45/4x + 26 = 0\n(x - -13/4)(x - -8) = 0\nx - -13/4 = 0 or x - -8 = 0\nx = -13/4\nx = -8"} {"input": "Solve the equations:\n8x + 9y = 119\n10x + 3y = 157", "output": "8x + 9y = 119\n10x + 3y = 157\n\nUsing elimination\n10*(8x + 9y = 119)\n8*(10x + 3y = 157)\n80x + 90y = 1190\n80x + 24y = 1256\nSubtract equations\n66y = -66\ny = -66/66\ny = -1\n\nSubstitute y\n8x + 9(-1) = 119\n8x = 128\nx = 128/8\nx = 16"} {"input": "Compute the solution of 1x + 6/5 = 0", "output": "1x + 6/5 = 0\n1x = -6/5\nx = -6/5 / 1\nx = -6/5"} {"input": "Find the solution to x^3 + 167/12x^2 + 695/24x - 275/8 = 0", "output": "x^3 + 167/12x^2 + 695/24x - 275/8 = 0\n(x - 5/6)(x - -11)(x - -15/4) = 0\nx - 5/6 = 0\nx - -11 = 0\nx - -15/4 = 0\nx = 5/6\nx = -11\nx = -15/4"} {"input": "Compute the solution of x^3 + 103/28x^2 + 27/28x - 45/14 = 0", "output": "x^3 + 103/28x^2 + 27/28x - 45/14 = 0\n(x - 3/4)(x - -10/7)(x - -3) = 0\nx - 3/4 = 0\nx - -10/7 = 0\nx - -3 = 0\nx = 3/4\nx = -10/7\nx = -3"} {"input": "Determine x in x^2 + 11/7x - 18/7 = 0", "output": "x^2 + 11/7x - 18/7 = 0\n(x - 1)(x - -18/7) = 0\nx - 1 = 0 or x - -18/7 = 0\nx = 1\nx = -18/7"} {"input": "What value of x satisfies x^2 - 48/5x + 64/5 = 0", "output": "x^2 - 48/5x + 64/5 = 0\n(x - 8/5)(x - 8) = 0\nx - 8/5 = 0 or x - 8 = 0\nx = 8/5\nx = 8"} {"input": "Solve the equation 5x - 11 = 0", "output": "5x - 11 = 0\n5x = 11\nx = 11 / 5\nx = 11/5"} {"input": "Solve the equation x^3 - 2x^2 - 25/4x + 25/2 = 0", "output": "x^3 - 2x^2 - 25/4x + 25/2 = 0\n(x - 5/2)(x - -5/2)(x - 2) = 0\nx - 5/2 = 0\nx - -5/2 = 0\nx - 2 = 0\nx = 5/2\nx = -5/2\nx = 2"} {"input": "Solve the equation x^2 - 3x - 18 = 0", "output": "x^2 - 3x - 18 = 0\n(x - -3)(x - 6) = 0\nx - -3 = 0 or x - 6 = 0\nx = -3\nx = 6"} {"input": "Solve the equations:\n9x + 1y = 54/5\n3x + 4y = -129/10", "output": "9x + 1y = 54/5\n3x + 4y = -129/10\n\nUsing elimination\n3*(9x + 1y = 54/5)\n9*(3x + 4y = -129/10)\n27x + 3y = 162/5\n27x + 36y = -1161/10\nSubtract equations\n-33y = 297/2\ny = 297/2/-33\ny = -9/2\n\nSubstitute y\n9x + 1(-9/2) = 54/5\n9x = 153/10\nx = 153/10/9\nx = 17/10"} {"input": "Solve 1x - 13/8 = 0", "output": "1x - 13/8 = 0\n1x = 13/8\nx = 13/8 / 1\nx = 13/8"} {"input": "Find x and y such that\n7x + 3y = 31\n7x + 7y = 63", "output": "7x + 3y = 31\n7x + 7y = 63\n\nUsing elimination\n7*(7x + 3y = 31)\n7*(7x + 7y = 63)\n49x + 21y = 217\n49x + 49y = 441\nSubtract equations\n-28y = -224\ny = -224/-28\ny = 8\n\nSubstitute y\n7x + 3(8) = 31\n7x = 7\nx = 7/7\nx = 1"} {"input": "Find x in x^2 + 67/45x + 8/15 = 0", "output": "x^2 + 67/45x + 8/15 = 0\n(x - -3/5)(x - -8/9) = 0\nx - -3/5 = 0 or x - -8/9 = 0\nx = -3/5\nx = -8/9"} {"input": "Solve simultaneously:\n4x + 8y = -34/5\n8x + 1y = -197/20", "output": "4x + 8y = -34/5\n8x + 1y = -197/20\n\nUsing elimination\n8*(4x + 8y = -34/5)\n4*(8x + 1y = -197/20)\n32x + 64y = -272/5\n32x + 4y = -197/5\nSubtract equations\n60y = -15\ny = -15/60\ny = -1/4\n\nSubstitute y\n4x + 8(-1/4) = -34/5\n4x = -24/5\nx = -24/5/4\nx = -6/5"} {"input": "Determine x in 6x - 33/5 = 0", "output": "6x - 33/5 = 0\n6x = 33/5\nx = 33/5 / 6\nx = 11/10"} {"input": "Find the solution to x^2 - 19x + 70 = 0", "output": "x^2 - 19x + 70 = 0\n(x - 5)(x - 14) = 0\nx - 5 = 0 or x - 14 = 0\nx = 5\nx = 14"} {"input": "Find x for x^3 - 481/140x^2 - 13/35x + 48/7 = 0", "output": "x^3 - 481/140x^2 - 13/35x + 48/7 = 0\n(x - -5/4)(x - 16/7)(x - 12/5) = 0\nx - -5/4 = 0\nx - 16/7 = 0\nx - 12/5 = 0\nx = -5/4\nx = 16/7\nx = 12/5"} {"input": "Solve quickly: x^3 + 87/20x^2 + 11/10x - 6/5 = 0", "output": "x^3 + 87/20x^2 + 11/10x - 6/5 = 0\n(x - -3/4)(x - 2/5)(x - -4) = 0\nx - -3/4 = 0\nx - 2/5 = 0\nx - -4 = 0\nx = -3/4\nx = 2/5\nx = -4"} {"input": "Solve the equation x^2 + 103/24x + 55/24 = 0", "output": "x^2 + 103/24x + 55/24 = 0\n(x - -5/8)(x - -11/3) = 0\nx - -5/8 = 0 or x - -11/3 = 0\nx = -5/8\nx = -11/3"} {"input": "Solve quickly: 10x - 140/3 = 0", "output": "10x - 140/3 = 0\n10x = 140/3\nx = 140/3 / 10\nx = 14/3"} {"input": "Solve x^3 + 77/24x^2 + 7/12x - 1/8 = 0", "output": "x^3 + 77/24x^2 + 7/12x - 1/8 = 0\n(x - -1/3)(x - 1/8)(x - -3) = 0\nx - -1/3 = 0\nx - 1/8 = 0\nx - -3 = 0\nx = -1/3\nx = 1/8\nx = -3"} {"input": "Solve the equation x^3 + 127/60x^2 - 683/120x + 13/8 = 0", "output": "x^3 + 127/60x^2 - 683/120x + 13/8 = 0\n(x - 13/10)(x - -15/4)(x - 1/3) = 0\nx - 13/10 = 0\nx - -15/4 = 0\nx - 1/3 = 0\nx = 13/10\nx = -15/4\nx = 1/3"} {"input": "Find x for 2x + 28 = 0", "output": "2x + 28 = 0\n2x = -28\nx = -28 / 2\nx = -14"} {"input": "Solve simultaneously:\n8x + 1y = 47/2\n4x + 8y = 23", "output": "8x + 1y = 47/2\n4x + 8y = 23\n\nUsing elimination\n4*(8x + 1y = 47/2)\n8*(4x + 8y = 23)\n32x + 4y = 94\n32x + 64y = 184\nSubtract equations\n-60y = -90\ny = -90/-60\ny = 3/2\n\nSubstitute y\n8x + 1(3/2) = 47/2\n8x = 22\nx = 22/8\nx = 11/4"} {"input": "Compute the solution of x^3 + 9/10x^2 - 93/25x - 76/25 = 0", "output": "x^3 + 9/10x^2 - 93/25x - 76/25 = 0\n(x - -2)(x - 19/10)(x - -4/5) = 0\nx - -2 = 0\nx - 19/10 = 0\nx - -4/5 = 0\nx = -2\nx = 19/10\nx = -4/5"} {"input": "Find x and y such that\n8x + 7y = 536/5\n10x + 5y = 74", "output": "8x + 7y = 536/5\n10x + 5y = 74\n\nUsing elimination\n10*(8x + 7y = 536/5)\n8*(10x + 5y = 74)\n80x + 70y = 1072\n80x + 40y = 592\nSubtract equations\n30y = 480\ny = 480/30\ny = 16\n\nSubstitute y\n8x + 7(16) = 536/5\n8x = -24/5\nx = -24/5/8\nx = -3/5"} {"input": "Find the solution to 1x + 19/2 = 0", "output": "1x + 19/2 = 0\n1x = -19/2\nx = -19/2 / 1\nx = -19/2"} {"input": "Determine x in x^3 + 25/21x^2 - 82/21x - 104/21 = 0", "output": "x^3 + 25/21x^2 - 82/21x - 104/21 = 0\n(x - -13/7)(x - 2)(x - -4/3) = 0\nx - -13/7 = 0\nx - 2 = 0\nx - -4/3 = 0\nx = -13/7\nx = 2\nx = -4/3"} {"input": "Solve quickly: x^3 + 7/18x^2 - 31/9x - 8/3 = 0", "output": "x^3 + 7/18x^2 - 31/9x - 8/3 = 0\n(x - -3/2)(x - -8/9)(x - 2) = 0\nx - -3/2 = 0\nx - -8/9 = 0\nx - 2 = 0\nx = -3/2\nx = -8/9\nx = 2"} {"input": "Solve quickly: x^3 - 9/2x^2 - 171/16x + 81/8 = 0", "output": "x^3 - 9/2x^2 - 171/16x + 81/8 = 0\n(x - 6)(x - 3/4)(x - -9/4) = 0\nx - 6 = 0\nx - 3/4 = 0\nx - -9/4 = 0\nx = 6\nx = 3/4\nx = -9/4"} {"input": "What value of x satisfies 3x + 9/4 = 0", "output": "3x + 9/4 = 0\n3x = -9/4\nx = -9/4 / 3\nx = -3/4"} {"input": "Solve the system:\n6x + 8y = 44/3\n8x + 2y = 50/3", "output": "6x + 8y = 44/3\n8x + 2y = 50/3\n\nUsing elimination\n8*(6x + 8y = 44/3)\n6*(8x + 2y = 50/3)\n48x + 64y = 352/3\n48x + 12y = 100\nSubtract equations\n52y = 52/3\ny = 52/3/52\ny = 1/3\n\nSubstitute y\n6x + 8(1/3) = 44/3\n6x = 12\nx = 12/6\nx = 2"} {"input": "Solve the equations:\n7x + 4y = -33/4\n5x + 1y = -5/4", "output": "7x + 4y = -33/4\n5x + 1y = -5/4\n\nUsing elimination\n5*(7x + 4y = -33/4)\n7*(5x + 1y = -5/4)\n35x + 20y = -165/4\n35x + 7y = -35/4\nSubtract equations\n13y = -65/2\ny = -65/2/13\ny = -5/2\n\nSubstitute y\n7x + 4(-5/2) = -33/4\n7x = 7/4\nx = 7/4/7\nx = 1/4"} {"input": "Solve 2x + 15 = 0", "output": "2x + 15 = 0\n2x = -15\nx = -15 / 2\nx = -15/2"} {"input": "Solve quickly: 10x + 35/4 = 0", "output": "10x + 35/4 = 0\n10x = -35/4\nx = -35/4 / 10\nx = -7/8"} {"input": "Find x and y such that\n6x + 1y = 121/40\n4x + 7y = 239/40", "output": "6x + 1y = 121/40\n4x + 7y = 239/40\n\nUsing elimination\n4*(6x + 1y = 121/40)\n6*(4x + 7y = 239/40)\n24x + 4y = 121/10\n24x + 42y = 717/20\nSubtract equations\n-38y = -95/4\ny = -95/4/-38\ny = 5/8\n\nSubstitute y\n6x + 1(5/8) = 121/40\n6x = 12/5\nx = 12/5/6\nx = 2/5"} {"input": "Find x in x^2 - 51/5x + 133/20 = 0", "output": "x^2 - 51/5x + 133/20 = 0\n(x - 7/10)(x - 19/2) = 0\nx - 7/10 = 0 or x - 19/2 = 0\nx = 7/10\nx = 19/2"} {"input": "Solve the system:\n7x + 1y = -33/7\n6x + 2y = -10/7", "output": "7x + 1y = -33/7\n6x + 2y = -10/7\n\nUsing elimination\n6*(7x + 1y = -33/7)\n7*(6x + 2y = -10/7)\n42x + 6y = -198/7\n42x + 14y = -10\nSubtract equations\n-8y = -128/7\ny = -128/7/-8\ny = 16/7\n\nSubstitute y\n7x + 1(16/7) = -33/7\n7x = -7\nx = -7/7\nx = -1"} {"input": "Solve x^2 + 2x = 0", "output": "x^2 + 2x = 0\n(x - 0)(x - -2) = 0\nx - 0 = 0 or x - -2 = 0\nx = 0\nx = -2"} {"input": "Find x and y such that\n3x + 8y = -293/10\n1x + 10y = -391/10", "output": "3x + 8y = -293/10\n1x + 10y = -391/10\n\nUsing elimination\n1*(3x + 8y = -293/10)\n3*(1x + 10y = -391/10)\n3x + 8y = -293/10\n3x + 30y = -1173/10\nSubtract equations\n-22y = 88\ny = 88/-22\ny = -4\n\nSubstitute y\n3x + 8(-4) = -293/10\n3x = 27/10\nx = 27/10/3\nx = 9/10"} {"input": "Find x and y such that\n1x + 4y = 4/3\n4x + 10y = 28/3", "output": "1x + 4y = 4/3\n4x + 10y = 28/3\n\nUsing elimination\n4*(1x + 4y = 4/3)\n1*(4x + 10y = 28/3)\n4x + 16y = 16/3\n4x + 10y = 28/3\nSubtract equations\n6y = -4\ny = -4/6\ny = -2/3\n\nSubstitute y\n1x + 4(-2/3) = 4/3\n1x = 4\nx = 4/1\nx = 4"} {"input": "Solve 1x - 3 = 0", "output": "1x - 3 = 0\n1x = 3\nx = 3 / 1\nx = 3"} {"input": "What value of x satisfies x^2 - 27/5x + 28/5 = 0", "output": "x^2 - 27/5x + 28/5 = 0\n(x - 7/5)(x - 4) = 0\nx - 7/5 = 0 or x - 4 = 0\nx = 7/5\nx = 4"} {"input": "Compute the solution of x^3 + 77/8x^2 + 189/8x + 45/4 = 0", "output": "x^3 + 77/8x^2 + 189/8x + 45/4 = 0\n(x - -6)(x - -3)(x - -5/8) = 0\nx - -6 = 0\nx - -3 = 0\nx - -5/8 = 0\nx = -6\nx = -3\nx = -5/8"} {"input": "Solve the system:\n8x + 2y = 126/5\n4x + 3y = 53/5", "output": "8x + 2y = 126/5\n4x + 3y = 53/5\n\nUsing elimination\n4*(8x + 2y = 126/5)\n8*(4x + 3y = 53/5)\n32x + 8y = 504/5\n32x + 24y = 424/5\nSubtract equations\n-16y = 16\ny = 16/-16\ny = -1\n\nSubstitute y\n8x + 2(-1) = 126/5\n8x = 136/5\nx = 136/5/8\nx = 17/5"} {"input": "Solve the equations:\n9x + 1y = 227/15\n10x + 3y = 25", "output": "9x + 1y = 227/15\n10x + 3y = 25\n\nUsing elimination\n10*(9x + 1y = 227/15)\n9*(10x + 3y = 25)\n90x + 10y = 454/3\n90x + 27y = 225\nSubtract equations\n-17y = -221/3\ny = -221/3/-17\ny = 13/3\n\nSubstitute y\n9x + 1(13/3) = 227/15\n9x = 54/5\nx = 54/5/9\nx = 6/5"} {"input": "Find x in x^2 + 149/40x + 117/40 = 0", "output": "x^2 + 149/40x + 117/40 = 0\n(x - -9/8)(x - -13/5) = 0\nx - -9/8 = 0 or x - -13/5 = 0\nx = -9/8\nx = -13/5"} {"input": "Find x and y such that\n5x + 2y = -739/63\n6x + 5y = -1087/63", "output": "5x + 2y = -739/63\n6x + 5y = -1087/63\n\nUsing elimination\n6*(5x + 2y = -739/63)\n5*(6x + 5y = -1087/63)\n30x + 12y = -1478/21\n30x + 25y = -5435/63\nSubtract equations\n-13y = 143/9\ny = 143/9/-13\ny = -11/9\n\nSubstitute y\n5x + 2(-11/9) = -739/63\n5x = -65/7\nx = -65/7/5\nx = -13/7"} {"input": "Solve the equations:\n5x + 2y = 209/3\n5x + 3y = 67", "output": "5x + 2y = 209/3\n5x + 3y = 67\n\nUsing elimination\n5*(5x + 2y = 209/3)\n5*(5x + 3y = 67)\n25x + 10y = 1045/3\n25x + 15y = 335\nSubtract equations\n-5y = 40/3\ny = 40/3/-5\ny = -8/3\n\nSubstitute y\n5x + 2(-8/3) = 209/3\n5x = 75\nx = 75/5\nx = 15"} {"input": "Solve the equations:\n3x + 4y = 151/30\n6x + 6y = 37/5", "output": "3x + 4y = 151/30\n6x + 6y = 37/5\n\nUsing elimination\n6*(3x + 4y = 151/30)\n3*(6x + 6y = 37/5)\n18x + 24y = 151/5\n18x + 18y = 111/5\nSubtract equations\n6y = 8\ny = 8/6\ny = 4/3\n\nSubstitute y\n3x + 4(4/3) = 151/30\n3x = -3/10\nx = -3/10/3\nx = -1/10"} {"input": "Compute the solution of 3x + 3 = 0", "output": "3x + 3 = 0\n3x = -3\nx = -3 / 3\nx = -1"} {"input": "Solve the equations:\n8x + 7y = 137/2\n7x + 5y = 103/2", "output": "8x + 7y = 137/2\n7x + 5y = 103/2\n\nUsing elimination\n7*(8x + 7y = 137/2)\n8*(7x + 5y = 103/2)\n56x + 49y = 959/2\n56x + 40y = 412\nSubtract equations\n9y = 135/2\ny = 135/2/9\ny = 15/2\n\nSubstitute y\n8x + 7(15/2) = 137/2\n8x = 16\nx = 16/8\nx = 2"} {"input": "Find x in 6x - 24/5 = 0", "output": "6x - 24/5 = 0\n6x = 24/5\nx = 24/5 / 6\nx = 4/5"} {"input": "Find x and y such that\n1x + 2y = -32/5\n3x + 5y = -177/10", "output": "1x + 2y = -32/5\n3x + 5y = -177/10\n\nUsing elimination\n3*(1x + 2y = -32/5)\n1*(3x + 5y = -177/10)\n3x + 6y = -96/5\n3x + 5y = -177/10\nSubtract equations\n1y = -3/2\ny = -3/2/1\ny = -3/2\n\nSubstitute y\n1x + 2(-3/2) = -32/5\n1x = -17/5\nx = -17/5/1\nx = -17/5"} {"input": "Determine x in 5x - 16 = 0", "output": "5x - 16 = 0\n5x = 16\nx = 16 / 5\nx = 16/5"} {"input": "Solve the system:\n5x + 8y = -31/12\n6x + 3y = 29/2", "output": "5x + 8y = -31/12\n6x + 3y = 29/2\n\nUsing elimination\n6*(5x + 8y = -31/12)\n5*(6x + 3y = 29/2)\n30x + 48y = -31/2\n30x + 15y = 145/2\nSubtract equations\n33y = -88\ny = -88/33\ny = -8/3\n\nSubstitute y\n5x + 8(-8/3) = -31/12\n5x = 75/4\nx = 75/4/5\nx = 15/4"} {"input": "Solve 1x - 16/3 = 0", "output": "1x - 16/3 = 0\n1x = 16/3\nx = 16/3 / 1\nx = 16/3"} {"input": "Find x and y such that\n7x + 8y = 92\n4x + 8y = 80", "output": "7x + 8y = 92\n4x + 8y = 80\n\nUsing elimination\n4*(7x + 8y = 92)\n7*(4x + 8y = 80)\n28x + 32y = 368\n28x + 56y = 560\nSubtract equations\n-24y = -192\ny = -192/-24\ny = 8\n\nSubstitute y\n7x + 8(8) = 92\n7x = 28\nx = 28/7\nx = 4"} {"input": "Find x and y such that\n8x + 5y = -170/9\n1x + 3y = -64/9", "output": "8x + 5y = -170/9\n1x + 3y = -64/9\n\nUsing elimination\n1*(8x + 5y = -170/9)\n8*(1x + 3y = -64/9)\n8x + 5y = -170/9\n8x + 24y = -512/9\nSubtract equations\n-19y = 38\ny = 38/-19\ny = -2\n\nSubstitute y\n8x + 5(-2) = -170/9\n8x = -80/9\nx = -80/9/8\nx = -10/9"} {"input": "Solve simultaneously:\n9x + 8y = 19\n4x + 5y = 7", "output": "9x + 8y = 19\n4x + 5y = 7\n\nUsing elimination\n4*(9x + 8y = 19)\n9*(4x + 5y = 7)\n36x + 32y = 76\n36x + 45y = 63\nSubtract equations\n-13y = 13\ny = 13/-13\ny = -1\n\nSubstitute y\n9x + 8(-1) = 19\n9x = 27\nx = 27/9\nx = 3"} {"input": "Find x in x^2 - 1/6x - 1/3 = 0", "output": "x^2 - 1/6x - 1/3 = 0\n(x - 2/3)(x - -1/2) = 0\nx - 2/3 = 0 or x - -1/2 = 0\nx = 2/3\nx = -1/2"} {"input": "What value of x satisfies 1x - 3/7 = 0", "output": "1x - 3/7 = 0\n1x = 3/7\nx = 3/7 / 1\nx = 3/7"} {"input": "Find x in x^2 + 11/3x - 20/3 = 0", "output": "x^2 + 11/3x - 20/3 = 0\n(x - 4/3)(x - -5) = 0\nx - 4/3 = 0 or x - -5 = 0\nx = 4/3\nx = -5"} {"input": "Solve simultaneously:\n9x + 8y = -51\n10x + 6y = -118/3", "output": "9x + 8y = -51\n10x + 6y = -118/3\n\nUsing elimination\n10*(9x + 8y = -51)\n9*(10x + 6y = -118/3)\n90x + 80y = -510\n90x + 54y = -354\nSubtract equations\n26y = -156\ny = -156/26\ny = -6\n\nSubstitute y\n9x + 8(-6) = -51\n9x = -3\nx = -3/9\nx = -1/3"} {"input": "Find x and y such that\n6x + 8y = 194/7\n8x + 7y = 389/14", "output": "6x + 8y = 194/7\n8x + 7y = 389/14\n\nUsing elimination\n8*(6x + 8y = 194/7)\n6*(8x + 7y = 389/14)\n48x + 64y = 1552/7\n48x + 42y = 1167/7\nSubtract equations\n22y = 55\ny = 55/22\ny = 5/2\n\nSubstitute y\n6x + 8(5/2) = 194/7\n6x = 54/7\nx = 54/7/6\nx = 9/7"} {"input": "Solve the equations:\n1x + 2y = -12\n5x + 3y = -127/2", "output": "1x + 2y = -12\n5x + 3y = -127/2\n\nUsing elimination\n5*(1x + 2y = -12)\n1*(5x + 3y = -127/2)\n5x + 10y = -60\n5x + 3y = -127/2\nSubtract equations\n7y = 7/2\ny = 7/2/7\ny = 1/2\n\nSubstitute y\n1x + 2(1/2) = -12\n1x = -13\nx = -13/1\nx = -13"} {"input": "Solve the equations:\n5x + 7y = -151/6\n8x + 8y = -92/3", "output": "5x + 7y = -151/6\n8x + 8y = -92/3\n\nUsing elimination\n8*(5x + 7y = -151/6)\n5*(8x + 8y = -92/3)\n40x + 56y = -604/3\n40x + 40y = -460/3\nSubtract equations\n16y = -48\ny = -48/16\ny = -3\n\nSubstitute y\n5x + 7(-3) = -151/6\n5x = -25/6\nx = -25/6/5\nx = -5/6"} {"input": "Solve the system:\n1x + 5y = 506/63\n4x + 7y = 122/9", "output": "1x + 5y = 506/63\n4x + 7y = 122/9\n\nUsing elimination\n4*(1x + 5y = 506/63)\n1*(4x + 7y = 122/9)\n4x + 20y = 2024/63\n4x + 7y = 122/9\nSubtract equations\n13y = 130/7\ny = 130/7/13\ny = 10/7\n\nSubstitute y\n1x + 5(10/7) = 506/63\n1x = 8/9\nx = 8/9/1\nx = 8/9"} {"input": "Find the solution to x^3 - 11/10x^2 - 2x + 114/125 = 0", "output": "x^3 - 11/10x^2 - 2x + 114/125 = 0\n(x - 2/5)(x - -6/5)(x - 19/10) = 0\nx - 2/5 = 0\nx - -6/5 = 0\nx - 19/10 = 0\nx = 2/5\nx = -6/5\nx = 19/10"} {"input": "Compute the solution of x^2 + 20/63x - 1/21 = 0", "output": "x^2 + 20/63x - 1/21 = 0\n(x - -3/7)(x - 1/9) = 0\nx - -3/7 = 0 or x - 1/9 = 0\nx = -3/7\nx = 1/9"} {"input": "Solve x^3 + 271/60x^2 + 16/3x + 16/15 = 0", "output": "x^3 + 271/60x^2 + 16/3x + 16/15 = 0\n(x - -8/3)(x - -8/5)(x - -1/4) = 0\nx - -8/3 = 0\nx - -8/5 = 0\nx - -1/4 = 0\nx = -8/3\nx = -8/5\nx = -1/4"} {"input": "Determine x in 8x - 24 = 0", "output": "8x - 24 = 0\n8x = 24\nx = 24 / 8\nx = 3"} {"input": "Find x and y such that\n1x + 1y = 4\n8x + 5y = 26", "output": "1x + 1y = 4\n8x + 5y = 26\n\nUsing elimination\n8*(1x + 1y = 4)\n1*(8x + 5y = 26)\n8x + 8y = 32\n8x + 5y = 26\nSubtract equations\n3y = 6\ny = 6/3\ny = 2\n\nSubstitute y\n1x + 1(2) = 4\n1x = 2\nx = 2/1\nx = 2"} {"input": "Determine x in x^3 + 23/9x^2 - 40/9x - 28/3 = 0", "output": "x^3 + 23/9x^2 - 40/9x - 28/3 = 0\n(x - -3)(x - -14/9)(x - 2) = 0\nx - -3 = 0\nx - -14/9 = 0\nx - 2 = 0\nx = -3\nx = -14/9\nx = 2"} {"input": "Solve quickly: x^2 + 37/12x - 12 = 0", "output": "x^2 + 37/12x - 12 = 0\n(x - 9/4)(x - -16/3) = 0\nx - 9/4 = 0 or x - -16/3 = 0\nx = 9/4\nx = -16/3"} {"input": "Solve the equation x^2 + 63/4x - 4 = 0", "output": "x^2 + 63/4x - 4 = 0\n(x - 1/4)(x - -16) = 0\nx - 1/4 = 0 or x - -16 = 0\nx = 1/4\nx = -16"} {"input": "Determine x in x^2 + 7x + 68/9 = 0", "output": "x^2 + 7x + 68/9 = 0\n(x - -17/3)(x - -4/3) = 0\nx - -17/3 = 0 or x - -4/3 = 0\nx = -17/3\nx = -4/3"} {"input": "Solve quickly: x^2 + 31/5x + 6/5 = 0", "output": "x^2 + 31/5x + 6/5 = 0\n(x - -1/5)(x - -6) = 0\nx - -1/5 = 0 or x - -6 = 0\nx = -1/5\nx = -6"} {"input": "Solve the equation x^2 + 51/40x - 27/10 = 0", "output": "x^2 + 51/40x - 27/10 = 0\n(x - -12/5)(x - 9/8) = 0\nx - -12/5 = 0 or x - 9/8 = 0\nx = -12/5\nx = 9/8"} {"input": "Compute the solution of x^2 + 104/7x - 15/7 = 0", "output": "x^2 + 104/7x - 15/7 = 0\n(x - 1/7)(x - -15) = 0\nx - 1/7 = 0 or x - -15 = 0\nx = 1/7\nx = -15"} {"input": "Find the solution to x^2 + 125/63x - 68/63 = 0", "output": "x^2 + 125/63x - 68/63 = 0\n(x - -17/7)(x - 4/9) = 0\nx - -17/7 = 0 or x - 4/9 = 0\nx = -17/7\nx = 4/9"} {"input": "Find x for x^2 - 58/3x + 247/3 = 0", "output": "x^2 - 58/3x + 247/3 = 0\n(x - 19/3)(x - 13) = 0\nx - 19/3 = 0 or x - 13 = 0\nx = 19/3\nx = 13"} {"input": "Solve x^2 - 43/15x - 44/15 = 0", "output": "x^2 - 43/15x - 44/15 = 0\n(x - 11/3)(x - -4/5) = 0\nx - 11/3 = 0 or x - -4/5 = 0\nx = 11/3\nx = -4/5"} {"input": "Find x for x^2 - 40/9x + 128/27 = 0", "output": "x^2 - 40/9x + 128/27 = 0\n(x - 16/9)(x - 8/3) = 0\nx - 16/9 = 0 or x - 8/3 = 0\nx = 16/9\nx = 8/3"} {"input": "Solve 8x + 80/3 = 0", "output": "8x + 80/3 = 0\n8x = -80/3\nx = -80/3 / 8\nx = -10/3"} {"input": "Solve simultaneously:\n10x + 9y = -194\n10x + 10y = -580/3", "output": "10x + 9y = -194\n10x + 10y = -580/3\n\nUsing elimination\n10*(10x + 9y = -194)\n10*(10x + 10y = -580/3)\n100x + 90y = -1940\n100x + 100y = -5800/3\nSubtract equations\n-10y = -20/3\ny = -20/3/-10\ny = 2/3\n\nSubstitute y\n10x + 9(2/3) = -194\n10x = -200\nx = -200/10\nx = -20"} {"input": "Solve the equation x^2 - 19/3x = 0", "output": "x^2 - 19/3x = 0\n(x - 0)(x - 19/3) = 0\nx - 0 = 0 or x - 19/3 = 0\nx = 0\nx = 19/3"} {"input": "Find the solution to 8x + 32/3 = 0", "output": "8x + 32/3 = 0\n8x = -32/3\nx = -32/3 / 8\nx = -4/3"} {"input": "Solve simultaneously:\n10x + 9y = -82/3\n4x + 5y = -44/3", "output": "10x + 9y = -82/3\n4x + 5y = -44/3\n\nUsing elimination\n4*(10x + 9y = -82/3)\n10*(4x + 5y = -44/3)\n40x + 36y = -328/3\n40x + 50y = -440/3\nSubtract equations\n-14y = 112/3\ny = 112/3/-14\ny = -8/3\n\nSubstitute y\n10x + 9(-8/3) = -82/3\n10x = -10/3\nx = -10/3/10\nx = -1/3"} {"input": "Compute the solution of 1x - 17/7 = 0", "output": "1x - 17/7 = 0\n1x = 17/7\nx = 17/7 / 1\nx = 17/7"} {"input": "Find x in x^2 + 173/9x - 140/9 = 0", "output": "x^2 + 173/9x - 140/9 = 0\n(x - 7/9)(x - -20) = 0\nx - 7/9 = 0 or x - -20 = 0\nx = 7/9\nx = -20"} {"input": "Solve x^2 - 7/4x + 3/8 = 0", "output": "x^2 - 7/4x + 3/8 = 0\n(x - 3/2)(x - 1/4) = 0\nx - 3/2 = 0 or x - 1/4 = 0\nx = 3/2\nx = 1/4"} {"input": "Solve the system:\n5x + 8y = 37\n3x + 6y = 24", "output": "5x + 8y = 37\n3x + 6y = 24\n\nUsing elimination\n3*(5x + 8y = 37)\n5*(3x + 6y = 24)\n15x + 24y = 111\n15x + 30y = 120\nSubtract equations\n-6y = -9\ny = -9/-6\ny = 3/2\n\nSubstitute y\n5x + 8(3/2) = 37\n5x = 25\nx = 25/5\nx = 5"} {"input": "Solve the equation x^2 + 87/8x - 11/8 = 0", "output": "x^2 + 87/8x - 11/8 = 0\n(x - -11)(x - 1/8) = 0\nx - -11 = 0 or x - 1/8 = 0\nx = -11\nx = 1/8"} {"input": "Find x and y such that\n6x + 5y = -51/7\n6x + 4y = -52/7", "output": "6x + 5y = -51/7\n6x + 4y = -52/7\n\nUsing elimination\n6*(6x + 5y = -51/7)\n6*(6x + 4y = -52/7)\n36x + 30y = -306/7\n36x + 24y = -312/7\nSubtract equations\n6y = 6/7\ny = 6/7/6\ny = 1/7\n\nSubstitute y\n6x + 5(1/7) = -51/7\n6x = -8\nx = -8/6\nx = -4/3"} {"input": "Solve quickly: 7x - 133/4 = 0", "output": "7x - 133/4 = 0\n7x = 133/4\nx = 133/4 / 7\nx = 19/4"} {"input": "What value of x satisfies 1x + 6/7 = 0", "output": "1x + 6/7 = 0\n1x = -6/7\nx = -6/7 / 1\nx = -6/7"} {"input": "Find the solution to x^2 - 69/20x - 17/5 = 0", "output": "x^2 - 69/20x - 17/5 = 0\n(x - -4/5)(x - 17/4) = 0\nx - -4/5 = 0 or x - 17/4 = 0\nx = -4/5\nx = 17/4"} {"input": "Find x and y such that\n2x + 6y = 2/35\n1x + 10y = 281/35", "output": "2x + 6y = 2/35\n1x + 10y = 281/35\n\nUsing elimination\n1*(2x + 6y = 2/35)\n2*(1x + 10y = 281/35)\n2x + 6y = 2/35\n2x + 20y = 562/35\nSubtract equations\n-14y = -16\ny = -16/-14\ny = 8/7\n\nSubstitute y\n2x + 6(8/7) = 2/35\n2x = -34/5\nx = -34/5/2\nx = -17/5"} {"input": "Determine x in 2x - 6 = 0", "output": "2x - 6 = 0\n2x = 6\nx = 6 / 2\nx = 3"} {"input": "Find the solution to 2x + 30/7 = 0", "output": "2x + 30/7 = 0\n2x = -30/7\nx = -30/7 / 2\nx = -15/7"} {"input": "Find x and y such that\n6x + 4y = 4\n1x + 8y = -7/6", "output": "6x + 4y = 4\n1x + 8y = -7/6\n\nUsing elimination\n1*(6x + 4y = 4)\n6*(1x + 8y = -7/6)\n6x + 4y = 4\n6x + 48y = -7\nSubtract equations\n-44y = 11\ny = 11/-44\ny = -1/4\n\nSubstitute y\n6x + 4(-1/4) = 4\n6x = 5\nx = 5/6\nx = 5/6"} {"input": "Solve the system:\n3x + 4y = 19/3\n6x + 1y = 52/3", "output": "3x + 4y = 19/3\n6x + 1y = 52/3\n\nUsing elimination\n6*(3x + 4y = 19/3)\n3*(6x + 1y = 52/3)\n18x + 24y = 38\n18x + 3y = 52\nSubtract equations\n21y = -14\ny = -14/21\ny = -2/3\n\nSubstitute y\n3x + 4(-2/3) = 19/3\n3x = 9\nx = 9/3\nx = 3"} {"input": "Determine x in x^3 - 917/45x^2 + 1199/45x - 133/15 = 0", "output": "x^3 - 917/45x^2 + 1199/45x - 133/15 = 0\n(x - 7/9)(x - 19)(x - 3/5) = 0\nx - 7/9 = 0\nx - 19 = 0\nx - 3/5 = 0\nx = 7/9\nx = 19\nx = 3/5"} {"input": "What value of x satisfies x^2 + 68/35x + 32/35 = 0", "output": "x^2 + 68/35x + 32/35 = 0\n(x - -8/7)(x - -4/5) = 0\nx - -8/7 = 0 or x - -4/5 = 0\nx = -8/7\nx = -4/5"} {"input": "Solve x^3 + 4/3x^2 - 20/3x = 0", "output": "x^3 + 4/3x^2 - 20/3x = 0\n(x - 0)(x - 2)(x - -10/3) = 0\nx - 0 = 0\nx - 2 = 0\nx - -10/3 = 0\nx = 0\nx = 2\nx = -10/3"} {"input": "What value of x satisfies x^3 - 97/30x^2 - 73/30x + 7 = 0", "output": "x^3 - 97/30x^2 - 73/30x + 7 = 0\n(x - 10/3)(x - 7/5)(x - -3/2) = 0\nx - 10/3 = 0\nx - 7/5 = 0\nx - -3/2 = 0\nx = 10/3\nx = 7/5\nx = -3/2"} {"input": "Solve the system:\n6x + 1y = 3/2\n4x + 6y = 9", "output": "6x + 1y = 3/2\n4x + 6y = 9\n\nUsing elimination\n4*(6x + 1y = 3/2)\n6*(4x + 6y = 9)\n24x + 4y = 6\n24x + 36y = 54\nSubtract equations\n-32y = -48\ny = -48/-32\ny = 3/2\n\nSubstitute y\n6x + 1(3/2) = 3/2\n6x = 0\nx = 0/6\nx = 0"} {"input": "Solve simultaneously:\n1x + 7y = 59/3\n7x + 7y = 161/3", "output": "1x + 7y = 59/3\n7x + 7y = 161/3\n\nUsing elimination\n7*(1x + 7y = 59/3)\n1*(7x + 7y = 161/3)\n7x + 49y = 413/3\n7x + 7y = 161/3\nSubtract equations\n42y = 84\ny = 84/42\ny = 2\n\nSubstitute y\n1x + 7(2) = 59/3\n1x = 17/3\nx = 17/3/1\nx = 17/3"} {"input": "Find x and y such that\n6x + 2y = 82/15\n3x + 4y = 194/15", "output": "6x + 2y = 82/15\n3x + 4y = 194/15\n\nUsing elimination\n3*(6x + 2y = 82/15)\n6*(3x + 4y = 194/15)\n18x + 6y = 82/5\n18x + 24y = 388/5\nSubtract equations\n-18y = -306/5\ny = -306/5/-18\ny = 17/5\n\nSubstitute y\n6x + 2(17/5) = 82/15\n6x = -4/3\nx = -4/3/6\nx = -2/9"} {"input": "Solve quickly: 1x - 7/10 = 0", "output": "1x - 7/10 = 0\n1x = 7/10\nx = 7/10 / 1\nx = 7/10"} {"input": "Solve 4x + 56/5 = 0", "output": "4x + 56/5 = 0\n4x = -56/5\nx = -56/5 / 4\nx = -14/5"} {"input": "Solve the equation 2x - 16/5 = 0", "output": "2x - 16/5 = 0\n2x = 16/5\nx = 16/5 / 2\nx = 8/5"} {"input": "Compute the solution of x^2 - 17/4x - 15/4 = 0", "output": "x^2 - 17/4x - 15/4 = 0\n(x - 5)(x - -3/4) = 0\nx - 5 = 0 or x - -3/4 = 0\nx = 5\nx = -3/4"} {"input": "Determine x in 1x + 6 = 0", "output": "1x + 6 = 0\n1x = -6\nx = -6 / 1\nx = -6"} {"input": "Find the solution to x^3 + 83/7x^2 - 116/7x - 156/7 = 0", "output": "x^3 + 83/7x^2 - 116/7x - 156/7 = 0\n(x - 2)(x - -6/7)(x - -13) = 0\nx - 2 = 0\nx - -6/7 = 0\nx - -13 = 0\nx = 2\nx = -6/7\nx = -13"} {"input": "Solve simultaneously:\n8x + 10y = -70/3\n5x + 6y = -43/3", "output": "8x + 10y = -70/3\n5x + 6y = -43/3\n\nUsing elimination\n5*(8x + 10y = -70/3)\n8*(5x + 6y = -43/3)\n40x + 50y = -350/3\n40x + 48y = -344/3\nSubtract equations\n2y = -2\ny = -2/2\ny = -1\n\nSubstitute y\n8x + 10(-1) = -70/3\n8x = -40/3\nx = -40/3/8\nx = -5/3"} {"input": "Find x in x^3 - 4x^2 - 35/4x + 75/4 = 0", "output": "x^3 - 4x^2 - 35/4x + 75/4 = 0\n(x - 3/2)(x - -5/2)(x - 5) = 0\nx - 3/2 = 0\nx - -5/2 = 0\nx - 5 = 0\nx = 3/2\nx = -5/2\nx = 5"} {"input": "Determine x in x^3 - 583/56x^2 - 135/7x + 18/7 = 0", "output": "x^3 - 583/56x^2 - 135/7x + 18/7 = 0\n(x - 12)(x - -12/7)(x - 1/8) = 0\nx - 12 = 0\nx - -12/7 = 0\nx - 1/8 = 0\nx = 12\nx = -12/7\nx = 1/8"} {"input": "Solve 5x - 8 = 0", "output": "5x - 8 = 0\n5x = 8\nx = 8 / 5\nx = 8/5"} {"input": "Determine x in 2x + 2/3 = 0", "output": "2x + 2/3 = 0\n2x = -2/3\nx = -2/3 / 2\nx = -1/3"} {"input": "Solve quickly: x^2 - 24/7x + 80/49 = 0", "output": "x^2 - 24/7x + 80/49 = 0\n(x - 4/7)(x - 20/7) = 0\nx - 4/7 = 0 or x - 20/7 = 0\nx = 4/7\nx = 20/7"} {"input": "Solve the equation x^3 - 7x^2 - 35/4x + 75/2 = 0", "output": "x^3 - 7x^2 - 35/4x + 75/2 = 0\n(x - -5/2)(x - 2)(x - 15/2) = 0\nx - -5/2 = 0\nx - 2 = 0\nx - 15/2 = 0\nx = -5/2\nx = 2\nx = 15/2"} {"input": "Find the solution to x^3 - 8x^2 + 17x - 10 = 0", "output": "x^3 - 8x^2 + 17x - 10 = 0\n(x - 1)(x - 2)(x - 5) = 0\nx - 1 = 0\nx - 2 = 0\nx - 5 = 0\nx = 1\nx = 2\nx = 5"} {"input": "Solve 9x + 21/2 = 0", "output": "9x + 21/2 = 0\n9x = -21/2\nx = -21/2 / 9\nx = -7/6"} {"input": "Solve simultaneously:\n9x + 1y = 19/2\n1x + 4y = 53/6", "output": "9x + 1y = 19/2\n1x + 4y = 53/6\n\nUsing elimination\n1*(9x + 1y = 19/2)\n9*(1x + 4y = 53/6)\n9x + 1y = 19/2\n9x + 36y = 159/2\nSubtract equations\n-35y = -70\ny = -70/-35\ny = 2\n\nSubstitute y\n9x + 1(2) = 19/2\n9x = 15/2\nx = 15/2/9\nx = 5/6"} {"input": "Find x in x^2 + 24/5x + 128/25 = 0", "output": "x^2 + 24/5x + 128/25 = 0\n(x - -8/5)(x - -16/5) = 0\nx - -8/5 = 0 or x - -16/5 = 0\nx = -8/5\nx = -16/5"} {"input": "Find x and y such that\n5x + 8y = 931/15\n6x + 5y = 57", "output": "5x + 8y = 931/15\n6x + 5y = 57\n\nUsing elimination\n6*(5x + 8y = 931/15)\n5*(6x + 5y = 57)\n30x + 48y = 1862/5\n30x + 25y = 285\nSubtract equations\n23y = 437/5\ny = 437/5/23\ny = 19/5\n\nSubstitute y\n5x + 8(19/5) = 931/15\n5x = 95/3\nx = 95/3/5\nx = 19/3"} {"input": "Solve the equations:\n9x + 5y = 570/7\n4x + 9y = 172/7", "output": "9x + 5y = 570/7\n4x + 9y = 172/7\n\nUsing elimination\n4*(9x + 5y = 570/7)\n9*(4x + 9y = 172/7)\n36x + 20y = 2280/7\n36x + 81y = 1548/7\nSubtract equations\n-61y = 732/7\ny = 732/7/-61\ny = -12/7\n\nSubstitute y\n9x + 5(-12/7) = 570/7\n9x = 90\nx = 90/9\nx = 10"} {"input": "Solve simultaneously:\n1x + 3y = 23/10\n8x + 4y = 282/5", "output": "1x + 3y = 23/10\n8x + 4y = 282/5\n\nUsing elimination\n8*(1x + 3y = 23/10)\n1*(8x + 4y = 282/5)\n8x + 24y = 92/5\n8x + 4y = 282/5\nSubtract equations\n20y = -38\ny = -38/20\ny = -19/10\n\nSubstitute y\n1x + 3(-19/10) = 23/10\n1x = 8\nx = 8/1\nx = 8"} {"input": "Find the solution to 5x - 11 = 0", "output": "5x - 11 = 0\n5x = 11\nx = 11 / 5\nx = 11/5"} {"input": "Solve 6x + 4 = 0", "output": "6x + 4 = 0\n6x = -4\nx = -4 / 6\nx = -2/3"} {"input": "Find x and y such that\n6x + 9y = 261/20\n4x + 4y = 41/5", "output": "6x + 9y = 261/20\n4x + 4y = 41/5\n\nUsing elimination\n4*(6x + 9y = 261/20)\n6*(4x + 4y = 41/5)\n24x + 36y = 261/5\n24x + 24y = 246/5\nSubtract equations\n12y = 3\ny = 3/12\ny = 1/4\n\nSubstitute y\n6x + 9(1/4) = 261/20\n6x = 54/5\nx = 54/5/6\nx = 9/5"} {"input": "Solve the equations:\n10x + 7y = 9/2\n3x + 9y = -9", "output": "10x + 7y = 9/2\n3x + 9y = -9\n\nUsing elimination\n3*(10x + 7y = 9/2)\n10*(3x + 9y = -9)\n30x + 21y = 27/2\n30x + 90y = -90\nSubtract equations\n-69y = 207/2\ny = 207/2/-69\ny = -3/2\n\nSubstitute y\n10x + 7(-3/2) = 9/2\n10x = 15\nx = 15/10\nx = 3/2"} {"input": "Find x for x^3 - 1/2x^2 - 255x + 1404 = 0", "output": "x^3 - 1/2x^2 - 255x + 1404 = 0\n(x - -18)(x - 13/2)(x - 12) = 0\nx - -18 = 0\nx - 13/2 = 0\nx - 12 = 0\nx = -18\nx = 13/2\nx = 12"} {"input": "Compute the solution of 7x - 21/2 = 0", "output": "7x - 21/2 = 0\n7x = 21/2\nx = 21/2 / 7\nx = 3/2"} {"input": "Solve x^3 - 10/7x^2 - 397/175x - 68/175 = 0", "output": "x^3 - 10/7x^2 - 397/175x - 68/175 = 0\n(x - -1/5)(x - 17/7)(x - -4/5) = 0\nx - -1/5 = 0\nx - 17/7 = 0\nx - -4/5 = 0\nx = -1/5\nx = 17/7\nx = -4/5"} {"input": "Solve the system:\n9x + 9y = -261/10\n6x + 5y = -31/2", "output": "9x + 9y = -261/10\n6x + 5y = -31/2\n\nUsing elimination\n6*(9x + 9y = -261/10)\n9*(6x + 5y = -31/2)\n54x + 54y = -783/5\n54x + 45y = -279/2\nSubtract equations\n9y = -171/10\ny = -171/10/9\ny = -19/10\n\nSubstitute y\n9x + 9(-19/10) = -261/10\n9x = -9\nx = -9/9\nx = -1"} {"input": "Solve the equations:\n7x + 5y = 149/14\n6x + 1y = 31/7", "output": "7x + 5y = 149/14\n6x + 1y = 31/7\n\nUsing elimination\n6*(7x + 5y = 149/14)\n7*(6x + 1y = 31/7)\n42x + 30y = 447/7\n42x + 7y = 31\nSubtract equations\n23y = 230/7\ny = 230/7/23\ny = 10/7\n\nSubstitute y\n7x + 5(10/7) = 149/14\n7x = 7/2\nx = 7/2/7\nx = 1/2"} {"input": "Find x and y such that\n4x + 8y = -16/7\n10x + 3y = 232/7", "output": "4x + 8y = -16/7\n10x + 3y = 232/7\n\nUsing elimination\n10*(4x + 8y = -16/7)\n4*(10x + 3y = 232/7)\n40x + 80y = -160/7\n40x + 12y = 928/7\nSubtract equations\n68y = -1088/7\ny = -1088/7/68\ny = -16/7\n\nSubstitute y\n4x + 8(-16/7) = -16/7\n4x = 16\nx = 16/4\nx = 4"} {"input": "Solve the equations:\n5x + 10y = -7\n3x + 2y = 19/5", "output": "5x + 10y = -7\n3x + 2y = 19/5\n\nUsing elimination\n3*(5x + 10y = -7)\n5*(3x + 2y = 19/5)\n15x + 30y = -21\n15x + 10y = 19\nSubtract equations\n20y = -40\ny = -40/20\ny = -2\n\nSubstitute y\n5x + 10(-2) = -7\n5x = 13\nx = 13/5\nx = 13/5"} {"input": "Solve x^2 + 18/7x = 0", "output": "x^2 + 18/7x = 0\n(x - 0)(x - -18/7) = 0\nx - 0 = 0 or x - -18/7 = 0\nx = 0\nx = -18/7"} {"input": "Solve the equations:\n7x + 3y = -23/8\n5x + 7y = -133/8", "output": "7x + 3y = -23/8\n5x + 7y = -133/8\n\nUsing elimination\n5*(7x + 3y = -23/8)\n7*(5x + 7y = -133/8)\n35x + 15y = -115/8\n35x + 49y = -931/8\nSubtract equations\n-34y = 102\ny = 102/-34\ny = -3\n\nSubstitute y\n7x + 3(-3) = -23/8\n7x = 49/8\nx = 49/8/7\nx = 7/8"} {"input": "Solve quickly: x^3 + 5/18x^2 - 28/9x + 2/3 = 0", "output": "x^3 + 5/18x^2 - 28/9x + 2/3 = 0\n(x - 2/9)(x - -2)(x - 3/2) = 0\nx - 2/9 = 0\nx - -2 = 0\nx - 3/2 = 0\nx = 2/9\nx = -2\nx = 3/2"} {"input": "Solve quickly: 9x + 180/7 = 0", "output": "9x + 180/7 = 0\n9x = -180/7\nx = -180/7 / 9\nx = -20/7"} {"input": "Find x for x^3 - 129/40x^2 + 1107/400x - 119/400 = 0", "output": "x^3 - 129/40x^2 + 1107/400x - 119/400 = 0\n(x - 17/10)(x - 1/8)(x - 7/5) = 0\nx - 17/10 = 0\nx - 1/8 = 0\nx - 7/5 = 0\nx = 17/10\nx = 1/8\nx = 7/5"} {"input": "What value of x satisfies x^2 + 41/6x - 76/3 = 0", "output": "x^2 + 41/6x - 76/3 = 0\n(x - -19/2)(x - 8/3) = 0\nx - -19/2 = 0 or x - 8/3 = 0\nx = -19/2\nx = 8/3"} {"input": "Solve the system:\n3x + 10y = -12\n1x + 4y = -68/15", "output": "3x + 10y = -12\n1x + 4y = -68/15\n\nUsing elimination\n1*(3x + 10y = -12)\n3*(1x + 4y = -68/15)\n3x + 10y = -12\n3x + 12y = -68/5\nSubtract equations\n-2y = 8/5\ny = 8/5/-2\ny = -4/5\n\nSubstitute y\n3x + 10(-4/5) = -12\n3x = -4\nx = -4/3\nx = -4/3"} {"input": "Solve the equations:\n1x + 6y = 113/8\n10x + 1y = 17/2", "output": "1x + 6y = 113/8\n10x + 1y = 17/2\n\nUsing elimination\n10*(1x + 6y = 113/8)\n1*(10x + 1y = 17/2)\n10x + 60y = 565/4\n10x + 1y = 17/2\nSubtract equations\n59y = 531/4\ny = 531/4/59\ny = 9/4\n\nSubstitute y\n1x + 6(9/4) = 113/8\n1x = 5/8\nx = 5/8/1\nx = 5/8"} {"input": "Find the solution to x^3 - 6x^2 + 8x = 0", "output": "x^3 - 6x^2 + 8x = 0\n(x - 0)(x - 2)(x - 4) = 0\nx - 0 = 0\nx - 2 = 0\nx - 4 = 0\nx = 0\nx = 2\nx = 4"} {"input": "Compute the solution of x^2 - 177/10x + 136/5 = 0", "output": "x^2 - 177/10x + 136/5 = 0\n(x - 16)(x - 17/10) = 0\nx - 16 = 0 or x - 17/10 = 0\nx = 16\nx = 17/10"} {"input": "Solve the equations:\n10x + 9y = 19/2\n6x + 6y = 27/5", "output": "10x + 9y = 19/2\n6x + 6y = 27/5\n\nUsing elimination\n6*(10x + 9y = 19/2)\n10*(6x + 6y = 27/5)\n60x + 54y = 57\n60x + 60y = 54\nSubtract equations\n-6y = 3\ny = 3/-6\ny = -1/2\n\nSubstitute y\n10x + 9(-1/2) = 19/2\n10x = 14\nx = 14/10\nx = 7/5"} {"input": "Solve simultaneously:\n5x + 8y = -92/7\n1x + 2y = -89/28", "output": "5x + 8y = -92/7\n1x + 2y = -89/28\n\nUsing elimination\n1*(5x + 8y = -92/7)\n5*(1x + 2y = -89/28)\n5x + 8y = -92/7\n5x + 10y = -445/28\nSubtract equations\n-2y = 11/4\ny = 11/4/-2\ny = -11/8\n\nSubstitute y\n5x + 8(-11/8) = -92/7\n5x = -15/7\nx = -15/7/5\nx = -3/7"} {"input": "Solve the system:\n6x + 1y = 66\n4x + 5y = 70", "output": "6x + 1y = 66\n4x + 5y = 70\n\nUsing elimination\n4*(6x + 1y = 66)\n6*(4x + 5y = 70)\n24x + 4y = 264\n24x + 30y = 420\nSubtract equations\n-26y = -156\ny = -156/-26\ny = 6\n\nSubstitute y\n6x + 1(6) = 66\n6x = 60\nx = 60/6\nx = 10"} {"input": "What value of x satisfies x^3 - 63/10x^2 - 11/2x + 21/5 = 0", "output": "x^3 - 63/10x^2 - 11/2x + 21/5 = 0\n(x - 1/2)(x - -6/5)(x - 7) = 0\nx - 1/2 = 0\nx - -6/5 = 0\nx - 7 = 0\nx = 1/2\nx = -6/5\nx = 7"} {"input": "Determine x in x^3 + 127/168x^2 - 103/24x + 15/7 = 0", "output": "x^3 + 127/168x^2 - 103/24x + 15/7 = 0\n(x - 9/7)(x - -8/3)(x - 5/8) = 0\nx - 9/7 = 0\nx - -8/3 = 0\nx - 5/8 = 0\nx = 9/7\nx = -8/3\nx = 5/8"} {"input": "Determine x in x^2 - 19/5x + 84/25 = 0", "output": "x^2 - 19/5x + 84/25 = 0\n(x - 12/5)(x - 7/5) = 0\nx - 12/5 = 0 or x - 7/5 = 0\nx = 12/5\nx = 7/5"} {"input": "Solve the equation 3x - 24 = 0", "output": "3x - 24 = 0\n3x = 24\nx = 24 / 3\nx = 8"} {"input": "Solve the equation x^3 + 24/7x^2 + 101/49x - 78/49 = 0", "output": "x^3 + 24/7x^2 + 101/49x - 78/49 = 0\n(x - 3/7)(x - -13/7)(x - -2) = 0\nx - 3/7 = 0\nx - -13/7 = 0\nx - -2 = 0\nx = 3/7\nx = -13/7\nx = -2"} {"input": "Solve the equation x^2 - 43/10x + 39/10 = 0", "output": "x^2 - 43/10x + 39/10 = 0\n(x - 13/10)(x - 3) = 0\nx - 13/10 = 0 or x - 3 = 0\nx = 13/10\nx = 3"} {"input": "Compute the solution of x^3 + 601/42x^2 - 79/3x + 80/7 = 0", "output": "x^3 + 601/42x^2 - 79/3x + 80/7 = 0\n(x - 6/7)(x - -16)(x - 5/6) = 0\nx - 6/7 = 0\nx - -16 = 0\nx - 5/6 = 0\nx = 6/7\nx = -16\nx = 5/6"} {"input": "Find the solution to 3x - 42 = 0", "output": "3x - 42 = 0\n3x = 42\nx = 42 / 3\nx = 14"} {"input": "Find x and y such that\n2x + 8y = 141/2\n6x + 3y = 45/2", "output": "2x + 8y = 141/2\n6x + 3y = 45/2\n\nUsing elimination\n6*(2x + 8y = 141/2)\n2*(6x + 3y = 45/2)\n12x + 48y = 423\n12x + 6y = 45\nSubtract equations\n42y = 378\ny = 378/42\ny = 9\n\nSubstitute y\n2x + 8(9) = 141/2\n2x = -3/2\nx = -3/2/2\nx = -3/4"} {"input": "Solve simultaneously:\n1x + 10y = -787/12\n6x + 1y = -119/6", "output": "1x + 10y = -787/12\n6x + 1y = -119/6\n\nUsing elimination\n6*(1x + 10y = -787/12)\n1*(6x + 1y = -119/6)\n6x + 60y = -787/2\n6x + 1y = -119/6\nSubtract equations\n59y = -1121/3\ny = -1121/3/59\ny = -19/3\n\nSubstitute y\n1x + 10(-19/3) = -787/12\n1x = -9/4\nx = -9/4/1\nx = -9/4"} {"input": "Find x and y such that\n4x + 6y = -32/5\n10x + 4y = -16", "output": "4x + 6y = -32/5\n10x + 4y = -16\n\nUsing elimination\n10*(4x + 6y = -32/5)\n4*(10x + 4y = -16)\n40x + 60y = -64\n40x + 16y = -64\nSubtract equations\n44y = 0\ny = 0/44\ny = 0\n\nSubstitute y\n4x + 6(0) = -32/5\n4x = -32/5\nx = -32/5/4\nx = -8/5"} {"input": "What value of x satisfies x^3 + 1/2x^2 - 18x + 45/2 = 0", "output": "x^3 + 1/2x^2 - 18x + 45/2 = 0\n(x - -5)(x - 3)(x - 3/2) = 0\nx - -5 = 0\nx - 3 = 0\nx - 3/2 = 0\nx = -5\nx = 3\nx = 3/2"} {"input": "Solve x^3 - 38/9x^2 - 121/12x + 605/36 = 0", "output": "x^3 - 38/9x^2 - 121/12x + 605/36 = 0\n(x - 11/2)(x - 11/9)(x - -5/2) = 0\nx - 11/2 = 0\nx - 11/9 = 0\nx - -5/2 = 0\nx = 11/2\nx = 11/9\nx = -5/2"} {"input": "Determine x in 6x - 18/5 = 0", "output": "6x - 18/5 = 0\n6x = 18/5\nx = 18/5 / 6\nx = 3/5"} {"input": "Determine x in x^2 - 223/56x + 45/14 = 0", "output": "x^2 - 223/56x + 45/14 = 0\n(x - 20/7)(x - 9/8) = 0\nx - 20/7 = 0 or x - 9/8 = 0\nx = 20/7\nx = 9/8"} {"input": "Determine x in x^2 - 33/8x - 121/16 = 0", "output": "x^2 - 33/8x - 121/16 = 0\n(x - -11/8)(x - 11/2) = 0\nx - -11/8 = 0 or x - 11/2 = 0\nx = -11/8\nx = 11/2"} {"input": "Compute the solution of x^3 - 484/45x^2 + 247/15x - 6 = 0", "output": "x^3 - 484/45x^2 + 247/15x - 6 = 0\n(x - 5/9)(x - 9)(x - 6/5) = 0\nx - 5/9 = 0\nx - 9 = 0\nx - 6/5 = 0\nx = 5/9\nx = 9\nx = 6/5"} {"input": "Determine x in x^3 + 53/5x^2 + 337/20x - 17/2 = 0", "output": "x^3 + 53/5x^2 + 337/20x - 17/2 = 0\n(x - 2/5)(x - -5/2)(x - -17/2) = 0\nx - 2/5 = 0\nx - -5/2 = 0\nx - -17/2 = 0\nx = 2/5\nx = -5/2\nx = -17/2"} {"input": "Find x and y such that\n10x + 8y = 544/9\n2x + 4y = 92/9", "output": "10x + 8y = 544/9\n2x + 4y = 92/9\n\nUsing elimination\n2*(10x + 8y = 544/9)\n10*(2x + 4y = 92/9)\n20x + 16y = 1088/9\n20x + 40y = 920/9\nSubtract equations\n-24y = 56/3\ny = 56/3/-24\ny = -7/9\n\nSubstitute y\n10x + 8(-7/9) = 544/9\n10x = 200/3\nx = 200/3/10\nx = 20/3"} {"input": "Find x in x^3 - 59/30x^2 + 53/150x + 28/75 = 0", "output": "x^3 - 59/30x^2 + 53/150x + 28/75 = 0\n(x - 8/5)(x - -1/3)(x - 7/10) = 0\nx - 8/5 = 0\nx - -1/3 = 0\nx - 7/10 = 0\nx = 8/5\nx = -1/3\nx = 7/10"} {"input": "What value of x satisfies x^3 - 5/28x^2 - 1997/448x + 855/224 = 0", "output": "x^3 - 5/28x^2 - 1997/448x + 855/224 = 0\n(x - 10/7)(x - 9/8)(x - -19/8) = 0\nx - 10/7 = 0\nx - 9/8 = 0\nx - -19/8 = 0\nx = 10/7\nx = 9/8\nx = -19/8"} {"input": "Solve simultaneously:\n8x + 5y = 53/8\n10x + 5y = 85/8", "output": "8x + 5y = 53/8\n10x + 5y = 85/8\n\nUsing elimination\n10*(8x + 5y = 53/8)\n8*(10x + 5y = 85/8)\n80x + 50y = 265/4\n80x + 40y = 85\nSubtract equations\n10y = -75/4\ny = -75/4/10\ny = -15/8\n\nSubstitute y\n8x + 5(-15/8) = 53/8\n8x = 16\nx = 16/8\nx = 2"} {"input": "Find the solution to x^2 - 3/10x - 7/10 = 0", "output": "x^2 - 3/10x - 7/10 = 0\n(x - -7/10)(x - 1) = 0\nx - -7/10 = 0 or x - 1 = 0\nx = -7/10\nx = 1"} {"input": "Find x and y such that\n9x + 10y = 4\n8x + 5y = 11/2", "output": "9x + 10y = 4\n8x + 5y = 11/2\n\nUsing elimination\n8*(9x + 10y = 4)\n9*(8x + 5y = 11/2)\n72x + 80y = 32\n72x + 45y = 99/2\nSubtract equations\n35y = -35/2\ny = -35/2/35\ny = -1/2\n\nSubstitute y\n9x + 10(-1/2) = 4\n9x = 9\nx = 9/9\nx = 1"} {"input": "Solve x^2 - 11/12x - 121/12 = 0", "output": "x^2 - 11/12x - 121/12 = 0\n(x - 11/3)(x - -11/4) = 0\nx - 11/3 = 0 or x - -11/4 = 0\nx = 11/3\nx = -11/4"} {"input": "Solve quickly: 3x - 33/2 = 0", "output": "3x - 33/2 = 0\n3x = 33/2\nx = 33/2 / 3\nx = 11/2"} {"input": "Find x for x^2 - 8/15x - 16/15 = 0", "output": "x^2 - 8/15x - 16/15 = 0\n(x - 4/3)(x - -4/5) = 0\nx - 4/3 = 0 or x - -4/5 = 0\nx = 4/3\nx = -4/5"} {"input": "Find x and y such that\n9x + 2y = 48/5\n4x + 4y = 164/45", "output": "9x + 2y = 48/5\n4x + 4y = 164/45\n\nUsing elimination\n4*(9x + 2y = 48/5)\n9*(4x + 4y = 164/45)\n36x + 8y = 192/5\n36x + 36y = 164/5\nSubtract equations\n-28y = 28/5\ny = 28/5/-28\ny = -1/5\n\nSubstitute y\n9x + 2(-1/5) = 48/5\n9x = 10\nx = 10/9\nx = 10/9"} {"input": "What value of x satisfies x^2 - 63/10x + 81/10 = 0", "output": "x^2 - 63/10x + 81/10 = 0\n(x - 9/2)(x - 9/5) = 0\nx - 9/2 = 0 or x - 9/5 = 0\nx = 9/2\nx = 9/5"} {"input": "Solve quickly: x^3 - 157/42x^2 - 173/42x - 1 = 0", "output": "x^3 - 157/42x^2 - 173/42x - 1 = 0\n(x - 14/3)(x - -1/2)(x - -3/7) = 0\nx - 14/3 = 0\nx - -1/2 = 0\nx - -3/7 = 0\nx = 14/3\nx = -1/2\nx = -3/7"} {"input": "Find the solution to 3x - 2 = 0", "output": "3x - 2 = 0\n3x = 2\nx = 2 / 3\nx = 2/3"} {"input": "Solve quickly: 7x + 49/6 = 0", "output": "7x + 49/6 = 0\n7x = -49/6\nx = -49/6 / 7\nx = -7/6"} {"input": "Solve quickly: x^2 - 22/5x + 96/25 = 0", "output": "x^2 - 22/5x + 96/25 = 0\n(x - 16/5)(x - 6/5) = 0\nx - 16/5 = 0 or x - 6/5 = 0\nx = 16/5\nx = 6/5"} {"input": "Find the solution to x^2 - 1/24x - 133/24 = 0", "output": "x^2 - 1/24x - 133/24 = 0\n(x - 19/8)(x - -7/3) = 0\nx - 19/8 = 0 or x - -7/3 = 0\nx = 19/8\nx = -7/3"} {"input": "What value of x satisfies x^2 + 11/8x = 0", "output": "x^2 + 11/8x = 0\n(x - 0)(x - -11/8) = 0\nx - 0 = 0 or x - -11/8 = 0\nx = 0\nx = -11/8"} {"input": "Find x in x^3 + 2/9x^2 - 19/36x - 7/36 = 0", "output": "x^3 + 2/9x^2 - 19/36x - 7/36 = 0\n(x - -1/2)(x - 7/9)(x - -1/2) = 0\nx - -1/2 = 0\nx - 7/9 = 0\nx - -1/2 = 0\nx = -1/2\nx = 7/9\nx = -1/2"} {"input": "Find x and y such that\n2x + 2y = -52/9\n7x + 10y = -317/9", "output": "2x + 2y = -52/9\n7x + 10y = -317/9\n\nUsing elimination\n7*(2x + 2y = -52/9)\n2*(7x + 10y = -317/9)\n14x + 14y = -364/9\n14x + 20y = -634/9\nSubtract equations\n-6y = 30\ny = 30/-6\ny = -5\n\nSubstitute y\n2x + 2(-5) = -52/9\n2x = 38/9\nx = 38/9/2\nx = 19/9"} {"input": "What value of x satisfies 4x + 64 = 0", "output": "4x + 64 = 0\n4x = -64\nx = -64 / 4\nx = -16"} {"input": "Solve quickly: 1x + 17 = 0", "output": "1x + 17 = 0\n1x = -17\nx = -17 / 1\nx = -17"} {"input": "Find x in x^3 - 3/5x^2 - 9/5x + 7/5 = 0", "output": "x^3 - 3/5x^2 - 9/5x + 7/5 = 0\n(x - 1)(x - 1)(x - -7/5) = 0\nx - 1 = 0\nx - 1 = 0\nx - -7/5 = 0\nx = 1\nx = 1\nx = -7/5"} {"input": "Find x in 1x + 1/5 = 0", "output": "1x + 1/5 = 0\n1x = -1/5\nx = -1/5 / 1\nx = -1/5"} {"input": "Find the solution to 5x - 14 = 0", "output": "5x - 14 = 0\n5x = 14\nx = 14 / 5\nx = 14/5"} {"input": "Find x in x^3 - 7/2x^2 - 47/2x + 26 = 0", "output": "x^3 - 7/2x^2 - 47/2x + 26 = 0\n(x - -4)(x - 1)(x - 13/2) = 0\nx - -4 = 0\nx - 1 = 0\nx - 13/2 = 0\nx = -4\nx = 1\nx = 13/2"} {"input": "Find x for 3x + 15/7 = 0", "output": "3x + 15/7 = 0\n3x = -15/7\nx = -15/7 / 3\nx = -5/7"} {"input": "Solve simultaneously:\n8x + 4y = -68/3\n1x + 7y = -17/6", "output": "8x + 4y = -68/3\n1x + 7y = -17/6\n\nUsing elimination\n1*(8x + 4y = -68/3)\n8*(1x + 7y = -17/6)\n8x + 4y = -68/3\n8x + 56y = -68/3\nSubtract equations\n-52y = 0\ny = 0/-52\ny = 0\n\nSubstitute y\n8x + 4(0) = -68/3\n8x = -68/3\nx = -68/3/8\nx = -17/6"} {"input": "Compute the solution of x^2 + 13/3x + 4 = 0", "output": "x^2 + 13/3x + 4 = 0\n(x - -3)(x - -4/3) = 0\nx - -3 = 0 or x - -4/3 = 0\nx = -3\nx = -4/3"} {"input": "Find x and y such that\n6x + 2y = -272/15\n2x + 9y = -58/5", "output": "6x + 2y = -272/15\n2x + 9y = -58/5\n\nUsing elimination\n2*(6x + 2y = -272/15)\n6*(2x + 9y = -58/5)\n12x + 4y = -544/15\n12x + 54y = -348/5\nSubtract equations\n-50y = 100/3\ny = 100/3/-50\ny = -2/3\n\nSubstitute y\n6x + 2(-2/3) = -272/15\n6x = -84/5\nx = -84/5/6\nx = -14/5"} {"input": "Solve the system:\n7x + 10y = 235/42\n8x + 3y = -68/21", "output": "7x + 10y = 235/42\n8x + 3y = -68/21\n\nUsing elimination\n8*(7x + 10y = 235/42)\n7*(8x + 3y = -68/21)\n56x + 80y = 940/21\n56x + 21y = -68/3\nSubtract equations\n59y = 472/7\ny = 472/7/59\ny = 8/7\n\nSubstitute y\n7x + 10(8/7) = 235/42\n7x = -35/6\nx = -35/6/7\nx = -5/6"} {"input": "Solve the equation 1x + 1/9 = 0", "output": "1x + 1/9 = 0\n1x = -1/9\nx = -1/9 / 1\nx = -1/9"} {"input": "Find x for x^3 - 121/40x^2 + 197/80x - 21/80 = 0", "output": "x^3 - 121/40x^2 + 197/80x - 21/80 = 0\n(x - 7/5)(x - 1/8)(x - 3/2) = 0\nx - 7/5 = 0\nx - 1/8 = 0\nx - 3/2 = 0\nx = 7/5\nx = 1/8\nx = 3/2"} {"input": "Find the solution to x^3 - 77/36x^2 - 71/72x + 35/12 = 0", "output": "x^3 - 77/36x^2 - 71/72x + 35/12 = 0\n(x - 3/2)(x - -10/9)(x - 7/4) = 0\nx - 3/2 = 0\nx - -10/9 = 0\nx - 7/4 = 0\nx = 3/2\nx = -10/9\nx = 7/4"} {"input": "Solve the system:\n4x + 8y = 4/3\n3x + 2y = -41/3", "output": "4x + 8y = 4/3\n3x + 2y = -41/3\n\nUsing elimination\n3*(4x + 8y = 4/3)\n4*(3x + 2y = -41/3)\n12x + 24y = 4\n12x + 8y = -164/3\nSubtract equations\n16y = 176/3\ny = 176/3/16\ny = 11/3\n\nSubstitute y\n4x + 8(11/3) = 4/3\n4x = -28\nx = -28/4\nx = -7"} {"input": "Find x in 9x + 5 = 0", "output": "9x + 5 = 0\n9x = -5\nx = -5 / 9\nx = -5/9"} {"input": "Compute the solution of x^2 + 39/4x + 19/8 = 0", "output": "x^2 + 39/4x + 19/8 = 0\n(x - -1/4)(x - -19/2) = 0\nx - -1/4 = 0 or x - -19/2 = 0\nx = -1/4\nx = -19/2"} {"input": "Solve quickly: x^2 - 17/12x + 1/2 = 0", "output": "x^2 - 17/12x + 1/2 = 0\n(x - 2/3)(x - 3/4) = 0\nx - 2/3 = 0 or x - 3/4 = 0\nx = 2/3\nx = 3/4"} {"input": "Solve the system:\n4x + 10y = 190/9\n4x + 7y = 187/9", "output": "4x + 10y = 190/9\n4x + 7y = 187/9\n\nUsing elimination\n4*(4x + 10y = 190/9)\n4*(4x + 7y = 187/9)\n16x + 40y = 760/9\n16x + 28y = 748/9\nSubtract equations\n12y = 4/3\ny = 4/3/12\ny = 1/9\n\nSubstitute y\n4x + 10(1/9) = 190/9\n4x = 20\nx = 20/4\nx = 5"} {"input": "Compute the solution of 4x + 76/9 = 0", "output": "4x + 76/9 = 0\n4x = -76/9\nx = -76/9 / 4\nx = -19/9"} {"input": "Find x in 3x + 51/4 = 0", "output": "3x + 51/4 = 0\n3x = -51/4\nx = -51/4 / 3\nx = -17/4"} {"input": "Compute the solution of 1x - 11/2 = 0", "output": "1x - 11/2 = 0\n1x = 11/2\nx = 11/2 / 1\nx = 11/2"} {"input": "Find x in x^3 + 4/35x^2 - 15/49x - 18/245 = 0", "output": "x^3 + 4/35x^2 - 15/49x - 18/245 = 0\n(x - -3/7)(x - 3/5)(x - -2/7) = 0\nx - -3/7 = 0\nx - 3/5 = 0\nx - -2/7 = 0\nx = -3/7\nx = 3/5\nx = -2/7"} {"input": "Determine x in 8x + 3 = 0", "output": "8x + 3 = 0\n8x = -3\nx = -3 / 8\nx = -3/8"} {"input": "Find the solution to x^3 + 247/36x^2 + 91/36x - 95/6 = 0", "output": "x^3 + 247/36x^2 + 91/36x - 95/6 = 0\n(x - 5/4)(x - -6)(x - -19/9) = 0\nx - 5/4 = 0\nx - -6 = 0\nx - -19/9 = 0\nx = 5/4\nx = -6\nx = -19/9"} {"input": "Solve the system:\n6x + 5y = -467/7\n1x + 4y = -366/7", "output": "6x + 5y = -467/7\n1x + 4y = -366/7\n\nUsing elimination\n1*(6x + 5y = -467/7)\n6*(1x + 4y = -366/7)\n6x + 5y = -467/7\n6x + 24y = -2196/7\nSubtract equations\n-19y = 247\ny = 247/-19\ny = -13\n\nSubstitute y\n6x + 5(-13) = -467/7\n6x = -12/7\nx = -12/7/6\nx = -2/7"} {"input": "Solve the equation 9x - 171/4 = 0", "output": "9x - 171/4 = 0\n9x = 171/4\nx = 171/4 / 9\nx = 19/4"} {"input": "Compute the solution of x^2 + 5/4x - 33/8 = 0", "output": "x^2 + 5/4x - 33/8 = 0\n(x - 3/2)(x - -11/4) = 0\nx - 3/2 = 0 or x - -11/4 = 0\nx = 3/2\nx = -11/4"} {"input": "Compute the solution of x^3 + 13/3x^2 + 50/81x - 2200/243 = 0", "output": "x^3 + 13/3x^2 + 50/81x - 2200/243 = 0\n(x - 11/9)(x - -10/3)(x - -20/9) = 0\nx - 11/9 = 0\nx - -10/3 = 0\nx - -20/9 = 0\nx = 11/9\nx = -10/3\nx = -20/9"} {"input": "Determine x in x^2 - 13/2x - 17 = 0", "output": "x^2 - 13/2x - 17 = 0\n(x - 17/2)(x - -2) = 0\nx - 17/2 = 0 or x - -2 = 0\nx = 17/2\nx = -2"} {"input": "Compute the solution of x^3 + 47/8x^2 + 135/32x - 567/64 = 0", "output": "x^3 + 47/8x^2 + 135/32x - 567/64 = 0\n(x - -9/2)(x - 7/8)(x - -9/4) = 0\nx - -9/2 = 0\nx - 7/8 = 0\nx - -9/4 = 0\nx = -9/2\nx = 7/8\nx = -9/4"} {"input": "Find the solution to 9x + 144/5 = 0", "output": "9x + 144/5 = 0\n9x = -144/5\nx = -144/5 / 9\nx = -16/5"} {"input": "Find x in 4x - 7 = 0", "output": "4x - 7 = 0\n4x = 7\nx = 7 / 4\nx = 7/4"} {"input": "Solve quickly: x^2 - 5x + 4 = 0", "output": "x^2 - 5x + 4 = 0\n(x - 4)(x - 1) = 0\nx - 4 = 0 or x - 1 = 0\nx = 4\nx = 1"} {"input": "Solve the equations:\n2x + 4y = 8/3\n1x + 4y = 8/3", "output": "2x + 4y = 8/3\n1x + 4y = 8/3\n\nUsing elimination\n1*(2x + 4y = 8/3)\n2*(1x + 4y = 8/3)\n2x + 4y = 8/3\n2x + 8y = 16/3\nSubtract equations\n-4y = -8/3\ny = -8/3/-4\ny = 2/3\n\nSubstitute y\n2x + 4(2/3) = 8/3\n2x = 0\nx = 0/2\nx = 0"} {"input": "Find x in x^2 + 3/4x - 7/4 = 0", "output": "x^2 + 3/4x - 7/4 = 0\n(x - -7/4)(x - 1) = 0\nx - -7/4 = 0 or x - 1 = 0\nx = -7/4\nx = 1"} {"input": "Compute the solution of 8x - 136/9 = 0", "output": "8x - 136/9 = 0\n8x = 136/9\nx = 136/9 / 8\nx = 17/9"} {"input": "Solve the system:\n1x + 9y = -49/20\n5x + 2y = -3/2", "output": "1x + 9y = -49/20\n5x + 2y = -3/2\n\nUsing elimination\n5*(1x + 9y = -49/20)\n1*(5x + 2y = -3/2)\n5x + 45y = -49/4\n5x + 2y = -3/2\nSubtract equations\n43y = -43/4\ny = -43/4/43\ny = -1/4\n\nSubstitute y\n1x + 9(-1/4) = -49/20\n1x = -1/5\nx = -1/5/1\nx = -1/5"} {"input": "Solve the system:\n8x + 1y = 13\n5x + 1y = 4", "output": "8x + 1y = 13\n5x + 1y = 4\n\nUsing elimination\n5*(8x + 1y = 13)\n8*(5x + 1y = 4)\n40x + 5y = 65\n40x + 8y = 32\nSubtract equations\n-3y = 33\ny = 33/-3\ny = -11\n\nSubstitute y\n8x + 1(-11) = 13\n8x = 24\nx = 24/8\nx = 3"} {"input": "Find x and y such that\n1x + 10y = 19\n8x + 5y = 2", "output": "1x + 10y = 19\n8x + 5y = 2\n\nUsing elimination\n8*(1x + 10y = 19)\n1*(8x + 5y = 2)\n8x + 80y = 152\n8x + 5y = 2\nSubtract equations\n75y = 150\ny = 150/75\ny = 2\n\nSubstitute y\n1x + 10(2) = 19\n1x = -1\nx = -1/1\nx = -1"} {"input": "Determine x in x^2 - 31/6x + 3 = 0", "output": "x^2 - 31/6x + 3 = 0\n(x - 2/3)(x - 9/2) = 0\nx - 2/3 = 0 or x - 9/2 = 0\nx = 2/3\nx = 9/2"} {"input": "Find x in x^2 + 6x + 9 = 0", "output": "x^2 + 6x + 9 = 0\n(x - -3)(x - -3) = 0\nx - -3 = 0 or x - -3 = 0\nx = -3\nx = -3"} {"input": "Find the solution to 7x + 42/5 = 0", "output": "7x + 42/5 = 0\n7x = -42/5\nx = -42/5 / 7\nx = -6/5"} {"input": "Solve the equations:\n6x + 1y = -92/7\n8x + 1y = -118/7", "output": "6x + 1y = -92/7\n8x + 1y = -118/7\n\nUsing elimination\n8*(6x + 1y = -92/7)\n6*(8x + 1y = -118/7)\n48x + 8y = -736/7\n48x + 6y = -708/7\nSubtract equations\n2y = -4\ny = -4/2\ny = -2\n\nSubstitute y\n6x + 1(-2) = -92/7\n6x = -78/7\nx = -78/7/6\nx = -13/7"} {"input": "Find x and y such that\n8x + 6y = -6\n3x + 3y = -27/4", "output": "8x + 6y = -6\n3x + 3y = -27/4\n\nUsing elimination\n3*(8x + 6y = -6)\n8*(3x + 3y = -27/4)\n24x + 18y = -18\n24x + 24y = -54\nSubtract equations\n-6y = 36\ny = 36/-6\ny = -6\n\nSubstitute y\n8x + 6(-6) = -6\n8x = 30\nx = 30/8\nx = 15/4"} {"input": "Determine x in x^3 + 19/6x^2 + 82/75x - 16/25 = 0", "output": "x^3 + 19/6x^2 + 82/75x - 16/25 = 0\n(x - -8/3)(x - -4/5)(x - 3/10) = 0\nx - -8/3 = 0\nx - -4/5 = 0\nx - 3/10 = 0\nx = -8/3\nx = -4/5\nx = 3/10"} {"input": "Find x in x^3 - 245/12x^2 + 467/12x + 165/2 = 0", "output": "x^3 - 245/12x^2 + 467/12x + 165/2 = 0\n(x - 11/3)(x - 18)(x - -5/4) = 0\nx - 11/3 = 0\nx - 18 = 0\nx - -5/4 = 0\nx = 11/3\nx = 18\nx = -5/4"} {"input": "Find x for 7x - 140/3 = 0", "output": "7x - 140/3 = 0\n7x = 140/3\nx = 140/3 / 7\nx = 20/3"} {"input": "Find x in x^2 + 163/35x + 26/5 = 0", "output": "x^2 + 163/35x + 26/5 = 0\n(x - -13/7)(x - -14/5) = 0\nx - -13/7 = 0 or x - -14/5 = 0\nx = -13/7\nx = -14/5"} {"input": "Find x and y such that\n3x + 9y = -201/4\n6x + 2y = -41/2", "output": "3x + 9y = -201/4\n6x + 2y = -41/2\n\nUsing elimination\n6*(3x + 9y = -201/4)\n3*(6x + 2y = -41/2)\n18x + 54y = -603/2\n18x + 6y = -123/2\nSubtract equations\n48y = -240\ny = -240/48\ny = -5\n\nSubstitute y\n3x + 9(-5) = -201/4\n3x = -21/4\nx = -21/4/3\nx = -7/4"} {"input": "Solve the equations:\n3x + 4y = -3/8\n1x + 10y = -79/8", "output": "3x + 4y = -3/8\n1x + 10y = -79/8\n\nUsing elimination\n1*(3x + 4y = -3/8)\n3*(1x + 10y = -79/8)\n3x + 4y = -3/8\n3x + 30y = -237/8\nSubtract equations\n-26y = 117/4\ny = 117/4/-26\ny = -9/8\n\nSubstitute y\n3x + 4(-9/8) = -3/8\n3x = 33/8\nx = 33/8/3\nx = 11/8"} {"input": "Solve quickly: 7x - 63/4 = 0", "output": "7x - 63/4 = 0\n7x = 63/4\nx = 63/4 / 7\nx = 9/4"} {"input": "Solve simultaneously:\n4x + 7y = 50/9\n8x + 6y = -4/3", "output": "4x + 7y = 50/9\n8x + 6y = -4/3\n\nUsing elimination\n8*(4x + 7y = 50/9)\n4*(8x + 6y = -4/3)\n32x + 56y = 400/9\n32x + 24y = -16/3\nSubtract equations\n32y = 448/9\ny = 448/9/32\ny = 14/9\n\nSubstitute y\n4x + 7(14/9) = 50/9\n4x = -16/3\nx = -16/3/4\nx = -4/3"} {"input": "Solve the equations:\n3x + 6y = 51/7\n3x + 8y = 75/7", "output": "3x + 6y = 51/7\n3x + 8y = 75/7\n\nUsing elimination\n3*(3x + 6y = 51/7)\n3*(3x + 8y = 75/7)\n9x + 18y = 153/7\n9x + 24y = 225/7\nSubtract equations\n-6y = -72/7\ny = -72/7/-6\ny = 12/7\n\nSubstitute y\n3x + 6(12/7) = 51/7\n3x = -3\nx = -3/3\nx = -1"} {"input": "Determine x in x^3 - 89/15x^2 + 146/15x - 24/5 = 0", "output": "x^3 - 89/15x^2 + 146/15x - 24/5 = 0\n(x - 18/5)(x - 4/3)(x - 1) = 0\nx - 18/5 = 0\nx - 4/3 = 0\nx - 1 = 0\nx = 18/5\nx = 4/3\nx = 1"} {"input": "Find the solution to x^2 + 11/9x - 16/3 = 0", "output": "x^2 + 11/9x - 16/3 = 0\n(x - 16/9)(x - -3) = 0\nx - 16/9 = 0 or x - -3 = 0\nx = 16/9\nx = -3"} {"input": "Find x for x^3 - 71/3x^2 + 62x + 680/3 = 0", "output": "x^3 - 71/3x^2 + 62x + 680/3 = 0\n(x - -2)(x - 20)(x - 17/3) = 0\nx - -2 = 0\nx - 20 = 0\nx - 17/3 = 0\nx = -2\nx = 20\nx = 17/3"} {"input": "Find the solution to x^3 + 19/2x^2 - 1043/18x + 637/9 = 0", "output": "x^3 + 19/2x^2 - 1043/18x + 637/9 = 0\n(x - 7/3)(x - 13/6)(x - -14) = 0\nx - 7/3 = 0\nx - 13/6 = 0\nx - -14 = 0\nx = 7/3\nx = 13/6\nx = -14"} {"input": "Find x in x^3 + 127/5x^2 + 767/5x - 507/5 = 0", "output": "x^3 + 127/5x^2 + 767/5x - 507/5 = 0\n(x - -13)(x - 3/5)(x - -13) = 0\nx - -13 = 0\nx - 3/5 = 0\nx - -13 = 0\nx = -13\nx = 3/5\nx = -13"} {"input": "Solve x^3 - 47/12x^2 - 99/4x + 595/6 = 0", "output": "x^3 - 47/12x^2 - 99/4x + 595/6 = 0\n(x - 14/3)(x - 17/4)(x - -5) = 0\nx - 14/3 = 0\nx - 17/4 = 0\nx - -5 = 0\nx = 14/3\nx = 17/4\nx = -5"} {"input": "Find x for 2x - 3/5 = 0", "output": "2x - 3/5 = 0\n2x = 3/5\nx = 3/5 / 2\nx = 3/10"} {"input": "Compute the solution of x^2 + 13/10x - 3 = 0", "output": "x^2 + 13/10x - 3 = 0\n(x - -5/2)(x - 6/5) = 0\nx - -5/2 = 0 or x - 6/5 = 0\nx = -5/2\nx = 6/5"} {"input": "Solve the system:\n4x + 5y = 15/2\n9x + 3y = 543/40", "output": "4x + 5y = 15/2\n9x + 3y = 543/40\n\nUsing elimination\n9*(4x + 5y = 15/2)\n4*(9x + 3y = 543/40)\n36x + 45y = 135/2\n36x + 12y = 543/10\nSubtract equations\n33y = 66/5\ny = 66/5/33\ny = 2/5\n\nSubstitute y\n4x + 5(2/5) = 15/2\n4x = 11/2\nx = 11/2/4\nx = 11/8"} {"input": "Solve 5x + 95/8 = 0", "output": "5x + 95/8 = 0\n5x = -95/8\nx = -95/8 / 5\nx = -19/8"} {"input": "Solve the system:\n1x + 1y = -157/40\n5x + 10y = -269/8", "output": "1x + 1y = -157/40\n5x + 10y = -269/8\n\nUsing elimination\n5*(1x + 1y = -157/40)\n1*(5x + 10y = -269/8)\n5x + 5y = -157/8\n5x + 10y = -269/8\nSubtract equations\n-5y = 14\ny = 14/-5\ny = -14/5\n\nSubstitute y\n1x + 1(-14/5) = -157/40\n1x = -9/8\nx = -9/8/1\nx = -9/8"} {"input": "Solve x^3 - 78/7x^2 + 5/7x + 66/7 = 0", "output": "x^3 - 78/7x^2 + 5/7x + 66/7 = 0\n(x - -6/7)(x - 11)(x - 1) = 0\nx - -6/7 = 0\nx - 11 = 0\nx - 1 = 0\nx = -6/7\nx = 11\nx = 1"} {"input": "What value of x satisfies x^2 - 28/15x - 247/60 = 0", "output": "x^2 - 28/15x - 247/60 = 0\n(x - -13/10)(x - 19/6) = 0\nx - -13/10 = 0 or x - 19/6 = 0\nx = -13/10\nx = 19/6"} {"input": "Find the solution to x^3 + 54/5x^2 + 17x + 36/5 = 0", "output": "x^3 + 54/5x^2 + 17x + 36/5 = 0\n(x - -4/5)(x - -9)(x - -1) = 0\nx - -4/5 = 0\nx - -9 = 0\nx - -1 = 0\nx = -4/5\nx = -9\nx = -1"} {"input": "Solve quickly: x^2 - 68/35x - 247/35 = 0", "output": "x^2 - 68/35x - 247/35 = 0\n(x - -13/7)(x - 19/5) = 0\nx - -13/7 = 0 or x - 19/5 = 0\nx = -13/7\nx = 19/5"} {"input": "Find x and y such that\n1x + 6y = 347/3\n5x + 2y = 139/3", "output": "1x + 6y = 347/3\n5x + 2y = 139/3\n\nUsing elimination\n5*(1x + 6y = 347/3)\n1*(5x + 2y = 139/3)\n5x + 30y = 1735/3\n5x + 2y = 139/3\nSubtract equations\n28y = 532\ny = 532/28\ny = 19\n\nSubstitute y\n1x + 6(19) = 347/3\n1x = 5/3\nx = 5/3/1\nx = 5/3"} {"input": "Solve the system:\n2x + 5y = -111/4\n2x + 8y = -30", "output": "2x + 5y = -111/4\n2x + 8y = -30\n\nUsing elimination\n2*(2x + 5y = -111/4)\n2*(2x + 8y = -30)\n4x + 10y = -111/2\n4x + 16y = -60\nSubtract equations\n-6y = 9/2\ny = 9/2/-6\ny = -3/4\n\nSubstitute y\n2x + 5(-3/4) = -111/4\n2x = -24\nx = -24/2\nx = -12"} {"input": "Determine x in x^2 - 3/8x - 11/8 = 0", "output": "x^2 - 3/8x - 11/8 = 0\n(x - 11/8)(x - -1) = 0\nx - 11/8 = 0 or x - -1 = 0\nx = 11/8\nx = -1"} {"input": "Solve 4x + 4/7 = 0", "output": "4x + 4/7 = 0\n4x = -4/7\nx = -4/7 / 4\nx = -1/7"} {"input": "Solve quickly: x^3 - 5/6x^2 - 1/2x + 1/3 = 0", "output": "x^3 - 5/6x^2 - 1/2x + 1/3 = 0\n(x - 1/2)(x - -2/3)(x - 1) = 0\nx - 1/2 = 0\nx - -2/3 = 0\nx - 1 = 0\nx = 1/2\nx = -2/3\nx = 1"} {"input": "Find x for x^2 - 179/30x + 17/10 = 0", "output": "x^2 - 179/30x + 17/10 = 0\n(x - 17/3)(x - 3/10) = 0\nx - 17/3 = 0 or x - 3/10 = 0\nx = 17/3\nx = 3/10"} {"input": "Find x and y such that\n4x + 9y = -132/7\n2x + 6y = -81/7", "output": "4x + 9y = -132/7\n2x + 6y = -81/7\n\nUsing elimination\n2*(4x + 9y = -132/7)\n4*(2x + 6y = -81/7)\n8x + 18y = -264/7\n8x + 24y = -324/7\nSubtract equations\n-6y = 60/7\ny = 60/7/-6\ny = -10/7\n\nSubstitute y\n4x + 9(-10/7) = -132/7\n4x = -6\nx = -6/4\nx = -3/2"} {"input": "Determine x in 3x - 51/4 = 0", "output": "3x - 51/4 = 0\n3x = 51/4\nx = 51/4 / 3\nx = 17/4"} {"input": "Solve simultaneously:\n10x + 7y = -117/8\n7x + 9y = -471/40", "output": "10x + 7y = -117/8\n7x + 9y = -471/40\n\nUsing elimination\n7*(10x + 7y = -117/8)\n10*(7x + 9y = -471/40)\n70x + 49y = -819/8\n70x + 90y = -471/4\nSubtract equations\n-41y = 123/8\ny = 123/8/-41\ny = -3/8\n\nSubstitute y\n10x + 7(-3/8) = -117/8\n10x = -12\nx = -12/10\nx = -6/5"} {"input": "Solve the equation x^2 + 23/28x - 15/28 = 0", "output": "x^2 + 23/28x - 15/28 = 0\n(x - 3/7)(x - -5/4) = 0\nx - 3/7 = 0 or x - -5/4 = 0\nx = 3/7\nx = -5/4"} {"input": "Solve quickly: 5x + 13/2 = 0", "output": "5x + 13/2 = 0\n5x = -13/2\nx = -13/2 / 5\nx = -13/10"} {"input": "Find x for 2x - 26 = 0", "output": "2x - 26 = 0\n2x = 26\nx = 26 / 2\nx = 13"} {"input": "Solve quickly: x^3 - 1/2x^2 - 14x = 0", "output": "x^3 - 1/2x^2 - 14x = 0\n(x - 0)(x - -7/2)(x - 4) = 0\nx - 0 = 0\nx - -7/2 = 0\nx - 4 = 0\nx = 0\nx = -7/2\nx = 4"} {"input": "Solve the equation x^3 + 20/3x^2 - 869/12x + 1547/12 = 0", "output": "x^3 + 20/3x^2 - 869/12x + 1547/12 = 0\n(x - 17/6)(x - 7/2)(x - -13) = 0\nx - 17/6 = 0\nx - 7/2 = 0\nx - -13 = 0\nx = 17/6\nx = 7/2\nx = -13"} {"input": "Solve the equation x^2 + 51/7x + 2 = 0", "output": "x^2 + 51/7x + 2 = 0\n(x - -7)(x - -2/7) = 0\nx - -7 = 0 or x - -2/7 = 0\nx = -7\nx = -2/7"} {"input": "Determine x in 5x + 40 = 0", "output": "5x + 40 = 0\n5x = -40\nx = -40 / 5\nx = -8"} {"input": "Solve the system:\n10x + 5y = 55/4\n6x + 10y = 69/2", "output": "10x + 5y = 55/4\n6x + 10y = 69/2\n\nUsing elimination\n6*(10x + 5y = 55/4)\n10*(6x + 10y = 69/2)\n60x + 30y = 165/2\n60x + 100y = 345\nSubtract equations\n-70y = -525/2\ny = -525/2/-70\ny = 15/4\n\nSubstitute y\n10x + 5(15/4) = 55/4\n10x = -5\nx = -5/10\nx = -1/2"} {"input": "Find x for x^3 + 17/14x^2 - 33/7x + 27/14 = 0", "output": "x^3 + 17/14x^2 - 33/7x + 27/14 = 0\n(x - 9/7)(x - -3)(x - 1/2) = 0\nx - 9/7 = 0\nx - -3 = 0\nx - 1/2 = 0\nx = 9/7\nx = -3\nx = 1/2"} {"input": "Find the solution to 9x + 54/5 = 0", "output": "9x + 54/5 = 0\n9x = -54/5\nx = -54/5 / 9\nx = -6/5"} {"input": "Find the solution to x^2 - 17x - 18 = 0", "output": "x^2 - 17x - 18 = 0\n(x - 18)(x - -1) = 0\nx - 18 = 0 or x - -1 = 0\nx = 18\nx = -1"} {"input": "What value of x satisfies x^2 - 29/7x + 4/7 = 0", "output": "x^2 - 29/7x + 4/7 = 0\n(x - 1/7)(x - 4) = 0\nx - 1/7 = 0 or x - 4 = 0\nx = 1/7\nx = 4"} {"input": "Determine x in x^2 - 32/9x + 64/27 = 0", "output": "x^2 - 32/9x + 64/27 = 0\n(x - 8/9)(x - 8/3) = 0\nx - 8/9 = 0 or x - 8/3 = 0\nx = 8/9\nx = 8/3"} {"input": "Find x for 1x + 4/7 = 0", "output": "1x + 4/7 = 0\n1x = -4/7\nx = -4/7 / 1\nx = -4/7"} {"input": "Find x for x^2 - 161/45x + 98/45 = 0", "output": "x^2 - 161/45x + 98/45 = 0\n(x - 7/9)(x - 14/5) = 0\nx - 7/9 = 0 or x - 14/5 = 0\nx = 7/9\nx = 14/5"} {"input": "Find x in 8x + 48 = 0", "output": "8x + 48 = 0\n8x = -48\nx = -48 / 8\nx = -6"} {"input": "Solve x^2 + 5/9x = 0", "output": "x^2 + 5/9x = 0\n(x - -5/9)(x - 0) = 0\nx - -5/9 = 0 or x - 0 = 0\nx = -5/9\nx = 0"} {"input": "What value of x satisfies x^2 - 107/7x + 30/7 = 0", "output": "x^2 - 107/7x + 30/7 = 0\n(x - 2/7)(x - 15) = 0\nx - 2/7 = 0 or x - 15 = 0\nx = 2/7\nx = 15"} {"input": "Solve quickly: x^3 + 97/4x^2 + 595/4x + 150 = 0", "output": "x^3 + 97/4x^2 + 595/4x + 150 = 0\n(x - -5/4)(x - -15)(x - -8) = 0\nx - -5/4 = 0\nx - -15 = 0\nx - -8 = 0\nx = -5/4\nx = -15\nx = -8"} {"input": "Solve simultaneously:\n9x + 9y = -477/5\n8x + 1y = -298/5", "output": "9x + 9y = -477/5\n8x + 1y = -298/5\n\nUsing elimination\n8*(9x + 9y = -477/5)\n9*(8x + 1y = -298/5)\n72x + 72y = -3816/5\n72x + 9y = -2682/5\nSubtract equations\n63y = -1134/5\ny = -1134/5/63\ny = -18/5\n\nSubstitute y\n9x + 9(-18/5) = -477/5\n9x = -63\nx = -63/9\nx = -7"} {"input": "Find x in x^3 + 268/35x^2 - 19/7x + 8/35 = 0", "output": "x^3 + 268/35x^2 - 19/7x + 8/35 = 0\n(x - 1/5)(x - 1/7)(x - -8) = 0\nx - 1/5 = 0\nx - 1/7 = 0\nx - -8 = 0\nx = 1/5\nx = 1/7\nx = -8"} {"input": "Find x for 6x + 8 = 0", "output": "6x + 8 = 0\n6x = -8\nx = -8 / 6\nx = -4/3"} {"input": "What value of x satisfies x^3 + 11/2x^2 + 433/50x + 104/25 = 0", "output": "x^3 + 11/2x^2 + 433/50x + 104/25 = 0\n(x - -13/10)(x - -1)(x - -16/5) = 0\nx - -13/10 = 0\nx - -1 = 0\nx - -16/5 = 0\nx = -13/10\nx = -1\nx = -16/5"} {"input": "What value of x satisfies x^2 + 4/5x - 28/5 = 0", "output": "x^2 + 4/5x - 28/5 = 0\n(x - -14/5)(x - 2) = 0\nx - -14/5 = 0 or x - 2 = 0\nx = -14/5\nx = 2"} {"input": "Find x and y such that\n1x + 10y = -4\n4x + 4y = 64/5", "output": "1x + 10y = -4\n4x + 4y = 64/5\n\nUsing elimination\n4*(1x + 10y = -4)\n1*(4x + 4y = 64/5)\n4x + 40y = -16\n4x + 4y = 64/5\nSubtract equations\n36y = -144/5\ny = -144/5/36\ny = -4/5\n\nSubstitute y\n1x + 10(-4/5) = -4\n1x = 4\nx = 4/1\nx = 4"} {"input": "Find x and y such that\n3x + 2y = -96/5\n4x + 9y = -508/5", "output": "3x + 2y = -96/5\n4x + 9y = -508/5\n\nUsing elimination\n4*(3x + 2y = -96/5)\n3*(4x + 9y = -508/5)\n12x + 8y = -384/5\n12x + 27y = -1524/5\nSubtract equations\n-19y = 228\ny = 228/-19\ny = -12\n\nSubstitute y\n3x + 2(-12) = -96/5\n3x = 24/5\nx = 24/5/3\nx = 8/5"} {"input": "Solve simultaneously:\n4x + 4y = -12/7\n1x + 9y = 29/7", "output": "4x + 4y = -12/7\n1x + 9y = 29/7\n\nUsing elimination\n1*(4x + 4y = -12/7)\n4*(1x + 9y = 29/7)\n4x + 4y = -12/7\n4x + 36y = 116/7\nSubtract equations\n-32y = -128/7\ny = -128/7/-32\ny = 4/7\n\nSubstitute y\n4x + 4(4/7) = -12/7\n4x = -4\nx = -4/4\nx = -1"} {"input": "Compute the solution of x^2 - 44/35x - 39/35 = 0", "output": "x^2 - 44/35x - 39/35 = 0\n(x - 13/7)(x - -3/5) = 0\nx - 13/7 = 0 or x - -3/5 = 0\nx = 13/7\nx = -3/5"} {"input": "Determine x in x^2 + 13/7x + 6/7 = 0", "output": "x^2 + 13/7x + 6/7 = 0\n(x - -1)(x - -6/7) = 0\nx - -1 = 0 or x - -6/7 = 0\nx = -1\nx = -6/7"} {"input": "Compute the solution of x^3 + 18/5x^2 - 8/5x = 0", "output": "x^3 + 18/5x^2 - 8/5x = 0\n(x - 0)(x - 2/5)(x - -4) = 0\nx - 0 = 0\nx - 2/5 = 0\nx - -4 = 0\nx = 0\nx = 2/5\nx = -4"} {"input": "What value of x satisfies 2x + 1/2 = 0", "output": "2x + 1/2 = 0\n2x = -1/2\nx = -1/2 / 2\nx = -1/4"} {"input": "Solve quickly: 4x - 56 = 0", "output": "4x - 56 = 0\n4x = 56\nx = 56 / 4\nx = 14"} {"input": "Solve the equations:\n2x + 1y = -44/9\n10x + 10y = -310/9", "output": "2x + 1y = -44/9\n10x + 10y = -310/9\n\nUsing elimination\n10*(2x + 1y = -44/9)\n2*(10x + 10y = -310/9)\n20x + 10y = -440/9\n20x + 20y = -620/9\nSubtract equations\n-10y = 20\ny = 20/-10\ny = -2\n\nSubstitute y\n2x + 1(-2) = -44/9\n2x = -26/9\nx = -26/9/2\nx = -13/9"} {"input": "Find x for 5x + 25 = 0", "output": "5x + 25 = 0\n5x = -25\nx = -25 / 5\nx = -5"} {"input": "Compute the solution of x^2 - 19/2x - 30 = 0", "output": "x^2 - 19/2x - 30 = 0\n(x - 12)(x - -5/2) = 0\nx - 12 = 0 or x - -5/2 = 0\nx = 12\nx = -5/2"} {"input": "Find x and y such that\n5x + 6y = -75\n9x + 4y = -135", "output": "5x + 6y = -75\n9x + 4y = -135\n\nUsing elimination\n9*(5x + 6y = -75)\n5*(9x + 4y = -135)\n45x + 54y = -675\n45x + 20y = -675\nSubtract equations\n34y = 0\ny = 0/34\ny = 0\n\nSubstitute y\n5x + 6(0) = -75\n5x = -75\nx = -75/5\nx = -15"} {"input": "Find x in x^2 + 19/4x = 0", "output": "x^2 + 19/4x = 0\n(x - 0)(x - -19/4) = 0\nx - 0 = 0 or x - -19/4 = 0\nx = 0\nx = -19/4"} {"input": "Find x for x^2 - 23/12x + 5/12 = 0", "output": "x^2 - 23/12x + 5/12 = 0\n(x - 1/4)(x - 5/3) = 0\nx - 1/4 = 0 or x - 5/3 = 0\nx = 1/4\nx = 5/3"} {"input": "Solve quickly: x^2 - 83/7x + 180/7 = 0", "output": "x^2 - 83/7x + 180/7 = 0\n(x - 9)(x - 20/7) = 0\nx - 9 = 0 or x - 20/7 = 0\nx = 9\nx = 20/7"} {"input": "Solve 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "Find the solution to x^3 - 23/6x^2 + 25/6x - 1 = 0", "output": "x^3 - 23/6x^2 + 25/6x - 1 = 0\n(x - 1/3)(x - 2)(x - 3/2) = 0\nx - 1/3 = 0\nx - 2 = 0\nx - 3/2 = 0\nx = 1/3\nx = 2\nx = 3/2"} {"input": "Compute the solution of 10x - 130/3 = 0", "output": "10x - 130/3 = 0\n10x = 130/3\nx = 130/3 / 10\nx = 13/3"} {"input": "Solve the system:\n7x + 10y = 198/5\n3x + 9y = 132/5", "output": "7x + 10y = 198/5\n3x + 9y = 132/5\n\nUsing elimination\n3*(7x + 10y = 198/5)\n7*(3x + 9y = 132/5)\n21x + 30y = 594/5\n21x + 63y = 924/5\nSubtract equations\n-33y = -66\ny = -66/-33\ny = 2\n\nSubstitute y\n7x + 10(2) = 198/5\n7x = 98/5\nx = 98/5/7\nx = 14/5"} {"input": "Solve the equation x^3 - 267/40x^2 + 491/40x - 63/10 = 0", "output": "x^3 - 267/40x^2 + 491/40x - 63/10 = 0\n(x - 9/5)(x - 7/8)(x - 4) = 0\nx - 9/5 = 0\nx - 7/8 = 0\nx - 4 = 0\nx = 9/5\nx = 7/8\nx = 4"} {"input": "Determine x in 1x + 3 = 0", "output": "1x + 3 = 0\n1x = -3\nx = -3 / 1\nx = -3"} {"input": "Find the solution to 7x + 91/6 = 0", "output": "7x + 91/6 = 0\n7x = -91/6\nx = -91/6 / 7\nx = -13/6"} {"input": "Compute the solution of 10x + 110/3 = 0", "output": "10x + 110/3 = 0\n10x = -110/3\nx = -110/3 / 10\nx = -11/3"} {"input": "Determine x in x^2 - 1/4x - 15/8 = 0", "output": "x^2 - 1/4x - 15/8 = 0\n(x - 3/2)(x - -5/4) = 0\nx - 3/2 = 0 or x - -5/4 = 0\nx = 3/2\nx = -5/4"} {"input": "Solve the equations:\n8x + 8y = -56\n5x + 7y = -45", "output": "8x + 8y = -56\n5x + 7y = -45\n\nUsing elimination\n5*(8x + 8y = -56)\n8*(5x + 7y = -45)\n40x + 40y = -280\n40x + 56y = -360\nSubtract equations\n-16y = 80\ny = 80/-16\ny = -5\n\nSubstitute y\n8x + 8(-5) = -56\n8x = -16\nx = -16/8\nx = -2"} {"input": "Solve quickly: x^3 + 11/10x^2 - 51/5x - 63/10 = 0", "output": "x^3 + 11/10x^2 - 51/5x - 63/10 = 0\n(x - 3)(x - -3/5)(x - -7/2) = 0\nx - 3 = 0\nx - -3/5 = 0\nx - -7/2 = 0\nx = 3\nx = -3/5\nx = -7/2"} {"input": "Find x for x^3 - 142/15x^2 - 9x + 110/3 = 0", "output": "x^3 - 142/15x^2 - 9x + 110/3 = 0\n(x - -11/5)(x - 5/3)(x - 10) = 0\nx - -11/5 = 0\nx - 5/3 = 0\nx - 10 = 0\nx = -11/5\nx = 5/3\nx = 10"} {"input": "Solve the equations:\n1x + 8y = -7/2\n10x + 1y = 9/2", "output": "1x + 8y = -7/2\n10x + 1y = 9/2\n\nUsing elimination\n10*(1x + 8y = -7/2)\n1*(10x + 1y = 9/2)\n10x + 80y = -35\n10x + 1y = 9/2\nSubtract equations\n79y = -79/2\ny = -79/2/79\ny = -1/2\n\nSubstitute y\n1x + 8(-1/2) = -7/2\n1x = 1/2\nx = 1/2/1\nx = 1/2"} {"input": "Determine x in 5x + 4 = 0", "output": "5x + 4 = 0\n5x = -4\nx = -4 / 5\nx = -4/5"} {"input": "Solve quickly: 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "What value of x satisfies x^3 + 37/7x^2 + 52/7x + 12/7 = 0", "output": "x^3 + 37/7x^2 + 52/7x + 12/7 = 0\n(x - -2)(x - -2/7)(x - -3) = 0\nx - -2 = 0\nx - -2/7 = 0\nx - -3 = 0\nx = -2\nx = -2/7\nx = -3"} {"input": "Find x in x^3 - 221/72x^2 + 169/72x = 0", "output": "x^3 - 221/72x^2 + 169/72x = 0\n(x - 0)(x - 13/8)(x - 13/9) = 0\nx - 0 = 0\nx - 13/8 = 0\nx - 13/9 = 0\nx = 0\nx = 13/8\nx = 13/9"} {"input": "Determine x in 7x + 7 = 0", "output": "7x + 7 = 0\n7x = -7\nx = -7 / 7\nx = -1"} {"input": "Solve 8x - 10 = 0", "output": "8x - 10 = 0\n8x = 10\nx = 10 / 8\nx = 5/4"} {"input": "Solve 9x - 36 = 0", "output": "9x - 36 = 0\n9x = 36\nx = 36 / 9\nx = 4"} {"input": "Find x in x^2 - 1/6x - 2 = 0", "output": "x^2 - 1/6x - 2 = 0\n(x - 3/2)(x - -4/3) = 0\nx - 3/2 = 0 or x - -4/3 = 0\nx = 3/2\nx = -4/3"} {"input": "Find x for x^3 - 245/72x^2 + 931/288x - 11/18 = 0", "output": "x^3 - 245/72x^2 + 931/288x - 11/18 = 0\n(x - 16/9)(x - 1/4)(x - 11/8) = 0\nx - 16/9 = 0\nx - 1/4 = 0\nx - 11/8 = 0\nx = 16/9\nx = 1/4\nx = 11/8"} {"input": "Find x for 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Solve the system:\n4x + 6y = -137/10\n5x + 4y = -18", "output": "4x + 6y = -137/10\n5x + 4y = -18\n\nUsing elimination\n5*(4x + 6y = -137/10)\n4*(5x + 4y = -18)\n20x + 30y = -137/2\n20x + 16y = -72\nSubtract equations\n14y = 7/2\ny = 7/2/14\ny = 1/4\n\nSubstitute y\n4x + 6(1/4) = -137/10\n4x = -76/5\nx = -76/5/4\nx = -19/5"} {"input": "Determine x in x^2 - 1/6x - 5/6 = 0", "output": "x^2 - 1/6x - 5/6 = 0\n(x - 1)(x - -5/6) = 0\nx - 1 = 0 or x - -5/6 = 0\nx = 1\nx = -5/6"} {"input": "Solve quickly: 9x - 108/5 = 0", "output": "9x - 108/5 = 0\n9x = 108/5\nx = 108/5 / 9\nx = 12/5"} {"input": "Solve x^2 + 19/5x + 14/5 = 0", "output": "x^2 + 19/5x + 14/5 = 0\n(x - -1)(x - -14/5) = 0\nx - -1 = 0 or x - -14/5 = 0\nx = -1\nx = -14/5"} {"input": "Solve the system:\n8x + 2y = 96/7\n8x + 6y = 32/7", "output": "8x + 2y = 96/7\n8x + 6y = 32/7\n\nUsing elimination\n8*(8x + 2y = 96/7)\n8*(8x + 6y = 32/7)\n64x + 16y = 768/7\n64x + 48y = 256/7\nSubtract equations\n-32y = 512/7\ny = 512/7/-32\ny = -16/7\n\nSubstitute y\n8x + 2(-16/7) = 96/7\n8x = 128/7\nx = 128/7/8\nx = 16/7"} {"input": "Find the solution to x^2 - 13/3x + 14/3 = 0", "output": "x^2 - 13/3x + 14/3 = 0\n(x - 2)(x - 7/3) = 0\nx - 2 = 0 or x - 7/3 = 0\nx = 2\nx = 7/3"} {"input": "Find the solution to x^2 + 55/6x - 25/3 = 0", "output": "x^2 + 55/6x - 25/3 = 0\n(x - -10)(x - 5/6) = 0\nx - -10 = 0 or x - 5/6 = 0\nx = -10\nx = 5/6"} {"input": "Find x for x^3 - 32/9x^2 + 61/27x + 8/27 = 0", "output": "x^3 - 32/9x^2 + 61/27x + 8/27 = 0\n(x - -1/9)(x - 8/3)(x - 1) = 0\nx - -1/9 = 0\nx - 8/3 = 0\nx - 1 = 0\nx = -1/9\nx = 8/3\nx = 1"} {"input": "Solve simultaneously:\n6x + 7y = 943/14\n4x + 2y = 137/7", "output": "6x + 7y = 943/14\n4x + 2y = 137/7\n\nUsing elimination\n4*(6x + 7y = 943/14)\n6*(4x + 2y = 137/7)\n24x + 28y = 1886/7\n24x + 12y = 822/7\nSubtract equations\n16y = 152\ny = 152/16\ny = 19/2\n\nSubstitute y\n6x + 7(19/2) = 943/14\n6x = 6/7\nx = 6/7/6\nx = 1/7"} {"input": "Solve quickly: x^2 - 32/7x + 16/7 = 0", "output": "x^2 - 32/7x + 16/7 = 0\n(x - 4)(x - 4/7) = 0\nx - 4 = 0 or x - 4/7 = 0\nx = 4\nx = 4/7"} {"input": "Compute the solution of x^2 - 19/5x - 6 = 0", "output": "x^2 - 19/5x - 6 = 0\n(x - 5)(x - -6/5) = 0\nx - 5 = 0 or x - -6/5 = 0\nx = 5\nx = -6/5"} {"input": "Determine x in 7x - 91/8 = 0", "output": "7x - 91/8 = 0\n7x = 91/8\nx = 91/8 / 7\nx = 13/8"} {"input": "Solve the equation x^3 + 41/24x^2 - 11/4x - 13/3 = 0", "output": "x^3 + 41/24x^2 - 11/4x - 13/3 = 0\n(x - -4/3)(x - 13/8)(x - -2) = 0\nx - -4/3 = 0\nx - 13/8 = 0\nx - -2 = 0\nx = -4/3\nx = 13/8\nx = -2"} {"input": "Solve quickly: 10x - 40/3 = 0", "output": "10x - 40/3 = 0\n10x = 40/3\nx = 40/3 / 10\nx = 4/3"} {"input": "Solve 7x + 7/3 = 0", "output": "7x + 7/3 = 0\n7x = -7/3\nx = -7/3 / 7\nx = -1/3"} {"input": "Find x for x^2 + 1/3x - 56/9 = 0", "output": "x^2 + 1/3x - 56/9 = 0\n(x - 7/3)(x - -8/3) = 0\nx - 7/3 = 0 or x - -8/3 = 0\nx = 7/3\nx = -8/3"} {"input": "Find x for x^2 + 116/45x + 7/5 = 0", "output": "x^2 + 116/45x + 7/5 = 0\n(x - -7/9)(x - -9/5) = 0\nx - -7/9 = 0 or x - -9/5 = 0\nx = -7/9\nx = -9/5"} {"input": "Find x in x^3 - 25/6x^2 + 1/2x + 2/3 = 0", "output": "x^3 - 25/6x^2 + 1/2x + 2/3 = 0\n(x - 1/2)(x - -1/3)(x - 4) = 0\nx - 1/2 = 0\nx - -1/3 = 0\nx - 4 = 0\nx = 1/2\nx = -1/3\nx = 4"} {"input": "Solve the system:\n5x + 9y = -109/4\n3x + 9y = -87/4", "output": "5x + 9y = -109/4\n3x + 9y = -87/4\n\nUsing elimination\n3*(5x + 9y = -109/4)\n5*(3x + 9y = -87/4)\n15x + 27y = -327/4\n15x + 45y = -435/4\nSubtract equations\n-18y = 27\ny = 27/-18\ny = -3/2\n\nSubstitute y\n5x + 9(-3/2) = -109/4\n5x = -55/4\nx = -55/4/5\nx = -11/4"} {"input": "Solve the equations:\n6x + 10y = -1\n2x + 2y = 1/5", "output": "6x + 10y = -1\n2x + 2y = 1/5\n\nUsing elimination\n2*(6x + 10y = -1)\n6*(2x + 2y = 1/5)\n12x + 20y = -2\n12x + 12y = 6/5\nSubtract equations\n8y = -16/5\ny = -16/5/8\ny = -2/5\n\nSubstitute y\n6x + 10(-2/5) = -1\n6x = 3\nx = 3/6\nx = 1/2"} {"input": "Compute the solution of 3x - 12 = 0", "output": "3x - 12 = 0\n3x = 12\nx = 12 / 3\nx = 4"} {"input": "What value of x satisfies x^2 - 1x = 0", "output": "x^2 - 1x = 0\n(x - 1)(x - 0) = 0\nx - 1 = 0 or x - 0 = 0\nx = 1\nx = 0"} {"input": "Find x in x^2 - 65/18x + 19/6 = 0", "output": "x^2 - 65/18x + 19/6 = 0\n(x - 19/9)(x - 3/2) = 0\nx - 19/9 = 0 or x - 3/2 = 0\nx = 19/9\nx = 3/2"} {"input": "Solve quickly: x^3 - 349/60x^2 + 417/40x - 27/5 = 0", "output": "x^3 - 349/60x^2 + 417/40x - 27/5 = 0\n(x - 8/3)(x - 9/10)(x - 9/4) = 0\nx - 8/3 = 0\nx - 9/10 = 0\nx - 9/4 = 0\nx = 8/3\nx = 9/10\nx = 9/4"} {"input": "What value of x satisfies 4x - 4/3 = 0", "output": "4x - 4/3 = 0\n4x = 4/3\nx = 4/3 / 4\nx = 1/3"} {"input": "Solve x^3 - 61/20x^2 - 249/40x + 513/40 = 0", "output": "x^3 - 61/20x^2 - 249/40x + 513/40 = 0\n(x - -9/4)(x - 3/2)(x - 19/5) = 0\nx - -9/4 = 0\nx - 3/2 = 0\nx - 19/5 = 0\nx = -9/4\nx = 3/2\nx = 19/5"} {"input": "Solve the equations:\n3x + 7y = -42\n1x + 1y = -114/7", "output": "3x + 7y = -42\n1x + 1y = -114/7\n\nUsing elimination\n1*(3x + 7y = -42)\n3*(1x + 1y = -114/7)\n3x + 7y = -42\n3x + 3y = -342/7\nSubtract equations\n4y = 48/7\ny = 48/7/4\ny = 12/7\n\nSubstitute y\n3x + 7(12/7) = -42\n3x = -54\nx = -54/3\nx = -18"} {"input": "Find x in x^2 + 22/3x - 15 = 0", "output": "x^2 + 22/3x - 15 = 0\n(x - 5/3)(x - -9) = 0\nx - 5/3 = 0 or x - -9 = 0\nx = 5/3\nx = -9"} {"input": "Solve the system:\n10x + 4y = -4/3\n2x + 7y = 55/3", "output": "10x + 4y = -4/3\n2x + 7y = 55/3\n\nUsing elimination\n2*(10x + 4y = -4/3)\n10*(2x + 7y = 55/3)\n20x + 8y = -8/3\n20x + 70y = 550/3\nSubtract equations\n-62y = -186\ny = -186/-62\ny = 3\n\nSubstitute y\n10x + 4(3) = -4/3\n10x = -40/3\nx = -40/3/10\nx = -4/3"} {"input": "Determine x in x^3 - 148/35x^2 - 127/7x - 44/5 = 0", "output": "x^3 - 148/35x^2 - 127/7x - 44/5 = 0\n(x - -4/7)(x - 7)(x - -11/5) = 0\nx - -4/7 = 0\nx - 7 = 0\nx - -11/5 = 0\nx = -4/7\nx = 7\nx = -11/5"} {"input": "Find x in x^3 + 27/4x^2 + 59/4x + 21/2 = 0", "output": "x^3 + 27/4x^2 + 59/4x + 21/2 = 0\n(x - -2)(x - -3)(x - -7/4) = 0\nx - -2 = 0\nx - -3 = 0\nx - -7/4 = 0\nx = -2\nx = -3\nx = -7/4"} {"input": "Compute the solution of x^3 - 23/20x^2 - 89/40x + 21/8 = 0", "output": "x^3 - 23/20x^2 - 89/40x + 21/8 = 0\n(x - 7/5)(x - 5/4)(x - -3/2) = 0\nx - 7/5 = 0\nx - 5/4 = 0\nx - -3/2 = 0\nx = 7/5\nx = 5/4\nx = -3/2"} {"input": "Compute the solution of x^2 - 3/2x + 7/18 = 0", "output": "x^2 - 3/2x + 7/18 = 0\n(x - 7/6)(x - 1/3) = 0\nx - 7/6 = 0 or x - 1/3 = 0\nx = 7/6\nx = 1/3"} {"input": "Solve quickly: x^2 - 127/30x + 3 = 0", "output": "x^2 - 127/30x + 3 = 0\n(x - 10/3)(x - 9/10) = 0\nx - 10/3 = 0 or x - 9/10 = 0\nx = 10/3\nx = 9/10"} {"input": "Find the solution to 4x + 32 = 0", "output": "4x + 32 = 0\n4x = -32\nx = -32 / 4\nx = -8"} {"input": "Solve simultaneously:\n10x + 4y = 118/3\n2x + 2y = 29/3", "output": "10x + 4y = 118/3\n2x + 2y = 29/3\n\nUsing elimination\n2*(10x + 4y = 118/3)\n10*(2x + 2y = 29/3)\n20x + 8y = 236/3\n20x + 20y = 290/3\nSubtract equations\n-12y = -18\ny = -18/-12\ny = 3/2\n\nSubstitute y\n10x + 4(3/2) = 118/3\n10x = 100/3\nx = 100/3/10\nx = 10/3"} {"input": "What value of x satisfies 7x + 7 = 0", "output": "7x + 7 = 0\n7x = -7\nx = -7 / 7\nx = -1"} {"input": "Find the solution to 3x - 21/10 = 0", "output": "3x - 21/10 = 0\n3x = 21/10\nx = 21/10 / 3\nx = 7/10"} {"input": "Find x in x^2 + 61/6x + 133/6 = 0", "output": "x^2 + 61/6x + 133/6 = 0\n(x - -7)(x - -19/6) = 0\nx - -7 = 0 or x - -19/6 = 0\nx = -7\nx = -19/6"} {"input": "Compute the solution of x^3 - 9/28x^2 - 267/98x + 11/28 = 0", "output": "x^3 - 9/28x^2 - 267/98x + 11/28 = 0\n(x - 7/4)(x - 1/7)(x - -11/7) = 0\nx - 7/4 = 0\nx - 1/7 = 0\nx - -11/7 = 0\nx = 7/4\nx = 1/7\nx = -11/7"} {"input": "Solve the system:\n5x + 7y = -59/10\n8x + 8y = -28/5", "output": "5x + 7y = -59/10\n8x + 8y = -28/5\n\nUsing elimination\n8*(5x + 7y = -59/10)\n5*(8x + 8y = -28/5)\n40x + 56y = -236/5\n40x + 40y = -28\nSubtract equations\n16y = -96/5\ny = -96/5/16\ny = -6/5\n\nSubstitute y\n5x + 7(-6/5) = -59/10\n5x = 5/2\nx = 5/2/5\nx = 1/2"} {"input": "What value of x satisfies x^2 - 7/2x + 3 = 0", "output": "x^2 - 7/2x + 3 = 0\n(x - 3/2)(x - 2) = 0\nx - 3/2 = 0 or x - 2 = 0\nx = 3/2\nx = 2"} {"input": "Determine x in x^2 + 14/5x - 19/5 = 0", "output": "x^2 + 14/5x - 19/5 = 0\n(x - -19/5)(x - 1) = 0\nx - -19/5 = 0 or x - 1 = 0\nx = -19/5\nx = 1"} {"input": "Find the solution to x^2 + 37/2x + 143/2 = 0", "output": "x^2 + 37/2x + 143/2 = 0\n(x - -11/2)(x - -13) = 0\nx - -11/2 = 0 or x - -13 = 0\nx = -11/2\nx = -13"} {"input": "Compute the solution of x^2 + 10x = 0", "output": "x^2 + 10x = 0\n(x - -10)(x - 0) = 0\nx - -10 = 0 or x - 0 = 0\nx = -10\nx = 0"} {"input": "Compute the solution of 4x - 24/7 = 0", "output": "4x - 24/7 = 0\n4x = 24/7\nx = 24/7 / 4\nx = 6/7"} {"input": "Compute the solution of x^2 - 73/14x + 45/14 = 0", "output": "x^2 - 73/14x + 45/14 = 0\n(x - 5/7)(x - 9/2) = 0\nx - 5/7 = 0 or x - 9/2 = 0\nx = 5/7\nx = 9/2"} {"input": "Find the solution to x^2 - 199/56x + 85/28 = 0", "output": "x^2 - 199/56x + 85/28 = 0\n(x - 10/7)(x - 17/8) = 0\nx - 10/7 = 0 or x - 17/8 = 0\nx = 10/7\nx = 17/8"} {"input": "What value of x satisfies 7x + 91 = 0", "output": "7x + 91 = 0\n7x = -91\nx = -91 / 7\nx = -13"} {"input": "Determine x in 7x + 19 = 0", "output": "7x + 19 = 0\n7x = -19\nx = -19 / 7\nx = -19/7"} {"input": "Find x for x^3 - 2/5x^2 - 63/25x = 0", "output": "x^3 - 2/5x^2 - 63/25x = 0\n(x - -7/5)(x - 9/5)(x - 0) = 0\nx - -7/5 = 0\nx - 9/5 = 0\nx - 0 = 0\nx = -7/5\nx = 9/5\nx = 0"} {"input": "Find the solution to x^3 - 15x^2 - 73x - 57 = 0", "output": "x^3 - 15x^2 - 73x - 57 = 0\n(x - 19)(x - -1)(x - -3) = 0\nx - 19 = 0\nx - -1 = 0\nx - -3 = 0\nx = 19\nx = -1\nx = -3"} {"input": "Find x and y such that\n9x + 5y = -136/3\n9x + 3y = -38", "output": "9x + 5y = -136/3\n9x + 3y = -38\n\nUsing elimination\n9*(9x + 5y = -136/3)\n9*(9x + 3y = -38)\n81x + 45y = -408\n81x + 27y = -342\nSubtract equations\n18y = -66\ny = -66/18\ny = -11/3\n\nSubstitute y\n9x + 5(-11/3) = -136/3\n9x = -27\nx = -27/9\nx = -3"} {"input": "Find the solution to x^3 + 33/20x^2 - 73/40x - 9/4 = 0", "output": "x^3 + 33/20x^2 - 73/40x - 9/4 = 0\n(x - -9/10)(x - 5/4)(x - -2) = 0\nx - -9/10 = 0\nx - 5/4 = 0\nx - -2 = 0\nx = -9/10\nx = 5/4\nx = -2"} {"input": "Solve 10x + 10 = 0", "output": "10x + 10 = 0\n10x = -10\nx = -10 / 10\nx = -1"} {"input": "What value of x satisfies x^3 + 497/90x^2 + 29/15x - 12 = 0", "output": "x^3 + 497/90x^2 + 29/15x - 12 = 0\n(x - -9/2)(x - -20/9)(x - 6/5) = 0\nx - -9/2 = 0\nx - -20/9 = 0\nx - 6/5 = 0\nx = -9/2\nx = -20/9\nx = 6/5"} {"input": "Compute the solution of 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Solve simultaneously:\n3x + 9y = -53/2\n10x + 6y = -97/3", "output": "3x + 9y = -53/2\n10x + 6y = -97/3\n\nUsing elimination\n10*(3x + 9y = -53/2)\n3*(10x + 6y = -97/3)\n30x + 90y = -265\n30x + 18y = -97\nSubtract equations\n72y = -168\ny = -168/72\ny = -7/3\n\nSubstitute y\n3x + 9(-7/3) = -53/2\n3x = -11/2\nx = -11/2/3\nx = -11/6"} {"input": "Solve the system:\n10x + 8y = -16/3\n4x + 10y = 116/3", "output": "10x + 8y = -16/3\n4x + 10y = 116/3\n\nUsing elimination\n4*(10x + 8y = -16/3)\n10*(4x + 10y = 116/3)\n40x + 32y = -64/3\n40x + 100y = 1160/3\nSubtract equations\n-68y = -408\ny = -408/-68\ny = 6\n\nSubstitute y\n10x + 8(6) = -16/3\n10x = -160/3\nx = -160/3/10\nx = -16/3"} {"input": "What value of x satisfies x^3 - 37/8x^2 + 151/32x + 95/64 = 0", "output": "x^3 - 37/8x^2 + 151/32x + 95/64 = 0\n(x - -1/4)(x - 5/2)(x - 19/8) = 0\nx - -1/4 = 0\nx - 5/2 = 0\nx - 19/8 = 0\nx = -1/4\nx = 5/2\nx = 19/8"} {"input": "Find x in x^3 - 23/10x^2 - 34/5x = 0", "output": "x^3 - 23/10x^2 - 34/5x = 0\n(x - -17/10)(x - 0)(x - 4) = 0\nx - -17/10 = 0\nx - 0 = 0\nx - 4 = 0\nx = -17/10\nx = 0\nx = 4"} {"input": "Find x in x^3 - 11/8x^2 - 717/32x - 513/16 = 0", "output": "x^3 - 11/8x^2 - 717/32x - 513/16 = 0\n(x - -19/8)(x - -9/4)(x - 6) = 0\nx - -19/8 = 0\nx - -9/4 = 0\nx - 6 = 0\nx = -19/8\nx = -9/4\nx = 6"} {"input": "What value of x satisfies x^3 + 21/4x^2 + 607/72x + 91/24 = 0", "output": "x^3 + 21/4x^2 + 607/72x + 91/24 = 0\n(x - -3/4)(x - -13/6)(x - -7/3) = 0\nx - -3/4 = 0\nx - -13/6 = 0\nx - -7/3 = 0\nx = -3/4\nx = -13/6\nx = -7/3"} {"input": "Solve the system:\n2x + 4y = -94/3\n1x + 4y = -101/3", "output": "2x + 4y = -94/3\n1x + 4y = -101/3\n\nUsing elimination\n1*(2x + 4y = -94/3)\n2*(1x + 4y = -101/3)\n2x + 4y = -94/3\n2x + 8y = -202/3\nSubtract equations\n-4y = 36\ny = 36/-4\ny = -9\n\nSubstitute y\n2x + 4(-9) = -94/3\n2x = 14/3\nx = 14/3/2\nx = 7/3"} {"input": "Solve x^2 + 53/24x + 55/48 = 0", "output": "x^2 + 53/24x + 55/48 = 0\n(x - -5/6)(x - -11/8) = 0\nx - -5/6 = 0 or x - -11/8 = 0\nx = -5/6\nx = -11/8"} {"input": "Find the solution to x^3 - 185/28x^2 + 53/7x + 65/28 = 0", "output": "x^3 - 185/28x^2 + 53/7x + 65/28 = 0\n(x - -1/4)(x - 13/7)(x - 5) = 0\nx - -1/4 = 0\nx - 13/7 = 0\nx - 5 = 0\nx = -1/4\nx = 13/7\nx = 5"} {"input": "Solve simultaneously:\n3x + 3y = -123/7\n9x + 2y = 23/7", "output": "3x + 3y = -123/7\n9x + 2y = 23/7\n\nUsing elimination\n9*(3x + 3y = -123/7)\n3*(9x + 2y = 23/7)\n27x + 27y = -1107/7\n27x + 6y = 69/7\nSubtract equations\n21y = -168\ny = -168/21\ny = -8\n\nSubstitute y\n3x + 3(-8) = -123/7\n3x = 45/7\nx = 45/7/3\nx = 15/7"} {"input": "Find x for 7x + 42 = 0", "output": "7x + 42 = 0\n7x = -42\nx = -42 / 7\nx = -6"} {"input": "Solve quickly: x^2 - 10x - 39 = 0", "output": "x^2 - 10x - 39 = 0\n(x - 13)(x - -3) = 0\nx - 13 = 0 or x - -3 = 0\nx = 13\nx = -3"} {"input": "Find x in 1x + 4/5 = 0", "output": "1x + 4/5 = 0\n1x = -4/5\nx = -4/5 / 1\nx = -4/5"} {"input": "Solve the equations:\n5x + 3y = 309/10\n9x + 4y = 517/10", "output": "5x + 3y = 309/10\n9x + 4y = 517/10\n\nUsing elimination\n9*(5x + 3y = 309/10)\n5*(9x + 4y = 517/10)\n45x + 27y = 2781/10\n45x + 20y = 517/2\nSubtract equations\n7y = 98/5\ny = 98/5/7\ny = 14/5\n\nSubstitute y\n5x + 3(14/5) = 309/10\n5x = 45/2\nx = 45/2/5\nx = 9/2"} {"input": "Find x in 9x + 117 = 0", "output": "9x + 117 = 0\n9x = -117\nx = -117 / 9\nx = -13"} {"input": "Solve simultaneously:\n1x + 9y = 49/40\n5x + 1y = 421/40", "output": "1x + 9y = 49/40\n5x + 1y = 421/40\n\nUsing elimination\n5*(1x + 9y = 49/40)\n1*(5x + 1y = 421/40)\n5x + 45y = 49/8\n5x + 1y = 421/40\nSubtract equations\n44y = -22/5\ny = -22/5/44\ny = -1/10\n\nSubstitute y\n1x + 9(-1/10) = 49/40\n1x = 17/8\nx = 17/8/1\nx = 17/8"} {"input": "What value of x satisfies x^3 + 5/6x^2 - 299/6x - 95 = 0", "output": "x^3 + 5/6x^2 - 299/6x - 95 = 0\n(x - -19/3)(x - -2)(x - 15/2) = 0\nx - -19/3 = 0\nx - -2 = 0\nx - 15/2 = 0\nx = -19/3\nx = -2\nx = 15/2"} {"input": "Find x and y such that\n5x + 4y = -27\n9x + 8y = -149/3", "output": "5x + 4y = -27\n9x + 8y = -149/3\n\nUsing elimination\n9*(5x + 4y = -27)\n5*(9x + 8y = -149/3)\n45x + 36y = -243\n45x + 40y = -745/3\nSubtract equations\n-4y = 16/3\ny = 16/3/-4\ny = -4/3\n\nSubstitute y\n5x + 4(-4/3) = -27\n5x = -65/3\nx = -65/3/5\nx = -13/3"} {"input": "Solve the system:\n6x + 6y = -24/7\n7x + 8y = -20/7", "output": "6x + 6y = -24/7\n7x + 8y = -20/7\n\nUsing elimination\n7*(6x + 6y = -24/7)\n6*(7x + 8y = -20/7)\n42x + 42y = -24\n42x + 48y = -120/7\nSubtract equations\n-6y = -48/7\ny = -48/7/-6\ny = 8/7\n\nSubstitute y\n6x + 6(8/7) = -24/7\n6x = -72/7\nx = -72/7/6\nx = -12/7"} {"input": "Solve 10x - 70 = 0", "output": "10x - 70 = 0\n10x = 70\nx = 70 / 10\nx = 7"} {"input": "Solve the equations:\n1x + 3y = 3\n4x + 4y = 28", "output": "1x + 3y = 3\n4x + 4y = 28\n\nUsing elimination\n4*(1x + 3y = 3)\n1*(4x + 4y = 28)\n4x + 12y = 12\n4x + 4y = 28\nSubtract equations\n8y = -16\ny = -16/8\ny = -2\n\nSubstitute y\n1x + 3(-2) = 3\n1x = 9\nx = 9/1\nx = 9"} {"input": "Find the solution to 10x + 160/7 = 0", "output": "10x + 160/7 = 0\n10x = -160/7\nx = -160/7 / 10\nx = -16/7"} {"input": "Find x and y such that\n1x + 8y = 157/3\n10x + 3y = 10", "output": "1x + 8y = 157/3\n10x + 3y = 10\n\nUsing elimination\n10*(1x + 8y = 157/3)\n1*(10x + 3y = 10)\n10x + 80y = 1570/3\n10x + 3y = 10\nSubtract equations\n77y = 1540/3\ny = 1540/3/77\ny = 20/3\n\nSubstitute y\n1x + 8(20/3) = 157/3\n1x = -1\nx = -1/1\nx = -1"} {"input": "Find x and y such that\n9x + 1y = 1369/9\n6x + 10y = 838/9", "output": "9x + 1y = 1369/9\n6x + 10y = 838/9\n\nUsing elimination\n6*(9x + 1y = 1369/9)\n9*(6x + 10y = 838/9)\n54x + 6y = 2738/3\n54x + 90y = 838\nSubtract equations\n-84y = 224/3\ny = 224/3/-84\ny = -8/9\n\nSubstitute y\n9x + 1(-8/9) = 1369/9\n9x = 153\nx = 153/9\nx = 17"} {"input": "Find x for 9x + 72/5 = 0", "output": "9x + 72/5 = 0\n9x = -72/5\nx = -72/5 / 9\nx = -8/5"} {"input": "Find x for x^3 + 146/15x^2 - 136/15x - 64 = 0", "output": "x^3 + 146/15x^2 - 136/15x - 64 = 0\n(x - -12/5)(x - -10)(x - 8/3) = 0\nx - -12/5 = 0\nx - -10 = 0\nx - 8/3 = 0\nx = -12/5\nx = -10\nx = 8/3"} {"input": "Solve the equations:\n7x + 7y = 175/6\n4x + 3y = 21", "output": "7x + 7y = 175/6\n4x + 3y = 21\n\nUsing elimination\n4*(7x + 7y = 175/6)\n7*(4x + 3y = 21)\n28x + 28y = 350/3\n28x + 21y = 147\nSubtract equations\n7y = -91/3\ny = -91/3/7\ny = -13/3\n\nSubstitute y\n7x + 7(-13/3) = 175/6\n7x = 119/2\nx = 119/2/7\nx = 17/2"} {"input": "Solve quickly: x^2 - 1/20x - 13/8 = 0", "output": "x^2 - 1/20x - 13/8 = 0\n(x - 13/10)(x - -5/4) = 0\nx - 13/10 = 0 or x - -5/4 = 0\nx = 13/10\nx = -5/4"} {"input": "Find x and y such that\n5x + 9y = -17\n9x + 1y = 301/15", "output": "5x + 9y = -17\n9x + 1y = 301/15\n\nUsing elimination\n9*(5x + 9y = -17)\n5*(9x + 1y = 301/15)\n45x + 81y = -153\n45x + 5y = 301/3\nSubtract equations\n76y = -760/3\ny = -760/3/76\ny = -10/3\n\nSubstitute y\n5x + 9(-10/3) = -17\n5x = 13\nx = 13/5\nx = 13/5"} {"input": "Find x and y such that\n1x + 10y = 292/21\n5x + 8y = 284/21", "output": "1x + 10y = 292/21\n5x + 8y = 284/21\n\nUsing elimination\n5*(1x + 10y = 292/21)\n1*(5x + 8y = 284/21)\n5x + 50y = 1460/21\n5x + 8y = 284/21\nSubtract equations\n42y = 56\ny = 56/42\ny = 4/3\n\nSubstitute y\n1x + 10(4/3) = 292/21\n1x = 4/7\nx = 4/7/1\nx = 4/7"} {"input": "Find x in x^3 + 81/4x^2 + 89/4x - 57/2 = 0", "output": "x^3 + 81/4x^2 + 89/4x - 57/2 = 0\n(x - -19)(x - -2)(x - 3/4) = 0\nx - -19 = 0\nx - -2 = 0\nx - 3/4 = 0\nx = -19\nx = -2\nx = 3/4"} {"input": "What value of x satisfies 4x - 6 = 0", "output": "4x - 6 = 0\n4x = 6\nx = 6 / 4\nx = 3/2"} {"input": "Determine x in 1x + 17/8 = 0", "output": "1x + 17/8 = 0\n1x = -17/8\nx = -17/8 / 1\nx = -17/8"} {"input": "Find the solution to 7x + 77/5 = 0", "output": "7x + 77/5 = 0\n7x = -77/5\nx = -77/5 / 7\nx = -11/5"} {"input": "Find x in x^2 - 104/63x + 20/63 = 0", "output": "x^2 - 104/63x + 20/63 = 0\n(x - 2/9)(x - 10/7) = 0\nx - 2/9 = 0 or x - 10/7 = 0\nx = 2/9\nx = 10/7"} {"input": "Solve quickly: 1x + 2 = 0", "output": "1x + 2 = 0\n1x = -2\nx = -2 / 1\nx = -2"} {"input": "Find x and y such that\n10x + 3y = 193/8\n9x + 8y = 29", "output": "10x + 3y = 193/8\n9x + 8y = 29\n\nUsing elimination\n9*(10x + 3y = 193/8)\n10*(9x + 8y = 29)\n90x + 27y = 1737/8\n90x + 80y = 290\nSubtract equations\n-53y = -583/8\ny = -583/8/-53\ny = 11/8\n\nSubstitute y\n10x + 3(11/8) = 193/8\n10x = 20\nx = 20/10\nx = 2"} {"input": "What value of x satisfies x^3 - 7/6x^2 - 53/3x + 12 = 0", "output": "x^3 - 7/6x^2 - 53/3x + 12 = 0\n(x - 9/2)(x - -4)(x - 2/3) = 0\nx - 9/2 = 0\nx - -4 = 0\nx - 2/3 = 0\nx = 9/2\nx = -4\nx = 2/3"} {"input": "Find x and y such that\n5x + 2y = 12\n6x + 10y = 148/5", "output": "5x + 2y = 12\n6x + 10y = 148/5\n\nUsing elimination\n6*(5x + 2y = 12)\n5*(6x + 10y = 148/5)\n30x + 12y = 72\n30x + 50y = 148\nSubtract equations\n-38y = -76\ny = -76/-38\ny = 2\n\nSubstitute y\n5x + 2(2) = 12\n5x = 8\nx = 8/5\nx = 8/5"} {"input": "Solve the system:\n10x + 10y = 275/6\n8x + 3y = 30", "output": "10x + 10y = 275/6\n8x + 3y = 30\n\nUsing elimination\n8*(10x + 10y = 275/6)\n10*(8x + 3y = 30)\n80x + 80y = 1100/3\n80x + 30y = 300\nSubtract equations\n50y = 200/3\ny = 200/3/50\ny = 4/3\n\nSubstitute y\n10x + 10(4/3) = 275/6\n10x = 65/2\nx = 65/2/10\nx = 13/4"} {"input": "Determine x in x^3 - 13/15x^2 - 706/15x + 56 = 0", "output": "x^3 - 13/15x^2 - 706/15x + 56 = 0\n(x - 20/3)(x - 6/5)(x - -7) = 0\nx - 20/3 = 0\nx - 6/5 = 0\nx - -7 = 0\nx = 20/3\nx = 6/5\nx = -7"} {"input": "Find the solution to x^3 - 121/40x^2 + 353/200x + 663/800 = 0", "output": "x^3 - 121/40x^2 + 353/200x + 663/800 = 0\n(x - -3/10)(x - 13/8)(x - 17/10) = 0\nx - -3/10 = 0\nx - 13/8 = 0\nx - 17/10 = 0\nx = -3/10\nx = 13/8\nx = 17/10"} {"input": "Find x in 8x + 8/9 = 0", "output": "8x + 8/9 = 0\n8x = -8/9\nx = -8/9 / 8\nx = -1/9"} {"input": "Find x in x^2 - 21/5x - 152/5 = 0", "output": "x^2 - 21/5x - 152/5 = 0\n(x - -19/5)(x - 8) = 0\nx - -19/5 = 0 or x - 8 = 0\nx = -19/5\nx = 8"} {"input": "Solve quickly: x^2 + 3x + 14/9 = 0", "output": "x^2 + 3x + 14/9 = 0\n(x - -2/3)(x - -7/3) = 0\nx - -2/3 = 0 or x - -7/3 = 0\nx = -2/3\nx = -7/3"} {"input": "Find the solution to x^3 + 7/10x^2 - 3/10x = 0", "output": "x^3 + 7/10x^2 - 3/10x = 0\n(x - 3/10)(x - -1)(x - 0) = 0\nx - 3/10 = 0\nx - -1 = 0\nx - 0 = 0\nx = 3/10\nx = -1\nx = 0"} {"input": "Find the solution to x^3 + 332/63x^2 + 1591/189x + 760/189 = 0", "output": "x^3 + 332/63x^2 + 1591/189x + 760/189 = 0\n(x - -8/9)(x - -19/7)(x - -5/3) = 0\nx - -8/9 = 0\nx - -19/7 = 0\nx - -5/3 = 0\nx = -8/9\nx = -19/7\nx = -5/3"} {"input": "Find x for x^3 + 51/4x^2 + 149/4x + 63/2 = 0", "output": "x^3 + 51/4x^2 + 149/4x + 63/2 = 0\n(x - -2)(x - -9)(x - -7/4) = 0\nx - -2 = 0\nx - -9 = 0\nx - -7/4 = 0\nx = -2\nx = -9\nx = -7/4"} {"input": "Solve quickly: x^2 - 15/2x - 27/2 = 0", "output": "x^2 - 15/2x - 27/2 = 0\n(x - -3/2)(x - 9) = 0\nx - -3/2 = 0 or x - 9 = 0\nx = -3/2\nx = 9"} {"input": "Find x for 7x + 7/2 = 0", "output": "7x + 7/2 = 0\n7x = -7/2\nx = -7/2 / 7\nx = -1/2"} {"input": "Find x and y such that\n10x + 10y = 1\n1x + 8y = 39/5", "output": "10x + 10y = 1\n1x + 8y = 39/5\n\nUsing elimination\n1*(10x + 10y = 1)\n10*(1x + 8y = 39/5)\n10x + 10y = 1\n10x + 80y = 78\nSubtract equations\n-70y = -77\ny = -77/-70\ny = 11/10\n\nSubstitute y\n10x + 10(11/10) = 1\n10x = -10\nx = -10/10\nx = -1"} {"input": "Determine x in x^3 + 59/6x^2 + 31/2x - 15 = 0", "output": "x^3 + 59/6x^2 + 31/2x - 15 = 0\n(x - -15/2)(x - -3)(x - 2/3) = 0\nx - -15/2 = 0\nx - -3 = 0\nx - 2/3 = 0\nx = -15/2\nx = -3\nx = 2/3"} {"input": "Find x for 2x - 20/3 = 0", "output": "2x - 20/3 = 0\n2x = 20/3\nx = 20/3 / 2\nx = 10/3"} {"input": "Solve the system:\n3x + 10y = 30\n1x + 7y = 115/6", "output": "3x + 10y = 30\n1x + 7y = 115/6\n\nUsing elimination\n1*(3x + 10y = 30)\n3*(1x + 7y = 115/6)\n3x + 10y = 30\n3x + 21y = 115/2\nSubtract equations\n-11y = -55/2\ny = -55/2/-11\ny = 5/2\n\nSubstitute y\n3x + 10(5/2) = 30\n3x = 5\nx = 5/3\nx = 5/3"} {"input": "Determine x in x^2 + 16/3x + 5/3 = 0", "output": "x^2 + 16/3x + 5/3 = 0\n(x - -1/3)(x - -5) = 0\nx - -1/3 = 0 or x - -5 = 0\nx = -1/3\nx = -5"} {"input": "Find x in x^3 + 17x^2 + 44x + 28 = 0", "output": "x^3 + 17x^2 + 44x + 28 = 0\n(x - -2)(x - -14)(x - -1) = 0\nx - -2 = 0\nx - -14 = 0\nx - -1 = 0\nx = -2\nx = -14\nx = -1"} {"input": "Find the solution to x^3 + 37/10x^2 + 8/5x = 0", "output": "x^3 + 37/10x^2 + 8/5x = 0\n(x - -1/2)(x - -16/5)(x - 0) = 0\nx - -1/2 = 0\nx - -16/5 = 0\nx - 0 = 0\nx = -1/2\nx = -16/5\nx = 0"} {"input": "Solve the equation x^3 - 44/3x^2 + 3539/81x - 2992/81 = 0", "output": "x^3 - 44/3x^2 + 3539/81x - 2992/81 = 0\n(x - 17/9)(x - 11)(x - 16/9) = 0\nx - 17/9 = 0\nx - 11 = 0\nx - 16/9 = 0\nx = 17/9\nx = 11\nx = 16/9"} {"input": "Solve the equations:\n10x + 5y = -40\n6x + 5y = -44", "output": "10x + 5y = -40\n6x + 5y = -44\n\nUsing elimination\n6*(10x + 5y = -40)\n10*(6x + 5y = -44)\n60x + 30y = -240\n60x + 50y = -440\nSubtract equations\n-20y = 200\ny = 200/-20\ny = -10\n\nSubstitute y\n10x + 5(-10) = -40\n10x = 10\nx = 10/10\nx = 1"} {"input": "Solve the system:\n5x + 1y = 37/2\n6x + 5y = 317/10", "output": "5x + 1y = 37/2\n6x + 5y = 317/10\n\nUsing elimination\n6*(5x + 1y = 37/2)\n5*(6x + 5y = 317/10)\n30x + 6y = 111\n30x + 25y = 317/2\nSubtract equations\n-19y = -95/2\ny = -95/2/-19\ny = 5/2\n\nSubstitute y\n5x + 1(5/2) = 37/2\n5x = 16\nx = 16/5\nx = 16/5"} {"input": "Find x in x^3 + 17/3x^2 + 94/9x + 56/9 = 0", "output": "x^3 + 17/3x^2 + 94/9x + 56/9 = 0\n(x - -7/3)(x - -4/3)(x - -2) = 0\nx - -7/3 = 0\nx - -4/3 = 0\nx - -2 = 0\nx = -7/3\nx = -4/3\nx = -2"} {"input": "Solve the equations:\n8x + 6y = 77\n3x + 4y = 42", "output": "8x + 6y = 77\n3x + 4y = 42\n\nUsing elimination\n3*(8x + 6y = 77)\n8*(3x + 4y = 42)\n24x + 18y = 231\n24x + 32y = 336\nSubtract equations\n-14y = -105\ny = -105/-14\ny = 15/2\n\nSubstitute y\n8x + 6(15/2) = 77\n8x = 32\nx = 32/8\nx = 4"} {"input": "Find the solution to x^2 - 7/9x = 0", "output": "x^2 - 7/9x = 0\n(x - 0)(x - 7/9) = 0\nx - 0 = 0 or x - 7/9 = 0\nx = 0\nx = 7/9"} {"input": "Solve 10x - 12 = 0", "output": "10x - 12 = 0\n10x = 12\nx = 12 / 10\nx = 6/5"} {"input": "Solve the system:\n4x + 10y = -604/5\n2x + 6y = -362/5", "output": "4x + 10y = -604/5\n2x + 6y = -362/5\n\nUsing elimination\n2*(4x + 10y = -604/5)\n4*(2x + 6y = -362/5)\n8x + 20y = -1208/5\n8x + 24y = -1448/5\nSubtract equations\n-4y = 48\ny = 48/-4\ny = -12\n\nSubstitute y\n4x + 10(-12) = -604/5\n4x = -4/5\nx = -4/5/4\nx = -1/5"} {"input": "Find the solution to 2x - 2/5 = 0", "output": "2x - 2/5 = 0\n2x = 2/5\nx = 2/5 / 2\nx = 1/5"} {"input": "Determine x in x^2 - 3/2x + 7/18 = 0", "output": "x^2 - 3/2x + 7/18 = 0\n(x - 7/6)(x - 1/3) = 0\nx - 7/6 = 0 or x - 1/3 = 0\nx = 7/6\nx = 1/3"} {"input": "Find x for x^3 + 65/18x^2 + 23/18x - 5/3 = 0", "output": "x^3 + 65/18x^2 + 23/18x - 5/3 = 0\n(x - 1/2)(x - -10/9)(x - -3) = 0\nx - 1/2 = 0\nx - -10/9 = 0\nx - -3 = 0\nx = 1/2\nx = -10/9\nx = -3"} {"input": "Solve quickly: x^3 - 77/10x^2 + 73/5x - 11/2 = 0", "output": "x^3 - 77/10x^2 + 73/5x - 11/2 = 0\n(x - 5)(x - 1/2)(x - 11/5) = 0\nx - 5 = 0\nx - 1/2 = 0\nx - 11/5 = 0\nx = 5\nx = 1/2\nx = 11/5"} {"input": "Find x for x^2 + 186/35x + 216/35 = 0", "output": "x^2 + 186/35x + 216/35 = 0\n(x - -18/5)(x - -12/7) = 0\nx - -18/5 = 0 or x - -12/7 = 0\nx = -18/5\nx = -12/7"} {"input": "Find x for x^3 - 61/10x^2 + 129/50x + 99/25 = 0", "output": "x^3 - 61/10x^2 + 129/50x + 99/25 = 0\n(x - 6/5)(x - -3/5)(x - 11/2) = 0\nx - 6/5 = 0\nx - -3/5 = 0\nx - 11/2 = 0\nx = 6/5\nx = -3/5\nx = 11/2"} {"input": "Solve the equations:\n9x + 2y = -93/2\n5x + 6y = -35", "output": "9x + 2y = -93/2\n5x + 6y = -35\n\nUsing elimination\n5*(9x + 2y = -93/2)\n9*(5x + 6y = -35)\n45x + 10y = -465/2\n45x + 54y = -315\nSubtract equations\n-44y = 165/2\ny = 165/2/-44\ny = -15/8\n\nSubstitute y\n9x + 2(-15/8) = -93/2\n9x = -171/4\nx = -171/4/9\nx = -19/4"} {"input": "Solve simultaneously:\n5x + 2y = 23\n5x + 4y = 53/3", "output": "5x + 2y = 23\n5x + 4y = 53/3\n\nUsing elimination\n5*(5x + 2y = 23)\n5*(5x + 4y = 53/3)\n25x + 10y = 115\n25x + 20y = 265/3\nSubtract equations\n-10y = 80/3\ny = 80/3/-10\ny = -8/3\n\nSubstitute y\n5x + 2(-8/3) = 23\n5x = 85/3\nx = 85/3/5\nx = 17/3"} {"input": "Determine x in x^2 - 38/21x + 5/21 = 0", "output": "x^2 - 38/21x + 5/21 = 0\n(x - 1/7)(x - 5/3) = 0\nx - 1/7 = 0 or x - 5/3 = 0\nx = 1/7\nx = 5/3"} {"input": "Solve quickly: x^2 - 16/7x - 57/49 = 0", "output": "x^2 - 16/7x - 57/49 = 0\n(x - -3/7)(x - 19/7) = 0\nx - -3/7 = 0 or x - 19/7 = 0\nx = -3/7\nx = 19/7"} {"input": "Determine x in x^3 + 127/56x^2 - 2617/392x - 2907/196 = 0", "output": "x^3 + 127/56x^2 - 2617/392x - 2907/196 = 0\n(x - 18/7)(x - -19/7)(x - -17/8) = 0\nx - 18/7 = 0\nx - -19/7 = 0\nx - -17/8 = 0\nx = 18/7\nx = -19/7\nx = -17/8"} {"input": "Solve x^3 - 2/9x^2 - 359/36x + 385/36 = 0", "output": "x^3 - 2/9x^2 - 359/36x + 385/36 = 0\n(x - 11/9)(x - -7/2)(x - 5/2) = 0\nx - 11/9 = 0\nx - -7/2 = 0\nx - 5/2 = 0\nx = 11/9\nx = -7/2\nx = 5/2"} {"input": "Find x for x^2 - 1/2x - 15/2 = 0", "output": "x^2 - 1/2x - 15/2 = 0\n(x - -5/2)(x - 3) = 0\nx - -5/2 = 0 or x - 3 = 0\nx = -5/2\nx = 3"} {"input": "Find the solution to 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Solve 10x - 70 = 0", "output": "10x - 70 = 0\n10x = 70\nx = 70 / 10\nx = 7"} {"input": "Solve the equations:\n4x + 7y = -7\n1x + 7y = -55/4", "output": "4x + 7y = -7\n1x + 7y = -55/4\n\nUsing elimination\n1*(4x + 7y = -7)\n4*(1x + 7y = -55/4)\n4x + 7y = -7\n4x + 28y = -55\nSubtract equations\n-21y = 48\ny = 48/-21\ny = -16/7\n\nSubstitute y\n4x + 7(-16/7) = -7\n4x = 9\nx = 9/4\nx = 9/4"} {"input": "Solve simultaneously:\n4x + 7y = -2/3\n2x + 8y = -10/3", "output": "4x + 7y = -2/3\n2x + 8y = -10/3\n\nUsing elimination\n2*(4x + 7y = -2/3)\n4*(2x + 8y = -10/3)\n8x + 14y = -4/3\n8x + 32y = -40/3\nSubtract equations\n-18y = 12\ny = 12/-18\ny = -2/3\n\nSubstitute y\n4x + 7(-2/3) = -2/3\n4x = 4\nx = 4/4\nx = 1"} {"input": "Solve the equations:\n3x + 10y = -421/21\n8x + 2y = 628/63", "output": "3x + 10y = -421/21\n8x + 2y = 628/63\n\nUsing elimination\n8*(3x + 10y = -421/21)\n3*(8x + 2y = 628/63)\n24x + 80y = -3368/21\n24x + 6y = 628/21\nSubtract equations\n74y = -1332/7\ny = -1332/7/74\ny = -18/7\n\nSubstitute y\n3x + 10(-18/7) = -421/21\n3x = 17/3\nx = 17/3/3\nx = 17/9"} {"input": "Find x in x^3 + 5/6x^2 - 26/9x = 0", "output": "x^3 + 5/6x^2 - 26/9x = 0\n(x - 4/3)(x - 0)(x - -13/6) = 0\nx - 4/3 = 0\nx - 0 = 0\nx - -13/6 = 0\nx = 4/3\nx = 0\nx = -13/6"} {"input": "Compute the solution of x^3 - 25/2x^2 + 2423/64x - 4199/128 = 0", "output": "x^3 - 25/2x^2 + 2423/64x - 4199/128 = 0\n(x - 13/8)(x - 17/2)(x - 19/8) = 0\nx - 13/8 = 0\nx - 17/2 = 0\nx - 19/8 = 0\nx = 13/8\nx = 17/2\nx = 19/8"} {"input": "Solve the equation x^3 + 59/4x^2 + 173/8x - 117/8 = 0", "output": "x^3 + 59/4x^2 + 173/8x - 117/8 = 0\n(x - 1/2)(x - -9/4)(x - -13) = 0\nx - 1/2 = 0\nx - -9/4 = 0\nx - -13 = 0\nx = 1/2\nx = -9/4\nx = -13"} {"input": "Find x for 5x - 15/8 = 0", "output": "5x - 15/8 = 0\n5x = 15/8\nx = 15/8 / 5\nx = 3/8"} {"input": "Compute the solution of 6x - 6/5 = 0", "output": "6x - 6/5 = 0\n6x = 6/5\nx = 6/5 / 6\nx = 1/5"} {"input": "Solve simultaneously:\n10x + 5y = 125/7\n10x + 7y = 17", "output": "10x + 5y = 125/7\n10x + 7y = 17\n\nUsing elimination\n10*(10x + 5y = 125/7)\n10*(10x + 7y = 17)\n100x + 50y = 1250/7\n100x + 70y = 170\nSubtract equations\n-20y = 60/7\ny = 60/7/-20\ny = -3/7\n\nSubstitute y\n10x + 5(-3/7) = 125/7\n10x = 20\nx = 20/10\nx = 2"} {"input": "Solve quickly: x^3 + 59/63x^2 - 1157/189x - 95/27 = 0", "output": "x^3 + 59/63x^2 - 1157/189x - 95/27 = 0\n(x - -19/7)(x - 7/3)(x - -5/9) = 0\nx - -19/7 = 0\nx - 7/3 = 0\nx - -5/9 = 0\nx = -19/7\nx = 7/3\nx = -5/9"} {"input": "Find the solution to x^2 + 25/2x - 247/2 = 0", "output": "x^2 + 25/2x - 247/2 = 0\n(x - 13/2)(x - -19) = 0\nx - 13/2 = 0 or x - -19 = 0\nx = 13/2\nx = -19"} {"input": "Solve the equation 8x + 12 = 0", "output": "8x + 12 = 0\n8x = -12\nx = -12 / 8\nx = -3/2"} {"input": "Solve quickly: x^3 - 699/56x^2 + 1455/56x - 325/28 = 0", "output": "x^3 - 699/56x^2 + 1455/56x - 325/28 = 0\n(x - 5/8)(x - 13/7)(x - 10) = 0\nx - 5/8 = 0\nx - 13/7 = 0\nx - 10 = 0\nx = 5/8\nx = 13/7\nx = 10"} {"input": "Find x for x^2 - 12x + 27 = 0", "output": "x^2 - 12x + 27 = 0\n(x - 3)(x - 9) = 0\nx - 3 = 0 or x - 9 = 0\nx = 3\nx = 9"} {"input": "Find x for x^3 + 35/4x^2 + 181/8x + 119/8 = 0", "output": "x^3 + 35/4x^2 + 181/8x + 119/8 = 0\n(x - -1)(x - -7/2)(x - -17/4) = 0\nx - -1 = 0\nx - -7/2 = 0\nx - -17/4 = 0\nx = -1\nx = -7/2\nx = -17/4"} {"input": "Determine x in x^3 + 69/7x^2 - 843/7x + 17 = 0", "output": "x^3 + 69/7x^2 - 843/7x + 17 = 0\n(x - -17)(x - 7)(x - 1/7) = 0\nx - -17 = 0\nx - 7 = 0\nx - 1/7 = 0\nx = -17\nx = 7\nx = 1/7"} {"input": "Solve quickly: x^3 - 9/2x^2 - 15/2x + 11 = 0", "output": "x^3 - 9/2x^2 - 15/2x + 11 = 0\n(x - -2)(x - 1)(x - 11/2) = 0\nx - -2 = 0\nx - 1 = 0\nx - 11/2 = 0\nx = -2\nx = 1\nx = 11/2"} {"input": "Determine x in x^2 + 41/10x - 9/2 = 0", "output": "x^2 + 41/10x - 9/2 = 0\n(x - -5)(x - 9/10) = 0\nx - -5 = 0 or x - 9/10 = 0\nx = -5\nx = 9/10"} {"input": "Find the solution to x^3 - 128/45x^2 + 343/135x - 98/135 = 0", "output": "x^3 - 128/45x^2 + 343/135x - 98/135 = 0\n(x - 2/3)(x - 7/9)(x - 7/5) = 0\nx - 2/3 = 0\nx - 7/9 = 0\nx - 7/5 = 0\nx = 2/3\nx = 7/9\nx = 7/5"} {"input": "Solve simultaneously:\n1x + 4y = 65\n5x + 3y = 70", "output": "1x + 4y = 65\n5x + 3y = 70\n\nUsing elimination\n5*(1x + 4y = 65)\n1*(5x + 3y = 70)\n5x + 20y = 325\n5x + 3y = 70\nSubtract equations\n17y = 255\ny = 255/17\ny = 15\n\nSubstitute y\n1x + 4(15) = 65\n1x = 5\nx = 5/1\nx = 5"} {"input": "Compute the solution of x^3 + 119/12x^2 + 91/24x - 19/12 = 0", "output": "x^3 + 119/12x^2 + 91/24x - 19/12 = 0\n(x - 1/4)(x - -19/2)(x - -2/3) = 0\nx - 1/4 = 0\nx - -19/2 = 0\nx - -2/3 = 0\nx = 1/4\nx = -19/2\nx = -2/3"} {"input": "Compute the solution of x^3 - 11/5x^2 + 2/5x = 0", "output": "x^3 - 11/5x^2 + 2/5x = 0\n(x - 2)(x - 0)(x - 1/5) = 0\nx - 2 = 0\nx - 0 = 0\nx - 1/5 = 0\nx = 2\nx = 0\nx = 1/5"} {"input": "Find x and y such that\n6x + 6y = -98/5\n3x + 9y = -97/5", "output": "6x + 6y = -98/5\n3x + 9y = -97/5\n\nUsing elimination\n3*(6x + 6y = -98/5)\n6*(3x + 9y = -97/5)\n18x + 18y = -294/5\n18x + 54y = -582/5\nSubtract equations\n-36y = 288/5\ny = 288/5/-36\ny = -8/5\n\nSubstitute y\n6x + 6(-8/5) = -98/5\n6x = -10\nx = -10/6\nx = -5/3"} {"input": "Find the solution to x^3 - 5/9x^2 - 122/9x + 56/3 = 0", "output": "x^3 - 5/9x^2 - 122/9x + 56/3 = 0\n(x - 3)(x - -4)(x - 14/9) = 0\nx - 3 = 0\nx - -4 = 0\nx - 14/9 = 0\nx = 3\nx = -4\nx = 14/9"} {"input": "Find x for x^3 + 3x^2 - 70x - 144 = 0", "output": "x^3 + 3x^2 - 70x - 144 = 0\n(x - -2)(x - -9)(x - 8) = 0\nx - -2 = 0\nx - -9 = 0\nx - 8 = 0\nx = -2\nx = -9\nx = 8"} {"input": "Solve the equation 6x - 42/5 = 0", "output": "6x - 42/5 = 0\n6x = 42/5\nx = 42/5 / 6\nx = 7/5"} {"input": "Solve the equation 4x - 68/9 = 0", "output": "4x - 68/9 = 0\n4x = 68/9\nx = 68/9 / 4\nx = 17/9"} {"input": "Solve the equations:\n3x + 9y = 183/10\n4x + 4y = 134/5", "output": "3x + 9y = 183/10\n4x + 4y = 134/5\n\nUsing elimination\n4*(3x + 9y = 183/10)\n3*(4x + 4y = 134/5)\n12x + 36y = 366/5\n12x + 12y = 402/5\nSubtract equations\n24y = -36/5\ny = -36/5/24\ny = -3/10\n\nSubstitute y\n3x + 9(-3/10) = 183/10\n3x = 21\nx = 21/3\nx = 7"} {"input": "Find the solution to x^2 + 5/3x - 50/3 = 0", "output": "x^2 + 5/3x - 50/3 = 0\n(x - 10/3)(x - -5) = 0\nx - 10/3 = 0 or x - -5 = 0\nx = 10/3\nx = -5"} {"input": "What value of x satisfies x^3 + 14/9x^2 - 37/12x - 65/36 = 0", "output": "x^3 + 14/9x^2 - 37/12x - 65/36 = 0\n(x - -1/2)(x - 13/9)(x - -5/2) = 0\nx - -1/2 = 0\nx - 13/9 = 0\nx - -5/2 = 0\nx = -1/2\nx = 13/9\nx = -5/2"} {"input": "Find x for x^2 + 10/21x - 200/21 = 0", "output": "x^2 + 10/21x - 200/21 = 0\n(x - -10/3)(x - 20/7) = 0\nx - -10/3 = 0 or x - 20/7 = 0\nx = -10/3\nx = 20/7"} {"input": "Find the solution to x^2 + 4/15x - 7/3 = 0", "output": "x^2 + 4/15x - 7/3 = 0\n(x - 7/5)(x - -5/3) = 0\nx - 7/5 = 0 or x - -5/3 = 0\nx = 7/5\nx = -5/3"} {"input": "What value of x satisfies x^3 + 9/8x^2 - 21/16x - 13/16 = 0", "output": "x^3 + 9/8x^2 - 21/16x - 13/16 = 0\n(x - 1)(x - -1/2)(x - -13/8) = 0\nx - 1 = 0\nx - -1/2 = 0\nx - -13/8 = 0\nx = 1\nx = -1/2\nx = -13/8"} {"input": "Solve the equation x^3 + 141/35x^2 + 29/7x + 39/35 = 0", "output": "x^3 + 141/35x^2 + 29/7x + 39/35 = 0\n(x - -13/5)(x - -1)(x - -3/7) = 0\nx - -13/5 = 0\nx - -1 = 0\nx - -3/7 = 0\nx = -13/5\nx = -1\nx = -3/7"} {"input": "Find x in x^3 - 47/6x^2 - 211/18x + 11 = 0", "output": "x^3 - 47/6x^2 - 211/18x + 11 = 0\n(x - -11/6)(x - 2/3)(x - 9) = 0\nx - -11/6 = 0\nx - 2/3 = 0\nx - 9 = 0\nx = -11/6\nx = 2/3\nx = 9"} {"input": "Solve 6x - 42 = 0", "output": "6x - 42 = 0\n6x = 42\nx = 42 / 6\nx = 7"} {"input": "Solve quickly: x^2 - 55/63x - 34/9 = 0", "output": "x^2 - 55/63x - 34/9 = 0\n(x - 17/7)(x - -14/9) = 0\nx - 17/7 = 0 or x - -14/9 = 0\nx = 17/7\nx = -14/9"} {"input": "Solve x^2 + 61/10x + 9 = 0", "output": "x^2 + 61/10x + 9 = 0\n(x - -5/2)(x - -18/5) = 0\nx - -5/2 = 0 or x - -18/5 = 0\nx = -5/2\nx = -18/5"} {"input": "Find x in x^3 - 7/2x^2 - 84x - 216 = 0", "output": "x^3 - 7/2x^2 - 84x - 216 = 0\n(x - 12)(x - -4)(x - -9/2) = 0\nx - 12 = 0\nx - -4 = 0\nx - -9/2 = 0\nx = 12\nx = -4\nx = -9/2"} {"input": "Compute the solution of x^3 - 23/63x^2 - 164/63x - 4/3 = 0", "output": "x^3 - 23/63x^2 - 164/63x - 4/3 = 0\n(x - -7/9)(x - 2)(x - -6/7) = 0\nx - -7/9 = 0\nx - 2 = 0\nx - -6/7 = 0\nx = -7/9\nx = 2\nx = -6/7"} {"input": "What value of x satisfies x^2 - 31/6x + 20/3 = 0", "output": "x^2 - 31/6x + 20/3 = 0\n(x - 8/3)(x - 5/2) = 0\nx - 8/3 = 0 or x - 5/2 = 0\nx = 8/3\nx = 5/2"} {"input": "Determine x in x^3 + 154/45x^2 + 79/75x - 84/25 = 0", "output": "x^3 + 154/45x^2 + 79/75x - 84/25 = 0\n(x - -9/5)(x - -12/5)(x - 7/9) = 0\nx - -9/5 = 0\nx - -12/5 = 0\nx - 7/9 = 0\nx = -9/5\nx = -12/5\nx = 7/9"} {"input": "Solve the equations:\n8x + 10y = 163/12\n8x + 1y = -25/24", "output": "8x + 10y = 163/12\n8x + 1y = -25/24\n\nUsing elimination\n8*(8x + 10y = 163/12)\n8*(8x + 1y = -25/24)\n64x + 80y = 326/3\n64x + 8y = -25/3\nSubtract equations\n72y = 117\ny = 117/72\ny = 13/8\n\nSubstitute y\n8x + 10(13/8) = 163/12\n8x = -8/3\nx = -8/3/8\nx = -1/3"} {"input": "Solve the equations:\n10x + 5y = 440/21\n9x + 3y = 139/7", "output": "10x + 5y = 440/21\n9x + 3y = 139/7\n\nUsing elimination\n9*(10x + 5y = 440/21)\n10*(9x + 3y = 139/7)\n90x + 45y = 1320/7\n90x + 30y = 1390/7\nSubtract equations\n15y = -10\ny = -10/15\ny = -2/3\n\nSubstitute y\n10x + 5(-2/3) = 440/21\n10x = 170/7\nx = 170/7/10\nx = 17/7"} {"input": "What value of x satisfies x^3 + 53/20x^2 + 8/5x - 3/16 = 0", "output": "x^3 + 53/20x^2 + 8/5x - 3/16 = 0\n(x - 1/10)(x - -3/2)(x - -5/4) = 0\nx - 1/10 = 0\nx - -3/2 = 0\nx - -5/4 = 0\nx = 1/10\nx = -3/2\nx = -5/4"} {"input": "Solve the system:\n9x + 5y = -53/8\n8x + 10y = -9/2", "output": "9x + 5y = -53/8\n8x + 10y = -9/2\n\nUsing elimination\n8*(9x + 5y = -53/8)\n9*(8x + 10y = -9/2)\n72x + 40y = -53\n72x + 90y = -81/2\nSubtract equations\n-50y = -25/2\ny = -25/2/-50\ny = 1/4\n\nSubstitute y\n9x + 5(1/4) = -53/8\n9x = -63/8\nx = -63/8/9\nx = -7/8"} {"input": "Solve x^3 + 109/60x^2 - 1109/120x + 187/40 = 0", "output": "x^3 + 109/60x^2 - 1109/120x + 187/40 = 0\n(x - 11/6)(x - -17/4)(x - 3/5) = 0\nx - 11/6 = 0\nx - -17/4 = 0\nx - 3/5 = 0\nx = 11/6\nx = -17/4\nx = 3/5"} {"input": "Solve the system:\n4x + 2y = 172/9\n9x + 7y = 422/9", "output": "4x + 2y = 172/9\n9x + 7y = 422/9\n\nUsing elimination\n9*(4x + 2y = 172/9)\n4*(9x + 7y = 422/9)\n36x + 18y = 172\n36x + 28y = 1688/9\nSubtract equations\n-10y = -140/9\ny = -140/9/-10\ny = 14/9\n\nSubstitute y\n4x + 2(14/9) = 172/9\n4x = 16\nx = 16/4\nx = 4"} {"input": "Find the solution to 6x + 6/5 = 0", "output": "6x + 6/5 = 0\n6x = -6/5\nx = -6/5 / 6\nx = -1/5"} {"input": "Solve quickly: x^3 - 1x^2 - 71/4x + 9 = 0", "output": "x^3 - 1x^2 - 71/4x + 9 = 0\n(x - 1/2)(x - 9/2)(x - -4) = 0\nx - 1/2 = 0\nx - 9/2 = 0\nx - -4 = 0\nx = 1/2\nx = 9/2\nx = -4"} {"input": "Solve the system:\n2x + 8y = 8/3\n3x + 1y = -7", "output": "2x + 8y = 8/3\n3x + 1y = -7\n\nUsing elimination\n3*(2x + 8y = 8/3)\n2*(3x + 1y = -7)\n6x + 24y = 8\n6x + 2y = -14\nSubtract equations\n22y = 22\ny = 22/22\ny = 1\n\nSubstitute y\n2x + 8(1) = 8/3\n2x = -16/3\nx = -16/3/2\nx = -8/3"} {"input": "Find x in x^3 + 581/90x^2 + 1127/90x + 343/45 = 0", "output": "x^3 + 581/90x^2 + 1127/90x + 343/45 = 0\n(x - -7/2)(x - -7/5)(x - -14/9) = 0\nx - -7/2 = 0\nx - -7/5 = 0\nx - -14/9 = 0\nx = -7/2\nx = -7/5\nx = -14/9"} {"input": "Compute the solution of 9x - 36 = 0", "output": "9x - 36 = 0\n9x = 36\nx = 36 / 9\nx = 4"} {"input": "What value of x satisfies x^2 + 37/7x + 36/7 = 0", "output": "x^2 + 37/7x + 36/7 = 0\n(x - -4)(x - -9/7) = 0\nx - -4 = 0 or x - -9/7 = 0\nx = -4\nx = -9/7"} {"input": "Compute the solution of x^3 - 163/35x^2 - 559/35x - 3 = 0", "output": "x^3 - 163/35x^2 - 559/35x - 3 = 0\n(x - 7)(x - -15/7)(x - -1/5) = 0\nx - 7 = 0\nx - -15/7 = 0\nx - -1/5 = 0\nx = 7\nx = -15/7\nx = -1/5"} {"input": "Find x for 2x - 8/5 = 0", "output": "2x - 8/5 = 0\n2x = 8/5\nx = 8/5 / 2\nx = 4/5"} {"input": "What value of x satisfies x^2 - 77/15x + 76/15 = 0", "output": "x^2 - 77/15x + 76/15 = 0\n(x - 19/5)(x - 4/3) = 0\nx - 19/5 = 0 or x - 4/3 = 0\nx = 19/5\nx = 4/3"} {"input": "Compute the solution of 6x + 78 = 0", "output": "6x + 78 = 0\n6x = -78\nx = -78 / 6\nx = -13"} {"input": "Find the solution to x^2 + 173/72x + 91/72 = 0", "output": "x^2 + 173/72x + 91/72 = 0\n(x - -7/9)(x - -13/8) = 0\nx - -7/9 = 0 or x - -13/8 = 0\nx = -7/9\nx = -13/8"} {"input": "Find x in x^2 - 17/5x - 38/25 = 0", "output": "x^2 - 17/5x - 38/25 = 0\n(x - 19/5)(x - -2/5) = 0\nx - 19/5 = 0 or x - -2/5 = 0\nx = 19/5\nx = -2/5"} {"input": "Find the solution to x^3 + 53/8x^2 + 327/32x + 189/64 = 0", "output": "x^3 + 53/8x^2 + 327/32x + 189/64 = 0\n(x - -9/2)(x - -7/4)(x - -3/8) = 0\nx - -9/2 = 0\nx - -7/4 = 0\nx - -3/8 = 0\nx = -9/2\nx = -7/4\nx = -3/8"} {"input": "Find x in 3x + 9/2 = 0", "output": "3x + 9/2 = 0\n3x = -9/2\nx = -9/2 / 3\nx = -3/2"} {"input": "Determine x in x^2 + 4/7x - 11/7 = 0", "output": "x^2 + 4/7x - 11/7 = 0\n(x - -11/7)(x - 1) = 0\nx - -11/7 = 0 or x - 1 = 0\nx = -11/7\nx = 1"} {"input": "Solve quickly: x^2 - 11/56x - 3/14 = 0", "output": "x^2 - 11/56x - 3/14 = 0\n(x - 4/7)(x - -3/8) = 0\nx - 4/7 = 0 or x - -3/8 = 0\nx = 4/7\nx = -3/8"} {"input": "What value of x satisfies x^3 - 2x^2 - 5x + 6 = 0", "output": "x^3 - 2x^2 - 5x + 6 = 0\n(x - 3)(x - 1)(x - -2) = 0\nx - 3 = 0\nx - 1 = 0\nx - -2 = 0\nx = 3\nx = 1\nx = -2"} {"input": "Find x for x^3 - 629/252x^2 + 305/252x + 1/6 = 0", "output": "x^3 - 629/252x^2 + 305/252x + 1/6 = 0\n(x - 6/7)(x - 7/4)(x - -1/9) = 0\nx - 6/7 = 0\nx - 7/4 = 0\nx - -1/9 = 0\nx = 6/7\nx = 7/4\nx = -1/9"} {"input": "Find x for x^2 + 12x - 64 = 0", "output": "x^2 + 12x - 64 = 0\n(x - -16)(x - 4) = 0\nx - -16 = 0 or x - 4 = 0\nx = -16\nx = 4"} {"input": "Solve the equation x^3 - 15x^2 - 54x = 0", "output": "x^3 - 15x^2 - 54x = 0\n(x - 18)(x - -3)(x - 0) = 0\nx - 18 = 0\nx - -3 = 0\nx - 0 = 0\nx = 18\nx = -3\nx = 0"} {"input": "Solve quickly: 4x - 76/9 = 0", "output": "4x - 76/9 = 0\n4x = 76/9\nx = 76/9 / 4\nx = 19/9"} {"input": "Solve the equation x^3 + 5/6x^2 - 68/9x + 56/9 = 0", "output": "x^3 + 5/6x^2 - 68/9x + 56/9 = 0\n(x - 4/3)(x - 4/3)(x - -7/2) = 0\nx - 4/3 = 0\nx - 4/3 = 0\nx - -7/2 = 0\nx = 4/3\nx = 4/3\nx = -7/2"} {"input": "Solve the equation 2x + 3 = 0", "output": "2x + 3 = 0\n2x = -3\nx = -3 / 2\nx = -3/2"} {"input": "Determine x in x^3 - 61/10x^2 - 443/25x + 504/25 = 0", "output": "x^3 - 61/10x^2 - 443/25x + 504/25 = 0\n(x - 9/10)(x - -14/5)(x - 8) = 0\nx - 9/10 = 0\nx - -14/5 = 0\nx - 8 = 0\nx = 9/10\nx = -14/5\nx = 8"} {"input": "What value of x satisfies 3x + 36 = 0", "output": "3x + 36 = 0\n3x = -36\nx = -36 / 3\nx = -12"} {"input": "Find x in x^2 - 6/7x - 1/7 = 0", "output": "x^2 - 6/7x - 1/7 = 0\n(x - -1/7)(x - 1) = 0\nx - -1/7 = 0 or x - 1 = 0\nx = -1/7\nx = 1"} {"input": "Find x for x^3 - 14x^2 - 95x + 1008 = 0", "output": "x^3 - 14x^2 - 95x + 1008 = 0\n(x - 16)(x - -9)(x - 7) = 0\nx - 16 = 0\nx - -9 = 0\nx - 7 = 0\nx = 16\nx = -9\nx = 7"} {"input": "Find x for x^3 + 64/9x^2 + 131/9x + 76/9 = 0", "output": "x^3 + 64/9x^2 + 131/9x + 76/9 = 0\n(x - -1)(x - -19/9)(x - -4) = 0\nx - -1 = 0\nx - -19/9 = 0\nx - -4 = 0\nx = -1\nx = -19/9\nx = -4"} {"input": "Find the solution to 1x - 3/2 = 0", "output": "1x - 3/2 = 0\n1x = 3/2\nx = 3/2 / 1\nx = 3/2"} {"input": "Find the solution to x^3 - 47/40x^2 - 2677/400x + 17/25 = 0", "output": "x^3 - 47/40x^2 - 2677/400x + 17/25 = 0\n(x - 1/10)(x - 16/5)(x - -17/8) = 0\nx - 1/10 = 0\nx - 16/5 = 0\nx - -17/8 = 0\nx = 1/10\nx = 16/5\nx = -17/8"} {"input": "Find x in x^3 - 37/3x^2 + 467/12x - 34 = 0", "output": "x^3 - 37/3x^2 + 467/12x - 34 = 0\n(x - 17/6)(x - 3/2)(x - 8) = 0\nx - 17/6 = 0\nx - 3/2 = 0\nx - 8 = 0\nx = 17/6\nx = 3/2\nx = 8"} {"input": "Find x and y such that\n3x + 4y = -8\n8x + 6y = -43/3", "output": "3x + 4y = -8\n8x + 6y = -43/3\n\nUsing elimination\n8*(3x + 4y = -8)\n3*(8x + 6y = -43/3)\n24x + 32y = -64\n24x + 18y = -43\nSubtract equations\n14y = -21\ny = -21/14\ny = -3/2\n\nSubstitute y\n3x + 4(-3/2) = -8\n3x = -2\nx = -2/3\nx = -2/3"} {"input": "Determine x in x^2 - 25/3x + 14 = 0", "output": "x^2 - 25/3x + 14 = 0\n(x - 6)(x - 7/3) = 0\nx - 6 = 0 or x - 7/3 = 0\nx = 6\nx = 7/3"} {"input": "Solve the system:\n5x + 2y = 729/56\n9x + 4y = 1325/56", "output": "5x + 2y = 729/56\n9x + 4y = 1325/56\n\nUsing elimination\n9*(5x + 2y = 729/56)\n5*(9x + 4y = 1325/56)\n45x + 18y = 6561/56\n45x + 20y = 6625/56\nSubtract equations\n-2y = -8/7\ny = -8/7/-2\ny = 4/7\n\nSubstitute y\n5x + 2(4/7) = 729/56\n5x = 95/8\nx = 95/8/5\nx = 19/8"} {"input": "Find the solution to x^3 + 63/4x^2 - 15/2x - 56 = 0", "output": "x^3 + 63/4x^2 - 15/2x - 56 = 0\n(x - -7/4)(x - 2)(x - -16) = 0\nx - -7/4 = 0\nx - 2 = 0\nx - -16 = 0\nx = -7/4\nx = 2\nx = -16"} {"input": "Solve x^3 + 45/8x^2 + 139/18x + 143/72 = 0", "output": "x^3 + 45/8x^2 + 139/18x + 143/72 = 0\n(x - -1/3)(x - -13/8)(x - -11/3) = 0\nx - -1/3 = 0\nx - -13/8 = 0\nx - -11/3 = 0\nx = -1/3\nx = -13/8\nx = -11/3"} {"input": "Solve the equation 10x - 50 = 0", "output": "10x - 50 = 0\n10x = 50\nx = 50 / 10\nx = 5"} {"input": "Solve x^2 - 160/21x + 256/21 = 0", "output": "x^2 - 160/21x + 256/21 = 0\n(x - 16/7)(x - 16/3) = 0\nx - 16/7 = 0 or x - 16/3 = 0\nx = 16/7\nx = 16/3"} {"input": "What value of x satisfies 6x + 7 = 0", "output": "6x + 7 = 0\n6x = -7\nx = -7 / 6\nx = -7/6"} {"input": "Determine x in 2x + 36 = 0", "output": "2x + 36 = 0\n2x = -36\nx = -36 / 2\nx = -18"} {"input": "Find x in x^2 - 19/2x = 0", "output": "x^2 - 19/2x = 0\n(x - 0)(x - 19/2) = 0\nx - 0 = 0 or x - 19/2 = 0\nx = 0\nx = 19/2"} {"input": "Solve x^3 + 13/6x^2 - 151/6x - 13 = 0", "output": "x^3 + 13/6x^2 - 151/6x - 13 = 0\n(x - -1/2)(x - -6)(x - 13/3) = 0\nx - -1/2 = 0\nx - -6 = 0\nx - 13/3 = 0\nx = -1/2\nx = -6\nx = 13/3"} {"input": "Solve 10x + 50 = 0", "output": "10x + 50 = 0\n10x = -50\nx = -50 / 10\nx = -5"} {"input": "Solve simultaneously:\n4x + 1y = 1/6\n2x + 3y = 53/6", "output": "4x + 1y = 1/6\n2x + 3y = 53/6\n\nUsing elimination\n2*(4x + 1y = 1/6)\n4*(2x + 3y = 53/6)\n8x + 2y = 1/3\n8x + 12y = 106/3\nSubtract equations\n-10y = -35\ny = -35/-10\ny = 7/2\n\nSubstitute y\n4x + 1(7/2) = 1/6\n4x = -10/3\nx = -10/3/4\nx = -5/6"} {"input": "Solve the equations:\n1x + 2y = 79/5\n7x + 3y = 391/10", "output": "1x + 2y = 79/5\n7x + 3y = 391/10\n\nUsing elimination\n7*(1x + 2y = 79/5)\n1*(7x + 3y = 391/10)\n7x + 14y = 553/5\n7x + 3y = 391/10\nSubtract equations\n11y = 143/2\ny = 143/2/11\ny = 13/2\n\nSubstitute y\n1x + 2(13/2) = 79/5\n1x = 14/5\nx = 14/5/1\nx = 14/5"} {"input": "Solve x^2 - 49/20x - 153/20 = 0", "output": "x^2 - 49/20x - 153/20 = 0\n(x - 17/4)(x - -9/5) = 0\nx - 17/4 = 0 or x - -9/5 = 0\nx = 17/4\nx = -9/5"} {"input": "Determine x in x^2 - 29/9x + 2/3 = 0", "output": "x^2 - 29/9x + 2/3 = 0\n(x - 3)(x - 2/9) = 0\nx - 3 = 0 or x - 2/9 = 0\nx = 3\nx = 2/9"} {"input": "Find x in x^2 - 44/5x - 9/5 = 0", "output": "x^2 - 44/5x - 9/5 = 0\n(x - 9)(x - -1/5) = 0\nx - 9 = 0 or x - -1/5 = 0\nx = 9\nx = -1/5"} {"input": "Solve quickly: x^2 - 111/40x + 19/20 = 0", "output": "x^2 - 111/40x + 19/20 = 0\n(x - 19/8)(x - 2/5) = 0\nx - 19/8 = 0 or x - 2/5 = 0\nx = 19/8\nx = 2/5"} {"input": "Compute the solution of x^3 + 46/15x^2 - 53/15x + 4/5 = 0", "output": "x^3 + 46/15x^2 - 53/15x + 4/5 = 0\n(x - -4)(x - 1/3)(x - 3/5) = 0\nx - -4 = 0\nx - 1/3 = 0\nx - 3/5 = 0\nx = -4\nx = 1/3\nx = 3/5"} {"input": "Determine x in x^2 + 135/7x + 38/7 = 0", "output": "x^2 + 135/7x + 38/7 = 0\n(x - -2/7)(x - -19) = 0\nx - -2/7 = 0 or x - -19 = 0\nx = -2/7\nx = -19"} {"input": "Find x and y such that\n10x + 2y = -98\n9x + 6y = -84", "output": "10x + 2y = -98\n9x + 6y = -84\n\nUsing elimination\n9*(10x + 2y = -98)\n10*(9x + 6y = -84)\n90x + 18y = -882\n90x + 60y = -840\nSubtract equations\n-42y = -42\ny = -42/-42\ny = 1\n\nSubstitute y\n10x + 2(1) = -98\n10x = -100\nx = -100/10\nx = -10"} {"input": "Find the solution to x^2 - 113/7x - 234/7 = 0", "output": "x^2 - 113/7x - 234/7 = 0\n(x - 18)(x - -13/7) = 0\nx - 18 = 0 or x - -13/7 = 0\nx = 18\nx = -13/7"} {"input": "Compute the solution of x^3 + 3/2x^2 - 135/16x = 0", "output": "x^3 + 3/2x^2 - 135/16x = 0\n(x - 9/4)(x - 0)(x - -15/4) = 0\nx - 9/4 = 0\nx - 0 = 0\nx - -15/4 = 0\nx = 9/4\nx = 0\nx = -15/4"} {"input": "Solve the system:\n8x + 10y = 84\n1x + 7y = 156/5", "output": "8x + 10y = 84\n1x + 7y = 156/5\n\nUsing elimination\n1*(8x + 10y = 84)\n8*(1x + 7y = 156/5)\n8x + 10y = 84\n8x + 56y = 1248/5\nSubtract equations\n-46y = -828/5\ny = -828/5/-46\ny = 18/5\n\nSubstitute y\n8x + 10(18/5) = 84\n8x = 48\nx = 48/8\nx = 6"} {"input": "Find x in 6x + 30 = 0", "output": "6x + 30 = 0\n6x = -30\nx = -30 / 6\nx = -5"} {"input": "Find x for x^2 - 2x = 0", "output": "x^2 - 2x = 0\n(x - 0)(x - 2) = 0\nx - 0 = 0 or x - 2 = 0\nx = 0\nx = 2"} {"input": "Compute the solution of 1x + 1/3 = 0", "output": "1x + 1/3 = 0\n1x = -1/3\nx = -1/3 / 1\nx = -1/3"} {"input": "Find x for x^2 - 92/9x + 160/9 = 0", "output": "x^2 - 92/9x + 160/9 = 0\n(x - 8)(x - 20/9) = 0\nx - 8 = 0 or x - 20/9 = 0\nx = 8\nx = 20/9"} {"input": "Determine x in 5x + 20/3 = 0", "output": "5x + 20/3 = 0\n5x = -20/3\nx = -20/3 / 5\nx = -4/3"} {"input": "What value of x satisfies 2x - 36/7 = 0", "output": "2x - 36/7 = 0\n2x = 36/7\nx = 36/7 / 2\nx = 18/7"} {"input": "Find x in x^3 - 221/24x^2 + 107/6x + 19/8 = 0", "output": "x^3 - 221/24x^2 + 107/6x + 19/8 = 0\n(x - 3)(x - -1/8)(x - 19/3) = 0\nx - 3 = 0\nx - -1/8 = 0\nx - 19/3 = 0\nx = 3\nx = -1/8\nx = 19/3"} {"input": "What value of x satisfies x^3 + 111/10x^2 + 467/25x - 99/50 = 0", "output": "x^3 + 111/10x^2 + 467/25x - 99/50 = 0\n(x - -11/5)(x - 1/10)(x - -9) = 0\nx - -11/5 = 0\nx - 1/10 = 0\nx - -9 = 0\nx = -11/5\nx = 1/10\nx = -9"} {"input": "Find x for 7x + 16 = 0", "output": "7x + 16 = 0\n7x = -16\nx = -16 / 7\nx = -16/7"} {"input": "What value of x satisfies 10x - 10/9 = 0", "output": "10x - 10/9 = 0\n10x = 10/9\nx = 10/9 / 10\nx = 1/9"} {"input": "Find x for x^3 + 367/168x^2 - 55/21x - 325/56 = 0", "output": "x^3 + 367/168x^2 - 55/21x - 325/56 = 0\n(x - -15/7)(x - -5/3)(x - 13/8) = 0\nx - -15/7 = 0\nx - -5/3 = 0\nx - 13/8 = 0\nx = -15/7\nx = -5/3\nx = 13/8"} {"input": "Find x in x^3 + 33/4x^2 + 25/2x - 231/16 = 0", "output": "x^3 + 33/4x^2 + 25/2x - 231/16 = 0\n(x - -11/2)(x - -7/2)(x - 3/4) = 0\nx - -11/2 = 0\nx - -7/2 = 0\nx - 3/4 = 0\nx = -11/2\nx = -7/2\nx = 3/4"} {"input": "Find x in x^2 + 2x + 21/25 = 0", "output": "x^2 + 2x + 21/25 = 0\n(x - -7/5)(x - -3/5) = 0\nx - -7/5 = 0 or x - -3/5 = 0\nx = -7/5\nx = -3/5"} {"input": "Find x and y such that\n1x + 10y = 670/21\n10x + 7y = 190/21", "output": "1x + 10y = 670/21\n10x + 7y = 190/21\n\nUsing elimination\n10*(1x + 10y = 670/21)\n1*(10x + 7y = 190/21)\n10x + 100y = 6700/21\n10x + 7y = 190/21\nSubtract equations\n93y = 310\ny = 310/93\ny = 10/3\n\nSubstitute y\n1x + 10(10/3) = 670/21\n1x = -10/7\nx = -10/7/1\nx = -10/7"} {"input": "Solve the equation 6x - 16 = 0", "output": "6x - 16 = 0\n6x = 16\nx = 16 / 6\nx = 8/3"} {"input": "Compute the solution of x^2 - 149/21x + 20/7 = 0", "output": "x^2 - 149/21x + 20/7 = 0\n(x - 3/7)(x - 20/3) = 0\nx - 3/7 = 0 or x - 20/3 = 0\nx = 3/7\nx = 20/3"} {"input": "Compute the solution of 5x + 50 = 0", "output": "5x + 50 = 0\n5x = -50\nx = -50 / 5\nx = -10"} {"input": "Solve simultaneously:\n8x + 4y = -424/5\n7x + 8y = -1597/10", "output": "8x + 4y = -424/5\n7x + 8y = -1597/10\n\nUsing elimination\n7*(8x + 4y = -424/5)\n8*(7x + 8y = -1597/10)\n56x + 28y = -2968/5\n56x + 64y = -6388/5\nSubtract equations\n-36y = 684\ny = 684/-36\ny = -19\n\nSubstitute y\n8x + 4(-19) = -424/5\n8x = -44/5\nx = -44/5/8\nx = -11/10"} {"input": "Determine x in 9x - 7 = 0", "output": "9x - 7 = 0\n9x = 7\nx = 7 / 9\nx = 7/9"} {"input": "Solve 2x - 14 = 0", "output": "2x - 14 = 0\n2x = 14\nx = 14 / 2\nx = 7"} {"input": "Solve the equation x^2 - 7/3x = 0", "output": "x^2 - 7/3x = 0\n(x - 7/3)(x - 0) = 0\nx - 7/3 = 0 or x - 0 = 0\nx = 7/3\nx = 0"} {"input": "Find the solution to 3x + 51/7 = 0", "output": "3x + 51/7 = 0\n3x = -51/7\nx = -51/7 / 3\nx = -17/7"} {"input": "Find x and y such that\n5x + 2y = -81/4\n7x + 1y = -99/4", "output": "5x + 2y = -81/4\n7x + 1y = -99/4\n\nUsing elimination\n7*(5x + 2y = -81/4)\n5*(7x + 1y = -99/4)\n35x + 14y = -567/4\n35x + 5y = -495/4\nSubtract equations\n9y = -18\ny = -18/9\ny = -2\n\nSubstitute y\n5x + 2(-2) = -81/4\n5x = -65/4\nx = -65/4/5\nx = -13/4"} {"input": "Find x in x^3 + 9/2x^2 - 35/2x = 0", "output": "x^3 + 9/2x^2 - 35/2x = 0\n(x - -7)(x - 5/2)(x - 0) = 0\nx - -7 = 0\nx - 5/2 = 0\nx - 0 = 0\nx = -7\nx = 5/2\nx = 0"} {"input": "Solve quickly: 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve the system:\n5x + 9y = -47/2\n6x + 5y = -335/9", "output": "5x + 9y = -47/2\n6x + 5y = -335/9\n\nUsing elimination\n6*(5x + 9y = -47/2)\n5*(6x + 5y = -335/9)\n30x + 54y = -141\n30x + 25y = -1675/9\nSubtract equations\n29y = 406/9\ny = 406/9/29\ny = 14/9\n\nSubstitute y\n5x + 9(14/9) = -47/2\n5x = -75/2\nx = -75/2/5\nx = -15/2"} {"input": "Find x and y such that\n3x + 5y = 103/2\n8x + 10y = 317/3", "output": "3x + 5y = 103/2\n8x + 10y = 317/3\n\nUsing elimination\n8*(3x + 5y = 103/2)\n3*(8x + 10y = 317/3)\n24x + 40y = 412\n24x + 30y = 317\nSubtract equations\n10y = 95\ny = 95/10\ny = 19/2\n\nSubstitute y\n3x + 5(19/2) = 103/2\n3x = 4\nx = 4/3\nx = 4/3"} {"input": "Find x in x^3 - 258/35x^2 + 473/28x - 117/10 = 0", "output": "x^3 - 258/35x^2 + 473/28x - 117/10 = 0\n(x - 7/2)(x - 18/7)(x - 13/10) = 0\nx - 7/2 = 0\nx - 18/7 = 0\nx - 13/10 = 0\nx = 7/2\nx = 18/7\nx = 13/10"} {"input": "Solve 10x + 14 = 0", "output": "10x + 14 = 0\n10x = -14\nx = -14 / 10\nx = -7/5"} {"input": "Find x in x^3 + 69/4x^2 + 757/8x + 165 = 0", "output": "x^3 + 69/4x^2 + 757/8x + 165 = 0\n(x - -11/2)(x - -15/4)(x - -8) = 0\nx - -11/2 = 0\nx - -15/4 = 0\nx - -8 = 0\nx = -11/2\nx = -15/4\nx = -8"} {"input": "Find x in x^3 - 452/63x^2 + 223/21x + 80/63 = 0", "output": "x^3 - 452/63x^2 + 223/21x + 80/63 = 0\n(x - 5)(x - 16/7)(x - -1/9) = 0\nx - 5 = 0\nx - 16/7 = 0\nx - -1/9 = 0\nx = 5\nx = 16/7\nx = -1/9"} {"input": "Solve the equation x^3 + 52/21x^2 + 32/21x = 0", "output": "x^3 + 52/21x^2 + 32/21x = 0\n(x - -8/7)(x - -4/3)(x - 0) = 0\nx - -8/7 = 0\nx - -4/3 = 0\nx - 0 = 0\nx = -8/7\nx = -4/3\nx = 0"} {"input": "Solve x^3 + 203/90x^2 + 31/50x - 182/225 = 0", "output": "x^3 + 203/90x^2 + 31/50x - 182/225 = 0\n(x - -7/5)(x - 4/9)(x - -13/10) = 0\nx - -7/5 = 0\nx - 4/9 = 0\nx - -13/10 = 0\nx = -7/5\nx = 4/9\nx = -13/10"} {"input": "Find x in 5x - 60/7 = 0", "output": "5x - 60/7 = 0\n5x = 60/7\nx = 60/7 / 5\nx = 12/7"} {"input": "Determine x in x^3 + 37/4x^2 + 43/4x - 105/2 = 0", "output": "x^3 + 37/4x^2 + 43/4x - 105/2 = 0\n(x - -5)(x - -6)(x - 7/4) = 0\nx - -5 = 0\nx - -6 = 0\nx - 7/4 = 0\nx = -5\nx = -6\nx = 7/4"} {"input": "Find x and y such that\n4x + 5y = -142/21\n1x + 1y = -32/21", "output": "4x + 5y = -142/21\n1x + 1y = -32/21\n\nUsing elimination\n1*(4x + 5y = -142/21)\n4*(1x + 1y = -32/21)\n4x + 5y = -142/21\n4x + 4y = -128/21\nSubtract equations\n1y = -2/3\ny = -2/3/1\ny = -2/3\n\nSubstitute y\n4x + 5(-2/3) = -142/21\n4x = -24/7\nx = -24/7/4\nx = -6/7"} {"input": "Find x and y such that\n6x + 5y = 50\n10x + 6y = 60", "output": "6x + 5y = 50\n10x + 6y = 60\n\nUsing elimination\n10*(6x + 5y = 50)\n6*(10x + 6y = 60)\n60x + 50y = 500\n60x + 36y = 360\nSubtract equations\n14y = 140\ny = 140/14\ny = 10\n\nSubstitute y\n6x + 5(10) = 50\n6x = 0\nx = 0/6\nx = 0"} {"input": "Determine x in x^3 + 38/21x^2 - 131/21x - 8 = 0", "output": "x^3 + 38/21x^2 - 131/21x - 8 = 0\n(x - 7/3)(x - -8/7)(x - -3) = 0\nx - 7/3 = 0\nx - -8/7 = 0\nx - -3 = 0\nx = 7/3\nx = -8/7\nx = -3"} {"input": "What value of x satisfies x^3 - 59/6x^2 + 565/18x - 884/27 = 0", "output": "x^3 - 59/6x^2 + 565/18x - 884/27 = 0\n(x - 13/3)(x - 8/3)(x - 17/6) = 0\nx - 13/3 = 0\nx - 8/3 = 0\nx - 17/6 = 0\nx = 13/3\nx = 8/3\nx = 17/6"} {"input": "Find the solution to x^2 + 4x + 15/16 = 0", "output": "x^2 + 4x + 15/16 = 0\n(x - -15/4)(x - -1/4) = 0\nx - -15/4 = 0 or x - -1/4 = 0\nx = -15/4\nx = -1/4"} {"input": "Compute the solution of 4x - 18/5 = 0", "output": "4x - 18/5 = 0\n4x = 18/5\nx = 18/5 / 4\nx = 9/10"} {"input": "Solve x^3 + 51/8x^2 + 45/8x - 25/4 = 0", "output": "x^3 + 51/8x^2 + 45/8x - 25/4 = 0\n(x - -2)(x - -5)(x - 5/8) = 0\nx - -2 = 0\nx - -5 = 0\nx - 5/8 = 0\nx = -2\nx = -5\nx = 5/8"} {"input": "Determine x in x^3 - 48/35x^2 - 87/25x + 26/35 = 0", "output": "x^3 - 48/35x^2 - 87/25x + 26/35 = 0\n(x - 1/5)(x - 13/5)(x - -10/7) = 0\nx - 1/5 = 0\nx - 13/5 = 0\nx - -10/7 = 0\nx = 1/5\nx = 13/5\nx = -10/7"} {"input": "Compute the solution of 2x + 19/4 = 0", "output": "2x + 19/4 = 0\n2x = -19/4\nx = -19/4 / 2\nx = -19/8"} {"input": "Find x for x^2 + 5/2x - 17/18 = 0", "output": "x^2 + 5/2x - 17/18 = 0\n(x - 1/3)(x - -17/6) = 0\nx - 1/3 = 0 or x - -17/6 = 0\nx = 1/3\nx = -17/6"} {"input": "Solve the equations:\n8x + 3y = -47/10\n7x + 7y = -539/30", "output": "8x + 3y = -47/10\n7x + 7y = -539/30\n\nUsing elimination\n7*(8x + 3y = -47/10)\n8*(7x + 7y = -539/30)\n56x + 21y = -329/10\n56x + 56y = -2156/15\nSubtract equations\n-35y = 665/6\ny = 665/6/-35\ny = -19/6\n\nSubstitute y\n8x + 3(-19/6) = -47/10\n8x = 24/5\nx = 24/5/8\nx = 3/5"} {"input": "Determine x in x^2 + 14/5x + 33/25 = 0", "output": "x^2 + 14/5x + 33/25 = 0\n(x - -11/5)(x - -3/5) = 0\nx - -11/5 = 0 or x - -3/5 = 0\nx = -11/5\nx = -3/5"} {"input": "Compute the solution of x^3 - 9/7x^2 - 76/49x + 12/49 = 0", "output": "x^3 - 9/7x^2 - 76/49x + 12/49 = 0\n(x - -6/7)(x - 1/7)(x - 2) = 0\nx - -6/7 = 0\nx - 1/7 = 0\nx - 2 = 0\nx = -6/7\nx = 1/7\nx = 2"} {"input": "Find x and y such that\n4x + 3y = -6/5\n2x + 2y = 2/5", "output": "4x + 3y = -6/5\n2x + 2y = 2/5\n\nUsing elimination\n2*(4x + 3y = -6/5)\n4*(2x + 2y = 2/5)\n8x + 6y = -12/5\n8x + 8y = 8/5\nSubtract equations\n-2y = -4\ny = -4/-2\ny = 2\n\nSubstitute y\n4x + 3(2) = -6/5\n4x = -36/5\nx = -36/5/4\nx = -9/5"} {"input": "Solve the system:\n4x + 2y = 14/3\n5x + 2y = 17/3", "output": "4x + 2y = 14/3\n5x + 2y = 17/3\n\nUsing elimination\n5*(4x + 2y = 14/3)\n4*(5x + 2y = 17/3)\n20x + 10y = 70/3\n20x + 8y = 68/3\nSubtract equations\n2y = 2/3\ny = 2/3/2\ny = 1/3\n\nSubstitute y\n4x + 2(1/3) = 14/3\n4x = 4\nx = 4/4\nx = 1"} {"input": "Compute the solution of 1x - 17/6 = 0", "output": "1x - 17/6 = 0\n1x = 17/6\nx = 17/6 / 1\nx = 17/6"} {"input": "Determine x in 9x - 20 = 0", "output": "9x - 20 = 0\n9x = 20\nx = 20 / 9\nx = 20/9"} {"input": "Compute the solution of x^3 - 106/5x^2 + 2213/25x - 2128/25 = 0", "output": "x^3 - 106/5x^2 + 2213/25x - 2128/25 = 0\n(x - 16)(x - 19/5)(x - 7/5) = 0\nx - 16 = 0\nx - 19/5 = 0\nx - 7/5 = 0\nx = 16\nx = 19/5\nx = 7/5"} {"input": "Solve the equation x^3 + 82/3x^2 + 201x + 1292/3 = 0", "output": "x^3 + 82/3x^2 + 201x + 1292/3 = 0\n(x - -4)(x - -19/3)(x - -17) = 0\nx - -4 = 0\nx - -19/3 = 0\nx - -17 = 0\nx = -4\nx = -19/3\nx = -17"} {"input": "Determine x in 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Compute the solution of x^2 + 11/10x - 57/10 = 0", "output": "x^2 + 11/10x - 57/10 = 0\n(x - 19/10)(x - -3) = 0\nx - 19/10 = 0 or x - -3 = 0\nx = 19/10\nx = -3"} {"input": "Solve x^3 - 259/40x^2 + 759/80x - 27/10 = 0", "output": "x^3 - 259/40x^2 + 759/80x - 27/10 = 0\n(x - 8/5)(x - 9/2)(x - 3/8) = 0\nx - 8/5 = 0\nx - 9/2 = 0\nx - 3/8 = 0\nx = 8/5\nx = 9/2\nx = 3/8"} {"input": "Find x in x^3 + 7/5x^2 - 14/5x - 16/5 = 0", "output": "x^3 + 7/5x^2 - 14/5x - 16/5 = 0\n(x - -1)(x - -2)(x - 8/5) = 0\nx - -1 = 0\nx - -2 = 0\nx - 8/5 = 0\nx = -1\nx = -2\nx = 8/5"} {"input": "Solve x^3 - 49/36x^2 - 3/4x + 10/9 = 0", "output": "x^3 - 49/36x^2 - 3/4x + 10/9 = 0\n(x - 5/4)(x - -8/9)(x - 1) = 0\nx - 5/4 = 0\nx - -8/9 = 0\nx - 1 = 0\nx = 5/4\nx = -8/9\nx = 1"} {"input": "Find the solution to 3x - 9/2 = 0", "output": "3x - 9/2 = 0\n3x = 9/2\nx = 9/2 / 3\nx = 3/2"} {"input": "Solve quickly: 5x + 95/4 = 0", "output": "5x + 95/4 = 0\n5x = -95/4\nx = -95/4 / 5\nx = -19/4"} {"input": "Find x for x^3 + 24/5x^2 + 37/5x + 18/5 = 0", "output": "x^3 + 24/5x^2 + 37/5x + 18/5 = 0\n(x - -9/5)(x - -1)(x - -2) = 0\nx - -9/5 = 0\nx - -1 = 0\nx - -2 = 0\nx = -9/5\nx = -1\nx = -2"} {"input": "Solve quickly: 2x - 32 = 0", "output": "2x - 32 = 0\n2x = 32\nx = 32 / 2\nx = 16"} {"input": "Find the solution to x^2 + 29/10x + 21/10 = 0", "output": "x^2 + 29/10x + 21/10 = 0\n(x - -7/5)(x - -3/2) = 0\nx - -7/5 = 0 or x - -3/2 = 0\nx = -7/5\nx = -3/2"} {"input": "Solve the equations:\n7x + 3y = 63\n5x + 1y = 143/3", "output": "7x + 3y = 63\n5x + 1y = 143/3\n\nUsing elimination\n5*(7x + 3y = 63)\n7*(5x + 1y = 143/3)\n35x + 15y = 315\n35x + 7y = 1001/3\nSubtract equations\n8y = -56/3\ny = -56/3/8\ny = -7/3\n\nSubstitute y\n7x + 3(-7/3) = 63\n7x = 70\nx = 70/7\nx = 10"} {"input": "Find x in x^3 + 99/56x^2 - 45/56x = 0", "output": "x^3 + 99/56x^2 - 45/56x = 0\n(x - 0)(x - 3/8)(x - -15/7) = 0\nx - 0 = 0\nx - 3/8 = 0\nx - -15/7 = 0\nx = 0\nx = 3/8\nx = -15/7"} {"input": "Solve simultaneously:\n5x + 8y = 31/6\n7x + 2y = 25/6", "output": "5x + 8y = 31/6\n7x + 2y = 25/6\n\nUsing elimination\n7*(5x + 8y = 31/6)\n5*(7x + 2y = 25/6)\n35x + 56y = 217/6\n35x + 10y = 125/6\nSubtract equations\n46y = 46/3\ny = 46/3/46\ny = 1/3\n\nSubstitute y\n5x + 8(1/3) = 31/6\n5x = 5/2\nx = 5/2/5\nx = 1/2"} {"input": "Solve quickly: x^3 + 18x^2 + 15x - 34 = 0", "output": "x^3 + 18x^2 + 15x - 34 = 0\n(x - -2)(x - -17)(x - 1) = 0\nx - -2 = 0\nx - -17 = 0\nx - 1 = 0\nx = -2\nx = -17\nx = 1"} {"input": "Find x in 9x - 18/7 = 0", "output": "9x - 18/7 = 0\n9x = 18/7\nx = 18/7 / 9\nx = 2/7"} {"input": "Solve x^2 + 151/30x - 8/5 = 0", "output": "x^2 + 151/30x - 8/5 = 0\n(x - 3/10)(x - -16/3) = 0\nx - 3/10 = 0 or x - -16/3 = 0\nx = 3/10\nx = -16/3"} {"input": "Solve the system:\n4x + 10y = -628/5\n8x + 7y = -346/5", "output": "4x + 10y = -628/5\n8x + 7y = -346/5\n\nUsing elimination\n8*(4x + 10y = -628/5)\n4*(8x + 7y = -346/5)\n32x + 80y = -5024/5\n32x + 28y = -1384/5\nSubtract equations\n52y = -728\ny = -728/52\ny = -14\n\nSubstitute y\n4x + 10(-14) = -628/5\n4x = 72/5\nx = 72/5/4\nx = 18/5"} {"input": "Solve the equation x^2 - 23/10x + 9/10 = 0", "output": "x^2 - 23/10x + 9/10 = 0\n(x - 9/5)(x - 1/2) = 0\nx - 9/5 = 0 or x - 1/2 = 0\nx = 9/5\nx = 1/2"} {"input": "Solve the equations:\n8x + 6y = 336/5\n5x + 6y = 246/5", "output": "8x + 6y = 336/5\n5x + 6y = 246/5\n\nUsing elimination\n5*(8x + 6y = 336/5)\n8*(5x + 6y = 246/5)\n40x + 30y = 336\n40x + 48y = 1968/5\nSubtract equations\n-18y = -288/5\ny = -288/5/-18\ny = 16/5\n\nSubstitute y\n8x + 6(16/5) = 336/5\n8x = 48\nx = 48/8\nx = 6"} {"input": "Find x and y such that\n9x + 3y = 981/14\n7x + 2y = 759/14", "output": "9x + 3y = 981/14\n7x + 2y = 759/14\n\nUsing elimination\n7*(9x + 3y = 981/14)\n9*(7x + 2y = 759/14)\n63x + 21y = 981/2\n63x + 18y = 6831/14\nSubtract equations\n3y = 18/7\ny = 18/7/3\ny = 6/7\n\nSubstitute y\n9x + 3(6/7) = 981/14\n9x = 135/2\nx = 135/2/9\nx = 15/2"} {"input": "Solve the equation 9x - 72 = 0", "output": "9x - 72 = 0\n9x = 72\nx = 72 / 9\nx = 8"} {"input": "Solve simultaneously:\n6x + 7y = -16\n10x + 5y = -20", "output": "6x + 7y = -16\n10x + 5y = -20\n\nUsing elimination\n10*(6x + 7y = -16)\n6*(10x + 5y = -20)\n60x + 70y = -160\n60x + 30y = -120\nSubtract equations\n40y = -40\ny = -40/40\ny = -1\n\nSubstitute y\n6x + 7(-1) = -16\n6x = -9\nx = -9/6\nx = -3/2"} {"input": "Solve the equation 10x + 15 = 0", "output": "10x + 15 = 0\n10x = -15\nx = -15 / 10\nx = -3/2"} {"input": "Solve quickly: x^3 - 115/21x^2 + 50/7x = 0", "output": "x^3 - 115/21x^2 + 50/7x = 0\n(x - 15/7)(x - 10/3)(x - 0) = 0\nx - 15/7 = 0\nx - 10/3 = 0\nx - 0 = 0\nx = 15/7\nx = 10/3\nx = 0"} {"input": "Find x in x^3 + 47/10x^2 + 34/5x + 14/5 = 0", "output": "x^3 + 47/10x^2 + 34/5x + 14/5 = 0\n(x - -7/10)(x - -2)(x - -2) = 0\nx - -7/10 = 0\nx - -2 = 0\nx - -2 = 0\nx = -7/10\nx = -2\nx = -2"} {"input": "Compute the solution of x^3 + 27/2x^2 - 576/25x - 81/10 = 0", "output": "x^3 + 27/2x^2 - 576/25x - 81/10 = 0\n(x - -15)(x - 9/5)(x - -3/10) = 0\nx - -15 = 0\nx - 9/5 = 0\nx - -3/10 = 0\nx = -15\nx = 9/5\nx = -3/10"} {"input": "Find the solution to x^3 + 39/5x^2 + 1711/180x + 247/180 = 0", "output": "x^3 + 39/5x^2 + 1711/180x + 247/180 = 0\n(x - -13/10)(x - -1/6)(x - -19/3) = 0\nx - -13/10 = 0\nx - -1/6 = 0\nx - -19/3 = 0\nx = -13/10\nx = -1/6\nx = -19/3"} {"input": "What value of x satisfies x^3 - 15/8x^2 - 71/32x + 99/32 = 0", "output": "x^3 - 15/8x^2 - 71/32x + 99/32 = 0\n(x - -11/8)(x - 9/4)(x - 1) = 0\nx - -11/8 = 0\nx - 9/4 = 0\nx - 1 = 0\nx = -11/8\nx = 9/4\nx = 1"} {"input": "Solve the system:\n4x + 9y = 175/4\n9x + 2y = 133/2", "output": "4x + 9y = 175/4\n9x + 2y = 133/2\n\nUsing elimination\n9*(4x + 9y = 175/4)\n4*(9x + 2y = 133/2)\n36x + 81y = 1575/4\n36x + 8y = 266\nSubtract equations\n73y = 511/4\ny = 511/4/73\ny = 7/4\n\nSubstitute y\n4x + 9(7/4) = 175/4\n4x = 28\nx = 28/4\nx = 7"} {"input": "Find x for x^2 + 13/3x + 40/9 = 0", "output": "x^2 + 13/3x + 40/9 = 0\n(x - -5/3)(x - -8/3) = 0\nx - -5/3 = 0 or x - -8/3 = 0\nx = -5/3\nx = -8/3"} {"input": "Compute the solution of x^3 + 205/36x^2 + 181/36x - 85/18 = 0", "output": "x^3 + 205/36x^2 + 181/36x - 85/18 = 0\n(x - -2)(x - -17/4)(x - 5/9) = 0\nx - -2 = 0\nx - -17/4 = 0\nx - 5/9 = 0\nx = -2\nx = -17/4\nx = 5/9"} {"input": "Solve the equation x^3 + 129/20x^2 + 279/40x - 209/40 = 0", "output": "x^3 + 129/20x^2 + 279/40x - 209/40 = 0\n(x - 1/2)(x - -11/5)(x - -19/4) = 0\nx - 1/2 = 0\nx - -11/5 = 0\nx - -19/4 = 0\nx = 1/2\nx = -11/5\nx = -19/4"} {"input": "Find the solution to x^2 + 1/6x = 0", "output": "x^2 + 1/6x = 0\n(x - -1/6)(x - 0) = 0\nx - -1/6 = 0 or x - 0 = 0\nx = -1/6\nx = 0"} {"input": "What value of x satisfies 8x + 32/9 = 0", "output": "8x + 32/9 = 0\n8x = -32/9\nx = -32/9 / 8\nx = -4/9"} {"input": "Solve the system:\n6x + 8y = -45\n9x + 2y = -135/2", "output": "6x + 8y = -45\n9x + 2y = -135/2\n\nUsing elimination\n9*(6x + 8y = -45)\n6*(9x + 2y = -135/2)\n54x + 72y = -405\n54x + 12y = -405\nSubtract equations\n60y = 0\ny = 0/60\ny = 0\n\nSubstitute y\n6x + 8(0) = -45\n6x = -45\nx = -45/6\nx = -15/2"} {"input": "Find x in 7x - 21 = 0", "output": "7x - 21 = 0\n7x = 21\nx = 21 / 7\nx = 3"} {"input": "Compute the solution of x^2 + 5/2x + 3/2 = 0", "output": "x^2 + 5/2x + 3/2 = 0\n(x - -1)(x - -3/2) = 0\nx - -1 = 0 or x - -3/2 = 0\nx = -1\nx = -3/2"} {"input": "Find the solution to x^2 - 67/30x + 6/5 = 0", "output": "x^2 - 67/30x + 6/5 = 0\n(x - 4/3)(x - 9/10) = 0\nx - 4/3 = 0 or x - 9/10 = 0\nx = 4/3\nx = 9/10"} {"input": "Find x in x^2 - 29/8x - 55/8 = 0", "output": "x^2 - 29/8x - 55/8 = 0\n(x - 5)(x - -11/8) = 0\nx - 5 = 0 or x - -11/8 = 0\nx = 5\nx = -11/8"} {"input": "Solve the equation 9x - 162/5 = 0", "output": "9x - 162/5 = 0\n9x = 162/5\nx = 162/5 / 9\nx = 18/5"} {"input": "Solve quickly: 4x + 80/3 = 0", "output": "4x + 80/3 = 0\n4x = -80/3\nx = -80/3 / 4\nx = -20/3"} {"input": "Determine x in 7x + 42 = 0", "output": "7x + 42 = 0\n7x = -42\nx = -42 / 7\nx = -6"} {"input": "Find the solution to x^2 - 4/5x = 0", "output": "x^2 - 4/5x = 0\n(x - 0)(x - 4/5) = 0\nx - 0 = 0 or x - 4/5 = 0\nx = 0\nx = 4/5"} {"input": "Find x and y such that\n9x + 2y = -65/8\n10x + 7y = -103/4", "output": "9x + 2y = -65/8\n10x + 7y = -103/4\n\nUsing elimination\n10*(9x + 2y = -65/8)\n9*(10x + 7y = -103/4)\n90x + 20y = -325/4\n90x + 63y = -927/4\nSubtract equations\n-43y = 301/2\ny = 301/2/-43\ny = -7/2\n\nSubstitute y\n9x + 2(-7/2) = -65/8\n9x = -9/8\nx = -9/8/9\nx = -1/8"} {"input": "Find x for 1x + 9/5 = 0", "output": "1x + 9/5 = 0\n1x = -9/5\nx = -9/5 / 1\nx = -9/5"} {"input": "Solve the equation x^3 + 14/5x^2 - 49/25x + 34/125 = 0", "output": "x^3 + 14/5x^2 - 49/25x + 34/125 = 0\n(x - 1/5)(x - -17/5)(x - 2/5) = 0\nx - 1/5 = 0\nx - -17/5 = 0\nx - 2/5 = 0\nx = 1/5\nx = -17/5\nx = 2/5"} {"input": "What value of x satisfies x^3 - 48/5x^2 + 151/5x - 156/5 = 0", "output": "x^3 - 48/5x^2 + 151/5x - 156/5 = 0\n(x - 3)(x - 4)(x - 13/5) = 0\nx - 3 = 0\nx - 4 = 0\nx - 13/5 = 0\nx = 3\nx = 4\nx = 13/5"} {"input": "Compute the solution of x^3 + 13/10x^2 + 1/50x - 7/25 = 0", "output": "x^3 + 13/10x^2 + 1/50x - 7/25 = 0\n(x - -1)(x - 2/5)(x - -7/10) = 0\nx - -1 = 0\nx - 2/5 = 0\nx - -7/10 = 0\nx = -1\nx = 2/5\nx = -7/10"} {"input": "Solve the equation 9x + 171/4 = 0", "output": "9x + 171/4 = 0\n9x = -171/4\nx = -171/4 / 9\nx = -19/4"} {"input": "Solve the equations:\n1x + 8y = -173/40\n9x + 8y = -533/40", "output": "1x + 8y = -173/40\n9x + 8y = -533/40\n\nUsing elimination\n9*(1x + 8y = -173/40)\n1*(9x + 8y = -533/40)\n9x + 72y = -1557/40\n9x + 8y = -533/40\nSubtract equations\n64y = -128/5\ny = -128/5/64\ny = -2/5\n\nSubstitute y\n1x + 8(-2/5) = -173/40\n1x = -9/8\nx = -9/8/1\nx = -9/8"} {"input": "Solve quickly: x^3 + 76/45x^2 - 49/45x - 8/5 = 0", "output": "x^3 + 76/45x^2 - 49/45x - 8/5 = 0\n(x - -8/9)(x - 1)(x - -9/5) = 0\nx - -8/9 = 0\nx - 1 = 0\nx - -9/5 = 0\nx = -8/9\nx = 1\nx = -9/5"} {"input": "Find x and y such that\n3x + 9y = -19\n10x + 1y = -193/9", "output": "3x + 9y = -19\n10x + 1y = -193/9\n\nUsing elimination\n10*(3x + 9y = -19)\n3*(10x + 1y = -193/9)\n30x + 90y = -190\n30x + 3y = -193/3\nSubtract equations\n87y = -377/3\ny = -377/3/87\ny = -13/9\n\nSubstitute y\n3x + 9(-13/9) = -19\n3x = -6\nx = -6/3\nx = -2"} {"input": "Solve quickly: 2x + 4/9 = 0", "output": "2x + 4/9 = 0\n2x = -4/9\nx = -4/9 / 2\nx = -2/9"} {"input": "Find x in x^3 - 38/9x^2 + 59/12x - 55/36 = 0", "output": "x^3 - 38/9x^2 + 59/12x - 55/36 = 0\n(x - 11/9)(x - 1/2)(x - 5/2) = 0\nx - 11/9 = 0\nx - 1/2 = 0\nx - 5/2 = 0\nx = 11/9\nx = 1/2\nx = 5/2"} {"input": "Find the solution to 10x + 200/3 = 0", "output": "10x + 200/3 = 0\n10x = -200/3\nx = -200/3 / 10\nx = -20/3"} {"input": "Solve quickly: 3x + 57/8 = 0", "output": "3x + 57/8 = 0\n3x = -57/8\nx = -57/8 / 3\nx = -19/8"} {"input": "Solve quickly: x^2 - 15/2x + 9 = 0", "output": "x^2 - 15/2x + 9 = 0\n(x - 3/2)(x - 6) = 0\nx - 3/2 = 0 or x - 6 = 0\nx = 3/2\nx = 6"} {"input": "Solve simultaneously:\n4x + 6y = 31/7\n10x + 5y = -55/14", "output": "4x + 6y = 31/7\n10x + 5y = -55/14\n\nUsing elimination\n10*(4x + 6y = 31/7)\n4*(10x + 5y = -55/14)\n40x + 60y = 310/7\n40x + 20y = -110/7\nSubtract equations\n40y = 60\ny = 60/40\ny = 3/2\n\nSubstitute y\n4x + 6(3/2) = 31/7\n4x = -32/7\nx = -32/7/4\nx = -8/7"} {"input": "What value of x satisfies 7x - 5 = 0", "output": "7x - 5 = 0\n7x = 5\nx = 5 / 7\nx = 5/7"} {"input": "Find x for x^3 + 13/20x^2 - 229/20x + 39/5 = 0", "output": "x^3 + 13/20x^2 - 229/20x + 39/5 = 0\n(x - 13/5)(x - -4)(x - 3/4) = 0\nx - 13/5 = 0\nx - -4 = 0\nx - 3/4 = 0\nx = 13/5\nx = -4\nx = 3/4"} {"input": "Solve simultaneously:\n1x + 10y = 95/9\n8x + 5y = 385/9", "output": "1x + 10y = 95/9\n8x + 5y = 385/9\n\nUsing elimination\n8*(1x + 10y = 95/9)\n1*(8x + 5y = 385/9)\n8x + 80y = 760/9\n8x + 5y = 385/9\nSubtract equations\n75y = 125/3\ny = 125/3/75\ny = 5/9\n\nSubstitute y\n1x + 10(5/9) = 95/9\n1x = 5\nx = 5/1\nx = 5"} {"input": "What value of x satisfies 7x + 49/8 = 0", "output": "7x + 49/8 = 0\n7x = -49/8\nx = -49/8 / 7\nx = -7/8"} {"input": "Find x and y such that\n7x + 8y = -28\n10x + 1y = -87/4", "output": "7x + 8y = -28\n10x + 1y = -87/4\n\nUsing elimination\n10*(7x + 8y = -28)\n7*(10x + 1y = -87/4)\n70x + 80y = -280\n70x + 7y = -609/4\nSubtract equations\n73y = -511/4\ny = -511/4/73\ny = -7/4\n\nSubstitute y\n7x + 8(-7/4) = -28\n7x = -14\nx = -14/7\nx = -2"} {"input": "Compute the solution of x^2 - 27/5x + 2 = 0", "output": "x^2 - 27/5x + 2 = 0\n(x - 2/5)(x - 5) = 0\nx - 2/5 = 0 or x - 5 = 0\nx = 2/5\nx = 5"} {"input": "What value of x satisfies x^2 - 19/8x - 15/8 = 0", "output": "x^2 - 19/8x - 15/8 = 0\n(x - 3)(x - -5/8) = 0\nx - 3 = 0 or x - -5/8 = 0\nx = 3\nx = -5/8"} {"input": "Find x for x^2 - 59/12x + 6 = 0", "output": "x^2 - 59/12x + 6 = 0\n(x - 8/3)(x - 9/4) = 0\nx - 8/3 = 0 or x - 9/4 = 0\nx = 8/3\nx = 9/4"} {"input": "Compute the solution of 6x - 36/5 = 0", "output": "6x - 36/5 = 0\n6x = 36/5\nx = 36/5 / 6\nx = 6/5"} {"input": "Solve the system:\n3x + 7y = -190/9\n1x + 7y = -82/9", "output": "3x + 7y = -190/9\n1x + 7y = -82/9\n\nUsing elimination\n1*(3x + 7y = -190/9)\n3*(1x + 7y = -82/9)\n3x + 7y = -190/9\n3x + 21y = -82/3\nSubtract equations\n-14y = 56/9\ny = 56/9/-14\ny = -4/9\n\nSubstitute y\n3x + 7(-4/9) = -190/9\n3x = -18\nx = -18/3\nx = -6"} {"input": "Find x for 9x + 12 = 0", "output": "9x + 12 = 0\n9x = -12\nx = -12 / 9\nx = -4/3"} {"input": "Solve the equation 3x + 33/8 = 0", "output": "3x + 33/8 = 0\n3x = -33/8\nx = -33/8 / 3\nx = -11/8"} {"input": "What value of x satisfies 7x - 16 = 0", "output": "7x - 16 = 0\n7x = 16\nx = 16 / 7\nx = 16/7"} {"input": "Determine x in x^3 - 3/5x^2 - 71/20x + 33/10 = 0", "output": "x^3 - 3/5x^2 - 71/20x + 33/10 = 0\n(x - 3/2)(x - -2)(x - 11/10) = 0\nx - 3/2 = 0\nx - -2 = 0\nx - 11/10 = 0\nx = 3/2\nx = -2\nx = 11/10"} {"input": "Compute the solution of x^2 - 151/10x + 3/2 = 0", "output": "x^2 - 151/10x + 3/2 = 0\n(x - 15)(x - 1/10) = 0\nx - 15 = 0 or x - 1/10 = 0\nx = 15\nx = 1/10"} {"input": "Solve the equations:\n1x + 1y = 86/63\n8x + 6y = 796/63", "output": "1x + 1y = 86/63\n8x + 6y = 796/63\n\nUsing elimination\n8*(1x + 1y = 86/63)\n1*(8x + 6y = 796/63)\n8x + 8y = 688/63\n8x + 6y = 796/63\nSubtract equations\n2y = -12/7\ny = -12/7/2\ny = -6/7\n\nSubstitute y\n1x + 1(-6/7) = 86/63\n1x = 20/9\nx = 20/9/1\nx = 20/9"} {"input": "Solve x^3 - 302/45x^2 - 29/45x + 442/15 = 0", "output": "x^3 - 302/45x^2 - 29/45x + 442/15 = 0\n(x - 13/5)(x - -17/9)(x - 6) = 0\nx - 13/5 = 0\nx - -17/9 = 0\nx - 6 = 0\nx = 13/5\nx = -17/9\nx = 6"} {"input": "Find x and y such that\n9x + 4y = 4\n10x + 10y = 145/12", "output": "9x + 4y = 4\n10x + 10y = 145/12\n\nUsing elimination\n10*(9x + 4y = 4)\n9*(10x + 10y = 145/12)\n90x + 40y = 40\n90x + 90y = 435/4\nSubtract equations\n-50y = -275/4\ny = -275/4/-50\ny = 11/8\n\nSubstitute y\n9x + 4(11/8) = 4\n9x = -3/2\nx = -3/2/9\nx = -1/6"} {"input": "Compute the solution of x^3 + 4/3x^2 + 1/9x - 2/9 = 0", "output": "x^3 + 4/3x^2 + 1/9x - 2/9 = 0\n(x - -2/3)(x - -1)(x - 1/3) = 0\nx - -2/3 = 0\nx - -1 = 0\nx - 1/3 = 0\nx = -2/3\nx = -1\nx = 1/3"} {"input": "Find x in x^2 + 7/10x - 6/5 = 0", "output": "x^2 + 7/10x - 6/5 = 0\n(x - 4/5)(x - -3/2) = 0\nx - 4/5 = 0 or x - -3/2 = 0\nx = 4/5\nx = -3/2"} {"input": "Find the solution to 3x - 45/7 = 0", "output": "3x - 45/7 = 0\n3x = 45/7\nx = 45/7 / 3\nx = 15/7"} {"input": "Solve the equation 3x - 36/7 = 0", "output": "3x - 36/7 = 0\n3x = 36/7\nx = 36/7 / 3\nx = 12/7"} {"input": "Solve x^3 - 19/5x^2 - 16x + 304/5 = 0", "output": "x^3 - 19/5x^2 - 16x + 304/5 = 0\n(x - -4)(x - 19/5)(x - 4) = 0\nx - -4 = 0\nx - 19/5 = 0\nx - 4 = 0\nx = -4\nx = 19/5\nx = 4"} {"input": "Solve quickly: x^3 + 61/21x^2 + 272/147x - 16/49 = 0", "output": "x^3 + 61/21x^2 + 272/147x - 16/49 = 0\n(x - -4/3)(x - 1/7)(x - -12/7) = 0\nx - -4/3 = 0\nx - 1/7 = 0\nx - -12/7 = 0\nx = -4/3\nx = 1/7\nx = -12/7"} {"input": "Solve the equations:\n3x + 10y = 174\n6x + 8y = 132", "output": "3x + 10y = 174\n6x + 8y = 132\n\nUsing elimination\n6*(3x + 10y = 174)\n3*(6x + 8y = 132)\n18x + 60y = 1044\n18x + 24y = 396\nSubtract equations\n36y = 648\ny = 648/36\ny = 18\n\nSubstitute y\n3x + 10(18) = 174\n3x = -6\nx = -6/3\nx = -2"} {"input": "Solve the system:\n2x + 5y = -13\n8x + 6y = 11", "output": "2x + 5y = -13\n8x + 6y = 11\n\nUsing elimination\n8*(2x + 5y = -13)\n2*(8x + 6y = 11)\n16x + 40y = -104\n16x + 12y = 22\nSubtract equations\n28y = -126\ny = -126/28\ny = -9/2\n\nSubstitute y\n2x + 5(-9/2) = -13\n2x = 19/2\nx = 19/2/2\nx = 19/4"} {"input": "What value of x satisfies x^3 + 5/6x^2 - 181/6x - 65 = 0", "output": "x^3 + 5/6x^2 - 181/6x - 65 = 0\n(x - -5/2)(x - -13/3)(x - 6) = 0\nx - -5/2 = 0\nx - -13/3 = 0\nx - 6 = 0\nx = -5/2\nx = -13/3\nx = 6"} {"input": "What value of x satisfies 10x + 20 = 0", "output": "10x + 20 = 0\n10x = -20\nx = -20 / 10\nx = -2"} {"input": "Solve the equation x^2 + 113/7x + 120/7 = 0", "output": "x^2 + 113/7x + 120/7 = 0\n(x - -8/7)(x - -15) = 0\nx - -8/7 = 0 or x - -15 = 0\nx = -8/7\nx = -15"} {"input": "Find the solution to x^3 + 55/7x^2 + 409/28x - 9/4 = 0", "output": "x^3 + 55/7x^2 + 409/28x - 9/4 = 0\n(x - -7/2)(x - 1/7)(x - -9/2) = 0\nx - -7/2 = 0\nx - 1/7 = 0\nx - -9/2 = 0\nx = -7/2\nx = 1/7\nx = -9/2"} {"input": "Compute the solution of x^2 - 13/5x - 171/20 = 0", "output": "x^2 - 13/5x - 171/20 = 0\n(x - 9/2)(x - -19/10) = 0\nx - 9/2 = 0 or x - -19/10 = 0\nx = 9/2\nx = -19/10"} {"input": "Find the solution to x^2 + 79/4x + 57/4 = 0", "output": "x^2 + 79/4x + 57/4 = 0\n(x - -19)(x - -3/4) = 0\nx - -19 = 0 or x - -3/4 = 0\nx = -19\nx = -3/4"} {"input": "Solve the equations:\n10x + 6y = -49/3\n10x + 7y = -154/9", "output": "10x + 6y = -49/3\n10x + 7y = -154/9\n\nUsing elimination\n10*(10x + 6y = -49/3)\n10*(10x + 7y = -154/9)\n100x + 60y = -490/3\n100x + 70y = -1540/9\nSubtract equations\n-10y = 70/9\ny = 70/9/-10\ny = -7/9\n\nSubstitute y\n10x + 6(-7/9) = -49/3\n10x = -35/3\nx = -35/3/10\nx = -7/6"} {"input": "Find the solution to x^2 + 5/18x - 7/18 = 0", "output": "x^2 + 5/18x - 7/18 = 0\n(x - 1/2)(x - -7/9) = 0\nx - 1/2 = 0 or x - -7/9 = 0\nx = 1/2\nx = -7/9"} {"input": "Solve x^2 + 39/14x + 5/7 = 0", "output": "x^2 + 39/14x + 5/7 = 0\n(x - -5/2)(x - -2/7) = 0\nx - -5/2 = 0 or x - -2/7 = 0\nx = -5/2\nx = -2/7"} {"input": "Solve simultaneously:\n2x + 9y = 201/8\n7x + 10y = 169/4", "output": "2x + 9y = 201/8\n7x + 10y = 169/4\n\nUsing elimination\n7*(2x + 9y = 201/8)\n2*(7x + 10y = 169/4)\n14x + 63y = 1407/8\n14x + 20y = 169/2\nSubtract equations\n43y = 731/8\ny = 731/8/43\ny = 17/8\n\nSubstitute y\n2x + 9(17/8) = 201/8\n2x = 6\nx = 6/2\nx = 3"} {"input": "Solve the system:\n3x + 6y = -41/2\n8x + 3y = -86/3", "output": "3x + 6y = -41/2\n8x + 3y = -86/3\n\nUsing elimination\n8*(3x + 6y = -41/2)\n3*(8x + 3y = -86/3)\n24x + 48y = -164\n24x + 9y = -86\nSubtract equations\n39y = -78\ny = -78/39\ny = -2\n\nSubstitute y\n3x + 6(-2) = -41/2\n3x = -17/2\nx = -17/2/3\nx = -17/6"} {"input": "Determine x in x^2 + 1/45x - 2/45 = 0", "output": "x^2 + 1/45x - 2/45 = 0\n(x - -2/9)(x - 1/5) = 0\nx - -2/9 = 0 or x - 1/5 = 0\nx = -2/9\nx = 1/5"} {"input": "Solve 7x + 20 = 0", "output": "7x + 20 = 0\n7x = -20\nx = -20 / 7\nx = -20/7"} {"input": "Solve x^3 + 657/40x^2 - 279/10x + 81/10 = 0", "output": "x^3 + 657/40x^2 - 279/10x + 81/10 = 0\n(x - 3/8)(x - 6/5)(x - -18) = 0\nx - 3/8 = 0\nx - 6/5 = 0\nx - -18 = 0\nx = 3/8\nx = 6/5\nx = -18"} {"input": "Determine x in x^3 + 41/2x^2 + 125x + 200 = 0", "output": "x^3 + 41/2x^2 + 125x + 200 = 0\n(x - -8)(x - -5/2)(x - -10) = 0\nx - -8 = 0\nx - -5/2 = 0\nx - -10 = 0\nx = -8\nx = -5/2\nx = -10"} {"input": "Solve quickly: 7x + 49/5 = 0", "output": "7x + 49/5 = 0\n7x = -49/5\nx = -49/5 / 7\nx = -7/5"} {"input": "Solve the equation x^3 + 113/63x^2 - 404/147x - 1760/441 = 0", "output": "x^3 + 113/63x^2 - 404/147x - 1760/441 = 0\n(x - 11/7)(x - -20/9)(x - -8/7) = 0\nx - 11/7 = 0\nx - -20/9 = 0\nx - -8/7 = 0\nx = 11/7\nx = -20/9\nx = -8/7"} {"input": "Solve x^2 + 11/6x + 2/3 = 0", "output": "x^2 + 11/6x + 2/3 = 0\n(x - -4/3)(x - -1/2) = 0\nx - -4/3 = 0 or x - -1/2 = 0\nx = -4/3\nx = -1/2"} {"input": "Solve the system:\n8x + 6y = -9/4\n10x + 7y = -17/8", "output": "8x + 6y = -9/4\n10x + 7y = -17/8\n\nUsing elimination\n10*(8x + 6y = -9/4)\n8*(10x + 7y = -17/8)\n80x + 60y = -45/2\n80x + 56y = -17\nSubtract equations\n4y = -11/2\ny = -11/2/4\ny = -11/8\n\nSubstitute y\n8x + 6(-11/8) = -9/4\n8x = 6\nx = 6/8\nx = 3/4"} {"input": "Find x and y such that\n3x + 4y = -24\n10x + 10y = -65", "output": "3x + 4y = -24\n10x + 10y = -65\n\nUsing elimination\n10*(3x + 4y = -24)\n3*(10x + 10y = -65)\n30x + 40y = -240\n30x + 30y = -195\nSubtract equations\n10y = -45\ny = -45/10\ny = -9/2\n\nSubstitute y\n3x + 4(-9/2) = -24\n3x = -6\nx = -6/3\nx = -2"} {"input": "Determine x in 7x - 35/4 = 0", "output": "7x - 35/4 = 0\n7x = 35/4\nx = 35/4 / 7\nx = 5/4"} {"input": "Find x for 4x - 10 = 0", "output": "4x - 10 = 0\n4x = 10\nx = 10 / 4\nx = 5/2"} {"input": "Solve x^2 + 22/5x - 3 = 0", "output": "x^2 + 22/5x - 3 = 0\n(x - 3/5)(x - -5) = 0\nx - 3/5 = 0 or x - -5 = 0\nx = 3/5\nx = -5"} {"input": "What value of x satisfies x^3 + 163/42x^2 - 5/6x - 76/7 = 0", "output": "x^3 + 163/42x^2 - 5/6x - 76/7 = 0\n(x - -19/7)(x - -8/3)(x - 3/2) = 0\nx - -19/7 = 0\nx - -8/3 = 0\nx - 3/2 = 0\nx = -19/7\nx = -8/3\nx = 3/2"} {"input": "Find the solution to x^2 - 5/2x + 3/2 = 0", "output": "x^2 - 5/2x + 3/2 = 0\n(x - 1)(x - 3/2) = 0\nx - 1 = 0 or x - 3/2 = 0\nx = 1\nx = 3/2"} {"input": "Solve x^3 - 5/2x^2 + 2x - 1/2 = 0", "output": "x^3 - 5/2x^2 + 2x - 1/2 = 0\n(x - 1)(x - 1/2)(x - 1) = 0\nx - 1 = 0\nx - 1/2 = 0\nx - 1 = 0\nx = 1\nx = 1/2\nx = 1"} {"input": "Solve the equations:\n2x + 1y = 33/20\n3x + 6y = -9/40", "output": "2x + 1y = 33/20\n3x + 6y = -9/40\n\nUsing elimination\n3*(2x + 1y = 33/20)\n2*(3x + 6y = -9/40)\n6x + 3y = 99/20\n6x + 12y = -9/20\nSubtract equations\n-9y = 27/5\ny = 27/5/-9\ny = -3/5\n\nSubstitute y\n2x + 1(-3/5) = 33/20\n2x = 9/4\nx = 9/4/2\nx = 9/8"} {"input": "Find x in 9x + 54/5 = 0", "output": "9x + 54/5 = 0\n9x = -54/5\nx = -54/5 / 9\nx = -6/5"} {"input": "Find x for 10x - 190 = 0", "output": "10x - 190 = 0\n10x = 190\nx = 190 / 10\nx = 19"} {"input": "Solve the system:\n1x + 8y = 184/9\n1x + 6y = 52/3", "output": "1x + 8y = 184/9\n1x + 6y = 52/3\n\nUsing elimination\n1*(1x + 8y = 184/9)\n1*(1x + 6y = 52/3)\n1x + 8y = 184/9\n1x + 6y = 52/3\nSubtract equations\n2y = 28/9\ny = 28/9/2\ny = 14/9\n\nSubstitute y\n1x + 8(14/9) = 184/9\n1x = 8\nx = 8/1\nx = 8"} {"input": "Solve the system:\n6x + 1y = -12\n6x + 5y = 4", "output": "6x + 1y = -12\n6x + 5y = 4\n\nUsing elimination\n6*(6x + 1y = -12)\n6*(6x + 5y = 4)\n36x + 6y = -72\n36x + 30y = 24\nSubtract equations\n-24y = -96\ny = -96/-24\ny = 4\n\nSubstitute y\n6x + 1(4) = -12\n6x = -16\nx = -16/6\nx = -8/3"} {"input": "Solve x^2 + 23/3x + 10 = 0", "output": "x^2 + 23/3x + 10 = 0\n(x - -5/3)(x - -6) = 0\nx - -5/3 = 0 or x - -6 = 0\nx = -5/3\nx = -6"} {"input": "Solve the equation x^2 - 10/3x - 8/3 = 0", "output": "x^2 - 10/3x - 8/3 = 0\n(x - 4)(x - -2/3) = 0\nx - 4 = 0 or x - -2/3 = 0\nx = 4\nx = -2/3"} {"input": "Find x in x^2 + 33/56x - 27/14 = 0", "output": "x^2 + 33/56x - 27/14 = 0\n(x - -12/7)(x - 9/8) = 0\nx - -12/7 = 0 or x - 9/8 = 0\nx = -12/7\nx = 9/8"} {"input": "What value of x satisfies x^3 - 5x^2 - 12x + 36 = 0", "output": "x^3 - 5x^2 - 12x + 36 = 0\n(x - 6)(x - -3)(x - 2) = 0\nx - 6 = 0\nx - -3 = 0\nx - 2 = 0\nx = 6\nx = -3\nx = 2"} {"input": "Determine x in 7x + 21/2 = 0", "output": "7x + 21/2 = 0\n7x = -21/2\nx = -21/2 / 7\nx = -3/2"} {"input": "Solve the equation 4x + 72/7 = 0", "output": "4x + 72/7 = 0\n4x = -72/7\nx = -72/7 / 4\nx = -18/7"} {"input": "Solve simultaneously:\n1x + 7y = -389/12\n1x + 4y = -221/12", "output": "1x + 7y = -389/12\n1x + 4y = -221/12\n\nUsing elimination\n1*(1x + 7y = -389/12)\n1*(1x + 4y = -221/12)\n1x + 7y = -389/12\n1x + 4y = -221/12\nSubtract equations\n3y = -14\ny = -14/3\ny = -14/3\n\nSubstitute y\n1x + 7(-14/3) = -389/12\n1x = 1/4\nx = 1/4/1\nx = 1/4"} {"input": "Solve the equations:\n10x + 5y = 85\n6x + 9y = 105", "output": "10x + 5y = 85\n6x + 9y = 105\n\nUsing elimination\n6*(10x + 5y = 85)\n10*(6x + 9y = 105)\n60x + 30y = 510\n60x + 90y = 1050\nSubtract equations\n-60y = -540\ny = -540/-60\ny = 9\n\nSubstitute y\n10x + 5(9) = 85\n10x = 40\nx = 40/10\nx = 4"} {"input": "Solve the equations:\n4x + 10y = -126\n1x + 4y = -45", "output": "4x + 10y = -126\n1x + 4y = -45\n\nUsing elimination\n1*(4x + 10y = -126)\n4*(1x + 4y = -45)\n4x + 10y = -126\n4x + 16y = -180\nSubtract equations\n-6y = 54\ny = 54/-6\ny = -9\n\nSubstitute y\n4x + 10(-9) = -126\n4x = -36\nx = -36/4\nx = -9"} {"input": "Solve the system:\n10x + 5y = -282/7\n1x + 5y = -129/7", "output": "10x + 5y = -282/7\n1x + 5y = -129/7\n\nUsing elimination\n1*(10x + 5y = -282/7)\n10*(1x + 5y = -129/7)\n10x + 5y = -282/7\n10x + 50y = -1290/7\nSubtract equations\n-45y = 144\ny = 144/-45\ny = -16/5\n\nSubstitute y\n10x + 5(-16/5) = -282/7\n10x = -170/7\nx = -170/7/10\nx = -17/7"} {"input": "Solve simultaneously:\n9x + 3y = -31/4\n9x + 4y = -8", "output": "9x + 3y = -31/4\n9x + 4y = -8\n\nUsing elimination\n9*(9x + 3y = -31/4)\n9*(9x + 4y = -8)\n81x + 27y = -279/4\n81x + 36y = -72\nSubtract equations\n-9y = 9/4\ny = 9/4/-9\ny = -1/4\n\nSubstitute y\n9x + 3(-1/4) = -31/4\n9x = -7\nx = -7/9\nx = -7/9"} {"input": "Solve the equations:\n4x + 5y = -131/8\n4x + 4y = -31/2", "output": "4x + 5y = -131/8\n4x + 4y = -31/2\n\nUsing elimination\n4*(4x + 5y = -131/8)\n4*(4x + 4y = -31/2)\n16x + 20y = -131/2\n16x + 16y = -62\nSubtract equations\n4y = -7/2\ny = -7/2/4\ny = -7/8\n\nSubstitute y\n4x + 5(-7/8) = -131/8\n4x = -12\nx = -12/4\nx = -3"} {"input": "Solve the equation x^2 + 19/6x + 35/18 = 0", "output": "x^2 + 19/6x + 35/18 = 0\n(x - -5/6)(x - -7/3) = 0\nx - -5/6 = 0 or x - -7/3 = 0\nx = -5/6\nx = -7/3"} {"input": "Find x and y such that\n9x + 2y = 49/4\n3x + 7y = 39/8", "output": "9x + 2y = 49/4\n3x + 7y = 39/8\n\nUsing elimination\n3*(9x + 2y = 49/4)\n9*(3x + 7y = 39/8)\n27x + 6y = 147/4\n27x + 63y = 351/8\nSubtract equations\n-57y = -57/8\ny = -57/8/-57\ny = 1/8\n\nSubstitute y\n9x + 2(1/8) = 49/4\n9x = 12\nx = 12/9\nx = 4/3"} {"input": "Find x for 7x - 105/8 = 0", "output": "7x - 105/8 = 0\n7x = 105/8\nx = 105/8 / 7\nx = 15/8"} {"input": "Solve 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Find x for x^3 + 499/21x^2 + 960/7x + 4352/21 = 0", "output": "x^3 + 499/21x^2 + 960/7x + 4352/21 = 0\n(x - -17/7)(x - -16/3)(x - -16) = 0\nx - -17/7 = 0\nx - -16/3 = 0\nx - -16 = 0\nx = -17/7\nx = -16/3\nx = -16"} {"input": "Find x for x^3 + 1255/56x^2 + 337/4x + 612/7 = 0", "output": "x^3 + 1255/56x^2 + 337/4x + 612/7 = 0\n(x - -17/8)(x - -16/7)(x - -18) = 0\nx - -17/8 = 0\nx - -16/7 = 0\nx - -18 = 0\nx = -17/8\nx = -16/7\nx = -18"} {"input": "Find x for 4x - 6 = 0", "output": "4x - 6 = 0\n4x = 6\nx = 6 / 4\nx = 3/2"} {"input": "Find x and y such that\n5x + 4y = -176/7\n2x + 4y = -188/7", "output": "5x + 4y = -176/7\n2x + 4y = -188/7\n\nUsing elimination\n2*(5x + 4y = -176/7)\n5*(2x + 4y = -188/7)\n10x + 8y = -352/7\n10x + 20y = -940/7\nSubtract equations\n-12y = 84\ny = 84/-12\ny = -7\n\nSubstitute y\n5x + 4(-7) = -176/7\n5x = 20/7\nx = 20/7/5\nx = 4/7"} {"input": "Find x for 1x + 7/2 = 0", "output": "1x + 7/2 = 0\n1x = -7/2\nx = -7/2 / 1\nx = -7/2"} {"input": "Find the solution to x^2 + 23/5x - 42/5 = 0", "output": "x^2 + 23/5x - 42/5 = 0\n(x - -6)(x - 7/5) = 0\nx - -6 = 0 or x - 7/5 = 0\nx = -6\nx = 7/5"} {"input": "Find x for 4x - 4/3 = 0", "output": "4x - 4/3 = 0\n4x = 4/3\nx = 4/3 / 4\nx = 1/3"} {"input": "Find the solution to x^3 + 1/8x^2 - 1x - 1/8 = 0", "output": "x^3 + 1/8x^2 - 1x - 1/8 = 0\n(x - -1/8)(x - 1)(x - -1) = 0\nx - -1/8 = 0\nx - 1 = 0\nx - -1 = 0\nx = -1/8\nx = 1\nx = -1"} {"input": "Solve the equation x^2 + 36/5x + 36/5 = 0", "output": "x^2 + 36/5x + 36/5 = 0\n(x - -6)(x - -6/5) = 0\nx - -6 = 0 or x - -6/5 = 0\nx = -6\nx = -6/5"} {"input": "Find x for x^3 - 127/12x^2 - 1085/24x - 147/4 = 0", "output": "x^3 - 127/12x^2 - 1085/24x - 147/4 = 0\n(x - -9/4)(x - -7/6)(x - 14) = 0\nx - -9/4 = 0\nx - -7/6 = 0\nx - 14 = 0\nx = -9/4\nx = -7/6\nx = 14"} {"input": "What value of x satisfies x^3 + 41/3x^2 - 655/12x + 425/12 = 0", "output": "x^3 + 41/3x^2 - 655/12x + 425/12 = 0\n(x - 5/2)(x - -17)(x - 5/6) = 0\nx - 5/2 = 0\nx - -17 = 0\nx - 5/6 = 0\nx = 5/2\nx = -17\nx = 5/6"} {"input": "Solve quickly: x^3 - 67/6x^2 - 334/3x - 210 = 0", "output": "x^3 - 67/6x^2 - 334/3x - 210 = 0\n(x - -7/2)(x - -10/3)(x - 18) = 0\nx - -7/2 = 0\nx - -10/3 = 0\nx - 18 = 0\nx = -7/2\nx = -10/3\nx = 18"} {"input": "Find the solution to x^2 - 23/3x + 40/3 = 0", "output": "x^2 - 23/3x + 40/3 = 0\n(x - 8/3)(x - 5) = 0\nx - 8/3 = 0 or x - 5 = 0\nx = 8/3\nx = 5"} {"input": "What value of x satisfies x^2 - 79/28x + 55/28 = 0", "output": "x^2 - 79/28x + 55/28 = 0\n(x - 11/7)(x - 5/4) = 0\nx - 11/7 = 0 or x - 5/4 = 0\nx = 11/7\nx = 5/4"} {"input": "Solve the equations:\n3x + 3y = -144/5\n6x + 1y = -13/5", "output": "3x + 3y = -144/5\n6x + 1y = -13/5\n\nUsing elimination\n6*(3x + 3y = -144/5)\n3*(6x + 1y = -13/5)\n18x + 18y = -864/5\n18x + 3y = -39/5\nSubtract equations\n15y = -165\ny = -165/15\ny = -11\n\nSubstitute y\n3x + 3(-11) = -144/5\n3x = 21/5\nx = 21/5/3\nx = 7/5"} {"input": "Find x and y such that\n6x + 3y = -73\n2x + 5y = -77/3", "output": "6x + 3y = -73\n2x + 5y = -77/3\n\nUsing elimination\n2*(6x + 3y = -73)\n6*(2x + 5y = -77/3)\n12x + 6y = -146\n12x + 30y = -154\nSubtract equations\n-24y = 8\ny = 8/-24\ny = -1/3\n\nSubstitute y\n6x + 3(-1/3) = -73\n6x = -72\nx = -72/6\nx = -12"} {"input": "Determine x in 6x - 33 = 0", "output": "6x - 33 = 0\n6x = 33\nx = 33 / 6\nx = 11/2"} {"input": "Determine x in 1x + 5/3 = 0", "output": "1x + 5/3 = 0\n1x = -5/3\nx = -5/3 / 1\nx = -5/3"} {"input": "Solve the equations:\n8x + 5y = -7/2\n2x + 7y = 27/2", "output": "8x + 5y = -7/2\n2x + 7y = 27/2\n\nUsing elimination\n2*(8x + 5y = -7/2)\n8*(2x + 7y = 27/2)\n16x + 10y = -7\n16x + 56y = 108\nSubtract equations\n-46y = -115\ny = -115/-46\ny = 5/2\n\nSubstitute y\n8x + 5(5/2) = -7/2\n8x = -16\nx = -16/8\nx = -2"} {"input": "Solve quickly: 6x + 33 = 0", "output": "6x + 33 = 0\n6x = -33\nx = -33 / 6\nx = -11/2"} {"input": "Solve x^2 + 4/3x - 5 = 0", "output": "x^2 + 4/3x - 5 = 0\n(x - 5/3)(x - -3) = 0\nx - 5/3 = 0 or x - -3 = 0\nx = 5/3\nx = -3"} {"input": "Compute the solution of x^2 + 94/15x - 8/3 = 0", "output": "x^2 + 94/15x - 8/3 = 0\n(x - -20/3)(x - 2/5) = 0\nx - -20/3 = 0 or x - 2/5 = 0\nx = -20/3\nx = 2/5"} {"input": "What value of x satisfies x^3 + 46/9x^2 - 49/9x - 2/3 = 0", "output": "x^3 + 46/9x^2 - 49/9x - 2/3 = 0\n(x - -1/9)(x - -6)(x - 1) = 0\nx - -1/9 = 0\nx - -6 = 0\nx - 1 = 0\nx = -1/9\nx = -6\nx = 1"} {"input": "What value of x satisfies 5x - 10/3 = 0", "output": "5x - 10/3 = 0\n5x = 10/3\nx = 10/3 / 5\nx = 2/3"} {"input": "Solve the system:\n10x + 10y = -172/3\n7x + 2y = -202/15", "output": "10x + 10y = -172/3\n7x + 2y = -202/15\n\nUsing elimination\n7*(10x + 10y = -172/3)\n10*(7x + 2y = -202/15)\n70x + 70y = -1204/3\n70x + 20y = -404/3\nSubtract equations\n50y = -800/3\ny = -800/3/50\ny = -16/3\n\nSubstitute y\n10x + 10(-16/3) = -172/3\n10x = -4\nx = -4/10\nx = -2/5"} {"input": "Solve the equation 6x - 20 = 0", "output": "6x - 20 = 0\n6x = 20\nx = 20 / 6\nx = 10/3"} {"input": "Compute the solution of x^2 + 7x + 38/9 = 0", "output": "x^2 + 7x + 38/9 = 0\n(x - -2/3)(x - -19/3) = 0\nx - -2/3 = 0 or x - -19/3 = 0\nx = -2/3\nx = -19/3"} {"input": "Find x for x^2 + 19/14x - 20/7 = 0", "output": "x^2 + 19/14x - 20/7 = 0\n(x - -5/2)(x - 8/7) = 0\nx - -5/2 = 0 or x - 8/7 = 0\nx = -5/2\nx = 8/7"} {"input": "Determine x in x^2 - 51/28x - 27/28 = 0", "output": "x^2 - 51/28x - 27/28 = 0\n(x - -3/7)(x - 9/4) = 0\nx - -3/7 = 0 or x - 9/4 = 0\nx = -3/7\nx = 9/4"} {"input": "Find x and y such that\n8x + 7y = 233/6\n3x + 8y = 28", "output": "8x + 7y = 233/6\n3x + 8y = 28\n\nUsing elimination\n3*(8x + 7y = 233/6)\n8*(3x + 8y = 28)\n24x + 21y = 233/2\n24x + 64y = 224\nSubtract equations\n-43y = -215/2\ny = -215/2/-43\ny = 5/2\n\nSubstitute y\n8x + 7(5/2) = 233/6\n8x = 64/3\nx = 64/3/8\nx = 8/3"} {"input": "Find x for x^2 - 53/35x - 12/35 = 0", "output": "x^2 - 53/35x - 12/35 = 0\n(x - -1/5)(x - 12/7) = 0\nx - -1/5 = 0 or x - 12/7 = 0\nx = -1/5\nx = 12/7"} {"input": "Find x in x^2 - 13/12x - 1/3 = 0", "output": "x^2 - 13/12x - 1/3 = 0\n(x - 4/3)(x - -1/4) = 0\nx - 4/3 = 0 or x - -1/4 = 0\nx = 4/3\nx = -1/4"} {"input": "Find x and y such that\n2x + 5y = -118/5\n9x + 3y = -141/5", "output": "2x + 5y = -118/5\n9x + 3y = -141/5\n\nUsing elimination\n9*(2x + 5y = -118/5)\n2*(9x + 3y = -141/5)\n18x + 45y = -1062/5\n18x + 6y = -282/5\nSubtract equations\n39y = -156\ny = -156/39\ny = -4\n\nSubstitute y\n2x + 5(-4) = -118/5\n2x = -18/5\nx = -18/5/2\nx = -9/5"} {"input": "What value of x satisfies x^2 + 4/3x - 4/3 = 0", "output": "x^2 + 4/3x - 4/3 = 0\n(x - 2/3)(x - -2) = 0\nx - 2/3 = 0 or x - -2 = 0\nx = 2/3\nx = -2"} {"input": "Solve simultaneously:\n10x + 9y = -205/4\n7x + 4y = -195/8", "output": "10x + 9y = -205/4\n7x + 4y = -195/8\n\nUsing elimination\n7*(10x + 9y = -205/4)\n10*(7x + 4y = -195/8)\n70x + 63y = -1435/4\n70x + 40y = -975/4\nSubtract equations\n23y = -115\ny = -115/23\ny = -5\n\nSubstitute y\n10x + 9(-5) = -205/4\n10x = -25/4\nx = -25/4/10\nx = -5/8"} {"input": "Solve quickly: x^2 - 14/3x - 5/3 = 0", "output": "x^2 - 14/3x - 5/3 = 0\n(x - -1/3)(x - 5) = 0\nx - -1/3 = 0 or x - 5 = 0\nx = -1/3\nx = 5"} {"input": "Solve x^2 + 13x + 30 = 0", "output": "x^2 + 13x + 30 = 0\n(x - -10)(x - -3) = 0\nx - -10 = 0 or x - -3 = 0\nx = -10\nx = -3"} {"input": "Solve simultaneously:\n3x + 9y = 51/2\n7x + 1y = 59/2", "output": "3x + 9y = 51/2\n7x + 1y = 59/2\n\nUsing elimination\n7*(3x + 9y = 51/2)\n3*(7x + 1y = 59/2)\n21x + 63y = 357/2\n21x + 3y = 177/2\nSubtract equations\n60y = 90\ny = 90/60\ny = 3/2\n\nSubstitute y\n3x + 9(3/2) = 51/2\n3x = 12\nx = 12/3\nx = 4"} {"input": "What value of x satisfies x^2 - 3/5x - 27/20 = 0", "output": "x^2 - 3/5x - 27/20 = 0\n(x - 3/2)(x - -9/10) = 0\nx - 3/2 = 0 or x - -9/10 = 0\nx = 3/2\nx = -9/10"} {"input": "Solve the system:\n5x + 9y = 571/40\n4x + 6y = 101/10", "output": "5x + 9y = 571/40\n4x + 6y = 101/10\n\nUsing elimination\n4*(5x + 9y = 571/40)\n5*(4x + 6y = 101/10)\n20x + 36y = 571/10\n20x + 30y = 101/2\nSubtract equations\n6y = 33/5\ny = 33/5/6\ny = 11/10\n\nSubstitute y\n5x + 9(11/10) = 571/40\n5x = 35/8\nx = 35/8/5\nx = 7/8"} {"input": "Find x in x^3 - 417/40x^2 - 53/5x + 1881/40 = 0", "output": "x^3 - 417/40x^2 - 53/5x + 1881/40 = 0\n(x - 9/5)(x - 11)(x - -19/8) = 0\nx - 9/5 = 0\nx - 11 = 0\nx - -19/8 = 0\nx = 9/5\nx = 11\nx = -19/8"} {"input": "Find the solution to x^3 - 17/3x^2 - 1x + 17/3 = 0", "output": "x^3 - 17/3x^2 - 1x + 17/3 = 0\n(x - 1)(x - 17/3)(x - -1) = 0\nx - 1 = 0\nx - 17/3 = 0\nx - -1 = 0\nx = 1\nx = 17/3\nx = -1"} {"input": "Solve the system:\n9x + 5y = 1847/70\n1x + 2y = 393/70", "output": "9x + 5y = 1847/70\n1x + 2y = 393/70\n\nUsing elimination\n1*(9x + 5y = 1847/70)\n9*(1x + 2y = 393/70)\n9x + 5y = 1847/70\n9x + 18y = 3537/70\nSubtract equations\n-13y = -169/7\ny = -169/7/-13\ny = 13/7\n\nSubstitute y\n9x + 5(13/7) = 1847/70\n9x = 171/10\nx = 171/10/9\nx = 19/10"} {"input": "Solve the equation x^2 - 8/3x + 143/81 = 0", "output": "x^2 - 8/3x + 143/81 = 0\n(x - 13/9)(x - 11/9) = 0\nx - 13/9 = 0 or x - 11/9 = 0\nx = 13/9\nx = 11/9"} {"input": "Find x for x^3 + 1/2x^2 - 37/2x - 18 = 0", "output": "x^3 + 1/2x^2 - 37/2x - 18 = 0\n(x - -1)(x - -4)(x - 9/2) = 0\nx - -1 = 0\nx - -4 = 0\nx - 9/2 = 0\nx = -1\nx = -4\nx = 9/2"} {"input": "Solve quickly: x^3 + 274/15x^2 - 23x - 2584/15 = 0", "output": "x^3 + 274/15x^2 - 23x - 2584/15 = 0\n(x - 17/5)(x - -8/3)(x - -19) = 0\nx - 17/5 = 0\nx - -8/3 = 0\nx - -19 = 0\nx = 17/5\nx = -8/3\nx = -19"} {"input": "Compute the solution of x^3 - 149/30x^2 + 1/10x + 91/15 = 0", "output": "x^3 - 149/30x^2 + 1/10x + 91/15 = 0\n(x - 14/3)(x - -1)(x - 13/10) = 0\nx - 14/3 = 0\nx - -1 = 0\nx - 13/10 = 0\nx = 14/3\nx = -1\nx = 13/10"} {"input": "What value of x satisfies x^3 - 13/18x^2 - 2/3x + 7/18 = 0", "output": "x^3 - 13/18x^2 - 2/3x + 7/18 = 0\n(x - -7/9)(x - 1)(x - 1/2) = 0\nx - -7/9 = 0\nx - 1 = 0\nx - 1/2 = 0\nx = -7/9\nx = 1\nx = 1/2"} {"input": "Solve the system:\n4x + 6y = 31/4\n8x + 1y = 201/8", "output": "4x + 6y = 31/4\n8x + 1y = 201/8\n\nUsing elimination\n8*(4x + 6y = 31/4)\n4*(8x + 1y = 201/8)\n32x + 48y = 62\n32x + 4y = 201/2\nSubtract equations\n44y = -77/2\ny = -77/2/44\ny = -7/8\n\nSubstitute y\n4x + 6(-7/8) = 31/4\n4x = 13\nx = 13/4\nx = 13/4"} {"input": "Solve quickly: x^2 + 1x - 6 = 0", "output": "x^2 + 1x - 6 = 0\n(x - 2)(x - -3) = 0\nx - 2 = 0 or x - -3 = 0\nx = 2\nx = -3"} {"input": "Determine x in x^3 - 59/30x^2 - 13/45x + 44/45 = 0", "output": "x^3 - 59/30x^2 - 13/45x + 44/45 = 0\n(x - 4/5)(x - 11/6)(x - -2/3) = 0\nx - 4/5 = 0\nx - 11/6 = 0\nx - -2/3 = 0\nx = 4/5\nx = 11/6\nx = -2/3"} {"input": "Solve the equations:\n10x + 9y = -150/7\n4x + 7y = -60/7", "output": "10x + 9y = -150/7\n4x + 7y = -60/7\n\nUsing elimination\n4*(10x + 9y = -150/7)\n10*(4x + 7y = -60/7)\n40x + 36y = -600/7\n40x + 70y = -600/7\nSubtract equations\n-34y = 0\ny = 0/-34\ny = 0\n\nSubstitute y\n10x + 9(0) = -150/7\n10x = -150/7\nx = -150/7/10\nx = -15/7"} {"input": "Determine x in x^2 + 11/6x - 38/9 = 0", "output": "x^2 + 11/6x - 38/9 = 0\n(x - -19/6)(x - 4/3) = 0\nx - -19/6 = 0 or x - 4/3 = 0\nx = -19/6\nx = 4/3"} {"input": "Solve simultaneously:\n3x + 1y = -15/2\n1x + 8y = -37", "output": "3x + 1y = -15/2\n1x + 8y = -37\n\nUsing elimination\n1*(3x + 1y = -15/2)\n3*(1x + 8y = -37)\n3x + 1y = -15/2\n3x + 24y = -111\nSubtract equations\n-23y = 207/2\ny = 207/2/-23\ny = -9/2\n\nSubstitute y\n3x + 1(-9/2) = -15/2\n3x = -3\nx = -3/3\nx = -1"} {"input": "Solve the equation 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Solve the equations:\n1x + 10y = -89/6\n9x + 10y = -161/6", "output": "1x + 10y = -89/6\n9x + 10y = -161/6\n\nUsing elimination\n9*(1x + 10y = -89/6)\n1*(9x + 10y = -161/6)\n9x + 90y = -267/2\n9x + 10y = -161/6\nSubtract equations\n80y = -320/3\ny = -320/3/80\ny = -4/3\n\nSubstitute y\n1x + 10(-4/3) = -89/6\n1x = -3/2\nx = -3/2/1\nx = -3/2"} {"input": "Solve the equation x^2 - 2x = 0", "output": "x^2 - 2x = 0\n(x - 2)(x - 0) = 0\nx - 2 = 0 or x - 0 = 0\nx = 2\nx = 0"} {"input": "Compute the solution of x^3 - 7/3x^2 - 131/3x + 455/3 = 0", "output": "x^3 - 7/3x^2 - 131/3x + 455/3 = 0\n(x - -7)(x - 13/3)(x - 5) = 0\nx - -7 = 0\nx - 13/3 = 0\nx - 5 = 0\nx = -7\nx = 13/3\nx = 5"} {"input": "What value of x satisfies x^2 + 39/10x - 2/5 = 0", "output": "x^2 + 39/10x - 2/5 = 0\n(x - -4)(x - 1/10) = 0\nx - -4 = 0 or x - 1/10 = 0\nx = -4\nx = 1/10"} {"input": "What value of x satisfies 8x - 8/9 = 0", "output": "8x - 8/9 = 0\n8x = 8/9\nx = 8/9 / 8\nx = 1/9"} {"input": "Compute the solution of x^2 - 151/24x + 85/24 = 0", "output": "x^2 - 151/24x + 85/24 = 0\n(x - 17/3)(x - 5/8) = 0\nx - 17/3 = 0 or x - 5/8 = 0\nx = 17/3\nx = 5/8"} {"input": "Find x for 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "What value of x satisfies x^3 - 263/70x^2 + 1529/350x - 39/25 = 0", "output": "x^3 - 263/70x^2 + 1529/350x - 39/25 = 0\n(x - 6/5)(x - 13/7)(x - 7/10) = 0\nx - 6/5 = 0\nx - 13/7 = 0\nx - 7/10 = 0\nx = 6/5\nx = 13/7\nx = 7/10"} {"input": "Determine x in x^2 - 20/7x = 0", "output": "x^2 - 20/7x = 0\n(x - 20/7)(x - 0) = 0\nx - 20/7 = 0 or x - 0 = 0\nx = 20/7\nx = 0"} {"input": "Solve quickly: x^2 - 261/56x + 38/7 = 0", "output": "x^2 - 261/56x + 38/7 = 0\n(x - 16/7)(x - 19/8) = 0\nx - 16/7 = 0 or x - 19/8 = 0\nx = 16/7\nx = 19/8"} {"input": "Solve the equation 7x - 119/3 = 0", "output": "7x - 119/3 = 0\n7x = 119/3\nx = 119/3 / 7\nx = 17/3"} {"input": "Solve quickly: x^3 + 179/72x^2 + 49/96x - 19/32 = 0", "output": "x^3 + 179/72x^2 + 49/96x - 19/32 = 0\n(x - -19/9)(x - 3/8)(x - -3/4) = 0\nx - -19/9 = 0\nx - 3/8 = 0\nx - -3/4 = 0\nx = -19/9\nx = 3/8\nx = -3/4"} {"input": "What value of x satisfies x^3 + 22/15x^2 - 721/60x + 147/20 = 0", "output": "x^3 + 22/15x^2 - 721/60x + 147/20 = 0\n(x - 7/10)(x - -9/2)(x - 7/3) = 0\nx - 7/10 = 0\nx - -9/2 = 0\nx - 7/3 = 0\nx = 7/10\nx = -9/2\nx = 7/3"} {"input": "Determine x in 4x + 36 = 0", "output": "4x + 36 = 0\n4x = -36\nx = -36 / 4\nx = -9"} {"input": "What value of x satisfies 7x - 63/4 = 0", "output": "7x - 63/4 = 0\n7x = 63/4\nx = 63/4 / 7\nx = 9/4"} {"input": "Find x in 6x - 14 = 0", "output": "6x - 14 = 0\n6x = 14\nx = 14 / 6\nx = 7/3"} {"input": "Find the solution to x^2 - 37/2x - 19/2 = 0", "output": "x^2 - 37/2x - 19/2 = 0\n(x - -1/2)(x - 19) = 0\nx - -1/2 = 0 or x - 19 = 0\nx = -1/2\nx = 19"} {"input": "What value of x satisfies 5x - 75/7 = 0", "output": "5x - 75/7 = 0\n5x = 75/7\nx = 75/7 / 5\nx = 15/7"} {"input": "Solve the equation 4x + 56/3 = 0", "output": "4x + 56/3 = 0\n4x = -56/3\nx = -56/3 / 4\nx = -14/3"} {"input": "Find x and y such that\n2x + 10y = 81/4\n2x + 9y = 149/8", "output": "2x + 10y = 81/4\n2x + 9y = 149/8\n\nUsing elimination\n2*(2x + 10y = 81/4)\n2*(2x + 9y = 149/8)\n4x + 20y = 81/2\n4x + 18y = 149/4\nSubtract equations\n2y = 13/4\ny = 13/4/2\ny = 13/8\n\nSubstitute y\n2x + 10(13/8) = 81/4\n2x = 4\nx = 4/2\nx = 2"} {"input": "Find the solution to x^2 - 18x + 17 = 0", "output": "x^2 - 18x + 17 = 0\n(x - 1)(x - 17) = 0\nx - 1 = 0 or x - 17 = 0\nx = 1\nx = 17"} {"input": "Solve the equations:\n8x + 4y = -19\n1x + 7y = -71/8", "output": "8x + 4y = -19\n1x + 7y = -71/8\n\nUsing elimination\n1*(8x + 4y = -19)\n8*(1x + 7y = -71/8)\n8x + 4y = -19\n8x + 56y = -71\nSubtract equations\n-52y = 52\ny = 52/-52\ny = -1\n\nSubstitute y\n8x + 4(-1) = -19\n8x = -15\nx = -15/8\nx = -15/8"} {"input": "Find x in 2x - 19 = 0", "output": "2x - 19 = 0\n2x = 19\nx = 19 / 2\nx = 19/2"} {"input": "Find x and y such that\n10x + 8y = 28\n6x + 5y = 18", "output": "10x + 8y = 28\n6x + 5y = 18\n\nUsing elimination\n6*(10x + 8y = 28)\n10*(6x + 5y = 18)\n60x + 48y = 168\n60x + 50y = 180\nSubtract equations\n-2y = -12\ny = -12/-2\ny = 6\n\nSubstitute y\n10x + 8(6) = 28\n10x = -20\nx = -20/10\nx = -2"} {"input": "Solve the equation 9x - 99/2 = 0", "output": "9x - 99/2 = 0\n9x = 99/2\nx = 99/2 / 9\nx = 11/2"} {"input": "Find x for x^2 + 41/5x - 36/5 = 0", "output": "x^2 + 41/5x - 36/5 = 0\n(x - 4/5)(x - -9) = 0\nx - 4/5 = 0 or x - -9 = 0\nx = 4/5\nx = -9"} {"input": "Compute the solution of x^2 + 75/14x + 50/7 = 0", "output": "x^2 + 75/14x + 50/7 = 0\n(x - -20/7)(x - -5/2) = 0\nx - -20/7 = 0 or x - -5/2 = 0\nx = -20/7\nx = -5/2"} {"input": "Solve simultaneously:\n1x + 1y = 20/7\n2x + 8y = 82/7", "output": "1x + 1y = 20/7\n2x + 8y = 82/7\n\nUsing elimination\n2*(1x + 1y = 20/7)\n1*(2x + 8y = 82/7)\n2x + 2y = 40/7\n2x + 8y = 82/7\nSubtract equations\n-6y = -6\ny = -6/-6\ny = 1\n\nSubstitute y\n1x + 1(1) = 20/7\n1x = 13/7\nx = 13/7/1\nx = 13/7"} {"input": "Solve the equation 7x = 0", "output": "7x = 0\n7x = 0\nx = 0 / 7\nx = 0"} {"input": "What value of x satisfies x^3 + 61/6x^2 + 13/2x - 36 = 0", "output": "x^3 + 61/6x^2 + 13/2x - 36 = 0\n(x - 3/2)(x - -8/3)(x - -9) = 0\nx - 3/2 = 0\nx - -8/3 = 0\nx - -9 = 0\nx = 3/2\nx = -8/3\nx = -9"} {"input": "Solve the equations:\n2x + 3y = 6\n5x + 1y = -1/6", "output": "2x + 3y = 6\n5x + 1y = -1/6\n\nUsing elimination\n5*(2x + 3y = 6)\n2*(5x + 1y = -1/6)\n10x + 15y = 30\n10x + 2y = -1/3\nSubtract equations\n13y = 91/3\ny = 91/3/13\ny = 7/3\n\nSubstitute y\n2x + 3(7/3) = 6\n2x = -1\nx = -1/2\nx = -1/2"} {"input": "Find x in 9x + 108/5 = 0", "output": "9x + 108/5 = 0\n9x = -108/5\nx = -108/5 / 9\nx = -12/5"} {"input": "Determine x in 7x + 35/9 = 0", "output": "7x + 35/9 = 0\n7x = -35/9\nx = -35/9 / 7\nx = -5/9"} {"input": "Solve simultaneously:\n1x + 4y = 20/9\n4x + 6y = -10/9", "output": "1x + 4y = 20/9\n4x + 6y = -10/9\n\nUsing elimination\n4*(1x + 4y = 20/9)\n1*(4x + 6y = -10/9)\n4x + 16y = 80/9\n4x + 6y = -10/9\nSubtract equations\n10y = 10\ny = 10/10\ny = 1\n\nSubstitute y\n1x + 4(1) = 20/9\n1x = -16/9\nx = -16/9/1\nx = -16/9"} {"input": "Find x and y such that\n2x + 7y = -5/3\n2x + 1y = -11/3", "output": "2x + 7y = -5/3\n2x + 1y = -11/3\n\nUsing elimination\n2*(2x + 7y = -5/3)\n2*(2x + 1y = -11/3)\n4x + 14y = -10/3\n4x + 2y = -22/3\nSubtract equations\n12y = 4\ny = 4/12\ny = 1/3\n\nSubstitute y\n2x + 7(1/3) = -5/3\n2x = -4\nx = -4/2\nx = -2"} {"input": "Solve the equations:\n9x + 2y = 242/9\n9x + 8y = 320/9", "output": "9x + 2y = 242/9\n9x + 8y = 320/9\n\nUsing elimination\n9*(9x + 2y = 242/9)\n9*(9x + 8y = 320/9)\n81x + 18y = 242\n81x + 72y = 320\nSubtract equations\n-54y = -78\ny = -78/-54\ny = 13/9\n\nSubstitute y\n9x + 2(13/9) = 242/9\n9x = 24\nx = 24/9\nx = 8/3"} {"input": "Determine x in 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "Solve simultaneously:\n9x + 4y = 322/5\n3x + 4y = 82/5", "output": "9x + 4y = 322/5\n3x + 4y = 82/5\n\nUsing elimination\n3*(9x + 4y = 322/5)\n9*(3x + 4y = 82/5)\n27x + 12y = 966/5\n27x + 36y = 738/5\nSubtract equations\n-24y = 228/5\ny = 228/5/-24\ny = -19/10\n\nSubstitute y\n9x + 4(-19/10) = 322/5\n9x = 72\nx = 72/9\nx = 8"} {"input": "What value of x satisfies x^2 + 37/5x - 72/5 = 0", "output": "x^2 + 37/5x - 72/5 = 0\n(x - -9)(x - 8/5) = 0\nx - -9 = 0 or x - 8/5 = 0\nx = -9\nx = 8/5"} {"input": "Find the solution to 5x - 25/4 = 0", "output": "5x - 25/4 = 0\n5x = 25/4\nx = 25/4 / 5\nx = 5/4"} {"input": "Find x in x^3 + 167/24x^2 + 46/3x + 65/6 = 0", "output": "x^3 + 167/24x^2 + 46/3x + 65/6 = 0\n(x - -13/8)(x - -2)(x - -10/3) = 0\nx - -13/8 = 0\nx - -2 = 0\nx - -10/3 = 0\nx = -13/8\nx = -2\nx = -10/3"} {"input": "Find x in x^3 - 26/15x^2 - 7/5x = 0", "output": "x^3 - 26/15x^2 - 7/5x = 0\n(x - -3/5)(x - 7/3)(x - 0) = 0\nx - -3/5 = 0\nx - 7/3 = 0\nx - 0 = 0\nx = -3/5\nx = 7/3\nx = 0"} {"input": "Find x for x^3 - 46/9x^2 + 112/27x + 32/27 = 0", "output": "x^3 - 46/9x^2 + 112/27x + 32/27 = 0\n(x - 4/3)(x - 4)(x - -2/9) = 0\nx - 4/3 = 0\nx - 4 = 0\nx - -2/9 = 0\nx = 4/3\nx = 4\nx = -2/9"} {"input": "What value of x satisfies x^3 + 317/45x^2 + 2126/135x + 304/27 = 0", "output": "x^3 + 317/45x^2 + 2126/135x + 304/27 = 0\n(x - -10/3)(x - -19/9)(x - -8/5) = 0\nx - -10/3 = 0\nx - -19/9 = 0\nx - -8/5 = 0\nx = -10/3\nx = -19/9\nx = -8/5"} {"input": "Find x for x^2 - 83/40x - 18/5 = 0", "output": "x^2 - 83/40x - 18/5 = 0\n(x - 16/5)(x - -9/8) = 0\nx - 16/5 = 0 or x - -9/8 = 0\nx = 16/5\nx = -9/8"} {"input": "Compute the solution of x^2 + 3/4x - 91/64 = 0", "output": "x^2 + 3/4x - 91/64 = 0\n(x - -13/8)(x - 7/8) = 0\nx - -13/8 = 0 or x - 7/8 = 0\nx = -13/8\nx = 7/8"} {"input": "What value of x satisfies x^2 + 89/9x - 10/9 = 0", "output": "x^2 + 89/9x - 10/9 = 0\n(x - -10)(x - 1/9) = 0\nx - -10 = 0 or x - 1/9 = 0\nx = -10\nx = 1/9"} {"input": "Find x and y such that\n3x + 8y = -275/4\n6x + 1y = -10", "output": "3x + 8y = -275/4\n6x + 1y = -10\n\nUsing elimination\n6*(3x + 8y = -275/4)\n3*(6x + 1y = -10)\n18x + 48y = -825/2\n18x + 3y = -30\nSubtract equations\n45y = -765/2\ny = -765/2/45\ny = -17/2\n\nSubstitute y\n3x + 8(-17/2) = -275/4\n3x = -3/4\nx = -3/4/3\nx = -1/4"} {"input": "Solve the system:\n4x + 8y = 160/3\n10x + 7y = 77", "output": "4x + 8y = 160/3\n10x + 7y = 77\n\nUsing elimination\n10*(4x + 8y = 160/3)\n4*(10x + 7y = 77)\n40x + 80y = 1600/3\n40x + 28y = 308\nSubtract equations\n52y = 676/3\ny = 676/3/52\ny = 13/3\n\nSubstitute y\n4x + 8(13/3) = 160/3\n4x = 56/3\nx = 56/3/4\nx = 14/3"} {"input": "Compute the solution of x^3 + 64/9x^2 + 25/3x + 68/81 = 0", "output": "x^3 + 64/9x^2 + 25/3x + 68/81 = 0\n(x - -1/9)(x - -17/3)(x - -4/3) = 0\nx - -1/9 = 0\nx - -17/3 = 0\nx - -4/3 = 0\nx = -1/9\nx = -17/3\nx = -4/3"} {"input": "Determine x in x^3 - 2/63x^2 - 331/189x + 104/189 = 0", "output": "x^3 - 2/63x^2 - 331/189x + 104/189 = 0\n(x - 8/7)(x - -13/9)(x - 1/3) = 0\nx - 8/7 = 0\nx - -13/9 = 0\nx - 1/3 = 0\nx = 8/7\nx = -13/9\nx = 1/3"} {"input": "Find the solution to 5x + 25/4 = 0", "output": "5x + 25/4 = 0\n5x = -25/4\nx = -25/4 / 5\nx = -5/4"} {"input": "Find x and y such that\n1x + 9y = 149/2\n2x + 3y = 29", "output": "1x + 9y = 149/2\n2x + 3y = 29\n\nUsing elimination\n2*(1x + 9y = 149/2)\n1*(2x + 3y = 29)\n2x + 18y = 149\n2x + 3y = 29\nSubtract equations\n15y = 120\ny = 120/15\ny = 8\n\nSubstitute y\n1x + 9(8) = 149/2\n1x = 5/2\nx = 5/2/1\nx = 5/2"} {"input": "Solve the system:\n4x + 2y = 119/18\n6x + 7y = 293/36", "output": "4x + 2y = 119/18\n6x + 7y = 293/36\n\nUsing elimination\n6*(4x + 2y = 119/18)\n4*(6x + 7y = 293/36)\n24x + 12y = 119/3\n24x + 28y = 293/9\nSubtract equations\n-16y = 64/9\ny = 64/9/-16\ny = -4/9\n\nSubstitute y\n4x + 2(-4/9) = 119/18\n4x = 15/2\nx = 15/2/4\nx = 15/8"} {"input": "Find x in x^3 + 91/20x^2 + 79/200x - 187/50 = 0", "output": "x^3 + 91/20x^2 + 79/200x - 187/50 = 0\n(x - -17/4)(x - 4/5)(x - -11/10) = 0\nx - -17/4 = 0\nx - 4/5 = 0\nx - -11/10 = 0\nx = -17/4\nx = 4/5\nx = -11/10"} {"input": "Determine x in x^2 - 43/7x - 6 = 0", "output": "x^2 - 43/7x - 6 = 0\n(x - -6/7)(x - 7) = 0\nx - -6/7 = 0 or x - 7 = 0\nx = -6/7\nx = 7"} {"input": "Solve the system:\n9x + 2y = -64\n10x + 5y = -60", "output": "9x + 2y = -64\n10x + 5y = -60\n\nUsing elimination\n10*(9x + 2y = -64)\n9*(10x + 5y = -60)\n90x + 20y = -640\n90x + 45y = -540\nSubtract equations\n-25y = -100\ny = -100/-25\ny = 4\n\nSubstitute y\n9x + 2(4) = -64\n9x = -72\nx = -72/9\nx = -8"} {"input": "Solve simultaneously:\n9x + 9y = -163/10\n3x + 9y = -121/10", "output": "9x + 9y = -163/10\n3x + 9y = -121/10\n\nUsing elimination\n3*(9x + 9y = -163/10)\n9*(3x + 9y = -121/10)\n27x + 27y = -489/10\n27x + 81y = -1089/10\nSubtract equations\n-54y = 60\ny = 60/-54\ny = -10/9\n\nSubstitute y\n9x + 9(-10/9) = -163/10\n9x = -63/10\nx = -63/10/9\nx = -7/10"} {"input": "Solve quickly: 4x - 2 = 0", "output": "4x - 2 = 0\n4x = 2\nx = 2 / 4\nx = 1/2"} {"input": "Find x and y such that\n3x + 6y = -37/3\n3x + 8y = -139/9", "output": "3x + 6y = -37/3\n3x + 8y = -139/9\n\nUsing elimination\n3*(3x + 6y = -37/3)\n3*(3x + 8y = -139/9)\n9x + 18y = -37\n9x + 24y = -139/3\nSubtract equations\n-6y = 28/3\ny = 28/3/-6\ny = -14/9\n\nSubstitute y\n3x + 6(-14/9) = -37/3\n3x = -3\nx = -3/3\nx = -1"} {"input": "Compute the solution of x^2 - 27/14x - 10/7 = 0", "output": "x^2 - 27/14x - 10/7 = 0\n(x - 5/2)(x - -4/7) = 0\nx - 5/2 = 0 or x - -4/7 = 0\nx = 5/2\nx = -4/7"} {"input": "Find x for 6x + 96 = 0", "output": "6x + 96 = 0\n6x = -96\nx = -96 / 6\nx = -16"} {"input": "What value of x satisfies x^3 - 1249/72x^2 + 353/18x + 280/9 = 0", "output": "x^3 - 1249/72x^2 + 353/18x + 280/9 = 0\n(x - 20/9)(x - 16)(x - -7/8) = 0\nx - 20/9 = 0\nx - 16 = 0\nx - -7/8 = 0\nx = 20/9\nx = 16\nx = -7/8"} {"input": "Find x in x^3 - 87/14x^2 - 139/49x + 312/49 = 0", "output": "x^3 - 87/14x^2 - 139/49x + 312/49 = 0\n(x - 13/2)(x - -8/7)(x - 6/7) = 0\nx - 13/2 = 0\nx - -8/7 = 0\nx - 6/7 = 0\nx = 13/2\nx = -8/7\nx = 6/7"} {"input": "Find x in x^2 - 3x + 2 = 0", "output": "x^2 - 3x + 2 = 0\n(x - 1)(x - 2) = 0\nx - 1 = 0 or x - 2 = 0\nx = 1\nx = 2"} {"input": "Solve the equation x^2 + 118/35x + 99/35 = 0", "output": "x^2 + 118/35x + 99/35 = 0\n(x - -9/5)(x - -11/7) = 0\nx - -9/5 = 0 or x - -11/7 = 0\nx = -9/5\nx = -11/7"} {"input": "Compute the solution of x^3 + 1171/210x^2 + 200/21x + 65/14 = 0", "output": "x^3 + 1171/210x^2 + 200/21x + 65/14 = 0\n(x - -5/6)(x - -15/7)(x - -13/5) = 0\nx - -5/6 = 0\nx - -15/7 = 0\nx - -13/5 = 0\nx = -5/6\nx = -15/7\nx = -13/5"} {"input": "What value of x satisfies 3x = 0", "output": "3x = 0\n3x = 0\nx = 0 / 3\nx = 0"} {"input": "Compute the solution of 7x = 0", "output": "7x = 0\n7x = 0\nx = 0 / 7\nx = 0"} {"input": "Solve the system:\n5x + 2y = 47/2\n7x + 8y = 19/2", "output": "5x + 2y = 47/2\n7x + 8y = 19/2\n\nUsing elimination\n7*(5x + 2y = 47/2)\n5*(7x + 8y = 19/2)\n35x + 14y = 329/2\n35x + 40y = 95/2\nSubtract equations\n-26y = 117\ny = 117/-26\ny = -9/2\n\nSubstitute y\n5x + 2(-9/2) = 47/2\n5x = 65/2\nx = 65/2/5\nx = 13/2"} {"input": "Find x for 5x - 10/7 = 0", "output": "5x - 10/7 = 0\n5x = 10/7\nx = 10/7 / 5\nx = 2/7"} {"input": "Solve quickly: 3x - 45/7 = 0", "output": "3x - 45/7 = 0\n3x = 45/7\nx = 45/7 / 3\nx = 15/7"} {"input": "Solve x^3 + 85/28x^2 - 339/56x + 135/56 = 0", "output": "x^3 + 85/28x^2 - 339/56x + 135/56 = 0\n(x - -9/2)(x - 5/7)(x - 3/4) = 0\nx - -9/2 = 0\nx - 5/7 = 0\nx - 3/4 = 0\nx = -9/2\nx = 5/7\nx = 3/4"} {"input": "Solve the system:\n6x + 1y = 68/7\n6x + 6y = -72/7", "output": "6x + 1y = 68/7\n6x + 6y = -72/7\n\nUsing elimination\n6*(6x + 1y = 68/7)\n6*(6x + 6y = -72/7)\n36x + 6y = 408/7\n36x + 36y = -432/7\nSubtract equations\n-30y = 120\ny = 120/-30\ny = -4\n\nSubstitute y\n6x + 1(-4) = 68/7\n6x = 96/7\nx = 96/7/6\nx = 16/7"} {"input": "Find x for 1x - 8/9 = 0", "output": "1x - 8/9 = 0\n1x = 8/9\nx = 8/9 / 1\nx = 8/9"} {"input": "What value of x satisfies 7x - 56/5 = 0", "output": "7x - 56/5 = 0\n7x = 56/5\nx = 56/5 / 7\nx = 8/5"} {"input": "Find x for 1x + 20/9 = 0", "output": "1x + 20/9 = 0\n1x = -20/9\nx = -20/9 / 1\nx = -20/9"} {"input": "Solve simultaneously:\n6x + 7y = -301/10\n4x + 9y = -641/30", "output": "6x + 7y = -301/10\n4x + 9y = -641/30\n\nUsing elimination\n4*(6x + 7y = -301/10)\n6*(4x + 9y = -641/30)\n24x + 28y = -602/5\n24x + 54y = -641/5\nSubtract equations\n-26y = 39/5\ny = 39/5/-26\ny = -3/10\n\nSubstitute y\n6x + 7(-3/10) = -301/10\n6x = -28\nx = -28/6\nx = -14/3"} {"input": "Solve x^2 + 2/3x = 0", "output": "x^2 + 2/3x = 0\n(x - -2/3)(x - 0) = 0\nx - -2/3 = 0 or x - 0 = 0\nx = -2/3\nx = 0"} {"input": "Solve the equations:\n6x + 1y = -149/10\n4x + 1y = -121/10", "output": "6x + 1y = -149/10\n4x + 1y = -121/10\n\nUsing elimination\n4*(6x + 1y = -149/10)\n6*(4x + 1y = -121/10)\n24x + 4y = -298/5\n24x + 6y = -363/5\nSubtract equations\n-2y = 13\ny = 13/-2\ny = -13/2\n\nSubstitute y\n6x + 1(-13/2) = -149/10\n6x = -42/5\nx = -42/5/6\nx = -7/5"} {"input": "What value of x satisfies x^3 + 40/9x^2 - 128/27x = 0", "output": "x^3 + 40/9x^2 - 128/27x = 0\n(x - -16/3)(x - 8/9)(x - 0) = 0\nx - -16/3 = 0\nx - 8/9 = 0\nx - 0 = 0\nx = -16/3\nx = 8/9\nx = 0"} {"input": "Solve the system:\n1x + 10y = 35/3\n4x + 3y = 29/3", "output": "1x + 10y = 35/3\n4x + 3y = 29/3\n\nUsing elimination\n4*(1x + 10y = 35/3)\n1*(4x + 3y = 29/3)\n4x + 40y = 140/3\n4x + 3y = 29/3\nSubtract equations\n37y = 37\ny = 37/37\ny = 1\n\nSubstitute y\n1x + 10(1) = 35/3\n1x = 5/3\nx = 5/3/1\nx = 5/3"} {"input": "Determine x in x^2 + 17/2x - 15 = 0", "output": "x^2 + 17/2x - 15 = 0\n(x - -10)(x - 3/2) = 0\nx - -10 = 0 or x - 3/2 = 0\nx = -10\nx = 3/2"} {"input": "Find x in 6x + 15 = 0", "output": "6x + 15 = 0\n6x = -15\nx = -15 / 6\nx = -5/2"} {"input": "Solve simultaneously:\n4x + 10y = -473/5\n5x + 8y = -151/2", "output": "4x + 10y = -473/5\n5x + 8y = -151/2\n\nUsing elimination\n5*(4x + 10y = -473/5)\n4*(5x + 8y = -151/2)\n20x + 50y = -473\n20x + 32y = -302\nSubtract equations\n18y = -171\ny = -171/18\ny = -19/2\n\nSubstitute y\n4x + 10(-19/2) = -473/5\n4x = 2/5\nx = 2/5/4\nx = 1/10"} {"input": "Find x in x^2 + 11x - 26 = 0", "output": "x^2 + 11x - 26 = 0\n(x - -13)(x - 2) = 0\nx - -13 = 0 or x - 2 = 0\nx = -13\nx = 2"} {"input": "Solve quickly: x^3 + 299/15x^2 + 269/15x + 19/5 = 0", "output": "x^3 + 299/15x^2 + 269/15x + 19/5 = 0\n(x - -3/5)(x - -19)(x - -1/3) = 0\nx - -3/5 = 0\nx - -19 = 0\nx - -1/3 = 0\nx = -3/5\nx = -19\nx = -1/3"} {"input": "Solve the system:\n9x + 3y = 3/2\n10x + 7y = 12/5", "output": "9x + 3y = 3/2\n10x + 7y = 12/5\n\nUsing elimination\n10*(9x + 3y = 3/2)\n9*(10x + 7y = 12/5)\n90x + 30y = 15\n90x + 63y = 108/5\nSubtract equations\n-33y = -33/5\ny = -33/5/-33\ny = 1/5\n\nSubstitute y\n9x + 3(1/5) = 3/2\n9x = 9/10\nx = 9/10/9\nx = 1/10"} {"input": "What value of x satisfies x^3 + 13/10x^2 - 627/50x - 459/25 = 0", "output": "x^3 + 13/10x^2 - 627/50x - 459/25 = 0\n(x - 18/5)(x - -3/2)(x - -17/5) = 0\nx - 18/5 = 0\nx - -3/2 = 0\nx - -17/5 = 0\nx = 18/5\nx = -3/2\nx = -17/5"} {"input": "Find x for x^3 + 34/15x^2 - 1864/75x + 448/15 = 0", "output": "x^3 + 34/15x^2 - 1864/75x + 448/15 = 0\n(x - 8/5)(x - 14/5)(x - -20/3) = 0\nx - 8/5 = 0\nx - 14/5 = 0\nx - -20/3 = 0\nx = 8/5\nx = 14/5\nx = -20/3"} {"input": "Find x and y such that\n1x + 5y = 11/4\n1x + 2y = 1/2", "output": "1x + 5y = 11/4\n1x + 2y = 1/2\n\nUsing elimination\n1*(1x + 5y = 11/4)\n1*(1x + 2y = 1/2)\n1x + 5y = 11/4\n1x + 2y = 1/2\nSubtract equations\n3y = 9/4\ny = 9/4/3\ny = 3/4\n\nSubstitute y\n1x + 5(3/4) = 11/4\n1x = -1\nx = -1/1\nx = -1"} {"input": "Solve the system:\n4x + 7y = 21\n9x + 5y = 339/14", "output": "4x + 7y = 21\n9x + 5y = 339/14\n\nUsing elimination\n9*(4x + 7y = 21)\n4*(9x + 5y = 339/14)\n36x + 63y = 189\n36x + 20y = 678/7\nSubtract equations\n43y = 645/7\ny = 645/7/43\ny = 15/7\n\nSubstitute y\n4x + 7(15/7) = 21\n4x = 6\nx = 6/4\nx = 3/2"} {"input": "Compute the solution of 3x - 7/3 = 0", "output": "3x - 7/3 = 0\n3x = 7/3\nx = 7/3 / 3\nx = 7/9"} {"input": "Solve the system:\n3x + 5y = 187/12\n4x + 5y = 49/3", "output": "3x + 5y = 187/12\n4x + 5y = 49/3\n\nUsing elimination\n4*(3x + 5y = 187/12)\n3*(4x + 5y = 49/3)\n12x + 20y = 187/3\n12x + 15y = 49\nSubtract equations\n5y = 40/3\ny = 40/3/5\ny = 8/3\n\nSubstitute y\n3x + 5(8/3) = 187/12\n3x = 9/4\nx = 9/4/3\nx = 3/4"} {"input": "Solve x^3 + 43/20x^2 - 29/20x - 7/2 = 0", "output": "x^3 + 43/20x^2 - 29/20x - 7/2 = 0\n(x - -2)(x - 5/4)(x - -7/5) = 0\nx - -2 = 0\nx - 5/4 = 0\nx - -7/5 = 0\nx = -2\nx = 5/4\nx = -7/5"} {"input": "What value of x satisfies x^2 + 47/36x - 7/18 = 0", "output": "x^2 + 47/36x - 7/18 = 0\n(x - -14/9)(x - 1/4) = 0\nx - -14/9 = 0 or x - 1/4 = 0\nx = -14/9\nx = 1/4"} {"input": "Solve quickly: x^2 - 71/10x + 33/5 = 0", "output": "x^2 - 71/10x + 33/5 = 0\n(x - 6)(x - 11/10) = 0\nx - 6 = 0 or x - 11/10 = 0\nx = 6\nx = 11/10"} {"input": "Compute the solution of x^2 + 3x - 34/25 = 0", "output": "x^2 + 3x - 34/25 = 0\n(x - 2/5)(x - -17/5) = 0\nx - 2/5 = 0 or x - -17/5 = 0\nx = 2/5\nx = -17/5"} {"input": "Solve x^3 - 159/10x^2 - 93/5x - 17/10 = 0", "output": "x^3 - 159/10x^2 - 93/5x - 17/10 = 0\n(x - 17)(x - -1/10)(x - -1) = 0\nx - 17 = 0\nx - -1/10 = 0\nx - -1 = 0\nx = 17\nx = -1/10\nx = -1"} {"input": "Find x and y such that\n10x + 4y = -296/9\n3x + 10y = -320/3", "output": "10x + 4y = -296/9\n3x + 10y = -320/3\n\nUsing elimination\n3*(10x + 4y = -296/9)\n10*(3x + 10y = -320/3)\n30x + 12y = -296/3\n30x + 100y = -3200/3\nSubtract equations\n-88y = 968\ny = 968/-88\ny = -11\n\nSubstitute y\n10x + 4(-11) = -296/9\n10x = 100/9\nx = 100/9/10\nx = 10/9"} {"input": "Solve 6x + 19 = 0", "output": "6x + 19 = 0\n6x = -19\nx = -19 / 6\nx = -19/6"} {"input": "Find x and y such that\n8x + 1y = 116/15\n9x + 7y = -7/10", "output": "8x + 1y = 116/15\n9x + 7y = -7/10\n\nUsing elimination\n9*(8x + 1y = 116/15)\n8*(9x + 7y = -7/10)\n72x + 9y = 348/5\n72x + 56y = -28/5\nSubtract equations\n-47y = 376/5\ny = 376/5/-47\ny = -8/5\n\nSubstitute y\n8x + 1(-8/5) = 116/15\n8x = 28/3\nx = 28/3/8\nx = 7/6"} {"input": "Solve the equations:\n7x + 10y = 559/12\n10x + 4y = 317/6", "output": "7x + 10y = 559/12\n10x + 4y = 317/6\n\nUsing elimination\n10*(7x + 10y = 559/12)\n7*(10x + 4y = 317/6)\n70x + 100y = 2795/6\n70x + 28y = 2219/6\nSubtract equations\n72y = 96\ny = 96/72\ny = 4/3\n\nSubstitute y\n7x + 10(4/3) = 559/12\n7x = 133/4\nx = 133/4/7\nx = 19/4"} {"input": "What value of x satisfies x^3 - 77/45x^2 - 10/9x + 16/15 = 0", "output": "x^3 - 77/45x^2 - 10/9x + 16/15 = 0\n(x - 3/5)(x - -8/9)(x - 2) = 0\nx - 3/5 = 0\nx - -8/9 = 0\nx - 2 = 0\nx = 3/5\nx = -8/9\nx = 2"} {"input": "Solve the system:\n8x + 3y = -239/3\n3x + 9y = -359/2", "output": "8x + 3y = -239/3\n3x + 9y = -359/2\n\nUsing elimination\n3*(8x + 3y = -239/3)\n8*(3x + 9y = -359/2)\n24x + 9y = -239\n24x + 72y = -1436\nSubtract equations\n-63y = 1197\ny = 1197/-63\ny = -19\n\nSubstitute y\n8x + 3(-19) = -239/3\n8x = -68/3\nx = -68/3/8\nx = -17/6"} {"input": "Solve 4x + 6 = 0", "output": "4x + 6 = 0\n4x = -6\nx = -6 / 4\nx = -3/2"} {"input": "Find x in x^2 + 21/4x + 17/4 = 0", "output": "x^2 + 21/4x + 17/4 = 0\n(x - -1)(x - -17/4) = 0\nx - -1 = 0 or x - -17/4 = 0\nx = -1\nx = -17/4"} {"input": "Find the solution to x^3 + 108/5x^2 + 247/5x = 0", "output": "x^3 + 108/5x^2 + 247/5x = 0\n(x - -13/5)(x - 0)(x - -19) = 0\nx - -13/5 = 0\nx - 0 = 0\nx - -19 = 0\nx = -13/5\nx = 0\nx = -19"} {"input": "Solve the system:\n10x + 3y = -59/6\n3x + 10y = -361/36", "output": "10x + 3y = -59/6\n3x + 10y = -361/36\n\nUsing elimination\n3*(10x + 3y = -59/6)\n10*(3x + 10y = -361/36)\n30x + 9y = -59/2\n30x + 100y = -1805/18\nSubtract equations\n-91y = 637/9\ny = 637/9/-91\ny = -7/9\n\nSubstitute y\n10x + 3(-7/9) = -59/6\n10x = -15/2\nx = -15/2/10\nx = -3/4"} {"input": "Solve the equations:\n3x + 6y = 47/6\n5x + 3y = 155/36", "output": "3x + 6y = 47/6\n5x + 3y = 155/36\n\nUsing elimination\n5*(3x + 6y = 47/6)\n3*(5x + 3y = 155/36)\n15x + 30y = 235/6\n15x + 9y = 155/12\nSubtract equations\n21y = 105/4\ny = 105/4/21\ny = 5/4\n\nSubstitute y\n3x + 6(5/4) = 47/6\n3x = 1/3\nx = 1/3/3\nx = 1/9"} {"input": "Find x for 4x - 3/2 = 0", "output": "4x - 3/2 = 0\n4x = 3/2\nx = 3/2 / 4\nx = 3/8"} {"input": "Find x in 5x - 8 = 0", "output": "5x - 8 = 0\n5x = 8\nx = 8 / 5\nx = 8/5"} {"input": "Solve the equation x^2 + 75/14x + 13/2 = 0", "output": "x^2 + 75/14x + 13/2 = 0\n(x - -7/2)(x - -13/7) = 0\nx - -7/2 = 0 or x - -13/7 = 0\nx = -7/2\nx = -13/7"} {"input": "Solve the equation x^3 + 3/14x^2 - 613/112x + 57/16 = 0", "output": "x^3 + 3/14x^2 - 613/112x + 57/16 = 0\n(x - -19/7)(x - 3/4)(x - 7/4) = 0\nx - -19/7 = 0\nx - 3/4 = 0\nx - 7/4 = 0\nx = -19/7\nx = 3/4\nx = 7/4"} {"input": "Find x and y such that\n3x + 8y = 75/14\n1x + 5y = 53/14", "output": "3x + 8y = 75/14\n1x + 5y = 53/14\n\nUsing elimination\n1*(3x + 8y = 75/14)\n3*(1x + 5y = 53/14)\n3x + 8y = 75/14\n3x + 15y = 159/14\nSubtract equations\n-7y = -6\ny = -6/-7\ny = 6/7\n\nSubstitute y\n3x + 8(6/7) = 75/14\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Solve the system:\n5x + 9y = 158/5\n10x + 2y = 124/5", "output": "5x + 9y = 158/5\n10x + 2y = 124/5\n\nUsing elimination\n10*(5x + 9y = 158/5)\n5*(10x + 2y = 124/5)\n50x + 90y = 316\n50x + 10y = 124\nSubtract equations\n80y = 192\ny = 192/80\ny = 12/5\n\nSubstitute y\n5x + 9(12/5) = 158/5\n5x = 10\nx = 10/5\nx = 2"} {"input": "Find x and y such that\n6x + 7y = 4/15\n2x + 5y = -52/15", "output": "6x + 7y = 4/15\n2x + 5y = -52/15\n\nUsing elimination\n2*(6x + 7y = 4/15)\n6*(2x + 5y = -52/15)\n12x + 14y = 8/15\n12x + 30y = -104/5\nSubtract equations\n-16y = 64/3\ny = 64/3/-16\ny = -4/3\n\nSubstitute y\n6x + 7(-4/3) = 4/15\n6x = 48/5\nx = 48/5/6\nx = 8/5"} {"input": "Solve the equation 6x - 3/2 = 0", "output": "6x - 3/2 = 0\n6x = 3/2\nx = 3/2 / 6\nx = 1/4"} {"input": "Solve the equations:\n4x + 9y = 629/10\n10x + 5y = 17/2", "output": "4x + 9y = 629/10\n10x + 5y = 17/2\n\nUsing elimination\n10*(4x + 9y = 629/10)\n4*(10x + 5y = 17/2)\n40x + 90y = 629\n40x + 20y = 34\nSubtract equations\n70y = 595\ny = 595/70\ny = 17/2\n\nSubstitute y\n4x + 9(17/2) = 629/10\n4x = -68/5\nx = -68/5/4\nx = -17/5"} {"input": "Find x in 10x - 20/7 = 0", "output": "10x - 20/7 = 0\n10x = 20/7\nx = 20/7 / 10\nx = 2/7"} {"input": "Solve x^2 - 23/5x + 26/5 = 0", "output": "x^2 - 23/5x + 26/5 = 0\n(x - 2)(x - 13/5) = 0\nx - 2 = 0 or x - 13/5 = 0\nx = 2\nx = 13/5"} {"input": "Find x in x^3 + 8/3x^2 - 77/3x + 98/3 = 0", "output": "x^3 + 8/3x^2 - 77/3x + 98/3 = 0\n(x - 7/3)(x - -7)(x - 2) = 0\nx - 7/3 = 0\nx - -7 = 0\nx - 2 = 0\nx = 7/3\nx = -7\nx = 2"} {"input": "Determine x in 10x - 5/4 = 0", "output": "10x - 5/4 = 0\n10x = 5/4\nx = 5/4 / 10\nx = 1/8"} {"input": "Solve x^3 - 727/180x^2 + 23/5x - 8/5 = 0", "output": "x^3 - 727/180x^2 + 23/5x - 8/5 = 0\n(x - 12/5)(x - 3/4)(x - 8/9) = 0\nx - 12/5 = 0\nx - 3/4 = 0\nx - 8/9 = 0\nx = 12/5\nx = 3/4\nx = 8/9"} {"input": "Find x and y such that\n6x + 10y = -118/21\n3x + 1y = -107/21", "output": "6x + 10y = -118/21\n3x + 1y = -107/21\n\nUsing elimination\n3*(6x + 10y = -118/21)\n6*(3x + 1y = -107/21)\n18x + 30y = -118/7\n18x + 6y = -214/7\nSubtract equations\n24y = 96/7\ny = 96/7/24\ny = 4/7\n\nSubstitute y\n6x + 10(4/7) = -118/21\n6x = -34/3\nx = -34/3/6\nx = -17/9"} {"input": "Find x for x^2 - 17/21x - 10/7 = 0", "output": "x^2 - 17/21x - 10/7 = 0\n(x - -6/7)(x - 5/3) = 0\nx - -6/7 = 0 or x - 5/3 = 0\nx = -6/7\nx = 5/3"} {"input": "Find x for x^3 - 53/18x^2 - 31/54x + 68/27 = 0", "output": "x^3 - 53/18x^2 - 31/54x + 68/27 = 0\n(x - 17/6)(x - -8/9)(x - 1) = 0\nx - 17/6 = 0\nx - -8/9 = 0\nx - 1 = 0\nx = 17/6\nx = -8/9\nx = 1"} {"input": "What value of x satisfies x^2 - 5/12x - 77/12 = 0", "output": "x^2 - 5/12x - 77/12 = 0\n(x - 11/4)(x - -7/3) = 0\nx - 11/4 = 0 or x - -7/3 = 0\nx = 11/4\nx = -7/3"} {"input": "Solve the equation x^2 + 3/5x - 26/5 = 0", "output": "x^2 + 3/5x - 26/5 = 0\n(x - -13/5)(x - 2) = 0\nx - -13/5 = 0 or x - 2 = 0\nx = -13/5\nx = 2"} {"input": "Compute the solution of x^2 + 16/21x - 85/21 = 0", "output": "x^2 + 16/21x - 85/21 = 0\n(x - 5/3)(x - -17/7) = 0\nx - 5/3 = 0 or x - -17/7 = 0\nx = 5/3\nx = -17/7"} {"input": "Find the solution to x^3 + 35/4x^2 + 77/8x + 15/8 = 0", "output": "x^3 + 35/4x^2 + 77/8x + 15/8 = 0\n(x - -1)(x - -1/4)(x - -15/2) = 0\nx - -1 = 0\nx - -1/4 = 0\nx - -15/2 = 0\nx = -1\nx = -1/4\nx = -15/2"} {"input": "Find x for x^2 + 9/2x + 9/2 = 0", "output": "x^2 + 9/2x + 9/2 = 0\n(x - -3)(x - -3/2) = 0\nx - -3 = 0 or x - -3/2 = 0\nx = -3\nx = -3/2"} {"input": "Solve simultaneously:\n7x + 3y = 23\n9x + 6y = 36", "output": "7x + 3y = 23\n9x + 6y = 36\n\nUsing elimination\n9*(7x + 3y = 23)\n7*(9x + 6y = 36)\n63x + 27y = 207\n63x + 42y = 252\nSubtract equations\n-15y = -45\ny = -45/-15\ny = 3\n\nSubstitute y\n7x + 3(3) = 23\n7x = 14\nx = 14/7\nx = 2"} {"input": "Solve x^3 - 11/2x^2 - 29/4x + 39/8 = 0", "output": "x^3 - 11/2x^2 - 29/4x + 39/8 = 0\n(x - 1/2)(x - -3/2)(x - 13/2) = 0\nx - 1/2 = 0\nx - -3/2 = 0\nx - 13/2 = 0\nx = 1/2\nx = -3/2\nx = 13/2"} {"input": "Solve the system:\n8x + 4y = 6\n10x + 6y = 3", "output": "8x + 4y = 6\n10x + 6y = 3\n\nUsing elimination\n10*(8x + 4y = 6)\n8*(10x + 6y = 3)\n80x + 40y = 60\n80x + 48y = 24\nSubtract equations\n-8y = 36\ny = 36/-8\ny = -9/2\n\nSubstitute y\n8x + 4(-9/2) = 6\n8x = 24\nx = 24/8\nx = 3"} {"input": "Determine x in 7x - 21/4 = 0", "output": "7x - 21/4 = 0\n7x = 21/4\nx = 21/4 / 7\nx = 3/4"} {"input": "Determine x in 5x - 5/4 = 0", "output": "5x - 5/4 = 0\n5x = 5/4\nx = 5/4 / 5\nx = 1/4"} {"input": "Solve x^3 + 187/18x^2 + 175/18x - 25 = 0", "output": "x^3 + 187/18x^2 + 175/18x - 25 = 0\n(x - 10/9)(x - -5/2)(x - -9) = 0\nx - 10/9 = 0\nx - -5/2 = 0\nx - -9 = 0\nx = 10/9\nx = -5/2\nx = -9"} {"input": "Solve the equation x^3 - 7/2x^2 - 231/16x + 765/16 = 0", "output": "x^3 - 7/2x^2 - 231/16x + 765/16 = 0\n(x - 17/4)(x - 3)(x - -15/4) = 0\nx - 17/4 = 0\nx - 3 = 0\nx - -15/4 = 0\nx = 17/4\nx = 3\nx = -15/4"} {"input": "Solve quickly: 5x + 95/2 = 0", "output": "5x + 95/2 = 0\n5x = -95/2\nx = -95/2 / 5\nx = -19/2"} {"input": "Solve the equation x^3 + 174/35x^2 + 207/35x + 68/35 = 0", "output": "x^3 + 174/35x^2 + 207/35x + 68/35 = 0\n(x - -17/5)(x - -1)(x - -4/7) = 0\nx - -17/5 = 0\nx - -1 = 0\nx - -4/7 = 0\nx = -17/5\nx = -1\nx = -4/7"} {"input": "Determine x in 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "Solve simultaneously:\n5x + 9y = -15/2\n8x + 7y = -83/10", "output": "5x + 9y = -15/2\n8x + 7y = -83/10\n\nUsing elimination\n8*(5x + 9y = -15/2)\n5*(8x + 7y = -83/10)\n40x + 72y = -60\n40x + 35y = -83/2\nSubtract equations\n37y = -37/2\ny = -37/2/37\ny = -1/2\n\nSubstitute y\n5x + 9(-1/2) = -15/2\n5x = -3\nx = -3/5\nx = -3/5"} {"input": "Find x in x^2 - 7/5x - 24/5 = 0", "output": "x^2 - 7/5x - 24/5 = 0\n(x - 3)(x - -8/5) = 0\nx - 3 = 0 or x - -8/5 = 0\nx = 3\nx = -8/5"} {"input": "Determine x in 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x in x^3 - 121/56x^2 - 1079/392x + 95/28 = 0", "output": "x^3 - 121/56x^2 - 1079/392x + 95/28 = 0\n(x - 7/8)(x - 19/7)(x - -10/7) = 0\nx - 7/8 = 0\nx - 19/7 = 0\nx - -10/7 = 0\nx = 7/8\nx = 19/7\nx = -10/7"} {"input": "Solve simultaneously:\n4x + 8y = 191/14\n5x + 9y = 835/56", "output": "4x + 8y = 191/14\n5x + 9y = 835/56\n\nUsing elimination\n5*(4x + 8y = 191/14)\n4*(5x + 9y = 835/56)\n20x + 40y = 955/14\n20x + 36y = 835/14\nSubtract equations\n4y = 60/7\ny = 60/7/4\ny = 15/7\n\nSubstitute y\n4x + 8(15/7) = 191/14\n4x = -7/2\nx = -7/2/4\nx = -7/8"} {"input": "Find x for x^3 - 401/210x^2 - 382/105x - 38/35 = 0", "output": "x^3 - 401/210x^2 - 382/105x - 38/35 = 0\n(x - 19/6)(x - -2/5)(x - -6/7) = 0\nx - 19/6 = 0\nx - -2/5 = 0\nx - -6/7 = 0\nx = 19/6\nx = -2/5\nx = -6/7"} {"input": "Solve x^2 + 10x + 24 = 0", "output": "x^2 + 10x + 24 = 0\n(x - -6)(x - -4) = 0\nx - -6 = 0 or x - -4 = 0\nx = -6\nx = -4"} {"input": "Determine x in x^2 + 5/8x - 51/16 = 0", "output": "x^2 + 5/8x - 51/16 = 0\n(x - -17/8)(x - 3/2) = 0\nx - -17/8 = 0 or x - 3/2 = 0\nx = -17/8\nx = 3/2"} {"input": "Solve the system:\n4x + 6y = 49/6\n1x + 9y = 123/8", "output": "4x + 6y = 49/6\n1x + 9y = 123/8\n\nUsing elimination\n1*(4x + 6y = 49/6)\n4*(1x + 9y = 123/8)\n4x + 6y = 49/6\n4x + 36y = 123/2\nSubtract equations\n-30y = -160/3\ny = -160/3/-30\ny = 16/9\n\nSubstitute y\n4x + 6(16/9) = 49/6\n4x = -5/2\nx = -5/2/4\nx = -5/8"} {"input": "Solve simultaneously:\n6x + 10y = 14\n7x + 2y = -3", "output": "6x + 10y = 14\n7x + 2y = -3\n\nUsing elimination\n7*(6x + 10y = 14)\n6*(7x + 2y = -3)\n42x + 70y = 98\n42x + 12y = -18\nSubtract equations\n58y = 116\ny = 116/58\ny = 2\n\nSubstitute y\n6x + 10(2) = 14\n6x = -6\nx = -6/6\nx = -1"} {"input": "Solve the equation 10x + 50/3 = 0", "output": "10x + 50/3 = 0\n10x = -50/3\nx = -50/3 / 10\nx = -5/3"} {"input": "Find the solution to x^2 - 51/7x + 2 = 0", "output": "x^2 - 51/7x + 2 = 0\n(x - 2/7)(x - 7) = 0\nx - 2/7 = 0 or x - 7 = 0\nx = 2/7\nx = 7"} {"input": "Solve the equation x^2 - 229/56x + 57/14 = 0", "output": "x^2 - 229/56x + 57/14 = 0\n(x - 19/8)(x - 12/7) = 0\nx - 19/8 = 0 or x - 12/7 = 0\nx = 19/8\nx = 12/7"} {"input": "Solve quickly: x^2 - 221/90x + 7/5 = 0", "output": "x^2 - 221/90x + 7/5 = 0\n(x - 9/10)(x - 14/9) = 0\nx - 9/10 = 0 or x - 14/9 = 0\nx = 9/10\nx = 14/9"} {"input": "Determine x in x^3 - 115/63x^2 - 11/3x + 3/7 = 0", "output": "x^3 - 115/63x^2 - 11/3x + 3/7 = 0\n(x - 1/9)(x - 3)(x - -9/7) = 0\nx - 1/9 = 0\nx - 3 = 0\nx - -9/7 = 0\nx = 1/9\nx = 3\nx = -9/7"} {"input": "Solve simultaneously:\n3x + 7y = 7/3\n4x + 5y = 5/3", "output": "3x + 7y = 7/3\n4x + 5y = 5/3\n\nUsing elimination\n4*(3x + 7y = 7/3)\n3*(4x + 5y = 5/3)\n12x + 28y = 28/3\n12x + 15y = 5\nSubtract equations\n13y = 13/3\ny = 13/3/13\ny = 1/3\n\nSubstitute y\n3x + 7(1/3) = 7/3\n3x = 0\nx = 0/3\nx = 0"} {"input": "Solve 8x - 2 = 0", "output": "8x - 2 = 0\n8x = 2\nx = 2 / 8\nx = 1/4"} {"input": "Solve the equation 10x - 40 = 0", "output": "10x - 40 = 0\n10x = 40\nx = 40 / 10\nx = 4"} {"input": "Solve the equation x^2 + 3/2x - 136/25 = 0", "output": "x^2 + 3/2x - 136/25 = 0\n(x - 17/10)(x - -16/5) = 0\nx - 17/10 = 0 or x - -16/5 = 0\nx = 17/10\nx = -16/5"} {"input": "Find x in 9x + 81/5 = 0", "output": "9x + 81/5 = 0\n9x = -81/5\nx = -81/5 / 9\nx = -9/5"} {"input": "Find the solution to x^3 + 29/10x^2 - 283/10x + 14/5 = 0", "output": "x^3 + 29/10x^2 - 283/10x + 14/5 = 0\n(x - 4)(x - 1/10)(x - -7) = 0\nx - 4 = 0\nx - 1/10 = 0\nx - -7 = 0\nx = 4\nx = 1/10\nx = -7"} {"input": "Find the solution to 8x + 14 = 0", "output": "8x + 14 = 0\n8x = -14\nx = -14 / 8\nx = -7/4"} {"input": "Determine x in 6x - 96/5 = 0", "output": "6x - 96/5 = 0\n6x = 96/5\nx = 96/5 / 6\nx = 16/5"} {"input": "Find x and y such that\n4x + 10y = 57/2\n1x + 4y = 429/40", "output": "4x + 10y = 57/2\n1x + 4y = 429/40\n\nUsing elimination\n1*(4x + 10y = 57/2)\n4*(1x + 4y = 429/40)\n4x + 10y = 57/2\n4x + 16y = 429/10\nSubtract equations\n-6y = -72/5\ny = -72/5/-6\ny = 12/5\n\nSubstitute y\n4x + 10(12/5) = 57/2\n4x = 9/2\nx = 9/2/4\nx = 9/8"} {"input": "What value of x satisfies x^3 + 23/5x^2 + 2x - 8/5 = 0", "output": "x^3 + 23/5x^2 + 2x - 8/5 = 0\n(x - -1)(x - -4)(x - 2/5) = 0\nx - -1 = 0\nx - -4 = 0\nx - 2/5 = 0\nx = -1\nx = -4\nx = 2/5"} {"input": "Solve quickly: x^2 - 29/8x + 13/4 = 0", "output": "x^2 - 29/8x + 13/4 = 0\n(x - 13/8)(x - 2) = 0\nx - 13/8 = 0 or x - 2 = 0\nx = 13/8\nx = 2"} {"input": "Find x in x^2 + 107/30x + 19/15 = 0", "output": "x^2 + 107/30x + 19/15 = 0\n(x - -2/5)(x - -19/6) = 0\nx - -2/5 = 0 or x - -19/6 = 0\nx = -2/5\nx = -19/6"} {"input": "Solve quickly: 6x - 3 = 0", "output": "6x - 3 = 0\n6x = 3\nx = 3 / 6\nx = 1/2"} {"input": "Solve 10x - 70 = 0", "output": "10x - 70 = 0\n10x = 70\nx = 70 / 10\nx = 7"} {"input": "Solve quickly: 9x + 27/5 = 0", "output": "9x + 27/5 = 0\n9x = -27/5\nx = -27/5 / 9\nx = -3/5"} {"input": "Solve simultaneously:\n2x + 6y = -27/7\n4x + 2y = 26/7", "output": "2x + 6y = -27/7\n4x + 2y = 26/7\n\nUsing elimination\n4*(2x + 6y = -27/7)\n2*(4x + 2y = 26/7)\n8x + 24y = -108/7\n8x + 4y = 52/7\nSubtract equations\n20y = -160/7\ny = -160/7/20\ny = -8/7\n\nSubstitute y\n2x + 6(-8/7) = -27/7\n2x = 3\nx = 3/2\nx = 3/2"} {"input": "Determine x in x^2 - 57/10x + 7/2 = 0", "output": "x^2 - 57/10x + 7/2 = 0\n(x - 7/10)(x - 5) = 0\nx - 7/10 = 0 or x - 5 = 0\nx = 7/10\nx = 5"} {"input": "Determine x in 7x - 28/5 = 0", "output": "7x - 28/5 = 0\n7x = 28/5\nx = 28/5 / 7\nx = 4/5"} {"input": "Compute the solution of x^3 - 1/4x^2 - 61/36x + 5/9 = 0", "output": "x^3 - 1/4x^2 - 61/36x + 5/9 = 0\n(x - -4/3)(x - 1/3)(x - 5/4) = 0\nx - -4/3 = 0\nx - 1/3 = 0\nx - 5/4 = 0\nx = -4/3\nx = 1/3\nx = 5/4"} {"input": "Find the solution to x^2 - 1/72x - 5/4 = 0", "output": "x^2 - 1/72x - 5/4 = 0\n(x - 9/8)(x - -10/9) = 0\nx - 9/8 = 0 or x - -10/9 = 0\nx = 9/8\nx = -10/9"} {"input": "Find the solution to x^2 - 19/12x - 34/3 = 0", "output": "x^2 - 19/12x - 34/3 = 0\n(x - 17/4)(x - -8/3) = 0\nx - 17/4 = 0 or x - -8/3 = 0\nx = 17/4\nx = -8/3"} {"input": "Find the solution to x^3 + 11/3x^2 + 32/9x + 28/27 = 0", "output": "x^3 + 11/3x^2 + 32/9x + 28/27 = 0\n(x - -7/3)(x - -2/3)(x - -2/3) = 0\nx - -7/3 = 0\nx - -2/3 = 0\nx - -2/3 = 0\nx = -7/3\nx = -2/3\nx = -2/3"} {"input": "Solve quickly: x^2 + 9x - 36 = 0", "output": "x^2 + 9x - 36 = 0\n(x - -12)(x - 3) = 0\nx - -12 = 0 or x - 3 = 0\nx = -12\nx = 3"} {"input": "Solve the system:\n3x + 4y = -7/3\n6x + 9y = -41/6", "output": "3x + 4y = -7/3\n6x + 9y = -41/6\n\nUsing elimination\n6*(3x + 4y = -7/3)\n3*(6x + 9y = -41/6)\n18x + 24y = -14\n18x + 27y = -41/2\nSubtract equations\n-3y = 13/2\ny = 13/2/-3\ny = -13/6\n\nSubstitute y\n3x + 4(-13/6) = -7/3\n3x = 19/3\nx = 19/3/3\nx = 19/9"} {"input": "Compute the solution of 4x - 48/5 = 0", "output": "4x - 48/5 = 0\n4x = 48/5\nx = 48/5 / 4\nx = 12/5"} {"input": "Solve the equation 8x - 56/9 = 0", "output": "8x - 56/9 = 0\n8x = 56/9\nx = 56/9 / 8\nx = 7/9"} {"input": "Solve the equation x^2 - 139/45x + 88/45 = 0", "output": "x^2 - 139/45x + 88/45 = 0\n(x - 11/5)(x - 8/9) = 0\nx - 11/5 = 0 or x - 8/9 = 0\nx = 11/5\nx = 8/9"} {"input": "Find the solution to 3x - 21/8 = 0", "output": "3x - 21/8 = 0\n3x = 21/8\nx = 21/8 / 3\nx = 7/8"} {"input": "Solve quickly: x^2 - 18/7x = 0", "output": "x^2 - 18/7x = 0\n(x - 0)(x - 18/7) = 0\nx - 0 = 0 or x - 18/7 = 0\nx = 0\nx = 18/7"} {"input": "Solve simultaneously:\n8x + 2y = 664/45\n3x + 7y = 749/45", "output": "8x + 2y = 664/45\n3x + 7y = 749/45\n\nUsing elimination\n3*(8x + 2y = 664/45)\n8*(3x + 7y = 749/45)\n24x + 6y = 664/15\n24x + 56y = 5992/45\nSubtract equations\n-50y = -800/9\ny = -800/9/-50\ny = 16/9\n\nSubstitute y\n8x + 2(16/9) = 664/45\n8x = 56/5\nx = 56/5/8\nx = 7/5"} {"input": "Solve quickly: 3x - 3/10 = 0", "output": "3x - 3/10 = 0\n3x = 3/10\nx = 3/10 / 3\nx = 1/10"} {"input": "Solve quickly: 1x - 7/5 = 0", "output": "1x - 7/5 = 0\n1x = 7/5\nx = 7/5 / 1\nx = 7/5"} {"input": "Find x in x^2 + 6/5x + 1/5 = 0", "output": "x^2 + 6/5x + 1/5 = 0\n(x - -1)(x - -1/5) = 0\nx - -1 = 0 or x - -1/5 = 0\nx = -1\nx = -1/5"} {"input": "Find x and y such that\n6x + 3y = 117/10\n4x + 10y = 23", "output": "6x + 3y = 117/10\n4x + 10y = 23\n\nUsing elimination\n4*(6x + 3y = 117/10)\n6*(4x + 10y = 23)\n24x + 12y = 234/5\n24x + 60y = 138\nSubtract equations\n-48y = -456/5\ny = -456/5/-48\ny = 19/10\n\nSubstitute y\n6x + 3(19/10) = 117/10\n6x = 6\nx = 6/6\nx = 1"} {"input": "Determine x in x^2 + 73/10x + 21/10 = 0", "output": "x^2 + 73/10x + 21/10 = 0\n(x - -3/10)(x - -7) = 0\nx - -3/10 = 0 or x - -7 = 0\nx = -3/10\nx = -7"} {"input": "Solve simultaneously:\n6x + 6y = -84/5\n6x + 9y = -111/5", "output": "6x + 6y = -84/5\n6x + 9y = -111/5\n\nUsing elimination\n6*(6x + 6y = -84/5)\n6*(6x + 9y = -111/5)\n36x + 36y = -504/5\n36x + 54y = -666/5\nSubtract equations\n-18y = 162/5\ny = 162/5/-18\ny = -9/5\n\nSubstitute y\n6x + 6(-9/5) = -84/5\n6x = -6\nx = -6/6\nx = -1"} {"input": "Find x and y such that\n3x + 7y = -23/8\n10x + 3y = -97/8", "output": "3x + 7y = -23/8\n10x + 3y = -97/8\n\nUsing elimination\n10*(3x + 7y = -23/8)\n3*(10x + 3y = -97/8)\n30x + 70y = -115/4\n30x + 9y = -291/8\nSubtract equations\n61y = 61/8\ny = 61/8/61\ny = 1/8\n\nSubstitute y\n3x + 7(1/8) = -23/8\n3x = -15/4\nx = -15/4/3\nx = -5/4"} {"input": "Find the solution to x^3 + 227/40x^2 + 253/40x - 3/2 = 0", "output": "x^3 + 227/40x^2 + 253/40x - 3/2 = 0\n(x - 1/5)(x - -4)(x - -15/8) = 0\nx - 1/5 = 0\nx - -4 = 0\nx - -15/8 = 0\nx = 1/5\nx = -4\nx = -15/8"} {"input": "Find x in x^3 - 2/5x^2 - 141/100x - 9/25 = 0", "output": "x^3 - 2/5x^2 - 141/100x - 9/25 = 0\n(x - -4/5)(x - 3/2)(x - -3/10) = 0\nx - -4/5 = 0\nx - 3/2 = 0\nx - -3/10 = 0\nx = -4/5\nx = 3/2\nx = -3/10"} {"input": "Solve x^3 - 11x^2 - 18x + 72 = 0", "output": "x^3 - 11x^2 - 18x + 72 = 0\n(x - 2)(x - -3)(x - 12) = 0\nx - 2 = 0\nx - -3 = 0\nx - 12 = 0\nx = 2\nx = -3\nx = 12"} {"input": "Solve the equation x^3 - 223/90x^2 - 388/135x + 238/45 = 0", "output": "x^3 - 223/90x^2 - 388/135x + 238/45 = 0\n(x - 17/6)(x - 6/5)(x - -14/9) = 0\nx - 17/6 = 0\nx - 6/5 = 0\nx - -14/9 = 0\nx = 17/6\nx = 6/5\nx = -14/9"} {"input": "Solve the equations:\n8x + 4y = 34\n4x + 7y = 19/2", "output": "8x + 4y = 34\n4x + 7y = 19/2\n\nUsing elimination\n4*(8x + 4y = 34)\n8*(4x + 7y = 19/2)\n32x + 16y = 136\n32x + 56y = 76\nSubtract equations\n-40y = 60\ny = 60/-40\ny = -3/2\n\nSubstitute y\n8x + 4(-3/2) = 34\n8x = 40\nx = 40/8\nx = 5"} {"input": "Find x in x^2 - 21/5x + 18/5 = 0", "output": "x^2 - 21/5x + 18/5 = 0\n(x - 6/5)(x - 3) = 0\nx - 6/5 = 0 or x - 3 = 0\nx = 6/5\nx = 3"} {"input": "Solve the equation x^3 + 29/20x^2 - 18/5x - 81/20 = 0", "output": "x^3 + 29/20x^2 - 18/5x - 81/20 = 0\n(x - 9/5)(x - -1)(x - -9/4) = 0\nx - 9/5 = 0\nx - -1 = 0\nx - -9/4 = 0\nx = 9/5\nx = -1\nx = -9/4"} {"input": "Compute the solution of x^2 + 38x + 360 = 0", "output": "x^2 + 38x + 360 = 0\n(x - -20)(x - -18) = 0\nx - -20 = 0 or x - -18 = 0\nx = -20\nx = -18"} {"input": "Solve x^3 + 125/12x^2 - 293/12x - 65 = 0", "output": "x^3 + 125/12x^2 - 293/12x - 65 = 0\n(x - 13/4)(x - -12)(x - -5/3) = 0\nx - 13/4 = 0\nx - -12 = 0\nx - -5/3 = 0\nx = 13/4\nx = -12\nx = -5/3"} {"input": "Solve quickly: x^3 + 107/6x^2 - 85/2x + 50/3 = 0", "output": "x^3 + 107/6x^2 - 85/2x + 50/3 = 0\n(x - 1/2)(x - -20)(x - 5/3) = 0\nx - 1/2 = 0\nx - -20 = 0\nx - 5/3 = 0\nx = 1/2\nx = -20\nx = 5/3"} {"input": "Compute the solution of x^2 - 25/3x + 16 = 0", "output": "x^2 - 25/3x + 16 = 0\n(x - 3)(x - 16/3) = 0\nx - 3 = 0 or x - 16/3 = 0\nx = 3\nx = 16/3"} {"input": "Solve the equations:\n6x + 5y = 502/21\n10x + 4y = 230/21", "output": "6x + 5y = 502/21\n10x + 4y = 230/21\n\nUsing elimination\n10*(6x + 5y = 502/21)\n6*(10x + 4y = 230/21)\n60x + 50y = 5020/21\n60x + 24y = 460/7\nSubtract equations\n26y = 520/3\ny = 520/3/26\ny = 20/3\n\nSubstitute y\n6x + 5(20/3) = 502/21\n6x = -66/7\nx = -66/7/6\nx = -11/7"} {"input": "Solve 1x - 14 = 0", "output": "1x - 14 = 0\n1x = 14\nx = 14 / 1\nx = 14"} {"input": "Find the solution to x^3 + 37/5x^2 + 216/25x + 36/25 = 0", "output": "x^3 + 37/5x^2 + 216/25x + 36/25 = 0\n(x - -6/5)(x - -1/5)(x - -6) = 0\nx - -6/5 = 0\nx - -1/5 = 0\nx - -6 = 0\nx = -6/5\nx = -1/5\nx = -6"} {"input": "What value of x satisfies x^2 - 3/10x - 9/5 = 0", "output": "x^2 - 3/10x - 9/5 = 0\n(x - -6/5)(x - 3/2) = 0\nx - -6/5 = 0 or x - 3/2 = 0\nx = -6/5\nx = 3/2"} {"input": "Solve the equation x^3 - 19/5x^2 - 187/20x = 0", "output": "x^3 - 19/5x^2 - 187/20x = 0\n(x - 11/2)(x - 0)(x - -17/10) = 0\nx - 11/2 = 0\nx - 0 = 0\nx - -17/10 = 0\nx = 11/2\nx = 0\nx = -17/10"} {"input": "Solve the equations:\n3x + 1y = 47/6\n5x + 8y = 74/3", "output": "3x + 1y = 47/6\n5x + 8y = 74/3\n\nUsing elimination\n5*(3x + 1y = 47/6)\n3*(5x + 8y = 74/3)\n15x + 5y = 235/6\n15x + 24y = 74\nSubtract equations\n-19y = -209/6\ny = -209/6/-19\ny = 11/6\n\nSubstitute y\n3x + 1(11/6) = 47/6\n3x = 6\nx = 6/3\nx = 2"} {"input": "Solve the equations:\n8x + 2y = -45\n8x + 4y = -50", "output": "8x + 2y = -45\n8x + 4y = -50\n\nUsing elimination\n8*(8x + 2y = -45)\n8*(8x + 4y = -50)\n64x + 16y = -360\n64x + 32y = -400\nSubtract equations\n-16y = 40\ny = 40/-16\ny = -5/2\n\nSubstitute y\n8x + 2(-5/2) = -45\n8x = -40\nx = -40/8\nx = -5"} {"input": "Find the solution to x^2 - 22/9x + 40/27 = 0", "output": "x^2 - 22/9x + 40/27 = 0\n(x - 10/9)(x - 4/3) = 0\nx - 10/9 = 0 or x - 4/3 = 0\nx = 10/9\nx = 4/3"} {"input": "Solve simultaneously:\n9x + 1y = -367/20\n3x + 10y = -91/5", "output": "9x + 1y = -367/20\n3x + 10y = -91/5\n\nUsing elimination\n3*(9x + 1y = -367/20)\n9*(3x + 10y = -91/5)\n27x + 3y = -1101/20\n27x + 90y = -819/5\nSubtract equations\n-87y = 435/4\ny = 435/4/-87\ny = -5/4\n\nSubstitute y\n9x + 1(-5/4) = -367/20\n9x = -171/10\nx = -171/10/9\nx = -19/10"} {"input": "Solve x^3 - 11/3x^2 - 20/3x = 0", "output": "x^3 - 11/3x^2 - 20/3x = 0\n(x - 5)(x - 0)(x - -4/3) = 0\nx - 5 = 0\nx - 0 = 0\nx - -4/3 = 0\nx = 5\nx = 0\nx = -4/3"} {"input": "Find x and y such that\n1x + 5y = 43/4\n4x + 8y = 59/5", "output": "1x + 5y = 43/4\n4x + 8y = 59/5\n\nUsing elimination\n4*(1x + 5y = 43/4)\n1*(4x + 8y = 59/5)\n4x + 20y = 43\n4x + 8y = 59/5\nSubtract equations\n12y = 156/5\ny = 156/5/12\ny = 13/5\n\nSubstitute y\n1x + 5(13/5) = 43/4\n1x = -9/4\nx = -9/4/1\nx = -9/4"} {"input": "Find x in 1x - 6 = 0", "output": "1x - 6 = 0\n1x = 6\nx = 6 / 1\nx = 6"} {"input": "Solve 6x + 12 = 0", "output": "6x + 12 = 0\n6x = -12\nx = -12 / 6\nx = -2"} {"input": "Solve the equation x^2 + 27/5x + 28/5 = 0", "output": "x^2 + 27/5x + 28/5 = 0\n(x - -4)(x - -7/5) = 0\nx - -4 = 0 or x - -7/5 = 0\nx = -4\nx = -7/5"} {"input": "Solve the equation x^3 - 269/90x^2 + 386/135x - 77/90 = 0", "output": "x^3 - 269/90x^2 + 386/135x - 77/90 = 0\n(x - 7/6)(x - 3/5)(x - 11/9) = 0\nx - 7/6 = 0\nx - 3/5 = 0\nx - 11/9 = 0\nx = 7/6\nx = 3/5\nx = 11/9"} {"input": "Solve the equations:\n9x + 2y = 67/3\n1x + 4y = -19/3", "output": "9x + 2y = 67/3\n1x + 4y = -19/3\n\nUsing elimination\n1*(9x + 2y = 67/3)\n9*(1x + 4y = -19/3)\n9x + 2y = 67/3\n9x + 36y = -57\nSubtract equations\n-34y = 238/3\ny = 238/3/-34\ny = -7/3\n\nSubstitute y\n9x + 2(-7/3) = 67/3\n9x = 27\nx = 27/9\nx = 3"} {"input": "Determine x in x^2 + 35/12x + 13/8 = 0", "output": "x^2 + 35/12x + 13/8 = 0\n(x - -3/4)(x - -13/6) = 0\nx - -3/4 = 0 or x - -13/6 = 0\nx = -3/4\nx = -13/6"} {"input": "Find x for 1x + 7 = 0", "output": "1x + 7 = 0\n1x = -7\nx = -7 / 1\nx = -7"} {"input": "Solve quickly: x^3 + 67/40x^2 - 941/200x + 14/25 = 0", "output": "x^3 + 67/40x^2 - 941/200x + 14/25 = 0\n(x - 1/8)(x - -16/5)(x - 7/5) = 0\nx - 1/8 = 0\nx - -16/5 = 0\nx - 7/5 = 0\nx = 1/8\nx = -16/5\nx = 7/5"} {"input": "Find the solution to x^3 - 45/7x^2 + 2x + 24/7 = 0", "output": "x^3 - 45/7x^2 + 2x + 24/7 = 0\n(x - 1)(x - 6)(x - -4/7) = 0\nx - 1 = 0\nx - 6 = 0\nx - -4/7 = 0\nx = 1\nx = 6\nx = -4/7"} {"input": "Solve the system:\n10x + 2y = 68\n3x + 4y = 85", "output": "10x + 2y = 68\n3x + 4y = 85\n\nUsing elimination\n3*(10x + 2y = 68)\n10*(3x + 4y = 85)\n30x + 6y = 204\n30x + 40y = 850\nSubtract equations\n-34y = -646\ny = -646/-34\ny = 19\n\nSubstitute y\n10x + 2(19) = 68\n10x = 30\nx = 30/10\nx = 3"} {"input": "Solve the equations:\n6x + 9y = -3/5\n4x + 4y = 0", "output": "6x + 9y = -3/5\n4x + 4y = 0\n\nUsing elimination\n4*(6x + 9y = -3/5)\n6*(4x + 4y = 0)\n24x + 36y = -12/5\n24x + 24y = 0\nSubtract equations\n12y = -12/5\ny = -12/5/12\ny = -1/5\n\nSubstitute y\n6x + 9(-1/5) = -3/5\n6x = 6/5\nx = 6/5/6\nx = 1/5"} {"input": "Solve the equation 1x + 1/6 = 0", "output": "1x + 1/6 = 0\n1x = -1/6\nx = -1/6 / 1\nx = -1/6"} {"input": "Solve quickly: 1x - 4/7 = 0", "output": "1x - 4/7 = 0\n1x = 4/7\nx = 4/7 / 1\nx = 4/7"} {"input": "Find x and y such that\n10x + 10y = 10/7\n1x + 2y = -5/7", "output": "10x + 10y = 10/7\n1x + 2y = -5/7\n\nUsing elimination\n1*(10x + 10y = 10/7)\n10*(1x + 2y = -5/7)\n10x + 10y = 10/7\n10x + 20y = -50/7\nSubtract equations\n-10y = 60/7\ny = 60/7/-10\ny = -6/7\n\nSubstitute y\n10x + 10(-6/7) = 10/7\n10x = 10\nx = 10/10\nx = 1"} {"input": "Solve quickly: x^2 + 7/2x + 5/2 = 0", "output": "x^2 + 7/2x + 5/2 = 0\n(x - -1)(x - -5/2) = 0\nx - -1 = 0 or x - -5/2 = 0\nx = -1\nx = -5/2"} {"input": "Solve x^2 - 7/2x + 3 = 0", "output": "x^2 - 7/2x + 3 = 0\n(x - 3/2)(x - 2) = 0\nx - 3/2 = 0 or x - 2 = 0\nx = 3/2\nx = 2"} {"input": "Solve the system:\n8x + 2y = 34\n9x + 1y = 69/2", "output": "8x + 2y = 34\n9x + 1y = 69/2\n\nUsing elimination\n9*(8x + 2y = 34)\n8*(9x + 1y = 69/2)\n72x + 18y = 306\n72x + 8y = 276\nSubtract equations\n10y = 30\ny = 30/10\ny = 3\n\nSubstitute y\n8x + 2(3) = 34\n8x = 28\nx = 28/8\nx = 7/2"} {"input": "Solve the system:\n7x + 8y = -104/5\n10x + 6y = -8", "output": "7x + 8y = -104/5\n10x + 6y = -8\n\nUsing elimination\n10*(7x + 8y = -104/5)\n7*(10x + 6y = -8)\n70x + 80y = -208\n70x + 42y = -56\nSubtract equations\n38y = -152\ny = -152/38\ny = -4\n\nSubstitute y\n7x + 8(-4) = -104/5\n7x = 56/5\nx = 56/5/7\nx = 8/5"} {"input": "Find x for x^2 - 22/3x + 7/3 = 0", "output": "x^2 - 22/3x + 7/3 = 0\n(x - 7)(x - 1/3) = 0\nx - 7 = 0 or x - 1/3 = 0\nx = 7\nx = 1/3"} {"input": "Find the solution to 2x - 14/3 = 0", "output": "2x - 14/3 = 0\n2x = 14/3\nx = 14/3 / 2\nx = 7/3"} {"input": "Find x in x^3 + 61/70x^2 - 17/10x - 33/35 = 0", "output": "x^3 + 61/70x^2 - 17/10x - 33/35 = 0\n(x - -1/2)(x - -11/7)(x - 6/5) = 0\nx - -1/2 = 0\nx - -11/7 = 0\nx - 6/5 = 0\nx = -1/2\nx = -11/7\nx = 6/5"} {"input": "Find x in 10x + 200/7 = 0", "output": "10x + 200/7 = 0\n10x = -200/7\nx = -200/7 / 10\nx = -20/7"} {"input": "Solve the equations:\n7x + 1y = -21/5\n6x + 4y = 4/5", "output": "7x + 1y = -21/5\n6x + 4y = 4/5\n\nUsing elimination\n6*(7x + 1y = -21/5)\n7*(6x + 4y = 4/5)\n42x + 6y = -126/5\n42x + 28y = 28/5\nSubtract equations\n-22y = -154/5\ny = -154/5/-22\ny = 7/5\n\nSubstitute y\n7x + 1(7/5) = -21/5\n7x = -28/5\nx = -28/5/7\nx = -4/5"} {"input": "Solve the equation 6x - 114/7 = 0", "output": "6x - 114/7 = 0\n6x = 114/7\nx = 114/7 / 6\nx = 19/7"} {"input": "Find x and y such that\n10x + 9y = -1254/7\n10x + 10y = -1380/7", "output": "10x + 9y = -1254/7\n10x + 10y = -1380/7\n\nUsing elimination\n10*(10x + 9y = -1254/7)\n10*(10x + 10y = -1380/7)\n100x + 90y = -12540/7\n100x + 100y = -13800/7\nSubtract equations\n-10y = 180\ny = 180/-10\ny = -18\n\nSubstitute y\n10x + 9(-18) = -1254/7\n10x = -120/7\nx = -120/7/10\nx = -12/7"} {"input": "Solve x^3 + 137/12x^2 + 69/8x - 665/12 = 0", "output": "x^3 + 137/12x^2 + 69/8x - 665/12 = 0\n(x - -19/6)(x - 7/4)(x - -10) = 0\nx - -19/6 = 0\nx - 7/4 = 0\nx - -10 = 0\nx = -19/6\nx = 7/4\nx = -10"} {"input": "Find the solution to x^2 - 21x + 98 = 0", "output": "x^2 - 21x + 98 = 0\n(x - 14)(x - 7) = 0\nx - 14 = 0 or x - 7 = 0\nx = 14\nx = 7"} {"input": "Find the solution to 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "Compute the solution of x^3 - 11/8x^2 - 1/16x + 7/16 = 0", "output": "x^3 - 11/8x^2 - 1/16x + 7/16 = 0\n(x - 1)(x - -1/2)(x - 7/8) = 0\nx - 1 = 0\nx - -1/2 = 0\nx - 7/8 = 0\nx = 1\nx = -1/2\nx = 7/8"} {"input": "Determine x in 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "Solve x^2 + 1x - 14/25 = 0", "output": "x^2 + 1x - 14/25 = 0\n(x - -7/5)(x - 2/5) = 0\nx - -7/5 = 0 or x - 2/5 = 0\nx = -7/5\nx = 2/5"} {"input": "Find x in x^3 + 161/30x^2 + 79/9x + 68/15 = 0", "output": "x^3 + 161/30x^2 + 79/9x + 68/15 = 0\n(x - -4/3)(x - -17/6)(x - -6/5) = 0\nx - -4/3 = 0\nx - -17/6 = 0\nx - -6/5 = 0\nx = -4/3\nx = -17/6\nx = -6/5"} {"input": "Solve simultaneously:\n3x + 8y = -131/5\n9x + 4y = -43/5", "output": "3x + 8y = -131/5\n9x + 4y = -43/5\n\nUsing elimination\n9*(3x + 8y = -131/5)\n3*(9x + 4y = -43/5)\n27x + 72y = -1179/5\n27x + 12y = -129/5\nSubtract equations\n60y = -210\ny = -210/60\ny = -7/2\n\nSubstitute y\n3x + 8(-7/2) = -131/5\n3x = 9/5\nx = 9/5/3\nx = 3/5"} {"input": "Solve simultaneously:\n3x + 6y = -49/2\n6x + 10y = -127/3", "output": "3x + 6y = -49/2\n6x + 10y = -127/3\n\nUsing elimination\n6*(3x + 6y = -49/2)\n3*(6x + 10y = -127/3)\n18x + 36y = -147\n18x + 30y = -127\nSubtract equations\n6y = -20\ny = -20/6\ny = -10/3\n\nSubstitute y\n3x + 6(-10/3) = -49/2\n3x = -9/2\nx = -9/2/3\nx = -3/2"} {"input": "Find x in x^3 - 83/24x^2 - 5/96x + 25/16 = 0", "output": "x^3 - 83/24x^2 - 5/96x + 25/16 = 0\n(x - 10/3)(x - 3/4)(x - -5/8) = 0\nx - 10/3 = 0\nx - 3/4 = 0\nx - -5/8 = 0\nx = 10/3\nx = 3/4\nx = -5/8"} {"input": "Solve quickly: x^3 - 18x^2 + 95x - 150 = 0", "output": "x^3 - 18x^2 + 95x - 150 = 0\n(x - 3)(x - 5)(x - 10) = 0\nx - 3 = 0\nx - 5 = 0\nx - 10 = 0\nx = 3\nx = 5\nx = 10"} {"input": "Find x in x^3 + 225/8x^2 + 2717/16x - 1083/16 = 0", "output": "x^3 + 225/8x^2 + 2717/16x - 1083/16 = 0\n(x - 3/8)(x - -19/2)(x - -19) = 0\nx - 3/8 = 0\nx - -19/2 = 0\nx - -19 = 0\nx = 3/8\nx = -19/2\nx = -19"} {"input": "Solve simultaneously:\n1x + 8y = -33\n8x + 1y = 141/4", "output": "1x + 8y = -33\n8x + 1y = 141/4\n\nUsing elimination\n8*(1x + 8y = -33)\n1*(8x + 1y = 141/4)\n8x + 64y = -264\n8x + 1y = 141/4\nSubtract equations\n63y = -1197/4\ny = -1197/4/63\ny = -19/4\n\nSubstitute y\n1x + 8(-19/4) = -33\n1x = 5\nx = 5/1\nx = 5"} {"input": "Find x and y such that\n5x + 7y = 27/4\n6x + 1y = 25/4", "output": "5x + 7y = 27/4\n6x + 1y = 25/4\n\nUsing elimination\n6*(5x + 7y = 27/4)\n5*(6x + 1y = 25/4)\n30x + 42y = 81/2\n30x + 5y = 125/4\nSubtract equations\n37y = 37/4\ny = 37/4/37\ny = 1/4\n\nSubstitute y\n5x + 7(1/4) = 27/4\n5x = 5\nx = 5/5\nx = 1"} {"input": "Solve the system:\n2x + 8y = 858/35\n10x + 5y = 221/7", "output": "2x + 8y = 858/35\n10x + 5y = 221/7\n\nUsing elimination\n10*(2x + 8y = 858/35)\n2*(10x + 5y = 221/7)\n20x + 80y = 1716/7\n20x + 10y = 442/7\nSubtract equations\n70y = 182\ny = 182/70\ny = 13/5\n\nSubstitute y\n2x + 8(13/5) = 858/35\n2x = 26/7\nx = 26/7/2\nx = 13/7"} {"input": "Find x and y such that\n9x + 6y = 87\n3x + 3y = 46", "output": "9x + 6y = 87\n3x + 3y = 46\n\nUsing elimination\n3*(9x + 6y = 87)\n9*(3x + 3y = 46)\n27x + 18y = 261\n27x + 27y = 414\nSubtract equations\n-9y = -153\ny = -153/-9\ny = 17\n\nSubstitute y\n9x + 6(17) = 87\n9x = -15\nx = -15/9\nx = -5/3"} {"input": "Find x for x^2 + 17/7x + 6/7 = 0", "output": "x^2 + 17/7x + 6/7 = 0\n(x - -2)(x - -3/7) = 0\nx - -2 = 0 or x - -3/7 = 0\nx = -2\nx = -3/7"} {"input": "Solve x^2 + 11/2x - 51/2 = 0", "output": "x^2 + 11/2x - 51/2 = 0\n(x - 3)(x - -17/2) = 0\nx - 3 = 0 or x - -17/2 = 0\nx = 3\nx = -17/2"} {"input": "Solve simultaneously:\n6x + 7y = -323/20\n9x + 10y = -185/8", "output": "6x + 7y = -323/20\n9x + 10y = -185/8\n\nUsing elimination\n9*(6x + 7y = -323/20)\n6*(9x + 10y = -185/8)\n54x + 63y = -2907/20\n54x + 60y = -555/4\nSubtract equations\n3y = -33/5\ny = -33/5/3\ny = -11/5\n\nSubstitute y\n6x + 7(-11/5) = -323/20\n6x = -3/4\nx = -3/4/6\nx = -1/8"} {"input": "Find x for x^2 + 3/4x - 1/4 = 0", "output": "x^2 + 3/4x - 1/4 = 0\n(x - 1/4)(x - -1) = 0\nx - 1/4 = 0 or x - -1 = 0\nx = 1/4\nx = -1"} {"input": "Solve the system:\n6x + 1y = -103/15\n3x + 4y = -383/30", "output": "6x + 1y = -103/15\n3x + 4y = -383/30\n\nUsing elimination\n3*(6x + 1y = -103/15)\n6*(3x + 4y = -383/30)\n18x + 3y = -103/5\n18x + 24y = -383/5\nSubtract equations\n-21y = 56\ny = 56/-21\ny = -8/3\n\nSubstitute y\n6x + 1(-8/3) = -103/15\n6x = -21/5\nx = -21/5/6\nx = -7/10"} {"input": "What value of x satisfies x^2 + 27/4x + 19/2 = 0", "output": "x^2 + 27/4x + 19/2 = 0\n(x - -2)(x - -19/4) = 0\nx - -2 = 0 or x - -19/4 = 0\nx = -2\nx = -19/4"} {"input": "Determine x in x^3 + 41/24x^2 - 641/144x + 19/36 = 0", "output": "x^3 + 41/24x^2 - 641/144x + 19/36 = 0\n(x - -19/6)(x - 4/3)(x - 1/8) = 0\nx - -19/6 = 0\nx - 4/3 = 0\nx - 1/8 = 0\nx = -19/6\nx = 4/3\nx = 1/8"} {"input": "Determine x in 9x - 36 = 0", "output": "9x - 36 = 0\n9x = 36\nx = 36 / 9\nx = 4"} {"input": "What value of x satisfies 10x + 65/3 = 0", "output": "10x + 65/3 = 0\n10x = -65/3\nx = -65/3 / 10\nx = -13/6"} {"input": "Solve x^2 - 7/2x - 9/2 = 0", "output": "x^2 - 7/2x - 9/2 = 0\n(x - -1)(x - 9/2) = 0\nx - -1 = 0 or x - 9/2 = 0\nx = -1\nx = 9/2"} {"input": "Solve simultaneously:\n10x + 10y = 185/6\n1x + 7y = 163/12", "output": "10x + 10y = 185/6\n1x + 7y = 163/12\n\nUsing elimination\n1*(10x + 10y = 185/6)\n10*(1x + 7y = 163/12)\n10x + 10y = 185/6\n10x + 70y = 815/6\nSubtract equations\n-60y = -105\ny = -105/-60\ny = 7/4\n\nSubstitute y\n10x + 10(7/4) = 185/6\n10x = 40/3\nx = 40/3/10\nx = 4/3"} {"input": "Solve the system:\n10x + 1y = 58/5\n10x + 10y = 8", "output": "10x + 1y = 58/5\n10x + 10y = 8\n\nUsing elimination\n10*(10x + 1y = 58/5)\n10*(10x + 10y = 8)\n100x + 10y = 116\n100x + 100y = 80\nSubtract equations\n-90y = 36\ny = 36/-90\ny = -2/5\n\nSubstitute y\n10x + 1(-2/5) = 58/5\n10x = 12\nx = 12/10\nx = 6/5"} {"input": "Solve simultaneously:\n7x + 9y = -1097/90\n1x + 4y = -286/45", "output": "7x + 9y = -1097/90\n1x + 4y = -286/45\n\nUsing elimination\n1*(7x + 9y = -1097/90)\n7*(1x + 4y = -286/45)\n7x + 9y = -1097/90\n7x + 28y = -2002/45\nSubtract equations\n-19y = 323/10\ny = 323/10/-19\ny = -17/10\n\nSubstitute y\n7x + 9(-17/10) = -1097/90\n7x = 28/9\nx = 28/9/7\nx = 4/9"} {"input": "Find x in x^2 - 116/63x - 64/63 = 0", "output": "x^2 - 116/63x - 64/63 = 0\n(x - 16/7)(x - -4/9) = 0\nx - 16/7 = 0 or x - -4/9 = 0\nx = 16/7\nx = -4/9"} {"input": "Find x for 7x + 28 = 0", "output": "7x + 28 = 0\n7x = -28\nx = -28 / 7\nx = -4"} {"input": "Solve quickly: x^3 + 884/63x^2 - 3065/63x + 646/21 = 0", "output": "x^3 + 884/63x^2 - 3065/63x + 646/21 = 0\n(x - 19/9)(x - 6/7)(x - -17) = 0\nx - 19/9 = 0\nx - 6/7 = 0\nx - -17 = 0\nx = 19/9\nx = 6/7\nx = -17"} {"input": "What value of x satisfies x^3 + 43/30x^2 - 57/10x - 42/5 = 0", "output": "x^3 + 43/30x^2 - 57/10x - 42/5 = 0\n(x - -7/3)(x - -3/2)(x - 12/5) = 0\nx - -7/3 = 0\nx - -3/2 = 0\nx - 12/5 = 0\nx = -7/3\nx = -3/2\nx = 12/5"} {"input": "Solve the equations:\n8x + 7y = 6\n6x + 7y = 23/2", "output": "8x + 7y = 6\n6x + 7y = 23/2\n\nUsing elimination\n6*(8x + 7y = 6)\n8*(6x + 7y = 23/2)\n48x + 42y = 36\n48x + 56y = 92\nSubtract equations\n-14y = -56\ny = -56/-14\ny = 4\n\nSubstitute y\n8x + 7(4) = 6\n8x = -22\nx = -22/8\nx = -11/4"} {"input": "Solve the equations:\n8x + 4y = 5/3\n5x + 6y = 1/6", "output": "8x + 4y = 5/3\n5x + 6y = 1/6\n\nUsing elimination\n5*(8x + 4y = 5/3)\n8*(5x + 6y = 1/6)\n40x + 20y = 25/3\n40x + 48y = 4/3\nSubtract equations\n-28y = 7\ny = 7/-28\ny = -1/4\n\nSubstitute y\n8x + 4(-1/4) = 5/3\n8x = 8/3\nx = 8/3/8\nx = 1/3"} {"input": "Find the solution to x^3 - 157/70x^2 + 44/35x = 0", "output": "x^3 - 157/70x^2 + 44/35x = 0\n(x - 11/10)(x - 0)(x - 8/7) = 0\nx - 11/10 = 0\nx - 0 = 0\nx - 8/7 = 0\nx = 11/10\nx = 0\nx = 8/7"} {"input": "What value of x satisfies x^2 - 23/10x + 9/10 = 0", "output": "x^2 - 23/10x + 9/10 = 0\n(x - 9/5)(x - 1/2) = 0\nx - 9/5 = 0 or x - 1/2 = 0\nx = 9/5\nx = 1/2"} {"input": "Compute the solution of x^3 + 22/5x^2 + 9/4x - 63/20 = 0", "output": "x^3 + 22/5x^2 + 9/4x - 63/20 = 0\n(x - -7/2)(x - 3/5)(x - -3/2) = 0\nx - -7/2 = 0\nx - 3/5 = 0\nx - -3/2 = 0\nx = -7/2\nx = 3/5\nx = -3/2"} {"input": "Solve x^3 + 5/24x^2 - 101/96x + 5/16 = 0", "output": "x^3 + 5/24x^2 - 101/96x + 5/16 = 0\n(x - -5/4)(x - 3/8)(x - 2/3) = 0\nx - -5/4 = 0\nx - 3/8 = 0\nx - 2/3 = 0\nx = -5/4\nx = 3/8\nx = 2/3"} {"input": "Solve the system:\n4x + 3y = -25\n9x + 2y = -4", "output": "4x + 3y = -25\n9x + 2y = -4\n\nUsing elimination\n9*(4x + 3y = -25)\n4*(9x + 2y = -4)\n36x + 27y = -225\n36x + 8y = -16\nSubtract equations\n19y = -209\ny = -209/19\ny = -11\n\nSubstitute y\n4x + 3(-11) = -25\n4x = 8\nx = 8/4\nx = 2"} {"input": "Solve quickly: x^3 + 17/5x^2 + 3/5x - 9/5 = 0", "output": "x^3 + 17/5x^2 + 3/5x - 9/5 = 0\n(x - -3)(x - -1)(x - 3/5) = 0\nx - -3 = 0\nx - -1 = 0\nx - 3/5 = 0\nx = -3\nx = -1\nx = 3/5"} {"input": "Solve simultaneously:\n1x + 6y = -13\n6x + 3y = -1", "output": "1x + 6y = -13\n6x + 3y = -1\n\nUsing elimination\n6*(1x + 6y = -13)\n1*(6x + 3y = -1)\n6x + 36y = -78\n6x + 3y = -1\nSubtract equations\n33y = -77\ny = -77/33\ny = -7/3\n\nSubstitute y\n1x + 6(-7/3) = -13\n1x = 1\nx = 1/1\nx = 1"} {"input": "Compute the solution of x^3 + 17/4x^2 + 9/2x = 0", "output": "x^3 + 17/4x^2 + 9/2x = 0\n(x - 0)(x - -9/4)(x - -2) = 0\nx - 0 = 0\nx - -9/4 = 0\nx - -2 = 0\nx = 0\nx = -9/4\nx = -2"} {"input": "Find x and y such that\n2x + 7y = -663/56\n4x + 5y = -885/56", "output": "2x + 7y = -663/56\n4x + 5y = -885/56\n\nUsing elimination\n4*(2x + 7y = -663/56)\n2*(4x + 5y = -885/56)\n8x + 28y = -663/14\n8x + 10y = -885/28\nSubtract equations\n18y = -63/4\ny = -63/4/18\ny = -7/8\n\nSubstitute y\n2x + 7(-7/8) = -663/56\n2x = -40/7\nx = -40/7/2\nx = -20/7"} {"input": "Find x for 10x - 200/9 = 0", "output": "10x - 200/9 = 0\n10x = 200/9\nx = 200/9 / 10\nx = 20/9"} {"input": "Find x and y such that\n7x + 10y = -109/2\n9x + 9y = -207/4", "output": "7x + 10y = -109/2\n9x + 9y = -207/4\n\nUsing elimination\n9*(7x + 10y = -109/2)\n7*(9x + 9y = -207/4)\n63x + 90y = -981/2\n63x + 63y = -1449/4\nSubtract equations\n27y = -513/4\ny = -513/4/27\ny = -19/4\n\nSubstitute y\n7x + 10(-19/4) = -109/2\n7x = -7\nx = -7/7\nx = -1"} {"input": "Solve the equations:\n3x + 5y = 25\n4x + 10y = 46", "output": "3x + 5y = 25\n4x + 10y = 46\n\nUsing elimination\n4*(3x + 5y = 25)\n3*(4x + 10y = 46)\n12x + 20y = 100\n12x + 30y = 138\nSubtract equations\n-10y = -38\ny = -38/-10\ny = 19/5\n\nSubstitute y\n3x + 5(19/5) = 25\n3x = 6\nx = 6/3\nx = 2"} {"input": "Solve the equations:\n4x + 5y = 785/21\n10x + 1y = 433/21", "output": "4x + 5y = 785/21\n10x + 1y = 433/21\n\nUsing elimination\n10*(4x + 5y = 785/21)\n4*(10x + 1y = 433/21)\n40x + 50y = 7850/21\n40x + 4y = 1732/21\nSubtract equations\n46y = 874/3\ny = 874/3/46\ny = 19/3\n\nSubstitute y\n4x + 5(19/3) = 785/21\n4x = 40/7\nx = 40/7/4\nx = 10/7"} {"input": "Compute the solution of x^3 + 37/9x^2 + 10/3x = 0", "output": "x^3 + 37/9x^2 + 10/3x = 0\n(x - -10/9)(x - 0)(x - -3) = 0\nx - -10/9 = 0\nx - 0 = 0\nx - -3 = 0\nx = -10/9\nx = 0\nx = -3"} {"input": "Solve the equations:\n8x + 7y = -113\n5x + 7y = -68", "output": "8x + 7y = -113\n5x + 7y = -68\n\nUsing elimination\n5*(8x + 7y = -113)\n8*(5x + 7y = -68)\n40x + 35y = -565\n40x + 56y = -544\nSubtract equations\n-21y = -21\ny = -21/-21\ny = 1\n\nSubstitute y\n8x + 7(1) = -113\n8x = -120\nx = -120/8\nx = -15"} {"input": "Solve the equation 5x - 55/3 = 0", "output": "5x - 55/3 = 0\n5x = 55/3\nx = 55/3 / 5\nx = 11/3"} {"input": "Solve simultaneously:\n1x + 8y = -17/3\n6x + 1y = 31/6", "output": "1x + 8y = -17/3\n6x + 1y = 31/6\n\nUsing elimination\n6*(1x + 8y = -17/3)\n1*(6x + 1y = 31/6)\n6x + 48y = -34\n6x + 1y = 31/6\nSubtract equations\n47y = -235/6\ny = -235/6/47\ny = -5/6\n\nSubstitute y\n1x + 8(-5/6) = -17/3\n1x = 1\nx = 1/1\nx = 1"} {"input": "Solve simultaneously:\n9x + 2y = 2\n1x + 1y = 1", "output": "9x + 2y = 2\n1x + 1y = 1\n\nUsing elimination\n1*(9x + 2y = 2)\n9*(1x + 1y = 1)\n9x + 2y = 2\n9x + 9y = 9\nSubtract equations\n-7y = -7\ny = -7/-7\ny = 1\n\nSubstitute y\n9x + 2(1) = 2\n9x = 0\nx = 0/9\nx = 0"} {"input": "Solve the system:\n4x + 7y = -94/3\n10x + 2y = 13/3", "output": "4x + 7y = -94/3\n10x + 2y = 13/3\n\nUsing elimination\n10*(4x + 7y = -94/3)\n4*(10x + 2y = 13/3)\n40x + 70y = -940/3\n40x + 8y = 52/3\nSubtract equations\n62y = -992/3\ny = -992/3/62\ny = -16/3\n\nSubstitute y\n4x + 7(-16/3) = -94/3\n4x = 6\nx = 6/4\nx = 3/2"} {"input": "Determine x in x^3 - 59/35x^2 + 13/28x + 9/140 = 0", "output": "x^3 - 59/35x^2 + 13/28x + 9/140 = 0\n(x - 1/2)(x - 9/7)(x - -1/10) = 0\nx - 1/2 = 0\nx - 9/7 = 0\nx - -1/10 = 0\nx = 1/2\nx = 9/7\nx = -1/10"} {"input": "Solve 4x + 68/9 = 0", "output": "4x + 68/9 = 0\n4x = -68/9\nx = -68/9 / 4\nx = -17/9"} {"input": "Solve simultaneously:\n9x + 6y = 54\n8x + 8y = 196/3", "output": "9x + 6y = 54\n8x + 8y = 196/3\n\nUsing elimination\n8*(9x + 6y = 54)\n9*(8x + 8y = 196/3)\n72x + 48y = 432\n72x + 72y = 588\nSubtract equations\n-24y = -156\ny = -156/-24\ny = 13/2\n\nSubstitute y\n9x + 6(13/2) = 54\n9x = 15\nx = 15/9\nx = 5/3"} {"input": "What value of x satisfies x^3 - 123/35x^2 - 323/35x + 1083/35 = 0", "output": "x^3 - 123/35x^2 - 323/35x + 1083/35 = 0\n(x - 19/7)(x - 19/5)(x - -3) = 0\nx - 19/7 = 0\nx - 19/5 = 0\nx - -3 = 0\nx = 19/7\nx = 19/5\nx = -3"} {"input": "Determine x in 10x - 190/3 = 0", "output": "10x - 190/3 = 0\n10x = 190/3\nx = 190/3 / 10\nx = 19/3"} {"input": "Solve the equations:\n10x + 5y = -85/3\n3x + 10y = -51", "output": "10x + 5y = -85/3\n3x + 10y = -51\n\nUsing elimination\n3*(10x + 5y = -85/3)\n10*(3x + 10y = -51)\n30x + 15y = -85\n30x + 100y = -510\nSubtract equations\n-85y = 425\ny = 425/-85\ny = -5\n\nSubstitute y\n10x + 5(-5) = -85/3\n10x = -10/3\nx = -10/3/10\nx = -1/3"} {"input": "Find the solution to x^2 - 23x + 120 = 0", "output": "x^2 - 23x + 120 = 0\n(x - 8)(x - 15) = 0\nx - 8 = 0 or x - 15 = 0\nx = 8\nx = 15"} {"input": "Solve the equation 5x + 65/9 = 0", "output": "5x + 65/9 = 0\n5x = -65/9\nx = -65/9 / 5\nx = -13/9"} {"input": "Find x and y such that\n8x + 1y = 9\n5x + 10y = -45/2", "output": "8x + 1y = 9\n5x + 10y = -45/2\n\nUsing elimination\n5*(8x + 1y = 9)\n8*(5x + 10y = -45/2)\n40x + 5y = 45\n40x + 80y = -180\nSubtract equations\n-75y = 225\ny = 225/-75\ny = -3\n\nSubstitute y\n8x + 1(-3) = 9\n8x = 12\nx = 12/8\nx = 3/2"} {"input": "Find x and y such that\n10x + 10y = -41/3\n5x + 4y = -199/30", "output": "10x + 10y = -41/3\n5x + 4y = -199/30\n\nUsing elimination\n5*(10x + 10y = -41/3)\n10*(5x + 4y = -199/30)\n50x + 50y = -205/3\n50x + 40y = -199/3\nSubtract equations\n10y = -2\ny = -2/10\ny = -1/5\n\nSubstitute y\n10x + 10(-1/5) = -41/3\n10x = -35/3\nx = -35/3/10\nx = -7/6"} {"input": "Compute the solution of x^3 + 53/2x^2 + 130x = 0", "output": "x^3 + 53/2x^2 + 130x = 0\n(x - -13/2)(x - 0)(x - -20) = 0\nx - -13/2 = 0\nx - 0 = 0\nx - -20 = 0\nx = -13/2\nx = 0\nx = -20"} {"input": "Solve the equation x^3 - 23/9x^2 + 40/81x + 100/81 = 0", "output": "x^3 - 23/9x^2 + 40/81x + 100/81 = 0\n(x - -5/9)(x - 10/9)(x - 2) = 0\nx - -5/9 = 0\nx - 10/9 = 0\nx - 2 = 0\nx = -5/9\nx = 10/9\nx = 2"} {"input": "Solve simultaneously:\n9x + 3y = 519/10\n3x + 7y = 563/10", "output": "9x + 3y = 519/10\n3x + 7y = 563/10\n\nUsing elimination\n3*(9x + 3y = 519/10)\n9*(3x + 7y = 563/10)\n27x + 9y = 1557/10\n27x + 63y = 5067/10\nSubtract equations\n-54y = -351\ny = -351/-54\ny = 13/2\n\nSubstitute y\n9x + 3(13/2) = 519/10\n9x = 162/5\nx = 162/5/9\nx = 18/5"} {"input": "Find x and y such that\n7x + 5y = -98/3\n2x + 5y = -53/3", "output": "7x + 5y = -98/3\n2x + 5y = -53/3\n\nUsing elimination\n2*(7x + 5y = -98/3)\n7*(2x + 5y = -53/3)\n14x + 10y = -196/3\n14x + 35y = -371/3\nSubtract equations\n-25y = 175/3\ny = 175/3/-25\ny = -7/3\n\nSubstitute y\n7x + 5(-7/3) = -98/3\n7x = -21\nx = -21/7\nx = -3"} {"input": "What value of x satisfies x^2 - 5/3x = 0", "output": "x^2 - 5/3x = 0\n(x - 5/3)(x - 0) = 0\nx - 5/3 = 0 or x - 0 = 0\nx = 5/3\nx = 0"} {"input": "Determine x in x^2 + 7/3x - 16 = 0", "output": "x^2 + 7/3x - 16 = 0\n(x - 3)(x - -16/3) = 0\nx - 3 = 0 or x - -16/3 = 0\nx = 3\nx = -16/3"} {"input": "Solve quickly: 3x + 48 = 0", "output": "3x + 48 = 0\n3x = -48\nx = -48 / 3\nx = -16"} {"input": "Find the solution to x^2 - 2/3x - 8/9 = 0", "output": "x^2 - 2/3x - 8/9 = 0\n(x - 4/3)(x - -2/3) = 0\nx - 4/3 = 0 or x - -2/3 = 0\nx = 4/3\nx = -2/3"} {"input": "Solve the equations:\n9x + 2y = 32/7\n7x + 5y = 23/21", "output": "9x + 2y = 32/7\n7x + 5y = 23/21\n\nUsing elimination\n7*(9x + 2y = 32/7)\n9*(7x + 5y = 23/21)\n63x + 14y = 32\n63x + 45y = 69/7\nSubtract equations\n-31y = 155/7\ny = 155/7/-31\ny = -5/7\n\nSubstitute y\n9x + 2(-5/7) = 32/7\n9x = 6\nx = 6/9\nx = 2/3"} {"input": "Solve 4x + 24/5 = 0", "output": "4x + 24/5 = 0\n4x = -24/5\nx = -24/5 / 4\nx = -6/5"} {"input": "What value of x satisfies x^2 + 34/15x + 16/15 = 0", "output": "x^2 + 34/15x + 16/15 = 0\n(x - -8/5)(x - -2/3) = 0\nx - -8/5 = 0 or x - -2/3 = 0\nx = -8/5\nx = -2/3"} {"input": "Solve x^3 + 1/14x^2 - 23/14x - 5/7 = 0", "output": "x^3 + 1/14x^2 - 23/14x - 5/7 = 0\n(x - 10/7)(x - -1/2)(x - -1) = 0\nx - 10/7 = 0\nx - -1/2 = 0\nx - -1 = 0\nx = 10/7\nx = -1/2\nx = -1"} {"input": "Solve quickly: x^2 - 11/4x - 19/2 = 0", "output": "x^2 - 11/4x - 19/2 = 0\n(x - -2)(x - 19/4) = 0\nx - -2 = 0 or x - 19/4 = 0\nx = -2\nx = 19/4"} {"input": "Determine x in 7x + 126/5 = 0", "output": "7x + 126/5 = 0\n7x = -126/5\nx = -126/5 / 7\nx = -18/5"} {"input": "Solve 4x + 28 = 0", "output": "4x + 28 = 0\n4x = -28\nx = -28 / 4\nx = -7"} {"input": "Solve simultaneously:\n10x + 8y = -1528/21\n9x + 8y = -472/7", "output": "10x + 8y = -1528/21\n9x + 8y = -472/7\n\nUsing elimination\n9*(10x + 8y = -1528/21)\n10*(9x + 8y = -472/7)\n90x + 72y = -4584/7\n90x + 80y = -4720/7\nSubtract equations\n-8y = 136/7\ny = 136/7/-8\ny = -17/7\n\nSubstitute y\n10x + 8(-17/7) = -1528/21\n10x = -160/3\nx = -160/3/10\nx = -16/3"} {"input": "Solve 4x - 44/3 = 0", "output": "4x - 44/3 = 0\n4x = 44/3\nx = 44/3 / 4\nx = 11/3"} {"input": "Determine x in x^3 + 153/56x^2 - 1151/224x - 765/56 = 0", "output": "x^3 + 153/56x^2 - 1151/224x - 765/56 = 0\n(x - 9/4)(x - -20/7)(x - -17/8) = 0\nx - 9/4 = 0\nx - -20/7 = 0\nx - -17/8 = 0\nx = 9/4\nx = -20/7\nx = -17/8"} {"input": "Find x for x^3 - 22/5x^2 - 152/5x + 64/5 = 0", "output": "x^3 - 22/5x^2 - 152/5x + 64/5 = 0\n(x - -4)(x - 2/5)(x - 8) = 0\nx - -4 = 0\nx - 2/5 = 0\nx - 8 = 0\nx = -4\nx = 2/5\nx = 8"} {"input": "Determine x in 5x - 45 = 0", "output": "5x - 45 = 0\n5x = 45\nx = 45 / 5\nx = 9"} {"input": "Solve the equations:\n1x + 3y = -127/35\n3x + 8y = -341/35", "output": "1x + 3y = -127/35\n3x + 8y = -341/35\n\nUsing elimination\n3*(1x + 3y = -127/35)\n1*(3x + 8y = -341/35)\n3x + 9y = -381/35\n3x + 8y = -341/35\nSubtract equations\n1y = -8/7\ny = -8/7/1\ny = -8/7\n\nSubstitute y\n1x + 3(-8/7) = -127/35\n1x = -1/5\nx = -1/5/1\nx = -1/5"} {"input": "Find x in x^2 + 5/36x - 2/3 = 0", "output": "x^2 + 5/36x - 2/3 = 0\n(x - 3/4)(x - -8/9) = 0\nx - 3/4 = 0 or x - -8/9 = 0\nx = 3/4\nx = -8/9"} {"input": "Solve the equations:\n2x + 1y = 81/5\n7x + 9y = 289/5", "output": "2x + 1y = 81/5\n7x + 9y = 289/5\n\nUsing elimination\n7*(2x + 1y = 81/5)\n2*(7x + 9y = 289/5)\n14x + 7y = 567/5\n14x + 18y = 578/5\nSubtract equations\n-11y = -11/5\ny = -11/5/-11\ny = 1/5\n\nSubstitute y\n2x + 1(1/5) = 81/5\n2x = 16\nx = 16/2\nx = 8"} {"input": "Find x in 5x - 11/2 = 0", "output": "5x - 11/2 = 0\n5x = 11/2\nx = 11/2 / 5\nx = 11/10"} {"input": "Solve quickly: x^2 + 43/30x - 91/30 = 0", "output": "x^2 + 43/30x - 91/30 = 0\n(x - -13/5)(x - 7/6) = 0\nx - -13/5 = 0 or x - 7/6 = 0\nx = -13/5\nx = 7/6"} {"input": "Solve the equations:\n2x + 8y = 986/35\n7x + 3y = 1201/35", "output": "2x + 8y = 986/35\n7x + 3y = 1201/35\n\nUsing elimination\n7*(2x + 8y = 986/35)\n2*(7x + 3y = 1201/35)\n14x + 56y = 986/5\n14x + 6y = 2402/35\nSubtract equations\n50y = 900/7\ny = 900/7/50\ny = 18/7\n\nSubstitute y\n2x + 8(18/7) = 986/35\n2x = 38/5\nx = 38/5/2\nx = 19/5"} {"input": "Solve quickly: x^3 - 187/10x^2 + 123/10x + 27/5 = 0", "output": "x^3 - 187/10x^2 + 123/10x + 27/5 = 0\n(x - 1)(x - 18)(x - -3/10) = 0\nx - 1 = 0\nx - 18 = 0\nx - -3/10 = 0\nx = 1\nx = 18\nx = -3/10"} {"input": "Solve simultaneously:\n7x + 8y = 341/10\n5x + 8y = 271/10", "output": "7x + 8y = 341/10\n5x + 8y = 271/10\n\nUsing elimination\n5*(7x + 8y = 341/10)\n7*(5x + 8y = 271/10)\n35x + 40y = 341/2\n35x + 56y = 1897/10\nSubtract equations\n-16y = -96/5\ny = -96/5/-16\ny = 6/5\n\nSubstitute y\n7x + 8(6/5) = 341/10\n7x = 49/2\nx = 49/2/7\nx = 7/2"} {"input": "Solve the system:\n6x + 1y = -92/5\n7x + 3y = -611/30", "output": "6x + 1y = -92/5\n7x + 3y = -611/30\n\nUsing elimination\n7*(6x + 1y = -92/5)\n6*(7x + 3y = -611/30)\n42x + 7y = -644/5\n42x + 18y = -611/5\nSubtract equations\n-11y = -33/5\ny = -33/5/-11\ny = 3/5\n\nSubstitute y\n6x + 1(3/5) = -92/5\n6x = -19\nx = -19/6\nx = -19/6"} {"input": "Find x for x^2 + 1/4x - 15/8 = 0", "output": "x^2 + 1/4x - 15/8 = 0\n(x - -3/2)(x - 5/4) = 0\nx - -3/2 = 0 or x - 5/4 = 0\nx = -3/2\nx = 5/4"} {"input": "Solve quickly: x^3 - 14/5x^2 + 71/100x + 1/10 = 0", "output": "x^3 - 14/5x^2 + 71/100x + 1/10 = 0\n(x - 2/5)(x - -1/10)(x - 5/2) = 0\nx - 2/5 = 0\nx - -1/10 = 0\nx - 5/2 = 0\nx = 2/5\nx = -1/10\nx = 5/2"} {"input": "Solve x^3 + 11/8x^2 - 185/32x - 475/64 = 0", "output": "x^3 + 11/8x^2 - 185/32x - 475/64 = 0\n(x - 19/8)(x - -5/4)(x - -5/2) = 0\nx - 19/8 = 0\nx - -5/4 = 0\nx - -5/2 = 0\nx = 19/8\nx = -5/4\nx = -5/2"} {"input": "Determine x in x^3 + 101/5x^2 + 16/5x - 16 = 0", "output": "x^3 + 101/5x^2 + 16/5x - 16 = 0\n(x - 4/5)(x - -1)(x - -20) = 0\nx - 4/5 = 0\nx - -1 = 0\nx - -20 = 0\nx = 4/5\nx = -1\nx = -20"} {"input": "Determine x in 7x + 35 = 0", "output": "7x + 35 = 0\n7x = -35\nx = -35 / 7\nx = -5"} {"input": "Determine x in x^3 - 23/15x^2 - 304/15x = 0", "output": "x^3 - 23/15x^2 - 304/15x = 0\n(x - -19/5)(x - 0)(x - 16/3) = 0\nx - -19/5 = 0\nx - 0 = 0\nx - 16/3 = 0\nx = -19/5\nx = 0\nx = 16/3"} {"input": "Determine x in x^2 + 13/4x - 15/8 = 0", "output": "x^2 + 13/4x - 15/8 = 0\n(x - 1/2)(x - -15/4) = 0\nx - 1/2 = 0 or x - -15/4 = 0\nx = 1/2\nx = -15/4"} {"input": "Determine x in x^2 - 11/5x + 28/25 = 0", "output": "x^2 - 11/5x + 28/25 = 0\n(x - 7/5)(x - 4/5) = 0\nx - 7/5 = 0 or x - 4/5 = 0\nx = 7/5\nx = 4/5"} {"input": "Solve x^2 - 1/18x - 1/27 = 0", "output": "x^2 - 1/18x - 1/27 = 0\n(x - 2/9)(x - -1/6) = 0\nx - 2/9 = 0 or x - -1/6 = 0\nx = 2/9\nx = -1/6"} {"input": "What value of x satisfies x^2 + 2/5x - 8/25 = 0", "output": "x^2 + 2/5x - 8/25 = 0\n(x - -4/5)(x - 2/5) = 0\nx - -4/5 = 0 or x - 2/5 = 0\nx = -4/5\nx = 2/5"} {"input": "What value of x satisfies 2x - 8/3 = 0", "output": "2x - 8/3 = 0\n2x = 8/3\nx = 8/3 / 2\nx = 4/3"} {"input": "Determine x in x^2 - 1 = 0", "output": "x^2 - 1 = 0\n(x - -1)(x - 1) = 0\nx - -1 = 0 or x - 1 = 0\nx = -1\nx = 1"} {"input": "Find the solution to 9x + 27/2 = 0", "output": "9x + 27/2 = 0\n9x = -27/2\nx = -27/2 / 9\nx = -3/2"} {"input": "Solve quickly: 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Find the solution to x^3 + 40/21x^2 - 92/21x - 48/7 = 0", "output": "x^3 + 40/21x^2 - 92/21x - 48/7 = 0\n(x - -18/7)(x - -4/3)(x - 2) = 0\nx - -18/7 = 0\nx - -4/3 = 0\nx - 2 = 0\nx = -18/7\nx = -4/3\nx = 2"} {"input": "Find x for x^3 + 133/10x^2 + 261/5x + 567/10 = 0", "output": "x^3 + 133/10x^2 + 261/5x + 567/10 = 0\n(x - -9/2)(x - -7)(x - -9/5) = 0\nx - -9/2 = 0\nx - -7 = 0\nx - -9/5 = 0\nx = -9/2\nx = -7\nx = -9/5"} {"input": "Find x and y such that\n2x + 3y = 1/2\n4x + 8y = -5", "output": "2x + 3y = 1/2\n4x + 8y = -5\n\nUsing elimination\n4*(2x + 3y = 1/2)\n2*(4x + 8y = -5)\n8x + 12y = 2\n8x + 16y = -10\nSubtract equations\n-4y = 12\ny = 12/-4\ny = -3\n\nSubstitute y\n2x + 3(-3) = 1/2\n2x = 19/2\nx = 19/2/2\nx = 19/4"} {"input": "Find x for x^2 + 9/4x - 13/4 = 0", "output": "x^2 + 9/4x - 13/4 = 0\n(x - -13/4)(x - 1) = 0\nx - -13/4 = 0 or x - 1 = 0\nx = -13/4\nx = 1"} {"input": "Solve simultaneously:\n4x + 1y = -46/5\n5x + 5y = -17/2", "output": "4x + 1y = -46/5\n5x + 5y = -17/2\n\nUsing elimination\n5*(4x + 1y = -46/5)\n4*(5x + 5y = -17/2)\n20x + 5y = -46\n20x + 20y = -34\nSubtract equations\n-15y = -12\ny = -12/-15\ny = 4/5\n\nSubstitute y\n4x + 1(4/5) = -46/5\n4x = -10\nx = -10/4\nx = -5/2"} {"input": "Solve x^3 + 181/45x^2 + 2891/540x + 637/270 = 0", "output": "x^3 + 181/45x^2 + 2891/540x + 637/270 = 0\n(x - -13/10)(x - -7/6)(x - -14/9) = 0\nx - -13/10 = 0\nx - -7/6 = 0\nx - -14/9 = 0\nx = -13/10\nx = -7/6\nx = -14/9"} {"input": "Solve the equations:\n2x + 1y = -35/6\n2x + 6y = -25/2", "output": "2x + 1y = -35/6\n2x + 6y = -25/2\n\nUsing elimination\n2*(2x + 1y = -35/6)\n2*(2x + 6y = -25/2)\n4x + 2y = -35/3\n4x + 12y = -25\nSubtract equations\n-10y = 40/3\ny = 40/3/-10\ny = -4/3\n\nSubstitute y\n2x + 1(-4/3) = -35/6\n2x = -9/2\nx = -9/2/2\nx = -9/4"} {"input": "What value of x satisfies 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve quickly: 1x + 13/3 = 0", "output": "1x + 13/3 = 0\n1x = -13/3\nx = -13/3 / 1\nx = -13/3"} {"input": "Solve the equations:\n7x + 10y = 278/45\n10x + 10y = 88/9", "output": "7x + 10y = 278/45\n10x + 10y = 88/9\n\nUsing elimination\n10*(7x + 10y = 278/45)\n7*(10x + 10y = 88/9)\n70x + 100y = 556/9\n70x + 70y = 616/9\nSubtract equations\n30y = -20/3\ny = -20/3/30\ny = -2/9\n\nSubstitute y\n7x + 10(-2/9) = 278/45\n7x = 42/5\nx = 42/5/7\nx = 6/5"} {"input": "Determine x in x^2 - 5/2x - 25/2 = 0", "output": "x^2 - 5/2x - 25/2 = 0\n(x - 5)(x - -5/2) = 0\nx - 5 = 0 or x - -5/2 = 0\nx = 5\nx = -5/2"} {"input": "Solve the equation x^2 - 23/10x - 21/10 = 0", "output": "x^2 - 23/10x - 21/10 = 0\n(x - 3)(x - -7/10) = 0\nx - 3 = 0 or x - -7/10 = 0\nx = 3\nx = -7/10"} {"input": "Determine x in 6x - 9/2 = 0", "output": "6x - 9/2 = 0\n6x = 9/2\nx = 9/2 / 6\nx = 3/4"} {"input": "Compute the solution of 2x - 12/5 = 0", "output": "2x - 12/5 = 0\n2x = 12/5\nx = 12/5 / 2\nx = 6/5"} {"input": "What value of x satisfies 8x - 9 = 0", "output": "8x - 9 = 0\n8x = 9\nx = 9 / 8\nx = 9/8"} {"input": "Solve quickly: 3x - 6 = 0", "output": "3x - 6 = 0\n3x = 6\nx = 6 / 3\nx = 2"} {"input": "Find x and y such that\n3x + 3y = -19/3\n2x + 10y = 98/9", "output": "3x + 3y = -19/3\n2x + 10y = 98/9\n\nUsing elimination\n2*(3x + 3y = -19/3)\n3*(2x + 10y = 98/9)\n6x + 6y = -38/3\n6x + 30y = 98/3\nSubtract equations\n-24y = -136/3\ny = -136/3/-24\ny = 17/9\n\nSubstitute y\n3x + 3(17/9) = -19/3\n3x = -12\nx = -12/3\nx = -4"} {"input": "Solve x^3 - 88/15x^2 + 39/5x - 4/3 = 0", "output": "x^3 - 88/15x^2 + 39/5x - 4/3 = 0\n(x - 5/3)(x - 1/5)(x - 4) = 0\nx - 5/3 = 0\nx - 1/5 = 0\nx - 4 = 0\nx = 5/3\nx = 1/5\nx = 4"} {"input": "Solve quickly: 9x - 54/5 = 0", "output": "9x - 54/5 = 0\n9x = 54/5\nx = 54/5 / 9\nx = 6/5"} {"input": "Find x in x^3 - 13/4x^2 - 9/8x + 45/8 = 0", "output": "x^3 - 13/4x^2 - 9/8x + 45/8 = 0\n(x - 3)(x - -5/4)(x - 3/2) = 0\nx - 3 = 0\nx - -5/4 = 0\nx - 3/2 = 0\nx = 3\nx = -5/4\nx = 3/2"} {"input": "Solve simultaneously:\n8x + 4y = 56/3\n7x + 2y = 53/6", "output": "8x + 4y = 56/3\n7x + 2y = 53/6\n\nUsing elimination\n7*(8x + 4y = 56/3)\n8*(7x + 2y = 53/6)\n56x + 28y = 392/3\n56x + 16y = 212/3\nSubtract equations\n12y = 60\ny = 60/12\ny = 5\n\nSubstitute y\n8x + 4(5) = 56/3\n8x = -4/3\nx = -4/3/8\nx = -1/6"} {"input": "Solve quickly: x^3 - 353/15x^2 + 1076/15x - 64/3 = 0", "output": "x^3 - 353/15x^2 + 1076/15x - 64/3 = 0\n(x - 20)(x - 1/3)(x - 16/5) = 0\nx - 20 = 0\nx - 1/3 = 0\nx - 16/5 = 0\nx = 20\nx = 1/3\nx = 16/5"} {"input": "Solve quickly: x^3 - 29/8x^2 - 7/16x + 49/16 = 0", "output": "x^3 - 29/8x^2 - 7/16x + 49/16 = 0\n(x - 7/2)(x - 1)(x - -7/8) = 0\nx - 7/2 = 0\nx - 1 = 0\nx - -7/8 = 0\nx = 7/2\nx = 1\nx = -7/8"} {"input": "What value of x satisfies 4x - 20/7 = 0", "output": "4x - 20/7 = 0\n4x = 20/7\nx = 20/7 / 4\nx = 5/7"} {"input": "Solve simultaneously:\n3x + 4y = 40/9\n8x + 7y = 9", "output": "3x + 4y = 40/9\n8x + 7y = 9\n\nUsing elimination\n8*(3x + 4y = 40/9)\n3*(8x + 7y = 9)\n24x + 32y = 320/9\n24x + 21y = 27\nSubtract equations\n11y = 77/9\ny = 77/9/11\ny = 7/9\n\nSubstitute y\n3x + 4(7/9) = 40/9\n3x = 4/3\nx = 4/3/3\nx = 4/9"} {"input": "Compute the solution of 10x + 70/3 = 0", "output": "10x + 70/3 = 0\n10x = -70/3\nx = -70/3 / 10\nx = -7/3"} {"input": "Find x for 9x + 45 = 0", "output": "9x + 45 = 0\n9x = -45\nx = -45 / 9\nx = -5"} {"input": "Solve x^2 - 85/36x - 26/9 = 0", "output": "x^2 - 85/36x - 26/9 = 0\n(x - 13/4)(x - -8/9) = 0\nx - 13/4 = 0 or x - -8/9 = 0\nx = 13/4\nx = -8/9"} {"input": "Find x and y such that\n5x + 1y = -16/9\n10x + 9y = 346/9", "output": "5x + 1y = -16/9\n10x + 9y = 346/9\n\nUsing elimination\n10*(5x + 1y = -16/9)\n5*(10x + 9y = 346/9)\n50x + 10y = -160/9\n50x + 45y = 1730/9\nSubtract equations\n-35y = -210\ny = -210/-35\ny = 6\n\nSubstitute y\n5x + 1(6) = -16/9\n5x = -70/9\nx = -70/9/5\nx = -14/9"} {"input": "Find x for x^3 + 439/168x^2 - 151/56x - 143/21 = 0", "output": "x^3 + 439/168x^2 - 151/56x - 143/21 = 0\n(x - -8/3)(x - 13/8)(x - -11/7) = 0\nx - -8/3 = 0\nx - 13/8 = 0\nx - -11/7 = 0\nx = -8/3\nx = 13/8\nx = -11/7"} {"input": "Solve quickly: 8x + 15 = 0", "output": "8x + 15 = 0\n8x = -15\nx = -15 / 8\nx = -15/8"} {"input": "Solve the equations:\n9x + 5y = -15/2\n5x + 9y = -27/2", "output": "9x + 5y = -15/2\n5x + 9y = -27/2\n\nUsing elimination\n5*(9x + 5y = -15/2)\n9*(5x + 9y = -27/2)\n45x + 25y = -75/2\n45x + 81y = -243/2\nSubtract equations\n-56y = 84\ny = 84/-56\ny = -3/2\n\nSubstitute y\n9x + 5(-3/2) = -15/2\n9x = 0\nx = 0/9\nx = 0"} {"input": "Find the solution to x^2 + 29/5x - 6/5 = 0", "output": "x^2 + 29/5x - 6/5 = 0\n(x - 1/5)(x - -6) = 0\nx - 1/5 = 0 or x - -6 = 0\nx = 1/5\nx = -6"} {"input": "What value of x satisfies x^3 - 47/4x^2 + 213/8x + 27 = 0", "output": "x^3 - 47/4x^2 + 213/8x + 27 = 0\n(x - 9/2)(x - -3/4)(x - 8) = 0\nx - 9/2 = 0\nx - -3/4 = 0\nx - 8 = 0\nx = 9/2\nx = -3/4\nx = 8"} {"input": "What value of x satisfies 4x - 4/3 = 0", "output": "4x - 4/3 = 0\n4x = 4/3\nx = 4/3 / 4\nx = 1/3"} {"input": "Find x and y such that\n4x + 10y = 137/3\n1x + 9y = 122/3", "output": "4x + 10y = 137/3\n1x + 9y = 122/3\n\nUsing elimination\n1*(4x + 10y = 137/3)\n4*(1x + 9y = 122/3)\n4x + 10y = 137/3\n4x + 36y = 488/3\nSubtract equations\n-26y = -117\ny = -117/-26\ny = 9/2\n\nSubstitute y\n4x + 10(9/2) = 137/3\n4x = 2/3\nx = 2/3/4\nx = 1/6"} {"input": "Find x for x^2 - 9/8x - 9/16 = 0", "output": "x^2 - 9/8x - 9/16 = 0\n(x - -3/8)(x - 3/2) = 0\nx - -3/8 = 0 or x - 3/2 = 0\nx = -3/8\nx = 3/2"} {"input": "Solve simultaneously:\n9x + 5y = 381/4\n3x + 6y = 48", "output": "9x + 5y = 381/4\n3x + 6y = 48\n\nUsing elimination\n3*(9x + 5y = 381/4)\n9*(3x + 6y = 48)\n27x + 15y = 1143/4\n27x + 54y = 432\nSubtract equations\n-39y = -585/4\ny = -585/4/-39\ny = 15/4\n\nSubstitute y\n9x + 5(15/4) = 381/4\n9x = 153/2\nx = 153/2/9\nx = 17/2"} {"input": "Solve the equation 5x + 15 = 0", "output": "5x + 15 = 0\n5x = -15\nx = -15 / 5\nx = -3"} {"input": "Find the solution to x^2 - 100/21x - 64/21 = 0", "output": "x^2 - 100/21x - 64/21 = 0\n(x - 16/3)(x - -4/7) = 0\nx - 16/3 = 0 or x - -4/7 = 0\nx = 16/3\nx = -4/7"} {"input": "Find x and y such that\n2x + 2y = 64/15\n1x + 4y = 137/15", "output": "2x + 2y = 64/15\n1x + 4y = 137/15\n\nUsing elimination\n1*(2x + 2y = 64/15)\n2*(1x + 4y = 137/15)\n2x + 2y = 64/15\n2x + 8y = 274/15\nSubtract equations\n-6y = -14\ny = -14/-6\ny = 7/3\n\nSubstitute y\n2x + 2(7/3) = 64/15\n2x = -2/5\nx = -2/5/2\nx = -1/5"} {"input": "Solve quickly: x^3 - 3/5x^2 - 225/49x + 135/49 = 0", "output": "x^3 - 3/5x^2 - 225/49x + 135/49 = 0\n(x - 15/7)(x - 3/5)(x - -15/7) = 0\nx - 15/7 = 0\nx - 3/5 = 0\nx - -15/7 = 0\nx = 15/7\nx = 3/5\nx = -15/7"} {"input": "Solve the equation x^3 + 79/6x^2 - 571/18x - 190/3 = 0", "output": "x^3 + 79/6x^2 - 571/18x - 190/3 = 0\n(x - -15)(x - -4/3)(x - 19/6) = 0\nx - -15 = 0\nx - -4/3 = 0\nx - 19/6 = 0\nx = -15\nx = -4/3\nx = 19/6"} {"input": "What value of x satisfies x^3 - 22/45x^2 - 404/45x - 8 = 0", "output": "x^3 - 22/45x^2 - 404/45x - 8 = 0\n(x - -2)(x - -10/9)(x - 18/5) = 0\nx - -2 = 0\nx - -10/9 = 0\nx - 18/5 = 0\nx = -2\nx = -10/9\nx = 18/5"} {"input": "Solve the system:\n8x + 7y = 98/9\n8x + 2y = 956/63", "output": "8x + 7y = 98/9\n8x + 2y = 956/63\n\nUsing elimination\n8*(8x + 7y = 98/9)\n8*(8x + 2y = 956/63)\n64x + 56y = 784/9\n64x + 16y = 7648/63\nSubtract equations\n40y = -240/7\ny = -240/7/40\ny = -6/7\n\nSubstitute y\n8x + 7(-6/7) = 98/9\n8x = 152/9\nx = 152/9/8\nx = 19/9"} {"input": "What value of x satisfies x^2 - 51/14x + 1/2 = 0", "output": "x^2 - 51/14x + 1/2 = 0\n(x - 1/7)(x - 7/2) = 0\nx - 1/7 = 0 or x - 7/2 = 0\nx = 1/7\nx = 7/2"} {"input": "Solve 5x + 75/7 = 0", "output": "5x + 75/7 = 0\n5x = -75/7\nx = -75/7 / 5\nx = -15/7"} {"input": "Determine x in x^3 + 7x^2 - 1665/16x + 3825/16 = 0", "output": "x^3 + 7x^2 - 1665/16x + 3825/16 = 0\n(x - 17/4)(x - -15)(x - 15/4) = 0\nx - 17/4 = 0\nx - -15 = 0\nx - 15/4 = 0\nx = 17/4\nx = -15\nx = 15/4"} {"input": "Solve quickly: 7x - 56/9 = 0", "output": "7x - 56/9 = 0\n7x = 56/9\nx = 56/9 / 7\nx = 8/9"} {"input": "Solve the equation x^2 + 19x = 0", "output": "x^2 + 19x = 0\n(x - -19)(x - 0) = 0\nx - -19 = 0 or x - 0 = 0\nx = -19\nx = 0"} {"input": "Solve the equations:\n6x + 10y = 0\n7x + 5y = 0", "output": "6x + 10y = 0\n7x + 5y = 0\n\nUsing elimination\n7*(6x + 10y = 0)\n6*(7x + 5y = 0)\n42x + 70y = 0\n42x + 30y = 0\nSubtract equations\n40y = 0\ny = 0/40\ny = 0\n\nSubstitute y\n6x + 10(0) = 0\n6x = 0\nx = 0/6\nx = 0"} {"input": "Determine x in x^2 + 145/28x + 57/28 = 0", "output": "x^2 + 145/28x + 57/28 = 0\n(x - -19/4)(x - -3/7) = 0\nx - -19/4 = 0 or x - -3/7 = 0\nx = -19/4\nx = -3/7"} {"input": "What value of x satisfies 7x - 63/2 = 0", "output": "7x - 63/2 = 0\n7x = 63/2\nx = 63/2 / 7\nx = 9/2"} {"input": "Solve the equations:\n1x + 8y = 62/9\n2x + 10y = 64/9", "output": "1x + 8y = 62/9\n2x + 10y = 64/9\n\nUsing elimination\n2*(1x + 8y = 62/9)\n1*(2x + 10y = 64/9)\n2x + 16y = 124/9\n2x + 10y = 64/9\nSubtract equations\n6y = 20/3\ny = 20/3/6\ny = 10/9\n\nSubstitute y\n1x + 8(10/9) = 62/9\n1x = -2\nx = -2/1\nx = -2"} {"input": "Solve the equation x^3 + 101/15x^2 - 466/15x + 16 = 0", "output": "x^3 + 101/15x^2 - 466/15x + 16 = 0\n(x - 8/3)(x - 3/5)(x - -10) = 0\nx - 8/3 = 0\nx - 3/5 = 0\nx - -10 = 0\nx = 8/3\nx = 3/5\nx = -10"} {"input": "Determine x in x^3 - 35/6x^2 - 213/4x + 4199/24 = 0", "output": "x^3 - 35/6x^2 - 213/4x + 4199/24 = 0\n(x - -13/2)(x - 17/6)(x - 19/2) = 0\nx - -13/2 = 0\nx - 17/6 = 0\nx - 19/2 = 0\nx = -13/2\nx = 17/6\nx = 19/2"} {"input": "Solve the equation 3x - 57/4 = 0", "output": "3x - 57/4 = 0\n3x = 57/4\nx = 57/4 / 3\nx = 19/4"} {"input": "Solve the system:\n3x + 6y = -27/2\n7x + 2y = -33/2", "output": "3x + 6y = -27/2\n7x + 2y = -33/2\n\nUsing elimination\n7*(3x + 6y = -27/2)\n3*(7x + 2y = -33/2)\n21x + 42y = -189/2\n21x + 6y = -99/2\nSubtract equations\n36y = -45\ny = -45/36\ny = -5/4\n\nSubstitute y\n3x + 6(-5/4) = -27/2\n3x = -6\nx = -6/3\nx = -2"} {"input": "Solve the equations:\n1x + 8y = -295/24\n10x + 8y = -323/12", "output": "1x + 8y = -295/24\n10x + 8y = -323/12\n\nUsing elimination\n10*(1x + 8y = -295/24)\n1*(10x + 8y = -323/12)\n10x + 80y = -1475/12\n10x + 8y = -323/12\nSubtract equations\n72y = -96\ny = -96/72\ny = -4/3\n\nSubstitute y\n1x + 8(-4/3) = -295/24\n1x = -13/8\nx = -13/8/1\nx = -13/8"} {"input": "Find x and y such that\n9x + 1y = -45/8\n10x + 1y = -469/72", "output": "9x + 1y = -45/8\n10x + 1y = -469/72\n\nUsing elimination\n10*(9x + 1y = -45/8)\n9*(10x + 1y = -469/72)\n90x + 10y = -225/4\n90x + 9y = -469/8\nSubtract equations\n1y = 19/8\ny = 19/8/1\ny = 19/8\n\nSubstitute y\n9x + 1(19/8) = -45/8\n9x = -8\nx = -8/9\nx = -8/9"} {"input": "Find x and y such that\n2x + 3y = 59/14\n7x + 4y = 5", "output": "2x + 3y = 59/14\n7x + 4y = 5\n\nUsing elimination\n7*(2x + 3y = 59/14)\n2*(7x + 4y = 5)\n14x + 21y = 59/2\n14x + 8y = 10\nSubtract equations\n13y = 39/2\ny = 39/2/13\ny = 3/2\n\nSubstitute y\n2x + 3(3/2) = 59/14\n2x = -2/7\nx = -2/7/2\nx = -1/7"} {"input": "Compute the solution of x^2 + 9/2x + 5 = 0", "output": "x^2 + 9/2x + 5 = 0\n(x - -2)(x - -5/2) = 0\nx - -2 = 0 or x - -5/2 = 0\nx = -2\nx = -5/2"} {"input": "Find x and y such that\n4x + 3y = 41\n4x + 8y = 86", "output": "4x + 3y = 41\n4x + 8y = 86\n\nUsing elimination\n4*(4x + 3y = 41)\n4*(4x + 8y = 86)\n16x + 12y = 164\n16x + 32y = 344\nSubtract equations\n-20y = -180\ny = -180/-20\ny = 9\n\nSubstitute y\n4x + 3(9) = 41\n4x = 14\nx = 14/4\nx = 7/2"} {"input": "Determine x in 8x + 128/7 = 0", "output": "8x + 128/7 = 0\n8x = -128/7\nx = -128/7 / 8\nx = -16/7"} {"input": "Compute the solution of x^2 - 1/2x - 35/18 = 0", "output": "x^2 - 1/2x - 35/18 = 0\n(x - -7/6)(x - 5/3) = 0\nx - -7/6 = 0 or x - 5/3 = 0\nx = -7/6\nx = 5/3"} {"input": "Find the solution to x^2 - 11/5x + 6/5 = 0", "output": "x^2 - 11/5x + 6/5 = 0\n(x - 1)(x - 6/5) = 0\nx - 1 = 0 or x - 6/5 = 0\nx = 1\nx = 6/5"} {"input": "Find x for x^2 + 16x - 57 = 0", "output": "x^2 + 16x - 57 = 0\n(x - 3)(x - -19) = 0\nx - 3 = 0 or x - -19 = 0\nx = 3\nx = -19"} {"input": "Find x in 10x - 22 = 0", "output": "10x - 22 = 0\n10x = 22\nx = 22 / 10\nx = 11/5"} {"input": "Find x in 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Determine x in x^3 - 19/12x^2 - 37/8x + 91/12 = 0", "output": "x^3 - 19/12x^2 - 37/8x + 91/12 = 0\n(x - 7/4)(x - 2)(x - -13/6) = 0\nx - 7/4 = 0\nx - 2 = 0\nx - -13/6 = 0\nx = 7/4\nx = 2\nx = -13/6"} {"input": "Solve the equations:\n9x + 9y = 291/8\n1x + 3y = 59/8", "output": "9x + 9y = 291/8\n1x + 3y = 59/8\n\nUsing elimination\n1*(9x + 9y = 291/8)\n9*(1x + 3y = 59/8)\n9x + 9y = 291/8\n9x + 27y = 531/8\nSubtract equations\n-18y = -30\ny = -30/-18\ny = 5/3\n\nSubstitute y\n9x + 9(5/3) = 291/8\n9x = 171/8\nx = 171/8/9\nx = 19/8"} {"input": "Solve simultaneously:\n1x + 10y = 655/12\n9x + 6y = 173/4", "output": "1x + 10y = 655/12\n9x + 6y = 173/4\n\nUsing elimination\n9*(1x + 10y = 655/12)\n1*(9x + 6y = 173/4)\n9x + 90y = 1965/4\n9x + 6y = 173/4\nSubtract equations\n84y = 448\ny = 448/84\ny = 16/3\n\nSubstitute y\n1x + 10(16/3) = 655/12\n1x = 5/4\nx = 5/4/1\nx = 5/4"} {"input": "Find x in 9x - 9/10 = 0", "output": "9x - 9/10 = 0\n9x = 9/10\nx = 9/10 / 9\nx = 1/10"} {"input": "Solve simultaneously:\n5x + 10y = 125/4\n10x + 7y = 99/2", "output": "5x + 10y = 125/4\n10x + 7y = 99/2\n\nUsing elimination\n10*(5x + 10y = 125/4)\n5*(10x + 7y = 99/2)\n50x + 100y = 625/2\n50x + 35y = 495/2\nSubtract equations\n65y = 65\ny = 65/65\ny = 1\n\nSubstitute y\n5x + 10(1) = 125/4\n5x = 85/4\nx = 85/4/5\nx = 17/4"} {"input": "Find x for x^2 + 11/10x - 7/2 = 0", "output": "x^2 + 11/10x - 7/2 = 0\n(x - 7/5)(x - -5/2) = 0\nx - 7/5 = 0 or x - -5/2 = 0\nx = 7/5\nx = -5/2"} {"input": "Find x and y such that\n10x + 2y = 13/2\n5x + 9y = 117/4", "output": "10x + 2y = 13/2\n5x + 9y = 117/4\n\nUsing elimination\n5*(10x + 2y = 13/2)\n10*(5x + 9y = 117/4)\n50x + 10y = 65/2\n50x + 90y = 585/2\nSubtract equations\n-80y = -260\ny = -260/-80\ny = 13/4\n\nSubstitute y\n10x + 2(13/4) = 13/2\n10x = 0\nx = 0/10\nx = 0"} {"input": "Find x for 6x + 9/4 = 0", "output": "6x + 9/4 = 0\n6x = -9/4\nx = -9/4 / 6\nx = -3/8"} {"input": "What value of x satisfies 5x + 11/2 = 0", "output": "5x + 11/2 = 0\n5x = -11/2\nx = -11/2 / 5\nx = -11/10"} {"input": "What value of x satisfies x^2 - 38/15x - 39/5 = 0", "output": "x^2 - 38/15x - 39/5 = 0\n(x - 13/3)(x - -9/5) = 0\nx - 13/3 = 0 or x - -9/5 = 0\nx = 13/3\nx = -9/5"} {"input": "Find x in x^3 + 223/120x^2 + 27/40x - 27/160 = 0", "output": "x^3 + 223/120x^2 + 27/40x - 27/160 = 0\n(x - 1/6)(x - -9/8)(x - -9/10) = 0\nx - 1/6 = 0\nx - -9/8 = 0\nx - -9/10 = 0\nx = 1/6\nx = -9/8\nx = -9/10"} {"input": "Solve quickly: x^3 - 131/120x^2 - 121/240x + 21/40 = 0", "output": "x^3 - 131/120x^2 - 121/240x + 21/40 = 0\n(x - -7/10)(x - 2/3)(x - 9/8) = 0\nx - -7/10 = 0\nx - 2/3 = 0\nx - 9/8 = 0\nx = -7/10\nx = 2/3\nx = 9/8"} {"input": "Solve quickly: x^3 + 225/7x^2 + 1574/7x - 3744/7 = 0", "output": "x^3 + 225/7x^2 + 1574/7x - 3744/7 = 0\n(x - 13/7)(x - -16)(x - -18) = 0\nx - 13/7 = 0\nx - -16 = 0\nx - -18 = 0\nx = 13/7\nx = -16\nx = -18"} {"input": "Find x for x^2 + 16/5x - 36/25 = 0", "output": "x^2 + 16/5x - 36/25 = 0\n(x - -18/5)(x - 2/5) = 0\nx - -18/5 = 0 or x - 2/5 = 0\nx = -18/5\nx = 2/5"} {"input": "What value of x satisfies x^3 - 9/2x^2 - 99/2x + 81 = 0", "output": "x^3 - 9/2x^2 - 99/2x + 81 = 0\n(x - 9)(x - -6)(x - 3/2) = 0\nx - 9 = 0\nx - -6 = 0\nx - 3/2 = 0\nx = 9\nx = -6\nx = 3/2"} {"input": "Solve simultaneously:\n6x + 9y = 177/7\n7x + 3y = 199/7", "output": "6x + 9y = 177/7\n7x + 3y = 199/7\n\nUsing elimination\n7*(6x + 9y = 177/7)\n6*(7x + 3y = 199/7)\n42x + 63y = 177\n42x + 18y = 1194/7\nSubtract equations\n45y = 45/7\ny = 45/7/45\ny = 1/7\n\nSubstitute y\n6x + 9(1/7) = 177/7\n6x = 24\nx = 24/6\nx = 4"} {"input": "Solve quickly: x^2 - 34/5x + 9 = 0", "output": "x^2 - 34/5x + 9 = 0\n(x - 5)(x - 9/5) = 0\nx - 5 = 0 or x - 9/5 = 0\nx = 5\nx = 9/5"} {"input": "Find x in x^3 + 37/8x^2 + 17/8x - 3/2 = 0", "output": "x^3 + 37/8x^2 + 17/8x - 3/2 = 0\n(x - -1)(x - -4)(x - 3/8) = 0\nx - -1 = 0\nx - -4 = 0\nx - 3/8 = 0\nx = -1\nx = -4\nx = 3/8"} {"input": "Solve quickly: 3x - 19 = 0", "output": "3x - 19 = 0\n3x = 19\nx = 19 / 3\nx = 19/3"} {"input": "Solve quickly: x^3 + 749/90x^2 + 343/18x + 110/9 = 0", "output": "x^3 + 749/90x^2 + 343/18x + 110/9 = 0\n(x - -5)(x - -20/9)(x - -11/10) = 0\nx - -5 = 0\nx - -20/9 = 0\nx - -11/10 = 0\nx = -5\nx = -20/9\nx = -11/10"} {"input": "What value of x satisfies x^2 + 31/7x - 20/7 = 0", "output": "x^2 + 31/7x - 20/7 = 0\n(x - 4/7)(x - -5) = 0\nx - 4/7 = 0 or x - -5 = 0\nx = 4/7\nx = -5"} {"input": "What value of x satisfies 4x - 14/3 = 0", "output": "4x - 14/3 = 0\n4x = 14/3\nx = 14/3 / 4\nx = 7/6"} {"input": "Solve simultaneously:\n1x + 3y = 35/2\n4x + 9y = 53", "output": "1x + 3y = 35/2\n4x + 9y = 53\n\nUsing elimination\n4*(1x + 3y = 35/2)\n1*(4x + 9y = 53)\n4x + 12y = 70\n4x + 9y = 53\nSubtract equations\n3y = 17\ny = 17/3\ny = 17/3\n\nSubstitute y\n1x + 3(17/3) = 35/2\n1x = 1/2\nx = 1/2/1\nx = 1/2"} {"input": "Find x and y such that\n1x + 8y = -149/7\n9x + 10y = -783/7", "output": "1x + 8y = -149/7\n9x + 10y = -783/7\n\nUsing elimination\n9*(1x + 8y = -149/7)\n1*(9x + 10y = -783/7)\n9x + 72y = -1341/7\n9x + 10y = -783/7\nSubtract equations\n62y = -558/7\ny = -558/7/62\ny = -9/7\n\nSubstitute y\n1x + 8(-9/7) = -149/7\n1x = -11\nx = -11/1\nx = -11"} {"input": "Compute the solution of 7x - 28/3 = 0", "output": "7x - 28/3 = 0\n7x = 28/3\nx = 28/3 / 7\nx = 4/3"} {"input": "Solve the equation x^3 + 1/9x^2 - 2125/36x + 3757/36 = 0", "output": "x^3 + 1/9x^2 - 2125/36x + 3757/36 = 0\n(x - -17/2)(x - 13/2)(x - 17/9) = 0\nx - -17/2 = 0\nx - 13/2 = 0\nx - 17/9 = 0\nx = -17/2\nx = 13/2\nx = 17/9"} {"input": "Find the solution to x^2 + 23/3x - 85/12 = 0", "output": "x^2 + 23/3x - 85/12 = 0\n(x - -17/2)(x - 5/6) = 0\nx - -17/2 = 0 or x - 5/6 = 0\nx = -17/2\nx = 5/6"} {"input": "Find x for x^3 + 47/36x^2 - 19/3x - 15/4 = 0", "output": "x^3 + 47/36x^2 - 19/3x - 15/4 = 0\n(x - -5/9)(x - -3)(x - 9/4) = 0\nx - -5/9 = 0\nx - -3 = 0\nx - 9/4 = 0\nx = -5/9\nx = -3\nx = 9/4"} {"input": "Compute the solution of x^3 + 169/36x^2 - 91/6x + 245/36 = 0", "output": "x^3 + 169/36x^2 - 91/6x + 245/36 = 0\n(x - 7/4)(x - 5/9)(x - -7) = 0\nx - 7/4 = 0\nx - 5/9 = 0\nx - -7 = 0\nx = 7/4\nx = 5/9\nx = -7"} {"input": "What value of x satisfies 8x - 12 = 0", "output": "8x - 12 = 0\n8x = 12\nx = 12 / 8\nx = 3/2"} {"input": "Compute the solution of x^2 + 136/7x + 180/7 = 0", "output": "x^2 + 136/7x + 180/7 = 0\n(x - -18)(x - -10/7) = 0\nx - -18 = 0 or x - -10/7 = 0\nx = -18\nx = -10/7"} {"input": "Solve the equation x^2 - 16/3x + 16/3 = 0", "output": "x^2 - 16/3x + 16/3 = 0\n(x - 4/3)(x - 4) = 0\nx - 4/3 = 0 or x - 4 = 0\nx = 4/3\nx = 4"} {"input": "Solve the equation 7x - 112/5 = 0", "output": "7x - 112/5 = 0\n7x = 112/5\nx = 112/5 / 7\nx = 16/5"} {"input": "Solve the system:\n3x + 5y = -2/3\n2x + 3y = -23/45", "output": "3x + 5y = -2/3\n2x + 3y = -23/45\n\nUsing elimination\n2*(3x + 5y = -2/3)\n3*(2x + 3y = -23/45)\n6x + 10y = -4/3\n6x + 9y = -23/15\nSubtract equations\n1y = 1/5\ny = 1/5/1\ny = 1/5\n\nSubstitute y\n3x + 5(1/5) = -2/3\n3x = -5/3\nx = -5/3/3\nx = -5/9"} {"input": "Determine x in x^2 + 35/2x + 117/2 = 0", "output": "x^2 + 35/2x + 117/2 = 0\n(x - -13)(x - -9/2) = 0\nx - -13 = 0 or x - -9/2 = 0\nx = -13\nx = -9/2"} {"input": "Solve the equation 3x + 21 = 0", "output": "3x + 21 = 0\n3x = -21\nx = -21 / 3\nx = -7"} {"input": "Solve the system:\n5x + 4y = 133/6\n3x + 8y = 49/2", "output": "5x + 4y = 133/6\n3x + 8y = 49/2\n\nUsing elimination\n3*(5x + 4y = 133/6)\n5*(3x + 8y = 49/2)\n15x + 12y = 133/2\n15x + 40y = 245/2\nSubtract equations\n-28y = -56\ny = -56/-28\ny = 2\n\nSubstitute y\n5x + 4(2) = 133/6\n5x = 85/6\nx = 85/6/5\nx = 17/6"} {"input": "Find x for x^2 - 1/6x - 5/2 = 0", "output": "x^2 - 1/6x - 5/2 = 0\n(x - 5/3)(x - -3/2) = 0\nx - 5/3 = 0 or x - -3/2 = 0\nx = 5/3\nx = -3/2"} {"input": "Solve quickly: x^3 + 2/5x^2 - 279/25x + 324/25 = 0", "output": "x^3 + 2/5x^2 - 279/25x + 324/25 = 0\n(x - 9/5)(x - 9/5)(x - -4) = 0\nx - 9/5 = 0\nx - 9/5 = 0\nx - -4 = 0\nx = 9/5\nx = 9/5\nx = -4"} {"input": "Solve x^3 + 127/6x^2 + 305/3x + 275/2 = 0", "output": "x^3 + 127/6x^2 + 305/3x + 275/2 = 0\n(x - -5/2)(x - -11/3)(x - -15) = 0\nx - -5/2 = 0\nx - -11/3 = 0\nx - -15 = 0\nx = -5/2\nx = -11/3\nx = -15"} {"input": "Solve the equation x^2 - 17/3x = 0", "output": "x^2 - 17/3x = 0\n(x - 17/3)(x - 0) = 0\nx - 17/3 = 0 or x - 0 = 0\nx = 17/3\nx = 0"} {"input": "Find x and y such that\n4x + 1y = 7/4\n4x + 6y = 21/2", "output": "4x + 1y = 7/4\n4x + 6y = 21/2\n\nUsing elimination\n4*(4x + 1y = 7/4)\n4*(4x + 6y = 21/2)\n16x + 4y = 7\n16x + 24y = 42\nSubtract equations\n-20y = -35\ny = -35/-20\ny = 7/4\n\nSubstitute y\n4x + 1(7/4) = 7/4\n4x = 0\nx = 0/4\nx = 0"} {"input": "Find x for 10x - 140/3 = 0", "output": "10x - 140/3 = 0\n10x = 140/3\nx = 140/3 / 10\nx = 14/3"} {"input": "Solve the equations:\n5x + 4y = -27/2\n3x + 6y = -333/20", "output": "5x + 4y = -27/2\n3x + 6y = -333/20\n\nUsing elimination\n3*(5x + 4y = -27/2)\n5*(3x + 6y = -333/20)\n15x + 12y = -81/2\n15x + 30y = -333/4\nSubtract equations\n-18y = 171/4\ny = 171/4/-18\ny = -19/8\n\nSubstitute y\n5x + 4(-19/8) = -27/2\n5x = -4\nx = -4/5\nx = -4/5"} {"input": "Find x and y such that\n9x + 7y = -247/3\n7x + 3y = -51", "output": "9x + 7y = -247/3\n7x + 3y = -51\n\nUsing elimination\n7*(9x + 7y = -247/3)\n9*(7x + 3y = -51)\n63x + 49y = -1729/3\n63x + 27y = -459\nSubtract equations\n22y = -352/3\ny = -352/3/22\ny = -16/3\n\nSubstitute y\n9x + 7(-16/3) = -247/3\n9x = -45\nx = -45/9\nx = -5"} {"input": "Find x in x^2 - 4/9x = 0", "output": "x^2 - 4/9x = 0\n(x - 4/9)(x - 0) = 0\nx - 4/9 = 0 or x - 0 = 0\nx = 4/9\nx = 0"} {"input": "Solve x^3 + 16/3x^2 - 80/9x = 0", "output": "x^3 + 16/3x^2 - 80/9x = 0\n(x - 4/3)(x - 0)(x - -20/3) = 0\nx - 4/3 = 0\nx - 0 = 0\nx - -20/3 = 0\nx = 4/3\nx = 0\nx = -20/3"} {"input": "Compute the solution of x^3 - 67/30x^2 - 149/30x + 28/15 = 0", "output": "x^3 - 67/30x^2 - 149/30x + 28/15 = 0\n(x - -8/5)(x - 7/2)(x - 1/3) = 0\nx - -8/5 = 0\nx - 7/2 = 0\nx - 1/3 = 0\nx = -8/5\nx = 7/2\nx = 1/3"} {"input": "Solve the system:\n2x + 7y = -327/28\n6x + 2y = -25/14", "output": "2x + 7y = -327/28\n6x + 2y = -25/14\n\nUsing elimination\n6*(2x + 7y = -327/28)\n2*(6x + 2y = -25/14)\n12x + 42y = -981/14\n12x + 4y = -25/7\nSubtract equations\n38y = -133/2\ny = -133/2/38\ny = -7/4\n\nSubstitute y\n2x + 7(-7/4) = -327/28\n2x = 4/7\nx = 4/7/2\nx = 2/7"} {"input": "Solve the equation x^2 - 20/3x - 187/12 = 0", "output": "x^2 - 20/3x - 187/12 = 0\n(x - 17/2)(x - -11/6) = 0\nx - 17/2 = 0 or x - -11/6 = 0\nx = 17/2\nx = -11/6"} {"input": "Solve the equation 9x - 3/2 = 0", "output": "9x - 3/2 = 0\n9x = 3/2\nx = 3/2 / 9\nx = 1/6"} {"input": "Solve the equations:\n3x + 2y = -123/10\n9x + 9y = -963/20", "output": "3x + 2y = -123/10\n9x + 9y = -963/20\n\nUsing elimination\n9*(3x + 2y = -123/10)\n3*(9x + 9y = -963/20)\n27x + 18y = -1107/10\n27x + 27y = -2889/20\nSubtract equations\n-9y = 135/4\ny = 135/4/-9\ny = -15/4\n\nSubstitute y\n3x + 2(-15/4) = -123/10\n3x = -24/5\nx = -24/5/3\nx = -8/5"} {"input": "Find x and y such that\n9x + 9y = -39/2\n3x + 4y = -23/3", "output": "9x + 9y = -39/2\n3x + 4y = -23/3\n\nUsing elimination\n3*(9x + 9y = -39/2)\n9*(3x + 4y = -23/3)\n27x + 27y = -117/2\n27x + 36y = -69\nSubtract equations\n-9y = 21/2\ny = 21/2/-9\ny = -7/6\n\nSubstitute y\n9x + 9(-7/6) = -39/2\n9x = -9\nx = -9/9\nx = -1"} {"input": "Solve the equations:\n4x + 9y = -37\n10x + 8y = -109/4", "output": "4x + 9y = -37\n10x + 8y = -109/4\n\nUsing elimination\n10*(4x + 9y = -37)\n4*(10x + 8y = -109/4)\n40x + 90y = -370\n40x + 32y = -109\nSubtract equations\n58y = -261\ny = -261/58\ny = -9/2\n\nSubstitute y\n4x + 9(-9/2) = -37\n4x = 7/2\nx = 7/2/4\nx = 7/8"} {"input": "Find x in 8x - 24 = 0", "output": "8x - 24 = 0\n8x = 24\nx = 24 / 8\nx = 3"} {"input": "Solve the equations:\n4x + 5y = -141/8\n8x + 9y = -289/8", "output": "4x + 5y = -141/8\n8x + 9y = -289/8\n\nUsing elimination\n8*(4x + 5y = -141/8)\n4*(8x + 9y = -289/8)\n32x + 40y = -141\n32x + 36y = -289/2\nSubtract equations\n4y = 7/2\ny = 7/2/4\ny = 7/8\n\nSubstitute y\n4x + 5(7/8) = -141/8\n4x = -22\nx = -22/4\nx = -11/2"} {"input": "Solve the equation 4x - 48 = 0", "output": "4x - 48 = 0\n4x = 48\nx = 48 / 4\nx = 12"} {"input": "Compute the solution of x^2 + 133/8x - 51/8 = 0", "output": "x^2 + 133/8x - 51/8 = 0\n(x - -17)(x - 3/8) = 0\nx - -17 = 0 or x - 3/8 = 0\nx = -17\nx = 3/8"} {"input": "What value of x satisfies x^2 + 43/7x + 40/7 = 0", "output": "x^2 + 43/7x + 40/7 = 0\n(x - -8/7)(x - -5) = 0\nx - -8/7 = 0 or x - -5 = 0\nx = -8/7\nx = -5"} {"input": "What value of x satisfies 1x + 8/7 = 0", "output": "1x + 8/7 = 0\n1x = -8/7\nx = -8/7 / 1\nx = -8/7"} {"input": "Compute the solution of x^2 - 5x + 6 = 0", "output": "x^2 - 5x + 6 = 0\n(x - 3)(x - 2) = 0\nx - 3 = 0 or x - 2 = 0\nx = 3\nx = 2"} {"input": "Solve simultaneously:\n8x + 8y = 116/5\n2x + 9y = -19/10", "output": "8x + 8y = 116/5\n2x + 9y = -19/10\n\nUsing elimination\n2*(8x + 8y = 116/5)\n8*(2x + 9y = -19/10)\n16x + 16y = 232/5\n16x + 72y = -76/5\nSubtract equations\n-56y = 308/5\ny = 308/5/-56\ny = -11/10\n\nSubstitute y\n8x + 8(-11/10) = 116/5\n8x = 32\nx = 32/8\nx = 4"} {"input": "Determine x in x^2 + 3/8x - 119/32 = 0", "output": "x^2 + 3/8x - 119/32 = 0\n(x - -17/8)(x - 7/4) = 0\nx - -17/8 = 0 or x - 7/4 = 0\nx = -17/8\nx = 7/4"} {"input": "Solve the system:\n8x + 4y = 110/3\n2x + 6y = 5", "output": "8x + 4y = 110/3\n2x + 6y = 5\n\nUsing elimination\n2*(8x + 4y = 110/3)\n8*(2x + 6y = 5)\n16x + 8y = 220/3\n16x + 48y = 40\nSubtract equations\n-40y = 100/3\ny = 100/3/-40\ny = -5/6\n\nSubstitute y\n8x + 4(-5/6) = 110/3\n8x = 40\nx = 40/8\nx = 5"} {"input": "Find x for 1x + 11/8 = 0", "output": "1x + 11/8 = 0\n1x = -11/8\nx = -11/8 / 1\nx = -11/8"} {"input": "Solve x^2 - 9/2x = 0", "output": "x^2 - 9/2x = 0\n(x - 0)(x - 9/2) = 0\nx - 0 = 0 or x - 9/2 = 0\nx = 0\nx = 9/2"} {"input": "What value of x satisfies x^3 - 407/24x^2 + 359/12x - 65/8 = 0", "output": "x^3 - 407/24x^2 + 359/12x - 65/8 = 0\n(x - 15)(x - 1/3)(x - 13/8) = 0\nx - 15 = 0\nx - 1/3 = 0\nx - 13/8 = 0\nx = 15\nx = 1/3\nx = 13/8"} {"input": "What value of x satisfies x^3 + 201/35x^2 + 19/5x + 3/7 = 0", "output": "x^3 + 201/35x^2 + 19/5x + 3/7 = 0\n(x - -3/5)(x - -5)(x - -1/7) = 0\nx - -3/5 = 0\nx - -5 = 0\nx - -1/7 = 0\nx = -3/5\nx = -5\nx = -1/7"} {"input": "Solve simultaneously:\n4x + 3y = -25/14\n7x + 3y = -373/56", "output": "4x + 3y = -25/14\n7x + 3y = -373/56\n\nUsing elimination\n7*(4x + 3y = -25/14)\n4*(7x + 3y = -373/56)\n28x + 21y = -25/2\n28x + 12y = -373/14\nSubtract equations\n9y = 99/7\ny = 99/7/9\ny = 11/7\n\nSubstitute y\n4x + 3(11/7) = -25/14\n4x = -13/2\nx = -13/2/4\nx = -13/8"} {"input": "Compute the solution of x^3 - 8x^2 + 1367/81x - 760/81 = 0", "output": "x^3 - 8x^2 + 1367/81x - 760/81 = 0\n(x - 8/9)(x - 5)(x - 19/9) = 0\nx - 8/9 = 0\nx - 5 = 0\nx - 19/9 = 0\nx = 8/9\nx = 5\nx = 19/9"} {"input": "What value of x satisfies x^2 - 55/12x - 4 = 0", "output": "x^2 - 55/12x - 4 = 0\n(x - -3/4)(x - 16/3) = 0\nx - -3/4 = 0 or x - 16/3 = 0\nx = -3/4\nx = 16/3"} {"input": "Solve simultaneously:\n6x + 10y = -400/3\n10x + 1y = -604/3", "output": "6x + 10y = -400/3\n10x + 1y = -604/3\n\nUsing elimination\n10*(6x + 10y = -400/3)\n6*(10x + 1y = -604/3)\n60x + 100y = -4000/3\n60x + 6y = -1208\nSubtract equations\n94y = -376/3\ny = -376/3/94\ny = -4/3\n\nSubstitute y\n6x + 10(-4/3) = -400/3\n6x = -120\nx = -120/6\nx = -20"} {"input": "Find x in 8x + 76 = 0", "output": "8x + 76 = 0\n8x = -76\nx = -76 / 8\nx = -19/2"} {"input": "Solve the system:\n2x + 4y = 79/6\n8x + 5y = 703/24", "output": "2x + 4y = 79/6\n8x + 5y = 703/24\n\nUsing elimination\n8*(2x + 4y = 79/6)\n2*(8x + 5y = 703/24)\n16x + 32y = 316/3\n16x + 10y = 703/12\nSubtract equations\n22y = 187/4\ny = 187/4/22\ny = 17/8\n\nSubstitute y\n2x + 4(17/8) = 79/6\n2x = 14/3\nx = 14/3/2\nx = 7/3"} {"input": "What value of x satisfies x^3 + 67/15x^2 + 4x - 28/15 = 0", "output": "x^3 + 67/15x^2 + 4x - 28/15 = 0\n(x - 1/3)(x - -14/5)(x - -2) = 0\nx - 1/3 = 0\nx - -14/5 = 0\nx - -2 = 0\nx = 1/3\nx = -14/5\nx = -2"} {"input": "Determine x in 9x + 45/4 = 0", "output": "9x + 45/4 = 0\n9x = -45/4\nx = -45/4 / 9\nx = -5/4"} {"input": "Find the solution to x^2 - 77/30x - 17/6 = 0", "output": "x^2 - 77/30x - 17/6 = 0\n(x - 17/5)(x - -5/6) = 0\nx - 17/5 = 0 or x - -5/6 = 0\nx = 17/5\nx = -5/6"} {"input": "Solve quickly: x^2 + 9x + 17/4 = 0", "output": "x^2 + 9x + 17/4 = 0\n(x - -1/2)(x - -17/2) = 0\nx - -1/2 = 0 or x - -17/2 = 0\nx = -1/2\nx = -17/2"} {"input": "Solve the equations:\n5x + 2y = 81/28\n2x + 6y = -15/14", "output": "5x + 2y = 81/28\n2x + 6y = -15/14\n\nUsing elimination\n2*(5x + 2y = 81/28)\n5*(2x + 6y = -15/14)\n10x + 4y = 81/14\n10x + 30y = -75/14\nSubtract equations\n-26y = 78/7\ny = 78/7/-26\ny = -3/7\n\nSubstitute y\n5x + 2(-3/7) = 81/28\n5x = 15/4\nx = 15/4/5\nx = 3/4"} {"input": "What value of x satisfies x^3 + 139/72x^2 - 479/27x + 4199/216 = 0", "output": "x^3 + 139/72x^2 - 479/27x + 4199/216 = 0\n(x - 19/9)(x - -17/3)(x - 13/8) = 0\nx - 19/9 = 0\nx - -17/3 = 0\nx - 13/8 = 0\nx = 19/9\nx = -17/3\nx = 13/8"} {"input": "Determine x in x^3 - 77/18x^2 - 1x = 0", "output": "x^3 - 77/18x^2 - 1x = 0\n(x - -2/9)(x - 0)(x - 9/2) = 0\nx - -2/9 = 0\nx - 0 = 0\nx - 9/2 = 0\nx = -2/9\nx = 0\nx = 9/2"} {"input": "Find the solution to 3x - 10/3 = 0", "output": "3x - 10/3 = 0\n3x = 10/3\nx = 10/3 / 3\nx = 10/9"} {"input": "Compute the solution of x^3 - 3x^2 - 46x - 72 = 0", "output": "x^3 - 3x^2 - 46x - 72 = 0\n(x - -2)(x - 9)(x - -4) = 0\nx - -2 = 0\nx - 9 = 0\nx - -4 = 0\nx = -2\nx = 9\nx = -4"} {"input": "Find the solution to x^3 + 17/6x^2 + 325/162x + 34/81 = 0", "output": "x^3 + 17/6x^2 + 325/162x + 34/81 = 0\n(x - -1/2)(x - -4/9)(x - -17/9) = 0\nx - -1/2 = 0\nx - -4/9 = 0\nx - -17/9 = 0\nx = -1/2\nx = -4/9\nx = -17/9"} {"input": "Determine x in 9x + 12 = 0", "output": "9x + 12 = 0\n9x = -12\nx = -12 / 9\nx = -4/3"} {"input": "Find the solution to 10x + 80/9 = 0", "output": "10x + 80/9 = 0\n10x = -80/9\nx = -80/9 / 10\nx = -8/9"} {"input": "Compute the solution of x^3 - 151/18x^2 + 40/9x + 50/3 = 0", "output": "x^3 - 151/18x^2 + 40/9x + 50/3 = 0\n(x - 15/2)(x - -10/9)(x - 2) = 0\nx - 15/2 = 0\nx - -10/9 = 0\nx - 2 = 0\nx = 15/2\nx = -10/9\nx = 2"} {"input": "Find x in x^2 + 12/5x = 0", "output": "x^2 + 12/5x = 0\n(x - 0)(x - -12/5) = 0\nx - 0 = 0 or x - -12/5 = 0\nx = 0\nx = -12/5"} {"input": "Solve quickly: x^3 + 175/12x^2 + 1279/24x + 95/2 = 0", "output": "x^3 + 175/12x^2 + 1279/24x + 95/2 = 0\n(x - -4/3)(x - -15/4)(x - -19/2) = 0\nx - -4/3 = 0\nx - -15/4 = 0\nx - -19/2 = 0\nx = -4/3\nx = -15/4\nx = -19/2"} {"input": "Solve the equation x^2 + 29/2x + 39/2 = 0", "output": "x^2 + 29/2x + 39/2 = 0\n(x - -13)(x - -3/2) = 0\nx - -13 = 0 or x - -3/2 = 0\nx = -13\nx = -3/2"} {"input": "Solve the equation x^3 - 6x^2 + 323/36x = 0", "output": "x^3 - 6x^2 + 323/36x = 0\n(x - 0)(x - 19/6)(x - 17/6) = 0\nx - 0 = 0\nx - 19/6 = 0\nx - 17/6 = 0\nx = 0\nx = 19/6\nx = 17/6"} {"input": "Solve quickly: x^3 - 152/21x^2 + 148/9x - 80/7 = 0", "output": "x^3 - 152/21x^2 + 148/9x - 80/7 = 0\n(x - 10/3)(x - 18/7)(x - 4/3) = 0\nx - 10/3 = 0\nx - 18/7 = 0\nx - 4/3 = 0\nx = 10/3\nx = 18/7\nx = 4/3"} {"input": "Solve the equations:\n3x + 5y = -37/4\n7x + 5y = -33/4", "output": "3x + 5y = -37/4\n7x + 5y = -33/4\n\nUsing elimination\n7*(3x + 5y = -37/4)\n3*(7x + 5y = -33/4)\n21x + 35y = -259/4\n21x + 15y = -99/4\nSubtract equations\n20y = -40\ny = -40/20\ny = -2\n\nSubstitute y\n3x + 5(-2) = -37/4\n3x = 3/4\nx = 3/4/3\nx = 1/4"} {"input": "Find x and y such that\n5x + 2y = 18/5\n10x + 6y = 49/5", "output": "5x + 2y = 18/5\n10x + 6y = 49/5\n\nUsing elimination\n10*(5x + 2y = 18/5)\n5*(10x + 6y = 49/5)\n50x + 20y = 36\n50x + 30y = 49\nSubtract equations\n-10y = -13\ny = -13/-10\ny = 13/10\n\nSubstitute y\n5x + 2(13/10) = 18/5\n5x = 1\nx = 1/5\nx = 1/5"} {"input": "Solve simultaneously:\n10x + 2y = -29/9\n9x + 8y = -6", "output": "10x + 2y = -29/9\n9x + 8y = -6\n\nUsing elimination\n9*(10x + 2y = -29/9)\n10*(9x + 8y = -6)\n90x + 18y = -29\n90x + 80y = -60\nSubtract equations\n-62y = 31\ny = 31/-62\ny = -1/2\n\nSubstitute y\n10x + 2(-1/2) = -29/9\n10x = -20/9\nx = -20/9/10\nx = -2/9"} {"input": "Find x in x^2 - 4/9 = 0", "output": "x^2 - 4/9 = 0\n(x - 2/3)(x - -2/3) = 0\nx - 2/3 = 0 or x - -2/3 = 0\nx = 2/3\nx = -2/3"} {"input": "Find the solution to x^2 - 6x - 7 = 0", "output": "x^2 - 6x - 7 = 0\n(x - -1)(x - 7) = 0\nx - -1 = 0 or x - 7 = 0\nx = -1\nx = 7"} {"input": "Solve the equations:\n9x + 10y = 241\n6x + 5y = 129", "output": "9x + 10y = 241\n6x + 5y = 129\n\nUsing elimination\n6*(9x + 10y = 241)\n9*(6x + 5y = 129)\n54x + 60y = 1446\n54x + 45y = 1161\nSubtract equations\n15y = 285\ny = 285/15\ny = 19\n\nSubstitute y\n9x + 10(19) = 241\n9x = 51\nx = 51/9\nx = 17/3"} {"input": "Solve quickly: 8x - 160/9 = 0", "output": "8x - 160/9 = 0\n8x = 160/9\nx = 160/9 / 8\nx = 20/9"} {"input": "What value of x satisfies 5x - 10/7 = 0", "output": "5x - 10/7 = 0\n5x = 10/7\nx = 10/7 / 5\nx = 2/7"} {"input": "Determine x in 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "Determine x in 10x + 20/7 = 0", "output": "10x + 20/7 = 0\n10x = -20/7\nx = -20/7 / 10\nx = -2/7"} {"input": "What value of x satisfies x^2 - 1x - 12 = 0", "output": "x^2 - 1x - 12 = 0\n(x - 4)(x - -3) = 0\nx - 4 = 0 or x - -3 = 0\nx = 4\nx = -3"} {"input": "Find x in x^2 + 139/40x + 3 = 0", "output": "x^2 + 139/40x + 3 = 0\n(x - -8/5)(x - -15/8) = 0\nx - -8/5 = 0 or x - -15/8 = 0\nx = -8/5\nx = -15/8"} {"input": "Find the solution to x^3 - 211/30x^2 + 182/15x - 33/10 = 0", "output": "x^3 - 211/30x^2 + 182/15x - 33/10 = 0\n(x - 11/5)(x - 9/2)(x - 1/3) = 0\nx - 11/5 = 0\nx - 9/2 = 0\nx - 1/3 = 0\nx = 11/5\nx = 9/2\nx = 1/3"} {"input": "Find x and y such that\n5x + 6y = -263/9\n2x + 6y = -251/9", "output": "5x + 6y = -263/9\n2x + 6y = -251/9\n\nUsing elimination\n2*(5x + 6y = -263/9)\n5*(2x + 6y = -251/9)\n10x + 12y = -526/9\n10x + 30y = -1255/9\nSubtract equations\n-18y = 81\ny = 81/-18\ny = -9/2\n\nSubstitute y\n5x + 6(-9/2) = -263/9\n5x = -20/9\nx = -20/9/5\nx = -4/9"} {"input": "Find x in 6x - 30 = 0", "output": "6x - 30 = 0\n6x = 30\nx = 30 / 6\nx = 5"} {"input": "Find the solution to 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "What value of x satisfies x^3 - 121/30x^2 - 977/150x - 56/25 = 0", "output": "x^3 - 121/30x^2 - 977/150x - 56/25 = 0\n(x - 16/3)(x - -3/5)(x - -7/10) = 0\nx - 16/3 = 0\nx - -3/5 = 0\nx - -7/10 = 0\nx = 16/3\nx = -3/5\nx = -7/10"} {"input": "Solve simultaneously:\n4x + 5y = 10\n3x + 10y = 65/4", "output": "4x + 5y = 10\n3x + 10y = 65/4\n\nUsing elimination\n3*(4x + 5y = 10)\n4*(3x + 10y = 65/4)\n12x + 15y = 30\n12x + 40y = 65\nSubtract equations\n-25y = -35\ny = -35/-25\ny = 7/5\n\nSubstitute y\n4x + 5(7/5) = 10\n4x = 3\nx = 3/4\nx = 3/4"} {"input": "Solve x^2 - 2x - 24 = 0", "output": "x^2 - 2x - 24 = 0\n(x - 6)(x - -4) = 0\nx - 6 = 0 or x - -4 = 0\nx = 6\nx = -4"} {"input": "Solve the equation x^3 - 26/5x^2 + 24/5x = 0", "output": "x^3 - 26/5x^2 + 24/5x = 0\n(x - 0)(x - 6/5)(x - 4) = 0\nx - 0 = 0\nx - 6/5 = 0\nx - 4 = 0\nx = 0\nx = 6/5\nx = 4"} {"input": "Solve the system:\n10x + 5y = -26\n10x + 9y = -34", "output": "10x + 5y = -26\n10x + 9y = -34\n\nUsing elimination\n10*(10x + 5y = -26)\n10*(10x + 9y = -34)\n100x + 50y = -260\n100x + 90y = -340\nSubtract equations\n-40y = 80\ny = 80/-40\ny = -2\n\nSubstitute y\n10x + 5(-2) = -26\n10x = -16\nx = -16/10\nx = -8/5"} {"input": "Find x and y such that\n5x + 6y = -151/9\n4x + 2y = -83/9", "output": "5x + 6y = -151/9\n4x + 2y = -83/9\n\nUsing elimination\n4*(5x + 6y = -151/9)\n5*(4x + 2y = -83/9)\n20x + 24y = -604/9\n20x + 10y = -415/9\nSubtract equations\n14y = -21\ny = -21/14\ny = -3/2\n\nSubstitute y\n5x + 6(-3/2) = -151/9\n5x = -70/9\nx = -70/9/5\nx = -14/9"} {"input": "Find x and y such that\n8x + 10y = 752/45\n10x + 7y = 232/9", "output": "8x + 10y = 752/45\n10x + 7y = 232/9\n\nUsing elimination\n10*(8x + 10y = 752/45)\n8*(10x + 7y = 232/9)\n80x + 100y = 1504/9\n80x + 56y = 1856/9\nSubtract equations\n44y = -352/9\ny = -352/9/44\ny = -8/9\n\nSubstitute y\n8x + 10(-8/9) = 752/45\n8x = 128/5\nx = 128/5/8\nx = 16/5"} {"input": "Solve the system:\n1x + 6y = 96/7\n6x + 4y = 64/7", "output": "1x + 6y = 96/7\n6x + 4y = 64/7\n\nUsing elimination\n6*(1x + 6y = 96/7)\n1*(6x + 4y = 64/7)\n6x + 36y = 576/7\n6x + 4y = 64/7\nSubtract equations\n32y = 512/7\ny = 512/7/32\ny = 16/7\n\nSubstitute y\n1x + 6(16/7) = 96/7\n1x = 0\nx = 0/1\nx = 0"} {"input": "Solve simultaneously:\n1x + 5y = 20/3\n6x + 2y = 8/3", "output": "1x + 5y = 20/3\n6x + 2y = 8/3\n\nUsing elimination\n6*(1x + 5y = 20/3)\n1*(6x + 2y = 8/3)\n6x + 30y = 40\n6x + 2y = 8/3\nSubtract equations\n28y = 112/3\ny = 112/3/28\ny = 4/3\n\nSubstitute y\n1x + 5(4/3) = 20/3\n1x = 0\nx = 0/1\nx = 0"} {"input": "Find the solution to 6x - 60/7 = 0", "output": "6x - 60/7 = 0\n6x = 60/7\nx = 60/7 / 6\nx = 10/7"} {"input": "Find x for x^3 + 41/12x^2 - 85/2x - 1463/12 = 0", "output": "x^3 + 41/12x^2 - 85/2x - 1463/12 = 0\n(x - -11/4)(x - -7)(x - 19/3) = 0\nx - -11/4 = 0\nx - -7 = 0\nx - 19/3 = 0\nx = -11/4\nx = -7\nx = 19/3"} {"input": "Solve quickly: x^3 + 41/7x^2 + 313/28x + 195/28 = 0", "output": "x^3 + 41/7x^2 + 313/28x + 195/28 = 0\n(x - -5/2)(x - -13/7)(x - -3/2) = 0\nx - -5/2 = 0\nx - -13/7 = 0\nx - -3/2 = 0\nx = -5/2\nx = -13/7\nx = -3/2"} {"input": "Determine x in x^2 + 8/9x = 0", "output": "x^2 + 8/9x = 0\n(x - -8/9)(x - 0) = 0\nx - -8/9 = 0 or x - 0 = 0\nx = -8/9\nx = 0"} {"input": "Solve simultaneously:\n8x + 6y = 37\n10x + 2y = 103/3", "output": "8x + 6y = 37\n10x + 2y = 103/3\n\nUsing elimination\n10*(8x + 6y = 37)\n8*(10x + 2y = 103/3)\n80x + 60y = 370\n80x + 16y = 824/3\nSubtract equations\n44y = 286/3\ny = 286/3/44\ny = 13/6\n\nSubstitute y\n8x + 6(13/6) = 37\n8x = 24\nx = 24/8\nx = 3"} {"input": "Find x for 4x + 26/3 = 0", "output": "4x + 26/3 = 0\n4x = -26/3\nx = -26/3 / 4\nx = -13/6"} {"input": "Solve x^2 - 21/2x + 17 = 0", "output": "x^2 - 21/2x + 17 = 0\n(x - 2)(x - 17/2) = 0\nx - 2 = 0 or x - 17/2 = 0\nx = 2\nx = 17/2"} {"input": "Find the solution to x^2 + 3/4x = 0", "output": "x^2 + 3/4x = 0\n(x - 0)(x - -3/4) = 0\nx - 0 = 0 or x - -3/4 = 0\nx = 0\nx = -3/4"} {"input": "Determine x in x^2 + 2/35x - 33/7 = 0", "output": "x^2 + 2/35x - 33/7 = 0\n(x - 15/7)(x - -11/5) = 0\nx - 15/7 = 0 or x - -11/5 = 0\nx = 15/7\nx = -11/5"} {"input": "Find x in x^2 + 28/3x + 160/9 = 0", "output": "x^2 + 28/3x + 160/9 = 0\n(x - -8/3)(x - -20/3) = 0\nx - -8/3 = 0 or x - -20/3 = 0\nx = -8/3\nx = -20/3"} {"input": "Find x and y such that\n1x + 6y = -154/5\n10x + 3y = 15", "output": "1x + 6y = -154/5\n10x + 3y = 15\n\nUsing elimination\n10*(1x + 6y = -154/5)\n1*(10x + 3y = 15)\n10x + 60y = -308\n10x + 3y = 15\nSubtract equations\n57y = -323\ny = -323/57\ny = -17/3\n\nSubstitute y\n1x + 6(-17/3) = -154/5\n1x = 16/5\nx = 16/5/1\nx = 16/5"} {"input": "Solve the system:\n8x + 9y = 84\n1x + 4y = 45", "output": "8x + 9y = 84\n1x + 4y = 45\n\nUsing elimination\n1*(8x + 9y = 84)\n8*(1x + 4y = 45)\n8x + 9y = 84\n8x + 32y = 360\nSubtract equations\n-23y = -276\ny = -276/-23\ny = 12\n\nSubstitute y\n8x + 9(12) = 84\n8x = -24\nx = -24/8\nx = -3"} {"input": "Compute the solution of x^3 + 9/4x^2 - 23/18x - 455/144 = 0", "output": "x^3 + 9/4x^2 - 23/18x - 455/144 = 0\n(x - -13/6)(x - 7/6)(x - -5/4) = 0\nx - -13/6 = 0\nx - 7/6 = 0\nx - -5/4 = 0\nx = -13/6\nx = 7/6\nx = -5/4"} {"input": "Find x for x^2 - 14/9x - 5/27 = 0", "output": "x^2 - 14/9x - 5/27 = 0\n(x - 5/3)(x - -1/9) = 0\nx - 5/3 = 0 or x - -1/9 = 0\nx = 5/3\nx = -1/9"} {"input": "Solve x^2 + 20/7x + 75/49 = 0", "output": "x^2 + 20/7x + 75/49 = 0\n(x - -5/7)(x - -15/7) = 0\nx - -5/7 = 0 or x - -15/7 = 0\nx = -5/7\nx = -15/7"} {"input": "Solve quickly: x^2 - 9/10x - 1/10 = 0", "output": "x^2 - 9/10x - 1/10 = 0\n(x - 1)(x - -1/10) = 0\nx - 1 = 0 or x - -1/10 = 0\nx = 1\nx = -1/10"} {"input": "Solve the equation x^2 + 131/9x - 208/9 = 0", "output": "x^2 + 131/9x - 208/9 = 0\n(x - -16)(x - 13/9) = 0\nx - -16 = 0 or x - 13/9 = 0\nx = -16\nx = 13/9"} {"input": "Determine x in x^2 + 81/10x - 19 = 0", "output": "x^2 + 81/10x - 19 = 0\n(x - -10)(x - 19/10) = 0\nx - -10 = 0 or x - 19/10 = 0\nx = -10\nx = 19/10"} {"input": "Find x in x^2 + 7/18x - 4/9 = 0", "output": "x^2 + 7/18x - 4/9 = 0\n(x - -8/9)(x - 1/2) = 0\nx - -8/9 = 0 or x - 1/2 = 0\nx = -8/9\nx = 1/2"} {"input": "Find x in x^3 - 1/3x^2 - 185/36x + 175/36 = 0", "output": "x^3 - 1/3x^2 - 185/36x + 175/36 = 0\n(x - 5/3)(x - 7/6)(x - -5/2) = 0\nx - 5/3 = 0\nx - 7/6 = 0\nx - -5/2 = 0\nx = 5/3\nx = 7/6\nx = -5/2"} {"input": "What value of x satisfies x^2 - 85/24x + 19/16 = 0", "output": "x^2 - 85/24x + 19/16 = 0\n(x - 19/6)(x - 3/8) = 0\nx - 19/6 = 0 or x - 3/8 = 0\nx = 19/6\nx = 3/8"} {"input": "Solve quickly: x^3 + 29/5x^2 + 41/4x + 5 = 0", "output": "x^3 + 29/5x^2 + 41/4x + 5 = 0\n(x - -5/2)(x - -4/5)(x - -5/2) = 0\nx - -5/2 = 0\nx - -4/5 = 0\nx - -5/2 = 0\nx = -5/2\nx = -4/5\nx = -5/2"} {"input": "Solve the equation 5x - 10 = 0", "output": "5x - 10 = 0\n5x = 10\nx = 10 / 5\nx = 2"} {"input": "Find x in x^3 - 2/15x^2 - 1313/405x - 266/135 = 0", "output": "x^3 - 2/15x^2 - 1313/405x - 266/135 = 0\n(x - -6/5)(x - 19/9)(x - -7/9) = 0\nx - -6/5 = 0\nx - 19/9 = 0\nx - -7/9 = 0\nx = -6/5\nx = 19/9\nx = -7/9"} {"input": "Solve the equations:\n9x + 2y = 40\n6x + 6y = 29", "output": "9x + 2y = 40\n6x + 6y = 29\n\nUsing elimination\n6*(9x + 2y = 40)\n9*(6x + 6y = 29)\n54x + 12y = 240\n54x + 54y = 261\nSubtract equations\n-42y = -21\ny = -21/-42\ny = 1/2\n\nSubstitute y\n9x + 2(1/2) = 40\n9x = 39\nx = 39/9\nx = 13/3"} {"input": "Find x in x^3 - 167/63x^2 - 82/21x + 680/63 = 0", "output": "x^3 - 167/63x^2 - 82/21x + 680/63 = 0\n(x - 20/9)(x - 17/7)(x - -2) = 0\nx - 20/9 = 0\nx - 17/7 = 0\nx - -2 = 0\nx = 20/9\nx = 17/7\nx = -2"} {"input": "Solve simultaneously:\n7x + 1y = -199/18\n5x + 7y = -205/18", "output": "7x + 1y = -199/18\n5x + 7y = -205/18\n\nUsing elimination\n5*(7x + 1y = -199/18)\n7*(5x + 7y = -205/18)\n35x + 5y = -995/18\n35x + 49y = -1435/18\nSubtract equations\n-44y = 220/9\ny = 220/9/-44\ny = -5/9\n\nSubstitute y\n7x + 1(-5/9) = -199/18\n7x = -21/2\nx = -21/2/7\nx = -3/2"} {"input": "Solve the equations:\n9x + 2y = -107/7\n7x + 9y = -61/2", "output": "9x + 2y = -107/7\n7x + 9y = -61/2\n\nUsing elimination\n7*(9x + 2y = -107/7)\n9*(7x + 9y = -61/2)\n63x + 14y = -107\n63x + 81y = -549/2\nSubtract equations\n-67y = 335/2\ny = 335/2/-67\ny = -5/2\n\nSubstitute y\n9x + 2(-5/2) = -107/7\n9x = -72/7\nx = -72/7/9\nx = -8/7"} {"input": "Compute the solution of x^2 + 29/6x + 10/3 = 0", "output": "x^2 + 29/6x + 10/3 = 0\n(x - -4)(x - -5/6) = 0\nx - -4 = 0 or x - -5/6 = 0\nx = -4\nx = -5/6"} {"input": "Find x in 2x + 2/3 = 0", "output": "2x + 2/3 = 0\n2x = -2/3\nx = -2/3 / 2\nx = -1/3"} {"input": "Compute the solution of x^2 - 39/8x + 45/8 = 0", "output": "x^2 - 39/8x + 45/8 = 0\n(x - 15/8)(x - 3) = 0\nx - 15/8 = 0 or x - 3 = 0\nx = 15/8\nx = 3"} {"input": "Find x in 7x - 77/3 = 0", "output": "7x - 77/3 = 0\n7x = 77/3\nx = 77/3 / 7\nx = 11/3"} {"input": "What value of x satisfies 5x - 20/7 = 0", "output": "5x - 20/7 = 0\n5x = 20/7\nx = 20/7 / 5\nx = 4/7"} {"input": "Find x for 4x + 76/9 = 0", "output": "4x + 76/9 = 0\n4x = -76/9\nx = -76/9 / 4\nx = -19/9"} {"input": "Solve the equations:\n7x + 8y = -142/5\n10x + 6y = -27", "output": "7x + 8y = -142/5\n10x + 6y = -27\n\nUsing elimination\n10*(7x + 8y = -142/5)\n7*(10x + 6y = -27)\n70x + 80y = -284\n70x + 42y = -189\nSubtract equations\n38y = -95\ny = -95/38\ny = -5/2\n\nSubstitute y\n7x + 8(-5/2) = -142/5\n7x = -42/5\nx = -42/5/7\nx = -6/5"} {"input": "Solve quickly: x^2 + 13x - 48 = 0", "output": "x^2 + 13x - 48 = 0\n(x - -16)(x - 3) = 0\nx - -16 = 0 or x - 3 = 0\nx = -16\nx = 3"} {"input": "Find x for x^2 + 1/6x - 35/6 = 0", "output": "x^2 + 1/6x - 35/6 = 0\n(x - -5/2)(x - 7/3) = 0\nx - -5/2 = 0 or x - 7/3 = 0\nx = -5/2\nx = 7/3"} {"input": "What value of x satisfies 9x - 33 = 0", "output": "9x - 33 = 0\n9x = 33\nx = 33 / 9\nx = 11/3"} {"input": "Solve x^3 + 89/30x^2 - 44/15x - 56/15 = 0", "output": "x^3 + 89/30x^2 - 44/15x - 56/15 = 0\n(x - -7/2)(x - -4/5)(x - 4/3) = 0\nx - -7/2 = 0\nx - -4/5 = 0\nx - 4/3 = 0\nx = -7/2\nx = -4/5\nx = 4/3"} {"input": "Find x for 8x + 20 = 0", "output": "8x + 20 = 0\n8x = -20\nx = -20 / 8\nx = -5/2"} {"input": "Determine x in x^3 + 629/168x^2 - 9/16x - 187/21 = 0", "output": "x^3 + 629/168x^2 - 9/16x - 187/21 = 0\n(x - -17/6)(x - -16/7)(x - 11/8) = 0\nx - -17/6 = 0\nx - -16/7 = 0\nx - 11/8 = 0\nx = -17/6\nx = -16/7\nx = 11/8"} {"input": "Solve simultaneously:\n1x + 3y = 9/5\n10x + 1y = 441/10", "output": "1x + 3y = 9/5\n10x + 1y = 441/10\n\nUsing elimination\n10*(1x + 3y = 9/5)\n1*(10x + 1y = 441/10)\n10x + 30y = 18\n10x + 1y = 441/10\nSubtract equations\n29y = -261/10\ny = -261/10/29\ny = -9/10\n\nSubstitute y\n1x + 3(-9/10) = 9/5\n1x = 9/2\nx = 9/2/1\nx = 9/2"} {"input": "Find x for x^3 + 391/28x^2 + 603/28x - 171/7 = 0", "output": "x^3 + 391/28x^2 + 603/28x - 171/7 = 0\n(x - 3/4)(x - -19/7)(x - -12) = 0\nx - 3/4 = 0\nx - -19/7 = 0\nx - -12 = 0\nx = 3/4\nx = -19/7\nx = -12"} {"input": "What value of x satisfies x^2 + 35/9x + 88/27 = 0", "output": "x^2 + 35/9x + 88/27 = 0\n(x - -11/9)(x - -8/3) = 0\nx - -11/9 = 0 or x - -8/3 = 0\nx = -11/9\nx = -8/3"} {"input": "Solve 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve the equations:\n5x + 9y = -15/7\n2x + 9y = -48/7", "output": "5x + 9y = -15/7\n2x + 9y = -48/7\n\nUsing elimination\n2*(5x + 9y = -15/7)\n5*(2x + 9y = -48/7)\n10x + 18y = -30/7\n10x + 45y = -240/7\nSubtract equations\n-27y = 30\ny = 30/-27\ny = -10/9\n\nSubstitute y\n5x + 9(-10/9) = -15/7\n5x = 55/7\nx = 55/7/5\nx = 11/7"} {"input": "Find x in x^3 + 817/56x^2 + 161/8x - 195/28 = 0", "output": "x^3 + 817/56x^2 + 161/8x - 195/28 = 0\n(x - 2/7)(x - -13)(x - -15/8) = 0\nx - 2/7 = 0\nx - -13 = 0\nx - -15/8 = 0\nx = 2/7\nx = -13\nx = -15/8"} {"input": "Solve x^3 - 81/28x^2 - 431/56x + 117/56 = 0", "output": "x^3 - 81/28x^2 - 431/56x + 117/56 = 0\n(x - 9/2)(x - -13/7)(x - 1/4) = 0\nx - 9/2 = 0\nx - -13/7 = 0\nx - 1/4 = 0\nx = 9/2\nx = -13/7\nx = 1/4"} {"input": "Solve simultaneously:\n5x + 1y = 68/5\n5x + 6y = 83/5", "output": "5x + 1y = 68/5\n5x + 6y = 83/5\n\nUsing elimination\n5*(5x + 1y = 68/5)\n5*(5x + 6y = 83/5)\n25x + 5y = 68\n25x + 30y = 83\nSubtract equations\n-25y = -15\ny = -15/-25\ny = 3/5\n\nSubstitute y\n5x + 1(3/5) = 68/5\n5x = 13\nx = 13/5\nx = 13/5"} {"input": "Find the solution to 10x + 40/3 = 0", "output": "10x + 40/3 = 0\n10x = -40/3\nx = -40/3 / 10\nx = -4/3"} {"input": "Determine x in 2x - 18/5 = 0", "output": "2x - 18/5 = 0\n2x = 18/5\nx = 18/5 / 2\nx = 9/5"} {"input": "Determine x in x^2 + 16/7x + 9/7 = 0", "output": "x^2 + 16/7x + 9/7 = 0\n(x - -9/7)(x - -1) = 0\nx - -9/7 = 0 or x - -1 = 0\nx = -9/7\nx = -1"} {"input": "Determine x in x^3 - 1241/120x^2 + 2207/80x - 247/12 = 0", "output": "x^3 - 1241/120x^2 + 2207/80x - 247/12 = 0\n(x - 20/3)(x - 19/8)(x - 13/10) = 0\nx - 20/3 = 0\nx - 19/8 = 0\nx - 13/10 = 0\nx = 20/3\nx = 19/8\nx = 13/10"} {"input": "Solve quickly: x^2 - 1/8x - 95/16 = 0", "output": "x^2 - 1/8x - 95/16 = 0\n(x - -19/8)(x - 5/2) = 0\nx - -19/8 = 0 or x - 5/2 = 0\nx = -19/8\nx = 5/2"} {"input": "Compute the solution of x^3 + 83/45x^2 + 46/45x + 8/45 = 0", "output": "x^3 + 83/45x^2 + 46/45x + 8/45 = 0\n(x - -2/5)(x - -4/9)(x - -1) = 0\nx - -2/5 = 0\nx - -4/9 = 0\nx - -1 = 0\nx = -2/5\nx = -4/9\nx = -1"} {"input": "Find x in x^3 - 287/72x^2 - 1657/288x + 323/32 = 0", "output": "x^3 - 287/72x^2 - 1657/288x + 323/32 = 0\n(x - -17/9)(x - 19/4)(x - 9/8) = 0\nx - -17/9 = 0\nx - 19/4 = 0\nx - 9/8 = 0\nx = -17/9\nx = 19/4\nx = 9/8"} {"input": "Solve the equation x^2 + 13/3x + 4/3 = 0", "output": "x^2 + 13/3x + 4/3 = 0\n(x - -1/3)(x - -4) = 0\nx - -1/3 = 0 or x - -4 = 0\nx = -1/3\nx = -4"} {"input": "Solve 7x + 77/9 = 0", "output": "7x + 77/9 = 0\n7x = -77/9\nx = -77/9 / 7\nx = -11/9"} {"input": "Solve quickly: 10x + 5/3 = 0", "output": "10x + 5/3 = 0\n10x = -5/3\nx = -5/3 / 10\nx = -1/6"} {"input": "Find x in x^3 - 55/28x^2 - 283/14x - 24 = 0", "output": "x^3 - 55/28x^2 - 283/14x - 24 = 0\n(x - -7/4)(x - -16/7)(x - 6) = 0\nx - -7/4 = 0\nx - -16/7 = 0\nx - 6 = 0\nx = -7/4\nx = -16/7\nx = 6"} {"input": "Compute the solution of 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x and y such that\n1x + 3y = -17/8\n8x + 7y = 187/8", "output": "1x + 3y = -17/8\n8x + 7y = 187/8\n\nUsing elimination\n8*(1x + 3y = -17/8)\n1*(8x + 7y = 187/8)\n8x + 24y = -17\n8x + 7y = 187/8\nSubtract equations\n17y = -323/8\ny = -323/8/17\ny = -19/8\n\nSubstitute y\n1x + 3(-19/8) = -17/8\n1x = 5\nx = 5/1\nx = 5"} {"input": "Find x in x^3 - 23/105x^2 - 398/105x - 32/15 = 0", "output": "x^3 - 23/105x^2 - 398/105x - 32/15 = 0\n(x - -7/5)(x - 16/7)(x - -2/3) = 0\nx - -7/5 = 0\nx - 16/7 = 0\nx - -2/3 = 0\nx = -7/5\nx = 16/7\nx = -2/3"} {"input": "Compute the solution of x^3 + 659/210x^2 + 6/5x - 16/105 = 0", "output": "x^3 + 659/210x^2 + 6/5x - 16/105 = 0\n(x - 1/10)(x - -8/3)(x - -4/7) = 0\nx - 1/10 = 0\nx - -8/3 = 0\nx - -4/7 = 0\nx = 1/10\nx = -8/3\nx = -4/7"} {"input": "Solve the equation 8x + 104/7 = 0", "output": "8x + 104/7 = 0\n8x = -104/7\nx = -104/7 / 8\nx = -13/7"} {"input": "Solve the equations:\n6x + 9y = -426/5\n4x + 8y = -374/5", "output": "6x + 9y = -426/5\n4x + 8y = -374/5\n\nUsing elimination\n4*(6x + 9y = -426/5)\n6*(4x + 8y = -374/5)\n24x + 36y = -1704/5\n24x + 48y = -2244/5\nSubtract equations\n-12y = 108\ny = 108/-12\ny = -9\n\nSubstitute y\n6x + 9(-9) = -426/5\n6x = -21/5\nx = -21/5/6\nx = -7/10"} {"input": "Solve the equation x^2 - 31/10x + 11/5 = 0", "output": "x^2 - 31/10x + 11/5 = 0\n(x - 11/10)(x - 2) = 0\nx - 11/10 = 0 or x - 2 = 0\nx = 11/10\nx = 2"} {"input": "What value of x satisfies 7x - 91/6 = 0", "output": "7x - 91/6 = 0\n7x = 91/6\nx = 91/6 / 7\nx = 13/6"} {"input": "Compute the solution of x^3 + 3/4x^2 - 61/4x - 15 = 0", "output": "x^3 + 3/4x^2 - 61/4x - 15 = 0\n(x - -1)(x - -15/4)(x - 4) = 0\nx - -1 = 0\nx - -15/4 = 0\nx - 4 = 0\nx = -1\nx = -15/4\nx = 4"} {"input": "Solve quickly: x^3 + 115/12x^2 + 24x + 65/12 = 0", "output": "x^3 + 115/12x^2 + 24x + 65/12 = 0\n(x - -13/3)(x - -1/4)(x - -5) = 0\nx - -13/3 = 0\nx - -1/4 = 0\nx - -5 = 0\nx = -13/3\nx = -1/4\nx = -5"} {"input": "Find x in x^2 + 5/6x - 17/3 = 0", "output": "x^2 + 5/6x - 17/3 = 0\n(x - -17/6)(x - 2) = 0\nx - -17/6 = 0 or x - 2 = 0\nx = -17/6\nx = 2"} {"input": "Solve the equation 3x + 12 = 0", "output": "3x + 12 = 0\n3x = -12\nx = -12 / 3\nx = -4"} {"input": "Compute the solution of 3x + 1 = 0", "output": "3x + 1 = 0\n3x = -1\nx = -1 / 3\nx = -1/3"} {"input": "Solve the system:\n4x + 1y = 17/3\n6x + 2y = 9", "output": "4x + 1y = 17/3\n6x + 2y = 9\n\nUsing elimination\n6*(4x + 1y = 17/3)\n4*(6x + 2y = 9)\n24x + 6y = 34\n24x + 8y = 36\nSubtract equations\n-2y = -2\ny = -2/-2\ny = 1\n\nSubstitute y\n4x + 1(1) = 17/3\n4x = 14/3\nx = 14/3/4\nx = 7/6"} {"input": "Find x for 5x + 13/2 = 0", "output": "5x + 13/2 = 0\n5x = -13/2\nx = -13/2 / 5\nx = -13/10"} {"input": "Find x for 7x - 35/6 = 0", "output": "7x - 35/6 = 0\n7x = 35/6\nx = 35/6 / 7\nx = 5/6"} {"input": "Determine x in x^3 + 2x^2 = 0", "output": "x^3 + 2x^2 = 0\n(x - -2)(x - 0)(x - 0) = 0\nx - -2 = 0\nx - 0 = 0\nx - 0 = 0\nx = -2\nx = 0\nx = 0"} {"input": "Find x in x^3 - 61/15x^2 - 199/15x + 119/5 = 0", "output": "x^3 - 61/15x^2 - 199/15x + 119/5 = 0\n(x - -3)(x - 7/5)(x - 17/3) = 0\nx - -3 = 0\nx - 7/5 = 0\nx - 17/3 = 0\nx = -3\nx = 7/5\nx = 17/3"} {"input": "Find the solution to x^3 - 289/90x^2 + 911/450x - 14/75 = 0", "output": "x^3 - 289/90x^2 + 911/450x - 14/75 = 0\n(x - 1/9)(x - 12/5)(x - 7/10) = 0\nx - 1/9 = 0\nx - 12/5 = 0\nx - 7/10 = 0\nx = 1/9\nx = 12/5\nx = 7/10"} {"input": "Solve the equation x^3 - 73/15x^2 - 376/75x + 68/25 = 0", "output": "x^3 - 73/15x^2 - 376/75x + 68/25 = 0\n(x - 2/5)(x - 17/3)(x - -6/5) = 0\nx - 2/5 = 0\nx - 17/3 = 0\nx - -6/5 = 0\nx = 2/5\nx = 17/3\nx = -6/5"} {"input": "Solve x^3 - 161/10x^2 - 81/5x + 153/10 = 0", "output": "x^3 - 161/10x^2 - 81/5x + 153/10 = 0\n(x - -3/2)(x - 17)(x - 3/5) = 0\nx - -3/2 = 0\nx - 17 = 0\nx - 3/5 = 0\nx = -3/2\nx = 17\nx = 3/5"} {"input": "Find the solution to x^2 + 2/35x - 1/35 = 0", "output": "x^2 + 2/35x - 1/35 = 0\n(x - -1/5)(x - 1/7) = 0\nx - -1/5 = 0 or x - 1/7 = 0\nx = -1/5\nx = 1/7"} {"input": "Solve simultaneously:\n1x + 5y = -111/7\n5x + 2y = -72/7", "output": "1x + 5y = -111/7\n5x + 2y = -72/7\n\nUsing elimination\n5*(1x + 5y = -111/7)\n1*(5x + 2y = -72/7)\n5x + 25y = -555/7\n5x + 2y = -72/7\nSubtract equations\n23y = -69\ny = -69/23\ny = -3\n\nSubstitute y\n1x + 5(-3) = -111/7\n1x = -6/7\nx = -6/7/1\nx = -6/7"} {"input": "Compute the solution of x^2 + 47/10x + 21/5 = 0", "output": "x^2 + 47/10x + 21/5 = 0\n(x - -6/5)(x - -7/2) = 0\nx - -6/5 = 0 or x - -7/2 = 0\nx = -6/5\nx = -7/2"} {"input": "Solve x^3 - 99/5x^2 + 487/5x - 117 = 0", "output": "x^3 - 99/5x^2 + 487/5x - 117 = 0\n(x - 5)(x - 13)(x - 9/5) = 0\nx - 5 = 0\nx - 13 = 0\nx - 9/5 = 0\nx = 5\nx = 13\nx = 9/5"} {"input": "Solve quickly: x^2 + 5/6x - 25/6 = 0", "output": "x^2 + 5/6x - 25/6 = 0\n(x - -5/2)(x - 5/3) = 0\nx - -5/2 = 0 or x - 5/3 = 0\nx = -5/2\nx = 5/3"} {"input": "Determine x in x^2 - 16/7x = 0", "output": "x^2 - 16/7x = 0\n(x - 16/7)(x - 0) = 0\nx - 16/7 = 0 or x - 0 = 0\nx = 16/7\nx = 0"} {"input": "Find x for x^2 - 8/5x - 4/5 = 0", "output": "x^2 - 8/5x - 4/5 = 0\n(x - -2/5)(x - 2) = 0\nx - -2/5 = 0 or x - 2 = 0\nx = -2/5\nx = 2"} {"input": "Solve simultaneously:\n4x + 6y = -3\n2x + 2y = 1/6", "output": "4x + 6y = -3\n2x + 2y = 1/6\n\nUsing elimination\n2*(4x + 6y = -3)\n4*(2x + 2y = 1/6)\n8x + 12y = -6\n8x + 8y = 2/3\nSubtract equations\n4y = -20/3\ny = -20/3/4\ny = -5/3\n\nSubstitute y\n4x + 6(-5/3) = -3\n4x = 7\nx = 7/4\nx = 7/4"} {"input": "Find x in 7x + 84 = 0", "output": "7x + 84 = 0\n7x = -84\nx = -84 / 7\nx = -12"} {"input": "Solve the equations:\n6x + 3y = -5/4\n8x + 2y = -13/6", "output": "6x + 3y = -5/4\n8x + 2y = -13/6\n\nUsing elimination\n8*(6x + 3y = -5/4)\n6*(8x + 2y = -13/6)\n48x + 24y = -10\n48x + 12y = -13\nSubtract equations\n12y = 3\ny = 3/12\ny = 1/4\n\nSubstitute y\n6x + 3(1/4) = -5/4\n6x = -2\nx = -2/6\nx = -1/3"} {"input": "What value of x satisfies 5x - 25/3 = 0", "output": "5x - 25/3 = 0\n5x = 25/3\nx = 25/3 / 5\nx = 5/3"} {"input": "Solve the equation x^2 + 6x = 0", "output": "x^2 + 6x = 0\n(x - -6)(x - 0) = 0\nx - -6 = 0 or x - 0 = 0\nx = -6\nx = 0"} {"input": "Find x for x^3 - 385/18x^2 + 2009/18x + 38/3 = 0", "output": "x^3 - 385/18x^2 + 2009/18x + 38/3 = 0\n(x - 19/2)(x - 12)(x - -1/9) = 0\nx - 19/2 = 0\nx - 12 = 0\nx - -1/9 = 0\nx = 19/2\nx = 12\nx = -1/9"} {"input": "Determine x in x^2 - 7/4x = 0", "output": "x^2 - 7/4x = 0\n(x - 0)(x - 7/4) = 0\nx - 0 = 0 or x - 7/4 = 0\nx = 0\nx = 7/4"} {"input": "Compute the solution of x^3 + 29/4x^2 - 7/4x - 49/2 = 0", "output": "x^3 + 29/4x^2 - 7/4x - 49/2 = 0\n(x - -2)(x - 7/4)(x - -7) = 0\nx - -2 = 0\nx - 7/4 = 0\nx - -7 = 0\nx = -2\nx = 7/4\nx = -7"} {"input": "Solve the equations:\n1x + 10y = 129/10\n8x + 8y = 84/5", "output": "1x + 10y = 129/10\n8x + 8y = 84/5\n\nUsing elimination\n8*(1x + 10y = 129/10)\n1*(8x + 8y = 84/5)\n8x + 80y = 516/5\n8x + 8y = 84/5\nSubtract equations\n72y = 432/5\ny = 432/5/72\ny = 6/5\n\nSubstitute y\n1x + 10(6/5) = 129/10\n1x = 9/10\nx = 9/10/1\nx = 9/10"} {"input": "Find the solution to 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Solve quickly: 3x - 9 = 0", "output": "3x - 9 = 0\n3x = 9\nx = 9 / 3\nx = 3"} {"input": "Find x in x^2 + 24/35x - 128/35 = 0", "output": "x^2 + 24/35x - 128/35 = 0\n(x - -16/7)(x - 8/5) = 0\nx - -16/7 = 0 or x - 8/5 = 0\nx = -16/7\nx = 8/5"} {"input": "Solve the equation x^3 - 218/21x^2 + 25/7x + 50/21 = 0", "output": "x^3 - 218/21x^2 + 25/7x + 50/21 = 0\n(x - 5/7)(x - 10)(x - -1/3) = 0\nx - 5/7 = 0\nx - 10 = 0\nx - -1/3 = 0\nx = 5/7\nx = 10\nx = -1/3"} {"input": "Compute the solution of 1x - 8/3 = 0", "output": "1x - 8/3 = 0\n1x = 8/3\nx = 8/3 / 1\nx = 8/3"} {"input": "Solve quickly: 8x + 64/5 = 0", "output": "8x + 64/5 = 0\n8x = -64/5\nx = -64/5 / 8\nx = -8/5"} {"input": "Find x in 8x - 136/9 = 0", "output": "8x - 136/9 = 0\n8x = 136/9\nx = 136/9 / 8\nx = 17/9"} {"input": "Solve the equations:\n5x + 8y = 13\n10x + 4y = 20", "output": "5x + 8y = 13\n10x + 4y = 20\n\nUsing elimination\n10*(5x + 8y = 13)\n5*(10x + 4y = 20)\n50x + 80y = 130\n50x + 20y = 100\nSubtract equations\n60y = 30\ny = 30/60\ny = 1/2\n\nSubstitute y\n5x + 8(1/2) = 13\n5x = 9\nx = 9/5\nx = 9/5"} {"input": "Find x and y such that\n9x + 7y = -61/5\n4x + 10y = -158/5", "output": "9x + 7y = -61/5\n4x + 10y = -158/5\n\nUsing elimination\n4*(9x + 7y = -61/5)\n9*(4x + 10y = -158/5)\n36x + 28y = -244/5\n36x + 90y = -1422/5\nSubtract equations\n-62y = 1178/5\ny = 1178/5/-62\ny = -19/5\n\nSubstitute y\n9x + 7(-19/5) = -61/5\n9x = 72/5\nx = 72/5/9\nx = 8/5"} {"input": "Determine x in x^2 + 7x - 30 = 0", "output": "x^2 + 7x - 30 = 0\n(x - -10)(x - 3) = 0\nx - -10 = 0 or x - 3 = 0\nx = -10\nx = 3"} {"input": "Find x in x^3 + 233/28x^2 + 67/28x - 969/14 = 0", "output": "x^3 + 233/28x^2 + 67/28x - 969/14 = 0\n(x - -19/4)(x - 17/7)(x - -6) = 0\nx - -19/4 = 0\nx - 17/7 = 0\nx - -6 = 0\nx = -19/4\nx = 17/7\nx = -6"} {"input": "Find x in x^3 - 19/10x^2 - 49/100x + 931/1000 = 0", "output": "x^3 - 19/10x^2 - 49/100x + 931/1000 = 0\n(x - 19/10)(x - -7/10)(x - 7/10) = 0\nx - 19/10 = 0\nx - -7/10 = 0\nx - 7/10 = 0\nx = 19/10\nx = -7/10\nx = 7/10"} {"input": "Find x for 9x - 27 = 0", "output": "9x - 27 = 0\n9x = 27\nx = 27 / 9\nx = 3"} {"input": "Find x in x^2 + 10/3x - 11/9 = 0", "output": "x^2 + 10/3x - 11/9 = 0\n(x - 1/3)(x - -11/3) = 0\nx - 1/3 = 0 or x - -11/3 = 0\nx = 1/3\nx = -11/3"} {"input": "Find x for 2x + 8 = 0", "output": "2x + 8 = 0\n2x = -8\nx = -8 / 2\nx = -4"} {"input": "Solve quickly: 7x - 77/6 = 0", "output": "7x - 77/6 = 0\n7x = 77/6\nx = 77/6 / 7\nx = 11/6"} {"input": "Solve the equations:\n5x + 3y = 544/7\n7x + 8y = 830/7", "output": "5x + 3y = 544/7\n7x + 8y = 830/7\n\nUsing elimination\n7*(5x + 3y = 544/7)\n5*(7x + 8y = 830/7)\n35x + 21y = 544\n35x + 40y = 4150/7\nSubtract equations\n-19y = -342/7\ny = -342/7/-19\ny = 18/7\n\nSubstitute y\n5x + 3(18/7) = 544/7\n5x = 70\nx = 70/5\nx = 14"} {"input": "Solve the equation x^3 - 35/24x^2 - 13/6x + 7/24 = 0", "output": "x^3 - 35/24x^2 - 13/6x + 7/24 = 0\n(x - 1/8)(x - 7/3)(x - -1) = 0\nx - 1/8 = 0\nx - 7/3 = 0\nx - -1 = 0\nx = 1/8\nx = 7/3\nx = -1"} {"input": "Solve simultaneously:\n3x + 9y = 163/21\n6x + 10y = 206/21", "output": "3x + 9y = 163/21\n6x + 10y = 206/21\n\nUsing elimination\n6*(3x + 9y = 163/21)\n3*(6x + 10y = 206/21)\n18x + 54y = 326/7\n18x + 30y = 206/7\nSubtract equations\n24y = 120/7\ny = 120/7/24\ny = 5/7\n\nSubstitute y\n3x + 9(5/7) = 163/21\n3x = 4/3\nx = 4/3/3\nx = 4/9"} {"input": "Solve the system:\n8x + 10y = 8\n5x + 7y = 5", "output": "8x + 10y = 8\n5x + 7y = 5\n\nUsing elimination\n5*(8x + 10y = 8)\n8*(5x + 7y = 5)\n40x + 50y = 40\n40x + 56y = 40\nSubtract equations\n-6y = 0\ny = 0/-6\ny = 0\n\nSubstitute y\n8x + 10(0) = 8\n8x = 8\nx = 8/8\nx = 1"} {"input": "What value of x satisfies 7x - 7 = 0", "output": "7x - 7 = 0\n7x = 7\nx = 7 / 7\nx = 1"} {"input": "Solve the equations:\n10x + 6y = -34\n10x + 8y = -72", "output": "10x + 6y = -34\n10x + 8y = -72\n\nUsing elimination\n10*(10x + 6y = -34)\n10*(10x + 8y = -72)\n100x + 60y = -340\n100x + 80y = -720\nSubtract equations\n-20y = 380\ny = 380/-20\ny = -19\n\nSubstitute y\n10x + 6(-19) = -34\n10x = 80\nx = 80/10\nx = 8"} {"input": "Compute the solution of x^3 - 257/10x^2 + 1151/10x - 22 = 0", "output": "x^3 - 257/10x^2 + 1151/10x - 22 = 0\n(x - 20)(x - 1/5)(x - 11/2) = 0\nx - 20 = 0\nx - 1/5 = 0\nx - 11/2 = 0\nx = 20\nx = 1/5\nx = 11/2"} {"input": "Determine x in 4x - 34 = 0", "output": "4x - 34 = 0\n4x = 34\nx = 34 / 4\nx = 17/2"} {"input": "Find the solution to x^3 - 83/20x^2 + 5x - 7/5 = 0", "output": "x^3 - 83/20x^2 + 5x - 7/5 = 0\n(x - 2)(x - 2/5)(x - 7/4) = 0\nx - 2 = 0\nx - 2/5 = 0\nx - 7/4 = 0\nx = 2\nx = 2/5\nx = 7/4"} {"input": "Find x in x^2 + 13/6x - 17/9 = 0", "output": "x^2 + 13/6x - 17/9 = 0\n(x - -17/6)(x - 2/3) = 0\nx - -17/6 = 0 or x - 2/3 = 0\nx = -17/6\nx = 2/3"} {"input": "Find x in 8x + 80/3 = 0", "output": "8x + 80/3 = 0\n8x = -80/3\nx = -80/3 / 8\nx = -10/3"} {"input": "Solve simultaneously:\n7x + 1y = -53/4\n10x + 2y = -39/2", "output": "7x + 1y = -53/4\n10x + 2y = -39/2\n\nUsing elimination\n10*(7x + 1y = -53/4)\n7*(10x + 2y = -39/2)\n70x + 10y = -265/2\n70x + 14y = -273/2\nSubtract equations\n-4y = 4\ny = 4/-4\ny = -1\n\nSubstitute y\n7x + 1(-1) = -53/4\n7x = -49/4\nx = -49/4/7\nx = -7/4"} {"input": "Solve quickly: x^2 + 49/9x + 52/9 = 0", "output": "x^2 + 49/9x + 52/9 = 0\n(x - -4)(x - -13/9) = 0\nx - -4 = 0 or x - -13/9 = 0\nx = -4\nx = -13/9"} {"input": "Solve the equations:\n10x + 2y = 143/3\n2x + 8y = 40/3", "output": "10x + 2y = 143/3\n2x + 8y = 40/3\n\nUsing elimination\n2*(10x + 2y = 143/3)\n10*(2x + 8y = 40/3)\n20x + 4y = 286/3\n20x + 80y = 400/3\nSubtract equations\n-76y = -38\ny = -38/-76\ny = 1/2\n\nSubstitute y\n10x + 2(1/2) = 143/3\n10x = 140/3\nx = 140/3/10\nx = 14/3"} {"input": "Determine x in 5x + 85/7 = 0", "output": "5x + 85/7 = 0\n5x = -85/7\nx = -85/7 / 5\nx = -17/7"} {"input": "Solve the equations:\n1x + 9y = -153\n1x + 2y = -20", "output": "1x + 9y = -153\n1x + 2y = -20\n\nUsing elimination\n1*(1x + 9y = -153)\n1*(1x + 2y = -20)\n1x + 9y = -153\n1x + 2y = -20\nSubtract equations\n7y = -133\ny = -133/7\ny = -19\n\nSubstitute y\n1x + 9(-19) = -153\n1x = 18\nx = 18/1\nx = 18"} {"input": "Compute the solution of x^2 - 103/14x - 15/14 = 0", "output": "x^2 - 103/14x - 15/14 = 0\n(x - -1/7)(x - 15/2) = 0\nx - -1/7 = 0 or x - 15/2 = 0\nx = -1/7\nx = 15/2"} {"input": "Find x and y such that\n5x + 8y = 43/7\n10x + 7y = 2", "output": "5x + 8y = 43/7\n10x + 7y = 2\n\nUsing elimination\n10*(5x + 8y = 43/7)\n5*(10x + 7y = 2)\n50x + 80y = 430/7\n50x + 35y = 10\nSubtract equations\n45y = 360/7\ny = 360/7/45\ny = 8/7\n\nSubstitute y\n5x + 8(8/7) = 43/7\n5x = -3\nx = -3/5\nx = -3/5"} {"input": "Find the solution to x^3 - 39/40x^2 - 269/80x - 9/8 = 0", "output": "x^3 - 39/40x^2 - 269/80x - 9/8 = 0\n(x - -9/8)(x - 5/2)(x - -2/5) = 0\nx - -9/8 = 0\nx - 5/2 = 0\nx - -2/5 = 0\nx = -9/8\nx = 5/2\nx = -2/5"} {"input": "Find x in 10x + 16 = 0", "output": "10x + 16 = 0\n10x = -16\nx = -16 / 10\nx = -8/5"} {"input": "What value of x satisfies x^2 + 5/14x - 39/14 = 0", "output": "x^2 + 5/14x - 39/14 = 0\n(x - -13/7)(x - 3/2) = 0\nx - -13/7 = 0 or x - 3/2 = 0\nx = -13/7\nx = 3/2"} {"input": "Solve the system:\n8x + 6y = -1144/7\n6x + 8y = -872/7", "output": "8x + 6y = -1144/7\n6x + 8y = -872/7\n\nUsing elimination\n6*(8x + 6y = -1144/7)\n8*(6x + 8y = -872/7)\n48x + 36y = -6864/7\n48x + 64y = -6976/7\nSubtract equations\n-28y = 16\ny = 16/-28\ny = -4/7\n\nSubstitute y\n8x + 6(-4/7) = -1144/7\n8x = -160\nx = -160/8\nx = -20"} {"input": "Find x in x^2 - 74/9x + 40/3 = 0", "output": "x^2 - 74/9x + 40/3 = 0\n(x - 6)(x - 20/9) = 0\nx - 6 = 0 or x - 20/9 = 0\nx = 6\nx = 20/9"} {"input": "Find x in x^2 - 11/4x - 15/4 = 0", "output": "x^2 - 11/4x - 15/4 = 0\n(x - -1)(x - 15/4) = 0\nx - -1 = 0 or x - 15/4 = 0\nx = -1\nx = 15/4"} {"input": "Solve the system:\n5x + 9y = -253/8\n7x + 10y = -917/24", "output": "5x + 9y = -253/8\n7x + 10y = -917/24\n\nUsing elimination\n7*(5x + 9y = -253/8)\n5*(7x + 10y = -917/24)\n35x + 63y = -1771/8\n35x + 50y = -4585/24\nSubtract equations\n13y = -91/3\ny = -91/3/13\ny = -7/3\n\nSubstitute y\n5x + 9(-7/3) = -253/8\n5x = -85/8\nx = -85/8/5\nx = -17/8"} {"input": "Solve x^2 - 5/3x + 56/81 = 0", "output": "x^2 - 5/3x + 56/81 = 0\n(x - 7/9)(x - 8/9) = 0\nx - 7/9 = 0 or x - 8/9 = 0\nx = 7/9\nx = 8/9"} {"input": "Solve quickly: x^2 - 3x - 7/4 = 0", "output": "x^2 - 3x - 7/4 = 0\n(x - -1/2)(x - 7/2) = 0\nx - -1/2 = 0 or x - 7/2 = 0\nx = -1/2\nx = 7/2"} {"input": "Solve simultaneously:\n3x + 4y = 37/10\n10x + 9y = 67/10", "output": "3x + 4y = 37/10\n10x + 9y = 67/10\n\nUsing elimination\n10*(3x + 4y = 37/10)\n3*(10x + 9y = 67/10)\n30x + 40y = 37\n30x + 27y = 201/10\nSubtract equations\n13y = 169/10\ny = 169/10/13\ny = 13/10\n\nSubstitute y\n3x + 4(13/10) = 37/10\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Compute the solution of 6x + 15/4 = 0", "output": "6x + 15/4 = 0\n6x = -15/4\nx = -15/4 / 6\nx = -5/8"} {"input": "Determine x in 5x - 5/2 = 0", "output": "5x - 5/2 = 0\n5x = 5/2\nx = 5/2 / 5\nx = 1/2"} {"input": "Find x for 7x + 56/5 = 0", "output": "7x + 56/5 = 0\n7x = -56/5\nx = -56/5 / 7\nx = -8/5"} {"input": "Solve quickly: 3x - 3/2 = 0", "output": "3x - 3/2 = 0\n3x = 3/2\nx = 3/2 / 3\nx = 1/2"} {"input": "Solve the system:\n5x + 9y = -29/2\n9x + 8y = -179/10", "output": "5x + 9y = -29/2\n9x + 8y = -179/10\n\nUsing elimination\n9*(5x + 9y = -29/2)\n5*(9x + 8y = -179/10)\n45x + 81y = -261/2\n45x + 40y = -179/2\nSubtract equations\n41y = -41\ny = -41/41\ny = -1\n\nSubstitute y\n5x + 9(-1) = -29/2\n5x = -11/2\nx = -11/2/5\nx = -11/10"} {"input": "Find the solution to x^3 - 157/42x^2 - 1/42x + 22/21 = 0", "output": "x^3 - 157/42x^2 - 1/42x + 22/21 = 0\n(x - 4/7)(x - 11/3)(x - -1/2) = 0\nx - 4/7 = 0\nx - 11/3 = 0\nx - -1/2 = 0\nx = 4/7\nx = 11/3\nx = -1/2"} {"input": "What value of x satisfies 5x + 11/2 = 0", "output": "5x + 11/2 = 0\n5x = -11/2\nx = -11/2 / 5\nx = -11/10"} {"input": "Solve 10x + 190 = 0", "output": "10x + 190 = 0\n10x = -190\nx = -190 / 10\nx = -19"} {"input": "Solve x^2 - 11/30x - 13/6 = 0", "output": "x^2 - 11/30x - 13/6 = 0\n(x - -13/10)(x - 5/3) = 0\nx - -13/10 = 0 or x - 5/3 = 0\nx = -13/10\nx = 5/3"} {"input": "Solve x^2 + 79/5x + 228/5 = 0", "output": "x^2 + 79/5x + 228/5 = 0\n(x - -19/5)(x - -12) = 0\nx - -19/5 = 0 or x - -12 = 0\nx = -19/5\nx = -12"} {"input": "Find x and y such that\n2x + 7y = -25/2\n4x + 6y = -47/3", "output": "2x + 7y = -25/2\n4x + 6y = -47/3\n\nUsing elimination\n4*(2x + 7y = -25/2)\n2*(4x + 6y = -47/3)\n8x + 28y = -50\n8x + 12y = -94/3\nSubtract equations\n16y = -56/3\ny = -56/3/16\ny = -7/6\n\nSubstitute y\n2x + 7(-7/6) = -25/2\n2x = -13/3\nx = -13/3/2\nx = -13/6"} {"input": "Determine x in 6x - 2 = 0", "output": "6x - 2 = 0\n6x = 2\nx = 2 / 6\nx = 1/3"} {"input": "Compute the solution of 9x - 27 = 0", "output": "9x - 27 = 0\n9x = 27\nx = 27 / 9\nx = 3"} {"input": "Determine x in 1x + 19/9 = 0", "output": "1x + 19/9 = 0\n1x = -19/9\nx = -19/9 / 1\nx = -19/9"} {"input": "Solve simultaneously:\n8x + 2y = 89/18\n8x + 5y = 205/36", "output": "8x + 2y = 89/18\n8x + 5y = 205/36\n\nUsing elimination\n8*(8x + 2y = 89/18)\n8*(8x + 5y = 205/36)\n64x + 16y = 356/9\n64x + 40y = 410/9\nSubtract equations\n-24y = -6\ny = -6/-24\ny = 1/4\n\nSubstitute y\n8x + 2(1/4) = 89/18\n8x = 40/9\nx = 40/9/8\nx = 5/9"} {"input": "Solve x^3 - 129/70x^2 - 68/35x + 39/14 = 0", "output": "x^3 - 129/70x^2 - 68/35x + 39/14 = 0\n(x - -13/10)(x - 1)(x - 15/7) = 0\nx - -13/10 = 0\nx - 1 = 0\nx - 15/7 = 0\nx = -13/10\nx = 1\nx = 15/7"} {"input": "Solve simultaneously:\n1x + 8y = -4\n3x + 3y = 13/3", "output": "1x + 8y = -4\n3x + 3y = 13/3\n\nUsing elimination\n3*(1x + 8y = -4)\n1*(3x + 3y = 13/3)\n3x + 24y = -12\n3x + 3y = 13/3\nSubtract equations\n21y = -49/3\ny = -49/3/21\ny = -7/9\n\nSubstitute y\n1x + 8(-7/9) = -4\n1x = 20/9\nx = 20/9/1\nx = 20/9"} {"input": "Solve simultaneously:\n1x + 7y = -82/3\n3x + 10y = -103/3", "output": "1x + 7y = -82/3\n3x + 10y = -103/3\n\nUsing elimination\n3*(1x + 7y = -82/3)\n1*(3x + 10y = -103/3)\n3x + 21y = -82\n3x + 10y = -103/3\nSubtract equations\n11y = -143/3\ny = -143/3/11\ny = -13/3\n\nSubstitute y\n1x + 7(-13/3) = -82/3\n1x = 3\nx = 3/1\nx = 3"} {"input": "Solve the system:\n2x + 2y = -4/5\n9x + 5y = -10", "output": "2x + 2y = -4/5\n9x + 5y = -10\n\nUsing elimination\n9*(2x + 2y = -4/5)\n2*(9x + 5y = -10)\n18x + 18y = -36/5\n18x + 10y = -20\nSubtract equations\n8y = 64/5\ny = 64/5/8\ny = 8/5\n\nSubstitute y\n2x + 2(8/5) = -4/5\n2x = -4\nx = -4/2\nx = -2"} {"input": "Compute the solution of x^3 + 61/30x^2 + 109/150x + 4/75 = 0", "output": "x^3 + 61/30x^2 + 109/150x + 4/75 = 0\n(x - -1/3)(x - -1/10)(x - -8/5) = 0\nx - -1/3 = 0\nx - -1/10 = 0\nx - -8/5 = 0\nx = -1/3\nx = -1/10\nx = -8/5"} {"input": "Solve 8x - 96 = 0", "output": "8x - 96 = 0\n8x = 96\nx = 96 / 8\nx = 12"} {"input": "Find the solution to x^3 - 36/5x^2 - 25/4x - 6/5 = 0", "output": "x^3 - 36/5x^2 - 25/4x - 6/5 = 0\n(x - -1/2)(x - 8)(x - -3/10) = 0\nx - -1/2 = 0\nx - 8 = 0\nx - -3/10 = 0\nx = -1/2\nx = 8\nx = -3/10"} {"input": "Find x in x^2 + 28/9x - 55/27 = 0", "output": "x^2 + 28/9x - 55/27 = 0\n(x - 5/9)(x - -11/3) = 0\nx - 5/9 = 0 or x - -11/3 = 0\nx = 5/9\nx = -11/3"} {"input": "Determine x in 6x + 3 = 0", "output": "6x + 3 = 0\n6x = -3\nx = -3 / 6\nx = -1/2"} {"input": "Solve 2x + 8/9 = 0", "output": "2x + 8/9 = 0\n2x = -8/9\nx = -8/9 / 2\nx = -4/9"} {"input": "Compute the solution of x^3 - 169/72x^2 - 263/216x + 35/12 = 0", "output": "x^3 - 169/72x^2 - 263/216x + 35/12 = 0\n(x - 7/3)(x - -10/9)(x - 9/8) = 0\nx - 7/3 = 0\nx - -10/9 = 0\nx - 9/8 = 0\nx = 7/3\nx = -10/9\nx = 9/8"} {"input": "What value of x satisfies x^2 - 21x + 38 = 0", "output": "x^2 - 21x + 38 = 0\n(x - 19)(x - 2) = 0\nx - 19 = 0 or x - 2 = 0\nx = 19\nx = 2"} {"input": "Find x for x^3 - 331/60x^2 + 63/8x - 11/15 = 0", "output": "x^3 - 331/60x^2 + 63/8x - 11/15 = 0\n(x - 8/3)(x - 1/10)(x - 11/4) = 0\nx - 8/3 = 0\nx - 1/10 = 0\nx - 11/4 = 0\nx = 8/3\nx = 1/10\nx = 11/4"} {"input": "Find x and y such that\n2x + 5y = 88/5\n2x + 2y = 58/5", "output": "2x + 5y = 88/5\n2x + 2y = 58/5\n\nUsing elimination\n2*(2x + 5y = 88/5)\n2*(2x + 2y = 58/5)\n4x + 10y = 176/5\n4x + 4y = 116/5\nSubtract equations\n6y = 12\ny = 12/6\ny = 2\n\nSubstitute y\n2x + 5(2) = 88/5\n2x = 38/5\nx = 38/5/2\nx = 19/5"} {"input": "Solve the system:\n6x + 7y = -7/3\n10x + 3y = 95/9", "output": "6x + 7y = -7/3\n10x + 3y = 95/9\n\nUsing elimination\n10*(6x + 7y = -7/3)\n6*(10x + 3y = 95/9)\n60x + 70y = -70/3\n60x + 18y = 190/3\nSubtract equations\n52y = -260/3\ny = -260/3/52\ny = -5/3\n\nSubstitute y\n6x + 7(-5/3) = -7/3\n6x = 28/3\nx = 28/3/6\nx = 14/9"} {"input": "Determine x in x^3 - 145/56x^2 - 1107/392x + 765/98 = 0", "output": "x^3 - 145/56x^2 - 1107/392x + 765/98 = 0\n(x - 17/7)(x - 15/8)(x - -12/7) = 0\nx - 17/7 = 0\nx - 15/8 = 0\nx - -12/7 = 0\nx = 17/7\nx = 15/8\nx = -12/7"} {"input": "Solve 6x + 54/7 = 0", "output": "6x + 54/7 = 0\n6x = -54/7\nx = -54/7 / 6\nx = -9/7"} {"input": "Find x for 10x + 130/7 = 0", "output": "10x + 130/7 = 0\n10x = -130/7\nx = -130/7 / 10\nx = -13/7"} {"input": "Solve quickly: 4x - 40/3 = 0", "output": "4x - 40/3 = 0\n4x = 40/3\nx = 40/3 / 4\nx = 10/3"} {"input": "Find the solution to x^3 - 106/5x^2 + 88x - 384/5 = 0", "output": "x^3 - 106/5x^2 + 88x - 384/5 = 0\n(x - 16)(x - 4)(x - 6/5) = 0\nx - 16 = 0\nx - 4 = 0\nx - 6/5 = 0\nx = 16\nx = 4\nx = 6/5"} {"input": "Solve x^2 - 15/4x - 27/2 = 0", "output": "x^2 - 15/4x - 27/2 = 0\n(x - 6)(x - -9/4) = 0\nx - 6 = 0 or x - -9/4 = 0\nx = 6\nx = -9/4"} {"input": "Find x for 1x + 6 = 0", "output": "1x + 6 = 0\n1x = -6\nx = -6 / 1\nx = -6"} {"input": "Solve simultaneously:\n2x + 4y = 130/9\n8x + 7y = 196/9", "output": "2x + 4y = 130/9\n8x + 7y = 196/9\n\nUsing elimination\n8*(2x + 4y = 130/9)\n2*(8x + 7y = 196/9)\n16x + 32y = 1040/9\n16x + 14y = 392/9\nSubtract equations\n18y = 72\ny = 72/18\ny = 4\n\nSubstitute y\n2x + 4(4) = 130/9\n2x = -14/9\nx = -14/9/2\nx = -7/9"} {"input": "Find x in x^3 - 29/36x^2 + 23/108x - 1/54 = 0", "output": "x^3 - 29/36x^2 + 23/108x - 1/54 = 0\n(x - 1/4)(x - 1/3)(x - 2/9) = 0\nx - 1/4 = 0\nx - 1/3 = 0\nx - 2/9 = 0\nx = 1/4\nx = 1/3\nx = 2/9"} {"input": "Solve 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Solve x^2 - 4/3x + 4/9 = 0", "output": "x^2 - 4/3x + 4/9 = 0\n(x - 2/3)(x - 2/3) = 0\nx - 2/3 = 0 or x - 2/3 = 0\nx = 2/3\nx = 2/3"} {"input": "Solve the system:\n2x + 7y = 12\n10x + 8y = 204/7", "output": "2x + 7y = 12\n10x + 8y = 204/7\n\nUsing elimination\n10*(2x + 7y = 12)\n2*(10x + 8y = 204/7)\n20x + 70y = 120\n20x + 16y = 408/7\nSubtract equations\n54y = 432/7\ny = 432/7/54\ny = 8/7\n\nSubstitute y\n2x + 7(8/7) = 12\n2x = 4\nx = 4/2\nx = 2"} {"input": "Find x for 10x + 85/2 = 0", "output": "10x + 85/2 = 0\n10x = -85/2\nx = -85/2 / 10\nx = -17/4"} {"input": "Solve quickly: x^2 - 97/14x + 153/14 = 0", "output": "x^2 - 97/14x + 153/14 = 0\n(x - 17/7)(x - 9/2) = 0\nx - 17/7 = 0 or x - 9/2 = 0\nx = 17/7\nx = 9/2"} {"input": "Determine x in 9x + 99/2 = 0", "output": "9x + 99/2 = 0\n9x = -99/2\nx = -99/2 / 9\nx = -11/2"} {"input": "Find x in x^2 + 85/24x + 19/16 = 0", "output": "x^2 + 85/24x + 19/16 = 0\n(x - -19/6)(x - -3/8) = 0\nx - -19/6 = 0 or x - -3/8 = 0\nx = -19/6\nx = -3/8"} {"input": "Solve quickly: x^3 - 47/3x^2 - 74x + 608/3 = 0", "output": "x^3 - 47/3x^2 - 74x + 608/3 = 0\n(x - 2)(x - 19)(x - -16/3) = 0\nx - 2 = 0\nx - 19 = 0\nx - -16/3 = 0\nx = 2\nx = 19\nx = -16/3"} {"input": "Solve simultaneously:\n2x + 5y = -8\n3x + 2y = -12", "output": "2x + 5y = -8\n3x + 2y = -12\n\nUsing elimination\n3*(2x + 5y = -8)\n2*(3x + 2y = -12)\n6x + 15y = -24\n6x + 4y = -24\nSubtract equations\n11y = 0\ny = 0/11\ny = 0\n\nSubstitute y\n2x + 5(0) = -8\n2x = -8\nx = -8/2\nx = -4"} {"input": "Find the solution to x^3 + 1/24x^2 - 3287/648x + 361/324 = 0", "output": "x^3 + 1/24x^2 - 3287/648x + 361/324 = 0\n(x - -19/8)(x - 19/9)(x - 2/9) = 0\nx - -19/8 = 0\nx - 19/9 = 0\nx - 2/9 = 0\nx = -19/8\nx = 19/9\nx = 2/9"} {"input": "Find x for x^2 - 5/7x - 38/7 = 0", "output": "x^2 - 5/7x - 38/7 = 0\n(x - 19/7)(x - -2) = 0\nx - 19/7 = 0 or x - -2 = 0\nx = 19/7\nx = -2"} {"input": "Find x for x^2 - 20/3x + 28/3 = 0", "output": "x^2 - 20/3x + 28/3 = 0\n(x - 14/3)(x - 2) = 0\nx - 14/3 = 0 or x - 2 = 0\nx = 14/3\nx = 2"} {"input": "Solve the equations:\n5x + 2y = 121/6\n1x + 7y = 77/6", "output": "5x + 2y = 121/6\n1x + 7y = 77/6\n\nUsing elimination\n1*(5x + 2y = 121/6)\n5*(1x + 7y = 77/6)\n5x + 2y = 121/6\n5x + 35y = 385/6\nSubtract equations\n-33y = -44\ny = -44/-33\ny = 4/3\n\nSubstitute y\n5x + 2(4/3) = 121/6\n5x = 35/2\nx = 35/2/5\nx = 7/2"} {"input": "Determine x in x^2 - 12/5x + 7/5 = 0", "output": "x^2 - 12/5x + 7/5 = 0\n(x - 7/5)(x - 1) = 0\nx - 7/5 = 0 or x - 1 = 0\nx = 7/5\nx = 1"} {"input": "Find x for x^3 + 18/7x^2 - 61/49x + 6/49 = 0", "output": "x^3 + 18/7x^2 - 61/49x + 6/49 = 0\n(x - -3)(x - 1/7)(x - 2/7) = 0\nx - -3 = 0\nx - 1/7 = 0\nx - 2/7 = 0\nx = -3\nx = 1/7\nx = 2/7"} {"input": "Determine x in x^2 - 53/36x - 5/3 = 0", "output": "x^2 - 53/36x - 5/3 = 0\n(x - -3/4)(x - 20/9) = 0\nx - -3/4 = 0 or x - 20/9 = 0\nx = -3/4\nx = 20/9"} {"input": "Solve simultaneously:\n8x + 4y = 104/3\n7x + 1y = 137/6", "output": "8x + 4y = 104/3\n7x + 1y = 137/6\n\nUsing elimination\n7*(8x + 4y = 104/3)\n8*(7x + 1y = 137/6)\n56x + 28y = 728/3\n56x + 8y = 548/3\nSubtract equations\n20y = 60\ny = 60/20\ny = 3\n\nSubstitute y\n8x + 4(3) = 104/3\n8x = 68/3\nx = 68/3/8\nx = 17/6"} {"input": "Solve x^3 - 8/3x^2 - 89/9x + 104/9 = 0", "output": "x^3 - 8/3x^2 - 89/9x + 104/9 = 0\n(x - -8/3)(x - 1)(x - 13/3) = 0\nx - -8/3 = 0\nx - 1 = 0\nx - 13/3 = 0\nx = -8/3\nx = 1\nx = 13/3"} {"input": "Solve the system:\n9x + 8y = 76/7\n8x + 4y = 73/7", "output": "9x + 8y = 76/7\n8x + 4y = 73/7\n\nUsing elimination\n8*(9x + 8y = 76/7)\n9*(8x + 4y = 73/7)\n72x + 64y = 608/7\n72x + 36y = 657/7\nSubtract equations\n28y = -7\ny = -7/28\ny = -1/4\n\nSubstitute y\n9x + 8(-1/4) = 76/7\n9x = 90/7\nx = 90/7/9\nx = 10/7"} {"input": "Solve simultaneously:\n9x + 9y = 63\n5x + 1y = 27", "output": "9x + 9y = 63\n5x + 1y = 27\n\nUsing elimination\n5*(9x + 9y = 63)\n9*(5x + 1y = 27)\n45x + 45y = 315\n45x + 9y = 243\nSubtract equations\n36y = 72\ny = 72/36\ny = 2\n\nSubstitute y\n9x + 9(2) = 63\n9x = 45\nx = 45/9\nx = 5"} {"input": "What value of x satisfies 6x - 42/5 = 0", "output": "6x - 42/5 = 0\n6x = 42/5\nx = 42/5 / 6\nx = 7/5"} {"input": "Solve simultaneously:\n2x + 10y = -2\n9x + 5y = -65", "output": "2x + 10y = -2\n9x + 5y = -65\n\nUsing elimination\n9*(2x + 10y = -2)\n2*(9x + 5y = -65)\n18x + 90y = -18\n18x + 10y = -130\nSubtract equations\n80y = 112\ny = 112/80\ny = 7/5\n\nSubstitute y\n2x + 10(7/5) = -2\n2x = -16\nx = -16/2\nx = -8"} {"input": "Find the solution to x^3 - 217/45x^2 + 128/45x + 28/5 = 0", "output": "x^3 - 217/45x^2 + 128/45x + 28/5 = 0\n(x - 2)(x - 18/5)(x - -7/9) = 0\nx - 2 = 0\nx - 18/5 = 0\nx - -7/9 = 0\nx = 2\nx = 18/5\nx = -7/9"} {"input": "Solve simultaneously:\n9x + 3y = 135/2\n7x + 9y = 65/2", "output": "9x + 3y = 135/2\n7x + 9y = 65/2\n\nUsing elimination\n7*(9x + 3y = 135/2)\n9*(7x + 9y = 65/2)\n63x + 21y = 945/2\n63x + 81y = 585/2\nSubtract equations\n-60y = 180\ny = 180/-60\ny = -3\n\nSubstitute y\n9x + 3(-3) = 135/2\n9x = 153/2\nx = 153/2/9\nx = 17/2"} {"input": "Determine x in 6x - 78/5 = 0", "output": "6x - 78/5 = 0\n6x = 78/5\nx = 78/5 / 6\nx = 13/5"} {"input": "Solve the equations:\n8x + 4y = 60\n7x + 2y = 81", "output": "8x + 4y = 60\n7x + 2y = 81\n\nUsing elimination\n7*(8x + 4y = 60)\n8*(7x + 2y = 81)\n56x + 28y = 420\n56x + 16y = 648\nSubtract equations\n12y = -228\ny = -228/12\ny = -19\n\nSubstitute y\n8x + 4(-19) = 60\n8x = 136\nx = 136/8\nx = 17"} {"input": "Solve x^3 + 911/252x^2 + 71/21x + 40/63 = 0", "output": "x^3 + 911/252x^2 + 71/21x + 40/63 = 0\n(x - -20/9)(x - -1/4)(x - -8/7) = 0\nx - -20/9 = 0\nx - -1/4 = 0\nx - -8/7 = 0\nx = -20/9\nx = -1/4\nx = -8/7"} {"input": "Solve quickly: x^2 - 14/3x + 8/3 = 0", "output": "x^2 - 14/3x + 8/3 = 0\n(x - 2/3)(x - 4) = 0\nx - 2/3 = 0 or x - 4 = 0\nx = 2/3\nx = 4"} {"input": "Find x and y such that\n6x + 8y = -26/3\n6x + 4y = 14/3", "output": "6x + 8y = -26/3\n6x + 4y = 14/3\n\nUsing elimination\n6*(6x + 8y = -26/3)\n6*(6x + 4y = 14/3)\n36x + 48y = -52\n36x + 24y = 28\nSubtract equations\n24y = -80\ny = -80/24\ny = -10/3\n\nSubstitute y\n6x + 8(-10/3) = -26/3\n6x = 18\nx = 18/6\nx = 3"} {"input": "What value of x satisfies x^2 - 2x - 7/9 = 0", "output": "x^2 - 2x - 7/9 = 0\n(x - 7/3)(x - -1/3) = 0\nx - 7/3 = 0 or x - -1/3 = 0\nx = 7/3\nx = -1/3"} {"input": "Determine x in x^2 - 13/3x + 4/3 = 0", "output": "x^2 - 13/3x + 4/3 = 0\n(x - 4)(x - 1/3) = 0\nx - 4 = 0 or x - 1/3 = 0\nx = 4\nx = 1/3"} {"input": "What value of x satisfies 8x + 32 = 0", "output": "8x + 32 = 0\n8x = -32\nx = -32 / 8\nx = -4"} {"input": "Determine x in 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Solve simultaneously:\n4x + 7y = -1138/9\n6x + 9y = -488/3", "output": "4x + 7y = -1138/9\n6x + 9y = -488/3\n\nUsing elimination\n6*(4x + 7y = -1138/9)\n4*(6x + 9y = -488/3)\n24x + 42y = -2276/3\n24x + 36y = -1952/3\nSubtract equations\n6y = -108\ny = -108/6\ny = -18\n\nSubstitute y\n4x + 7(-18) = -1138/9\n4x = -4/9\nx = -4/9/4\nx = -1/9"} {"input": "Solve the system:\n1x + 10y = -118/5\n5x + 2y = -10", "output": "1x + 10y = -118/5\n5x + 2y = -10\n\nUsing elimination\n5*(1x + 10y = -118/5)\n1*(5x + 2y = -10)\n5x + 50y = -118\n5x + 2y = -10\nSubtract equations\n48y = -108\ny = -108/48\ny = -9/4\n\nSubstitute y\n1x + 10(-9/4) = -118/5\n1x = -11/10\nx = -11/10/1\nx = -11/10"} {"input": "Determine x in x^2 + 19/8x + 3/4 = 0", "output": "x^2 + 19/8x + 3/4 = 0\n(x - -2)(x - -3/8) = 0\nx - -2 = 0 or x - -3/8 = 0\nx = -2\nx = -3/8"} {"input": "Find x in x^3 - 39/5x^2 + 319/20x - 39/4 = 0", "output": "x^3 - 39/5x^2 + 319/20x - 39/4 = 0\n(x - 5)(x - 3/2)(x - 13/10) = 0\nx - 5 = 0\nx - 3/2 = 0\nx - 13/10 = 0\nx = 5\nx = 3/2\nx = 13/10"} {"input": "Solve the equation x^2 - 151/90x - 19/45 = 0", "output": "x^2 - 151/90x - 19/45 = 0\n(x - -2/9)(x - 19/10) = 0\nx - -2/9 = 0 or x - 19/10 = 0\nx = -2/9\nx = 19/10"} {"input": "Find x and y such that\n1x + 9y = -99/2\n8x + 1y = -41", "output": "1x + 9y = -99/2\n8x + 1y = -41\n\nUsing elimination\n8*(1x + 9y = -99/2)\n1*(8x + 1y = -41)\n8x + 72y = -396\n8x + 1y = -41\nSubtract equations\n71y = -355\ny = -355/71\ny = -5\n\nSubstitute y\n1x + 9(-5) = -99/2\n1x = -9/2\nx = -9/2/1\nx = -9/2"} {"input": "Solve the equations:\n4x + 7y = 1315/56\n3x + 1y = 421/56", "output": "4x + 7y = 1315/56\n3x + 1y = 421/56\n\nUsing elimination\n3*(4x + 7y = 1315/56)\n4*(3x + 1y = 421/56)\n12x + 21y = 3945/56\n12x + 4y = 421/14\nSubtract equations\n17y = 323/8\ny = 323/8/17\ny = 19/8\n\nSubstitute y\n4x + 7(19/8) = 1315/56\n4x = 48/7\nx = 48/7/4\nx = 12/7"} {"input": "Solve 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Find x for x^3 - 39/40x^2 - 23/20x + 33/40 = 0", "output": "x^3 - 39/40x^2 - 23/20x + 33/40 = 0\n(x - -1)(x - 3/5)(x - 11/8) = 0\nx - -1 = 0\nx - 3/5 = 0\nx - 11/8 = 0\nx = -1\nx = 3/5\nx = 11/8"} {"input": "Solve 6x - 15/4 = 0", "output": "6x - 15/4 = 0\n6x = 15/4\nx = 15/4 / 6\nx = 5/8"} {"input": "Find x and y such that\n1x + 2y = -17/10\n7x + 5y = -193/20", "output": "1x + 2y = -17/10\n7x + 5y = -193/20\n\nUsing elimination\n7*(1x + 2y = -17/10)\n1*(7x + 5y = -193/20)\n7x + 14y = -119/10\n7x + 5y = -193/20\nSubtract equations\n9y = -9/4\ny = -9/4/9\ny = -1/4\n\nSubstitute y\n1x + 2(-1/4) = -17/10\n1x = -6/5\nx = -6/5/1\nx = -6/5"} {"input": "Compute the solution of x^3 + 21/5x^2 + 91/20x + 3/4 = 0", "output": "x^3 + 21/5x^2 + 91/20x + 3/4 = 0\n(x - -5/2)(x - -3/2)(x - -1/5) = 0\nx - -5/2 = 0\nx - -3/2 = 0\nx - -1/5 = 0\nx = -5/2\nx = -3/2\nx = -1/5"} {"input": "Find the solution to x^3 - 7x^2 + 55/4x - 21/4 = 0", "output": "x^3 - 7x^2 + 55/4x - 21/4 = 0\n(x - 7/2)(x - 1/2)(x - 3) = 0\nx - 7/2 = 0\nx - 1/2 = 0\nx - 3 = 0\nx = 7/2\nx = 1/2\nx = 3"} {"input": "Solve the equations:\n9x + 2y = 97/6\n5x + 2y = 29/6", "output": "9x + 2y = 97/6\n5x + 2y = 29/6\n\nUsing elimination\n5*(9x + 2y = 97/6)\n9*(5x + 2y = 29/6)\n45x + 10y = 485/6\n45x + 18y = 87/2\nSubtract equations\n-8y = 112/3\ny = 112/3/-8\ny = -14/3\n\nSubstitute y\n9x + 2(-14/3) = 97/6\n9x = 51/2\nx = 51/2/9\nx = 17/6"} {"input": "Solve the equations:\n6x + 1y = 119/10\n7x + 1y = 139/10", "output": "6x + 1y = 119/10\n7x + 1y = 139/10\n\nUsing elimination\n7*(6x + 1y = 119/10)\n6*(7x + 1y = 139/10)\n42x + 7y = 833/10\n42x + 6y = 417/5\nSubtract equations\n1y = -1/10\ny = -1/10/1\ny = -1/10\n\nSubstitute y\n6x + 1(-1/10) = 119/10\n6x = 12\nx = 12/6\nx = 2"} {"input": "Solve the equations:\n3x + 1y = 9\n7x + 9y = 1", "output": "3x + 1y = 9\n7x + 9y = 1\n\nUsing elimination\n7*(3x + 1y = 9)\n3*(7x + 9y = 1)\n21x + 7y = 63\n21x + 27y = 3\nSubtract equations\n-20y = 60\ny = 60/-20\ny = -3\n\nSubstitute y\n3x + 1(-3) = 9\n3x = 12\nx = 12/3\nx = 4"} {"input": "Find x for x^3 + 33/10x^2 - 7x - 36/5 = 0", "output": "x^3 + 33/10x^2 - 7x - 36/5 = 0\n(x - 2)(x - -4/5)(x - -9/2) = 0\nx - 2 = 0\nx - -4/5 = 0\nx - -9/2 = 0\nx = 2\nx = -4/5\nx = -9/2"} {"input": "Find x for 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Solve the equation x^3 - 267/56x^2 + 225/32x - 675/224 = 0", "output": "x^3 - 267/56x^2 + 225/32x - 675/224 = 0\n(x - 15/8)(x - 3/4)(x - 15/7) = 0\nx - 15/8 = 0\nx - 3/4 = 0\nx - 15/7 = 0\nx = 15/8\nx = 3/4\nx = 15/7"} {"input": "Solve 9x + 99/8 = 0", "output": "9x + 99/8 = 0\n9x = -99/8\nx = -99/8 / 9\nx = -11/8"} {"input": "Find x in x^3 + 197/42x^2 + 305/42x + 26/7 = 0", "output": "x^3 + 197/42x^2 + 305/42x + 26/7 = 0\n(x - -13/7)(x - -3/2)(x - -4/3) = 0\nx - -13/7 = 0\nx - -3/2 = 0\nx - -4/3 = 0\nx = -13/7\nx = -3/2\nx = -4/3"} {"input": "What value of x satisfies x^3 + 309/140x^2 + 1/2x - 39/140 = 0", "output": "x^3 + 309/140x^2 + 1/2x - 39/140 = 0\n(x - -13/7)(x - 1/4)(x - -3/5) = 0\nx - -13/7 = 0\nx - 1/4 = 0\nx - -3/5 = 0\nx = -13/7\nx = 1/4\nx = -3/5"} {"input": "Solve 6x - 102 = 0", "output": "6x - 102 = 0\n6x = 102\nx = 102 / 6\nx = 17"} {"input": "Solve the equations:\n4x + 3y = 25/6\n7x + 9y = 55/6", "output": "4x + 3y = 25/6\n7x + 9y = 55/6\n\nUsing elimination\n7*(4x + 3y = 25/6)\n4*(7x + 9y = 55/6)\n28x + 21y = 175/6\n28x + 36y = 110/3\nSubtract equations\n-15y = -15/2\ny = -15/2/-15\ny = 1/2\n\nSubstitute y\n4x + 3(1/2) = 25/6\n4x = 8/3\nx = 8/3/4\nx = 2/3"} {"input": "Solve the equations:\n10x + 6y = 25/3\n9x + 9y = -3/2", "output": "10x + 6y = 25/3\n9x + 9y = -3/2\n\nUsing elimination\n9*(10x + 6y = 25/3)\n10*(9x + 9y = -3/2)\n90x + 54y = 75\n90x + 90y = -15\nSubtract equations\n-36y = 90\ny = 90/-36\ny = -5/2\n\nSubstitute y\n10x + 6(-5/2) = 25/3\n10x = 70/3\nx = 70/3/10\nx = 7/3"} {"input": "Solve simultaneously:\n6x + 9y = -1/2\n2x + 8y = -83/18", "output": "6x + 9y = -1/2\n2x + 8y = -83/18\n\nUsing elimination\n2*(6x + 9y = -1/2)\n6*(2x + 8y = -83/18)\n12x + 18y = -1\n12x + 48y = -83/3\nSubtract equations\n-30y = 80/3\ny = 80/3/-30\ny = -8/9\n\nSubstitute y\n6x + 9(-8/9) = -1/2\n6x = 15/2\nx = 15/2/6\nx = 5/4"} {"input": "Find x for x^3 - 153/5x^2 + 227x - 627/5 = 0", "output": "x^3 - 153/5x^2 + 227x - 627/5 = 0\n(x - 11)(x - 3/5)(x - 19) = 0\nx - 11 = 0\nx - 3/5 = 0\nx - 19 = 0\nx = 11\nx = 3/5\nx = 19"} {"input": "Find x and y such that\n5x + 9y = 185/8\n9x + 2y = 15", "output": "5x + 9y = 185/8\n9x + 2y = 15\n\nUsing elimination\n9*(5x + 9y = 185/8)\n5*(9x + 2y = 15)\n45x + 81y = 1665/8\n45x + 10y = 75\nSubtract equations\n71y = 1065/8\ny = 1065/8/71\ny = 15/8\n\nSubstitute y\n5x + 9(15/8) = 185/8\n5x = 25/4\nx = 25/4/5\nx = 5/4"} {"input": "What value of x satisfies x^3 - 163/72x^2 - 323/72x + 361/36 = 0", "output": "x^3 - 163/72x^2 - 323/72x + 361/36 = 0\n(x - -19/9)(x - 2)(x - 19/8) = 0\nx - -19/9 = 0\nx - 2 = 0\nx - 19/8 = 0\nx = -19/9\nx = 2\nx = 19/8"} {"input": "Find x in 2x - 5 = 0", "output": "2x - 5 = 0\n2x = 5\nx = 5 / 2\nx = 5/2"} {"input": "Solve the equation x^2 + 40/7x - 9 = 0", "output": "x^2 + 40/7x - 9 = 0\n(x - 9/7)(x - -7) = 0\nx - 9/7 = 0 or x - -7 = 0\nx = 9/7\nx = -7"} {"input": "Find the solution to x^2 + 2/3x = 0", "output": "x^2 + 2/3x = 0\n(x - 0)(x - -2/3) = 0\nx - 0 = 0 or x - -2/3 = 0\nx = 0\nx = -2/3"} {"input": "Solve the equation x^2 + 19/36x - 7/36 = 0", "output": "x^2 + 19/36x - 7/36 = 0\n(x - 1/4)(x - -7/9) = 0\nx - 1/4 = 0 or x - -7/9 = 0\nx = 1/4\nx = -7/9"} {"input": "Find x and y such that\n7x + 8y = -173/7\n4x + 10y = -50/7", "output": "7x + 8y = -173/7\n4x + 10y = -50/7\n\nUsing elimination\n4*(7x + 8y = -173/7)\n7*(4x + 10y = -50/7)\n28x + 32y = -692/7\n28x + 70y = -50\nSubtract equations\n-38y = -342/7\ny = -342/7/-38\ny = 9/7\n\nSubstitute y\n7x + 8(9/7) = -173/7\n7x = -35\nx = -35/7\nx = -5"} {"input": "Solve 6x + 3 = 0", "output": "6x + 3 = 0\n6x = -3\nx = -3 / 6\nx = -1/2"} {"input": "Solve simultaneously:\n6x + 7y = 253/6\n2x + 1y = 31/6", "output": "6x + 7y = 253/6\n2x + 1y = 31/6\n\nUsing elimination\n2*(6x + 7y = 253/6)\n6*(2x + 1y = 31/6)\n12x + 14y = 253/3\n12x + 6y = 31\nSubtract equations\n8y = 160/3\ny = 160/3/8\ny = 20/3\n\nSubstitute y\n6x + 7(20/3) = 253/6\n6x = -9/2\nx = -9/2/6\nx = -3/4"} {"input": "What value of x satisfies 4x + 9/2 = 0", "output": "4x + 9/2 = 0\n4x = -9/2\nx = -9/2 / 4\nx = -9/8"} {"input": "Compute the solution of x^3 - 365/63x^2 - 91/27x - 19/63 = 0", "output": "x^3 - 365/63x^2 - 91/27x - 19/63 = 0\n(x - -1/9)(x - -3/7)(x - 19/3) = 0\nx - -1/9 = 0\nx - -3/7 = 0\nx - 19/3 = 0\nx = -1/9\nx = -3/7\nx = 19/3"} {"input": "Find x in x^3 - 211/30x^2 + 133/30x = 0", "output": "x^3 - 211/30x^2 + 133/30x = 0\n(x - 19/3)(x - 7/10)(x - 0) = 0\nx - 19/3 = 0\nx - 7/10 = 0\nx - 0 = 0\nx = 19/3\nx = 7/10\nx = 0"} {"input": "Compute the solution of x^3 - 137/40x^2 - 1117/80x - 357/40 = 0", "output": "x^3 - 137/40x^2 - 1117/80x - 357/40 = 0\n(x - -7/8)(x - 6)(x - -17/10) = 0\nx - -7/8 = 0\nx - 6 = 0\nx - -17/10 = 0\nx = -7/8\nx = 6\nx = -17/10"} {"input": "Solve the system:\n5x + 3y = 107/6\n3x + 1y = 167/18", "output": "5x + 3y = 107/6\n3x + 1y = 167/18\n\nUsing elimination\n3*(5x + 3y = 107/6)\n5*(3x + 1y = 167/18)\n15x + 9y = 107/2\n15x + 5y = 835/18\nSubtract equations\n4y = 64/9\ny = 64/9/4\ny = 16/9\n\nSubstitute y\n5x + 3(16/9) = 107/6\n5x = 25/2\nx = 25/2/5\nx = 5/2"} {"input": "Find x and y such that\n5x + 8y = 164/7\n5x + 2y = 146/7", "output": "5x + 8y = 164/7\n5x + 2y = 146/7\n\nUsing elimination\n5*(5x + 8y = 164/7)\n5*(5x + 2y = 146/7)\n25x + 40y = 820/7\n25x + 10y = 730/7\nSubtract equations\n30y = 90/7\ny = 90/7/30\ny = 3/7\n\nSubstitute y\n5x + 8(3/7) = 164/7\n5x = 20\nx = 20/5\nx = 4"} {"input": "What value of x satisfies 5x + 19/2 = 0", "output": "5x + 19/2 = 0\n5x = -19/2\nx = -19/2 / 5\nx = -19/10"} {"input": "Solve simultaneously:\n7x + 5y = -268/3\n8x + 4y = -272/3", "output": "7x + 5y = -268/3\n8x + 4y = -272/3\n\nUsing elimination\n8*(7x + 5y = -268/3)\n7*(8x + 4y = -272/3)\n56x + 40y = -2144/3\n56x + 28y = -1904/3\nSubtract equations\n12y = -80\ny = -80/12\ny = -20/3\n\nSubstitute y\n7x + 5(-20/3) = -268/3\n7x = -56\nx = -56/7\nx = -8"} {"input": "Determine x in 5x - 5/3 = 0", "output": "5x - 5/3 = 0\n5x = 5/3\nx = 5/3 / 5\nx = 1/3"} {"input": "Compute the solution of 10x + 18 = 0", "output": "10x + 18 = 0\n10x = -18\nx = -18 / 10\nx = -9/5"} {"input": "Solve simultaneously:\n8x + 6y = -43\n10x + 5y = -65/2", "output": "8x + 6y = -43\n10x + 5y = -65/2\n\nUsing elimination\n10*(8x + 6y = -43)\n8*(10x + 5y = -65/2)\n80x + 60y = -430\n80x + 40y = -260\nSubtract equations\n20y = -170\ny = -170/20\ny = -17/2\n\nSubstitute y\n8x + 6(-17/2) = -43\n8x = 8\nx = 8/8\nx = 1"} {"input": "Find the solution to x^3 + 1x^2 + 7/64x = 0", "output": "x^3 + 1x^2 + 7/64x = 0\n(x - -7/8)(x - -1/8)(x - 0) = 0\nx - -7/8 = 0\nx - -1/8 = 0\nx - 0 = 0\nx = -7/8\nx = -1/8\nx = 0"} {"input": "Solve quickly: x^2 - 16x - 17 = 0", "output": "x^2 - 16x - 17 = 0\n(x - -1)(x - 17) = 0\nx - -1 = 0 or x - 17 = 0\nx = -1\nx = 17"} {"input": "Find x in x^2 - 1/2x - 15/2 = 0", "output": "x^2 - 1/2x - 15/2 = 0\n(x - 3)(x - -5/2) = 0\nx - 3 = 0 or x - -5/2 = 0\nx = 3\nx = -5/2"} {"input": "Solve simultaneously:\n2x + 5y = 49/5\n5x + 9y = 189/10", "output": "2x + 5y = 49/5\n5x + 9y = 189/10\n\nUsing elimination\n5*(2x + 5y = 49/5)\n2*(5x + 9y = 189/10)\n10x + 25y = 49\n10x + 18y = 189/5\nSubtract equations\n7y = 56/5\ny = 56/5/7\ny = 8/5\n\nSubstitute y\n2x + 5(8/5) = 49/5\n2x = 9/5\nx = 9/5/2\nx = 9/10"} {"input": "Solve quickly: 2x + 10/3 = 0", "output": "2x + 10/3 = 0\n2x = -10/3\nx = -10/3 / 2\nx = -5/3"} {"input": "Solve quickly: 9x + 72/5 = 0", "output": "9x + 72/5 = 0\n9x = -72/5\nx = -72/5 / 9\nx = -8/5"} {"input": "Find the solution to 4x - 16/5 = 0", "output": "4x - 16/5 = 0\n4x = 16/5\nx = 16/5 / 4\nx = 4/5"} {"input": "Find x and y such that\n8x + 1y = -140/9\n3x + 5y = -295/3", "output": "8x + 1y = -140/9\n3x + 5y = -295/3\n\nUsing elimination\n3*(8x + 1y = -140/9)\n8*(3x + 5y = -295/3)\n24x + 3y = -140/3\n24x + 40y = -2360/3\nSubtract equations\n-37y = 740\ny = 740/-37\ny = -20\n\nSubstitute y\n8x + 1(-20) = -140/9\n8x = 40/9\nx = 40/9/8\nx = 5/9"} {"input": "Find x and y such that\n5x + 1y = 248/3\n1x + 6y = 3", "output": "5x + 1y = 248/3\n1x + 6y = 3\n\nUsing elimination\n1*(5x + 1y = 248/3)\n5*(1x + 6y = 3)\n5x + 1y = 248/3\n5x + 30y = 15\nSubtract equations\n-29y = 203/3\ny = 203/3/-29\ny = -7/3\n\nSubstitute y\n5x + 1(-7/3) = 248/3\n5x = 85\nx = 85/5\nx = 17"} {"input": "Determine x in 7x + 133/8 = 0", "output": "7x + 133/8 = 0\n7x = -133/8\nx = -133/8 / 7\nx = -19/8"} {"input": "Solve the equations:\n6x + 7y = -131/12\n3x + 3y = -67/12", "output": "6x + 7y = -131/12\n3x + 3y = -67/12\n\nUsing elimination\n3*(6x + 7y = -131/12)\n6*(3x + 3y = -67/12)\n18x + 21y = -131/4\n18x + 18y = -67/2\nSubtract equations\n3y = 3/4\ny = 3/4/3\ny = 1/4\n\nSubstitute y\n6x + 7(1/4) = -131/12\n6x = -38/3\nx = -38/3/6\nx = -19/9"} {"input": "Find x for x^3 + 23/60x^2 - 29/12x - 5/3 = 0", "output": "x^3 + 23/60x^2 - 29/12x - 5/3 = 0\n(x - -5/4)(x - -4/5)(x - 5/3) = 0\nx - -5/4 = 0\nx - -4/5 = 0\nx - 5/3 = 0\nx = -5/4\nx = -4/5\nx = 5/3"} {"input": "Solve x^2 - 43/8x + 57/8 = 0", "output": "x^2 - 43/8x + 57/8 = 0\n(x - 3)(x - 19/8) = 0\nx - 3 = 0 or x - 19/8 = 0\nx = 3\nx = 19/8"} {"input": "Compute the solution of 1x + 1/5 = 0", "output": "1x + 1/5 = 0\n1x = -1/5\nx = -1/5 / 1\nx = -1/5"} {"input": "Find x in x^3 - 307/120x^2 + 103/60x - 13/40 = 0", "output": "x^3 - 307/120x^2 + 103/60x - 13/40 = 0\n(x - 3/5)(x - 1/3)(x - 13/8) = 0\nx - 3/5 = 0\nx - 1/3 = 0\nx - 13/8 = 0\nx = 3/5\nx = 1/3\nx = 13/8"} {"input": "What value of x satisfies x^2 - 8/9x + 16/81 = 0", "output": "x^2 - 8/9x + 16/81 = 0\n(x - 4/9)(x - 4/9) = 0\nx - 4/9 = 0 or x - 4/9 = 0\nx = 4/9\nx = 4/9"} {"input": "Solve the equation x^2 + 4x - 320 = 0", "output": "x^2 + 4x - 320 = 0\n(x - -20)(x - 16) = 0\nx - -20 = 0 or x - 16 = 0\nx = -20\nx = 16"} {"input": "Solve x^3 - 101/30x^2 + 89/30x - 7/15 = 0", "output": "x^3 - 101/30x^2 + 89/30x - 7/15 = 0\n(x - 2)(x - 1/5)(x - 7/6) = 0\nx - 2 = 0\nx - 1/5 = 0\nx - 7/6 = 0\nx = 2\nx = 1/5\nx = 7/6"} {"input": "Compute the solution of x^2 + 19/5x + 18/5 = 0", "output": "x^2 + 19/5x + 18/5 = 0\n(x - -2)(x - -9/5) = 0\nx - -2 = 0 or x - -9/5 = 0\nx = -2\nx = -9/5"} {"input": "Solve the system:\n5x + 4y = -23/10\n5x + 10y = 5/2", "output": "5x + 4y = -23/10\n5x + 10y = 5/2\n\nUsing elimination\n5*(5x + 4y = -23/10)\n5*(5x + 10y = 5/2)\n25x + 20y = -23/2\n25x + 50y = 25/2\nSubtract equations\n-30y = -24\ny = -24/-30\ny = 4/5\n\nSubstitute y\n5x + 4(4/5) = -23/10\n5x = -11/2\nx = -11/2/5\nx = -11/10"} {"input": "Solve 3x - 17/3 = 0", "output": "3x - 17/3 = 0\n3x = 17/3\nx = 17/3 / 3\nx = 17/9"} {"input": "Solve the equation 3x - 13/2 = 0", "output": "3x - 13/2 = 0\n3x = 13/2\nx = 13/2 / 3\nx = 13/6"} {"input": "Solve 9x + 1 = 0", "output": "9x + 1 = 0\n9x = -1\nx = -1 / 9\nx = -1/9"} {"input": "Compute the solution of x^3 - 10/3x^2 - 257/36x + 77/18 = 0", "output": "x^3 - 10/3x^2 - 257/36x + 77/18 = 0\n(x - 14/3)(x - 1/2)(x - -11/6) = 0\nx - 14/3 = 0\nx - 1/2 = 0\nx - -11/6 = 0\nx = 14/3\nx = 1/2\nx = -11/6"} {"input": "Determine x in 10x + 65/3 = 0", "output": "10x + 65/3 = 0\n10x = -65/3\nx = -65/3 / 10\nx = -13/6"} {"input": "Solve the system:\n6x + 5y = 35/3\n3x + 2y = 37/6", "output": "6x + 5y = 35/3\n3x + 2y = 37/6\n\nUsing elimination\n3*(6x + 5y = 35/3)\n6*(3x + 2y = 37/6)\n18x + 15y = 35\n18x + 12y = 37\nSubtract equations\n3y = -2\ny = -2/3\ny = -2/3\n\nSubstitute y\n6x + 5(-2/3) = 35/3\n6x = 15\nx = 15/6\nx = 5/2"} {"input": "Find x in x^2 - 14/3x - 39 = 0", "output": "x^2 - 14/3x - 39 = 0\n(x - 9)(x - -13/3) = 0\nx - 9 = 0 or x - -13/3 = 0\nx = 9\nx = -13/3"} {"input": "Solve quickly: x^3 + 107/30x^2 - 211/30x + 2/3 = 0", "output": "x^3 + 107/30x^2 - 211/30x + 2/3 = 0\n(x - 4/3)(x - 1/10)(x - -5) = 0\nx - 4/3 = 0\nx - 1/10 = 0\nx - -5 = 0\nx = 4/3\nx = 1/10\nx = -5"} {"input": "What value of x satisfies 5x + 30 = 0", "output": "5x + 30 = 0\n5x = -30\nx = -30 / 5\nx = -6"} {"input": "Determine x in x^2 + 41/40x + 1/4 = 0", "output": "x^2 + 41/40x + 1/4 = 0\n(x - -5/8)(x - -2/5) = 0\nx - -5/8 = 0 or x - -2/5 = 0\nx = -5/8\nx = -2/5"} {"input": "Solve simultaneously:\n4x + 5y = 143/9\n3x + 2y = 317/36", "output": "4x + 5y = 143/9\n3x + 2y = 317/36\n\nUsing elimination\n3*(4x + 5y = 143/9)\n4*(3x + 2y = 317/36)\n12x + 15y = 143/3\n12x + 8y = 317/9\nSubtract equations\n7y = 112/9\ny = 112/9/7\ny = 16/9\n\nSubstitute y\n4x + 5(16/9) = 143/9\n4x = 7\nx = 7/4\nx = 7/4"} {"input": "Solve the system:\n9x + 6y = 15\n1x + 7y = -11", "output": "9x + 6y = 15\n1x + 7y = -11\n\nUsing elimination\n1*(9x + 6y = 15)\n9*(1x + 7y = -11)\n9x + 6y = 15\n9x + 63y = -99\nSubtract equations\n-57y = 114\ny = 114/-57\ny = -2\n\nSubstitute y\n9x + 6(-2) = 15\n9x = 27\nx = 27/9\nx = 3"} {"input": "What value of x satisfies x^2 + 19/2x + 39/2 = 0", "output": "x^2 + 19/2x + 39/2 = 0\n(x - -13/2)(x - -3) = 0\nx - -13/2 = 0 or x - -3 = 0\nx = -13/2\nx = -3"} {"input": "Find x for x^2 - 65/21x + 34/21 = 0", "output": "x^2 - 65/21x + 34/21 = 0\n(x - 17/7)(x - 2/3) = 0\nx - 17/7 = 0 or x - 2/3 = 0\nx = 17/7\nx = 2/3"} {"input": "Find x and y such that\n4x + 8y = 38\n2x + 8y = 43", "output": "4x + 8y = 38\n2x + 8y = 43\n\nUsing elimination\n2*(4x + 8y = 38)\n4*(2x + 8y = 43)\n8x + 16y = 76\n8x + 32y = 172\nSubtract equations\n-16y = -96\ny = -96/-16\ny = 6\n\nSubstitute y\n4x + 8(6) = 38\n4x = -10\nx = -10/4\nx = -5/2"} {"input": "Find the solution to 9x - 117/2 = 0", "output": "9x - 117/2 = 0\n9x = 117/2\nx = 117/2 / 9\nx = 13/2"} {"input": "Find x and y such that\n3x + 4y = 318/7\n5x + 3y = 508/7", "output": "3x + 4y = 318/7\n5x + 3y = 508/7\n\nUsing elimination\n5*(3x + 4y = 318/7)\n3*(5x + 3y = 508/7)\n15x + 20y = 1590/7\n15x + 9y = 1524/7\nSubtract equations\n11y = 66/7\ny = 66/7/11\ny = 6/7\n\nSubstitute y\n3x + 4(6/7) = 318/7\n3x = 42\nx = 42/3\nx = 14"} {"input": "Solve x^3 + 317/280x^2 - 151/80x - 57/70 = 0", "output": "x^3 + 317/280x^2 - 151/80x - 57/70 = 0\n(x - 8/7)(x - -19/10)(x - -3/8) = 0\nx - 8/7 = 0\nx - -19/10 = 0\nx - -3/8 = 0\nx = 8/7\nx = -19/10\nx = -3/8"} {"input": "Find x for 10x - 40 = 0", "output": "10x - 40 = 0\n10x = 40\nx = 40 / 10\nx = 4"} {"input": "Solve the equations:\n10x + 1y = 62/3\n4x + 3y = -2/5", "output": "10x + 1y = 62/3\n4x + 3y = -2/5\n\nUsing elimination\n4*(10x + 1y = 62/3)\n10*(4x + 3y = -2/5)\n40x + 4y = 248/3\n40x + 30y = -4\nSubtract equations\n-26y = 260/3\ny = 260/3/-26\ny = -10/3\n\nSubstitute y\n10x + 1(-10/3) = 62/3\n10x = 24\nx = 24/10\nx = 12/5"} {"input": "Find x for x^3 + 7/2x^2 + 49/25x = 0", "output": "x^3 + 7/2x^2 + 49/25x = 0\n(x - 0)(x - -14/5)(x - -7/10) = 0\nx - 0 = 0\nx - -14/5 = 0\nx - -7/10 = 0\nx = 0\nx = -14/5\nx = -7/10"} {"input": "Compute the solution of x^2 - 7/12x - 143/24 = 0", "output": "x^2 - 7/12x - 143/24 = 0\n(x - -13/6)(x - 11/4) = 0\nx - -13/6 = 0 or x - 11/4 = 0\nx = -13/6\nx = 11/4"} {"input": "What value of x satisfies x^3 + 61/8x^2 + 12x - 45/8 = 0", "output": "x^3 + 61/8x^2 + 12x - 45/8 = 0\n(x - 3/8)(x - -5)(x - -3) = 0\nx - 3/8 = 0\nx - -5 = 0\nx - -3 = 0\nx = 3/8\nx = -5\nx = -3"} {"input": "Solve the equations:\n5x + 8y = 21\n1x + 2y = 5", "output": "5x + 8y = 21\n1x + 2y = 5\n\nUsing elimination\n1*(5x + 8y = 21)\n5*(1x + 2y = 5)\n5x + 8y = 21\n5x + 10y = 25\nSubtract equations\n-2y = -4\ny = -4/-2\ny = 2\n\nSubstitute y\n5x + 8(2) = 21\n5x = 5\nx = 5/5\nx = 1"} {"input": "Solve x^3 - 35/12x^2 + 7/24x + 11/24 = 0", "output": "x^3 - 35/12x^2 + 7/24x + 11/24 = 0\n(x - 1/2)(x - 11/4)(x - -1/3) = 0\nx - 1/2 = 0\nx - 11/4 = 0\nx - -1/3 = 0\nx = 1/2\nx = 11/4\nx = -1/3"} {"input": "Solve the equations:\n2x + 1y = 43/24\n9x + 3y = 75/8", "output": "2x + 1y = 43/24\n9x + 3y = 75/8\n\nUsing elimination\n9*(2x + 1y = 43/24)\n2*(9x + 3y = 75/8)\n18x + 9y = 129/8\n18x + 6y = 75/4\nSubtract equations\n3y = -21/8\ny = -21/8/3\ny = -7/8\n\nSubstitute y\n2x + 1(-7/8) = 43/24\n2x = 8/3\nx = 8/3/2\nx = 4/3"} {"input": "Solve simultaneously:\n6x + 7y = 25/3\n10x + 10y = 50/3", "output": "6x + 7y = 25/3\n10x + 10y = 50/3\n\nUsing elimination\n10*(6x + 7y = 25/3)\n6*(10x + 10y = 50/3)\n60x + 70y = 250/3\n60x + 60y = 100\nSubtract equations\n10y = -50/3\ny = -50/3/10\ny = -5/3\n\nSubstitute y\n6x + 7(-5/3) = 25/3\n6x = 20\nx = 20/6\nx = 10/3"} {"input": "Find the solution to x^2 + 32/5x + 7 = 0", "output": "x^2 + 32/5x + 7 = 0\n(x - -7/5)(x - -5) = 0\nx - -7/5 = 0 or x - -5 = 0\nx = -7/5\nx = -5"} {"input": "What value of x satisfies x^3 + 2939/504x^2 + 803/72x + 442/63 = 0", "output": "x^3 + 2939/504x^2 + 803/72x + 442/63 = 0\n(x - -17/7)(x - -13/8)(x - -16/9) = 0\nx - -17/7 = 0\nx - -13/8 = 0\nx - -16/9 = 0\nx = -17/7\nx = -13/8\nx = -16/9"} {"input": "Solve x^2 - 32/35x + 1/7 = 0", "output": "x^2 - 32/35x + 1/7 = 0\n(x - 5/7)(x - 1/5) = 0\nx - 5/7 = 0 or x - 1/5 = 0\nx = 5/7\nx = 1/5"} {"input": "What value of x satisfies x^2 - 1/5x - 42/5 = 0", "output": "x^2 - 1/5x - 42/5 = 0\n(x - -14/5)(x - 3) = 0\nx - -14/5 = 0 or x - 3 = 0\nx = -14/5\nx = 3"} {"input": "Solve the equations:\n8x + 9y = 197/3\n5x + 10y = 395/6", "output": "8x + 9y = 197/3\n5x + 10y = 395/6\n\nUsing elimination\n5*(8x + 9y = 197/3)\n8*(5x + 10y = 395/6)\n40x + 45y = 985/3\n40x + 80y = 1580/3\nSubtract equations\n-35y = -595/3\ny = -595/3/-35\ny = 17/3\n\nSubstitute y\n8x + 9(17/3) = 197/3\n8x = 44/3\nx = 44/3/8\nx = 11/6"} {"input": "Compute the solution of x^2 - 1/3x - 2/3 = 0", "output": "x^2 - 1/3x - 2/3 = 0\n(x - -2/3)(x - 1) = 0\nx - -2/3 = 0 or x - 1 = 0\nx = -2/3\nx = 1"} {"input": "Solve 2x - 13/3 = 0", "output": "2x - 13/3 = 0\n2x = 13/3\nx = 13/3 / 2\nx = 13/6"} {"input": "What value of x satisfies x^2 + 17/14x - 3/7 = 0", "output": "x^2 + 17/14x - 3/7 = 0\n(x - 2/7)(x - -3/2) = 0\nx - 2/7 = 0 or x - -3/2 = 0\nx = 2/7\nx = -3/2"} {"input": "Solve quickly: x^3 - 14x^2 + 1949/36x - 2261/36 = 0", "output": "x^3 - 14x^2 + 1949/36x - 2261/36 = 0\n(x - 7/3)(x - 17/2)(x - 19/6) = 0\nx - 7/3 = 0\nx - 17/2 = 0\nx - 19/6 = 0\nx = 7/3\nx = 17/2\nx = 19/6"} {"input": "Solve the equation x^2 - 91/5x + 18/5 = 0", "output": "x^2 - 91/5x + 18/5 = 0\n(x - 1/5)(x - 18) = 0\nx - 1/5 = 0 or x - 18 = 0\nx = 1/5\nx = 18"} {"input": "Solve the system:\n9x + 7y = -164/5\n5x + 3y = -268/15", "output": "9x + 7y = -164/5\n5x + 3y = -268/15\n\nUsing elimination\n5*(9x + 7y = -164/5)\n9*(5x + 3y = -268/15)\n45x + 35y = -164\n45x + 27y = -804/5\nSubtract equations\n8y = -16/5\ny = -16/5/8\ny = -2/5\n\nSubstitute y\n9x + 7(-2/5) = -164/5\n9x = -30\nx = -30/9\nx = -10/3"} {"input": "Compute the solution of 9x - 72/5 = 0", "output": "9x - 72/5 = 0\n9x = 72/5\nx = 72/5 / 9\nx = 8/5"} {"input": "Find the solution to 4x - 16/3 = 0", "output": "4x - 16/3 = 0\n4x = 16/3\nx = 16/3 / 4\nx = 4/3"} {"input": "Solve quickly: 10x + 80 = 0", "output": "10x + 80 = 0\n10x = -80\nx = -80 / 10\nx = -8"} {"input": "Find x in 3x - 27 = 0", "output": "3x - 27 = 0\n3x = 27\nx = 27 / 3\nx = 9"} {"input": "Solve simultaneously:\n10x + 1y = -61/4\n5x + 8y = -17", "output": "10x + 1y = -61/4\n5x + 8y = -17\n\nUsing elimination\n5*(10x + 1y = -61/4)\n10*(5x + 8y = -17)\n50x + 5y = -305/4\n50x + 80y = -170\nSubtract equations\n-75y = 375/4\ny = 375/4/-75\ny = -5/4\n\nSubstitute y\n10x + 1(-5/4) = -61/4\n10x = -14\nx = -14/10\nx = -7/5"} {"input": "What value of x satisfies x^3 + 19/4x^2 + 55/8x + 25/8 = 0", "output": "x^3 + 19/4x^2 + 55/8x + 25/8 = 0\n(x - -1)(x - -5/2)(x - -5/4) = 0\nx - -1 = 0\nx - -5/2 = 0\nx - -5/4 = 0\nx = -1\nx = -5/2\nx = -5/4"} {"input": "Find x and y such that\n2x + 2y = 14\n1x + 6y = 32", "output": "2x + 2y = 14\n1x + 6y = 32\n\nUsing elimination\n1*(2x + 2y = 14)\n2*(1x + 6y = 32)\n2x + 2y = 14\n2x + 12y = 64\nSubtract equations\n-10y = -50\ny = -50/-10\ny = 5\n\nSubstitute y\n2x + 2(5) = 14\n2x = 4\nx = 4/2\nx = 2"} {"input": "Find x and y such that\n8x + 8y = 56/5\n3x + 9y = 33/5", "output": "8x + 8y = 56/5\n3x + 9y = 33/5\n\nUsing elimination\n3*(8x + 8y = 56/5)\n8*(3x + 9y = 33/5)\n24x + 24y = 168/5\n24x + 72y = 264/5\nSubtract equations\n-48y = -96/5\ny = -96/5/-48\ny = 2/5\n\nSubstitute y\n8x + 8(2/5) = 56/5\n8x = 8\nx = 8/8\nx = 1"} {"input": "Find x in 2x + 2/3 = 0", "output": "2x + 2/3 = 0\n2x = -2/3\nx = -2/3 / 2\nx = -1/3"} {"input": "What value of x satisfies 8x + 8 = 0", "output": "8x + 8 = 0\n8x = -8\nx = -8 / 8\nx = -1"} {"input": "Solve quickly: 4x - 44/5 = 0", "output": "4x - 44/5 = 0\n4x = 44/5\nx = 44/5 / 4\nx = 11/5"} {"input": "Solve simultaneously:\n1x + 9y = -77/6\n10x + 3y = 13/6", "output": "1x + 9y = -77/6\n10x + 3y = 13/6\n\nUsing elimination\n10*(1x + 9y = -77/6)\n1*(10x + 3y = 13/6)\n10x + 90y = -385/3\n10x + 3y = 13/6\nSubtract equations\n87y = -261/2\ny = -261/2/87\ny = -3/2\n\nSubstitute y\n1x + 9(-3/2) = -77/6\n1x = 2/3\nx = 2/3/1\nx = 2/3"} {"input": "Determine x in x^2 + 5/2x + 3/2 = 0", "output": "x^2 + 5/2x + 3/2 = 0\n(x - -1)(x - -3/2) = 0\nx - -1 = 0 or x - -3/2 = 0\nx = -1\nx = -3/2"} {"input": "Find x in x^2 + 46/5x + 119/20 = 0", "output": "x^2 + 46/5x + 119/20 = 0\n(x - -7/10)(x - -17/2) = 0\nx - -7/10 = 0 or x - -17/2 = 0\nx = -7/10\nx = -17/2"} {"input": "Solve quickly: 8x + 96 = 0", "output": "8x + 96 = 0\n8x = -96\nx = -96 / 8\nx = -12"} {"input": "What value of x satisfies 7x + 112/5 = 0", "output": "7x + 112/5 = 0\n7x = -112/5\nx = -112/5 / 7\nx = -16/5"} {"input": "Solve quickly: x^3 + 169/180x^2 - 2021/360x - 209/120 = 0", "output": "x^3 + 169/180x^2 - 2021/360x - 209/120 = 0\n(x - -3/10)(x - 19/9)(x - -11/4) = 0\nx - -3/10 = 0\nx - 19/9 = 0\nx - -11/4 = 0\nx = -3/10\nx = 19/9\nx = -11/4"} {"input": "Solve the equations:\n9x + 3y = -174/7\n1x + 7y = -346/7", "output": "9x + 3y = -174/7\n1x + 7y = -346/7\n\nUsing elimination\n1*(9x + 3y = -174/7)\n9*(1x + 7y = -346/7)\n9x + 3y = -174/7\n9x + 63y = -3114/7\nSubtract equations\n-60y = 420\ny = 420/-60\ny = -7\n\nSubstitute y\n9x + 3(-7) = -174/7\n9x = -27/7\nx = -27/7/9\nx = -3/7"} {"input": "Solve quickly: 4x + 72 = 0", "output": "4x + 72 = 0\n4x = -72\nx = -72 / 4\nx = -18"} {"input": "Solve x^2 - 83/10x - 57/5 = 0", "output": "x^2 - 83/10x - 57/5 = 0\n(x - 19/2)(x - -6/5) = 0\nx - 19/2 = 0 or x - -6/5 = 0\nx = 19/2\nx = -6/5"} {"input": "Find the solution to x^2 - 88/15x - 16/3 = 0", "output": "x^2 - 88/15x - 16/3 = 0\n(x - -4/5)(x - 20/3) = 0\nx - -4/5 = 0 or x - 20/3 = 0\nx = -4/5\nx = 20/3"} {"input": "Solve the equations:\n9x + 6y = -63/5\n8x + 10y = -56/3", "output": "9x + 6y = -63/5\n8x + 10y = -56/3\n\nUsing elimination\n8*(9x + 6y = -63/5)\n9*(8x + 10y = -56/3)\n72x + 48y = -504/5\n72x + 90y = -168\nSubtract equations\n-42y = 336/5\ny = 336/5/-42\ny = -8/5\n\nSubstitute y\n9x + 6(-8/5) = -63/5\n9x = -3\nx = -3/9\nx = -1/3"} {"input": "Solve the system:\n10x + 5y = 475/12\n4x + 3y = 43/2", "output": "10x + 5y = 475/12\n4x + 3y = 43/2\n\nUsing elimination\n4*(10x + 5y = 475/12)\n10*(4x + 3y = 43/2)\n40x + 20y = 475/3\n40x + 30y = 215\nSubtract equations\n-10y = -170/3\ny = -170/3/-10\ny = 17/3\n\nSubstitute y\n10x + 5(17/3) = 475/12\n10x = 45/4\nx = 45/4/10\nx = 9/8"} {"input": "Find x and y such that\n8x + 1y = -47/12\n9x + 4y = -8", "output": "8x + 1y = -47/12\n9x + 4y = -8\n\nUsing elimination\n9*(8x + 1y = -47/12)\n8*(9x + 4y = -8)\n72x + 9y = -141/4\n72x + 32y = -64\nSubtract equations\n-23y = 115/4\ny = 115/4/-23\ny = -5/4\n\nSubstitute y\n8x + 1(-5/4) = -47/12\n8x = -8/3\nx = -8/3/8\nx = -1/3"} {"input": "Solve the equation 6x + 14 = 0", "output": "6x + 14 = 0\n6x = -14\nx = -14 / 6\nx = -7/3"} {"input": "Find x in 2x - 36/7 = 0", "output": "2x - 36/7 = 0\n2x = 36/7\nx = 36/7 / 2\nx = 18/7"} {"input": "Find the solution to 5x - 50/7 = 0", "output": "5x - 50/7 = 0\n5x = 50/7\nx = 50/7 / 5\nx = 10/7"} {"input": "Solve x^2 - 26/9x + 160/81 = 0", "output": "x^2 - 26/9x + 160/81 = 0\n(x - 16/9)(x - 10/9) = 0\nx - 16/9 = 0 or x - 10/9 = 0\nx = 16/9\nx = 10/9"} {"input": "Solve the equation 5x + 20 = 0", "output": "5x + 20 = 0\n5x = -20\nx = -20 / 5\nx = -4"} {"input": "Determine x in x^2 - 131/7x - 180/7 = 0", "output": "x^2 - 131/7x - 180/7 = 0\n(x - 20)(x - -9/7) = 0\nx - 20 = 0 or x - -9/7 = 0\nx = 20\nx = -9/7"} {"input": "Determine x in x^3 + 17/10x^2 - 9/10x - 9/5 = 0", "output": "x^3 + 17/10x^2 - 9/10x - 9/5 = 0\n(x - -6/5)(x - -3/2)(x - 1) = 0\nx - -6/5 = 0\nx - -3/2 = 0\nx - 1 = 0\nx = -6/5\nx = -3/2\nx = 1"} {"input": "Find x for x^3 + 109/28x^2 - 21/2x - 855/28 = 0", "output": "x^3 + 109/28x^2 - 21/2x - 855/28 = 0\n(x - 3)(x - -15/7)(x - -19/4) = 0\nx - 3 = 0\nx - -15/7 = 0\nx - -19/4 = 0\nx = 3\nx = -15/7\nx = -19/4"} {"input": "Solve the system:\n10x + 9y = -707/20\n3x + 6y = -741/40", "output": "10x + 9y = -707/20\n3x + 6y = -741/40\n\nUsing elimination\n3*(10x + 9y = -707/20)\n10*(3x + 6y = -741/40)\n30x + 27y = -2121/20\n30x + 60y = -741/4\nSubtract equations\n-33y = 396/5\ny = 396/5/-33\ny = -12/5\n\nSubstitute y\n10x + 9(-12/5) = -707/20\n10x = -55/4\nx = -55/4/10\nx = -11/8"} {"input": "Solve quickly: x^3 + 27/10x^2 - 53/5x + 9/2 = 0", "output": "x^3 + 27/10x^2 - 53/5x + 9/2 = 0\n(x - -5)(x - 9/5)(x - 1/2) = 0\nx - -5 = 0\nx - 9/5 = 0\nx - 1/2 = 0\nx = -5\nx = 9/5\nx = 1/2"} {"input": "Solve the system:\n2x + 10y = -2\n9x + 5y = 31", "output": "2x + 10y = -2\n9x + 5y = 31\n\nUsing elimination\n9*(2x + 10y = -2)\n2*(9x + 5y = 31)\n18x + 90y = -18\n18x + 10y = 62\nSubtract equations\n80y = -80\ny = -80/80\ny = -1\n\nSubstitute y\n2x + 10(-1) = -2\n2x = 8\nx = 8/2\nx = 4"} {"input": "Find the solution to x^3 - 25/6x^2 + 29/6x - 5/3 = 0", "output": "x^3 - 25/6x^2 + 29/6x - 5/3 = 0\n(x - 2/3)(x - 5/2)(x - 1) = 0\nx - 2/3 = 0\nx - 5/2 = 0\nx - 1 = 0\nx = 2/3\nx = 5/2\nx = 1"} {"input": "Find x in 7x + 133/5 = 0", "output": "7x + 133/5 = 0\n7x = -133/5\nx = -133/5 / 7\nx = -19/5"} {"input": "Solve the equation x^2 - 41/35x - 22/35 = 0", "output": "x^2 - 41/35x - 22/35 = 0\n(x - -2/5)(x - 11/7) = 0\nx - -2/5 = 0 or x - 11/7 = 0\nx = -2/5\nx = 11/7"} {"input": "Solve simultaneously:\n4x + 2y = 23/10\n9x + 6y = 33/10", "output": "4x + 2y = 23/10\n9x + 6y = 33/10\n\nUsing elimination\n9*(4x + 2y = 23/10)\n4*(9x + 6y = 33/10)\n36x + 18y = 207/10\n36x + 24y = 66/5\nSubtract equations\n-6y = 15/2\ny = 15/2/-6\ny = -5/4\n\nSubstitute y\n4x + 2(-5/4) = 23/10\n4x = 24/5\nx = 24/5/4\nx = 6/5"} {"input": "Compute the solution of 5x - 5/4 = 0", "output": "5x - 5/4 = 0\n5x = 5/4\nx = 5/4 / 5\nx = 1/4"} {"input": "Determine x in x^2 - 5/4x - 51/4 = 0", "output": "x^2 - 5/4x - 51/4 = 0\n(x - 17/4)(x - -3) = 0\nx - 17/4 = 0 or x - -3 = 0\nx = 17/4\nx = -3"} {"input": "Compute the solution of x^3 + 101/56x^2 - 249/112x - 135/112 = 0", "output": "x^3 + 101/56x^2 - 249/112x - 135/112 = 0\n(x - 9/8)(x - -3/7)(x - -5/2) = 0\nx - 9/8 = 0\nx - -3/7 = 0\nx - -5/2 = 0\nx = 9/8\nx = -3/7\nx = -5/2"} {"input": "Find x for 4x + 38/5 = 0", "output": "4x + 38/5 = 0\n4x = -38/5\nx = -38/5 / 4\nx = -19/10"} {"input": "Find the solution to 4x + 10/3 = 0", "output": "4x + 10/3 = 0\n4x = -10/3\nx = -10/3 / 4\nx = -5/6"} {"input": "Solve the equation x^2 + 109/36x + 7/4 = 0", "output": "x^2 + 109/36x + 7/4 = 0\n(x - -7/9)(x - -9/4) = 0\nx - -7/9 = 0 or x - -9/4 = 0\nx = -7/9\nx = -9/4"} {"input": "Find x and y such that\n3x + 2y = 127/10\n2x + 8y = 209/5", "output": "3x + 2y = 127/10\n2x + 8y = 209/5\n\nUsing elimination\n2*(3x + 2y = 127/10)\n3*(2x + 8y = 209/5)\n6x + 4y = 127/5\n6x + 24y = 627/5\nSubtract equations\n-20y = -100\ny = -100/-20\ny = 5\n\nSubstitute y\n3x + 2(5) = 127/10\n3x = 27/10\nx = 27/10/3\nx = 9/10"} {"input": "Solve the system:\n3x + 1y = -91/15\n7x + 8y = 241/15", "output": "3x + 1y = -91/15\n7x + 8y = 241/15\n\nUsing elimination\n7*(3x + 1y = -91/15)\n3*(7x + 8y = 241/15)\n21x + 7y = -637/15\n21x + 24y = 241/5\nSubtract equations\n-17y = -272/3\ny = -272/3/-17\ny = 16/3\n\nSubstitute y\n3x + 1(16/3) = -91/15\n3x = -57/5\nx = -57/5/3\nx = -19/5"} {"input": "Find the solution to x^2 + 4/3x - 160/81 = 0", "output": "x^2 + 4/3x - 160/81 = 0\n(x - 8/9)(x - -20/9) = 0\nx - 8/9 = 0 or x - -20/9 = 0\nx = 8/9\nx = -20/9"} {"input": "Find the solution to x^2 - 251/72x + 209/72 = 0", "output": "x^2 - 251/72x + 209/72 = 0\n(x - 11/8)(x - 19/9) = 0\nx - 11/8 = 0 or x - 19/9 = 0\nx = 11/8\nx = 19/9"} {"input": "Find the solution to x^3 - 59/7x^2 - 23/28x + 51/28 = 0", "output": "x^3 - 59/7x^2 - 23/28x + 51/28 = 0\n(x - -1/2)(x - 17/2)(x - 3/7) = 0\nx - -1/2 = 0\nx - 17/2 = 0\nx - 3/7 = 0\nx = -1/2\nx = 17/2\nx = 3/7"} {"input": "Compute the solution of x^2 - 157/36x + 65/18 = 0", "output": "x^2 - 157/36x + 65/18 = 0\n(x - 13/4)(x - 10/9) = 0\nx - 13/4 = 0 or x - 10/9 = 0\nx = 13/4\nx = 10/9"} {"input": "Find x for 3x + 9 = 0", "output": "3x + 9 = 0\n3x = -9\nx = -9 / 3\nx = -3"} {"input": "Find the solution to x^3 - 131/30x^2 + 1601/300x - 247/200 = 0", "output": "x^3 - 131/30x^2 + 1601/300x - 247/200 = 0\n(x - 19/10)(x - 13/6)(x - 3/10) = 0\nx - 19/10 = 0\nx - 13/6 = 0\nx - 3/10 = 0\nx = 19/10\nx = 13/6\nx = 3/10"} {"input": "Solve x^2 + 16/3x - 4 = 0", "output": "x^2 + 16/3x - 4 = 0\n(x - 2/3)(x - -6) = 0\nx - 2/3 = 0 or x - -6 = 0\nx = 2/3\nx = -6"} {"input": "Solve the system:\n6x + 3y = 153/20\n8x + 1y = 279/20", "output": "6x + 3y = 153/20\n8x + 1y = 279/20\n\nUsing elimination\n8*(6x + 3y = 153/20)\n6*(8x + 1y = 279/20)\n48x + 24y = 306/5\n48x + 6y = 837/10\nSubtract equations\n18y = -45/2\ny = -45/2/18\ny = -5/4\n\nSubstitute y\n6x + 3(-5/4) = 153/20\n6x = 57/5\nx = 57/5/6\nx = 19/10"} {"input": "Solve the equations:\n4x + 1y = -25/18\n10x + 7y = -319/18", "output": "4x + 1y = -25/18\n10x + 7y = -319/18\n\nUsing elimination\n10*(4x + 1y = -25/18)\n4*(10x + 7y = -319/18)\n40x + 10y = -125/9\n40x + 28y = -638/9\nSubtract equations\n-18y = 57\ny = 57/-18\ny = -19/6\n\nSubstitute y\n4x + 1(-19/6) = -25/18\n4x = 16/9\nx = 16/9/4\nx = 4/9"} {"input": "Compute the solution of 4x + 2 = 0", "output": "4x + 2 = 0\n4x = -2\nx = -2 / 4\nx = -1/2"} {"input": "Determine x in x^2 + 7/4x - 65/4 = 0", "output": "x^2 + 7/4x - 65/4 = 0\n(x - -5)(x - 13/4) = 0\nx - -5 = 0 or x - 13/4 = 0\nx = -5\nx = 13/4"} {"input": "Solve the equations:\n3x + 9y = -315/2\n7x + 10y = -339/2", "output": "3x + 9y = -315/2\n7x + 10y = -339/2\n\nUsing elimination\n7*(3x + 9y = -315/2)\n3*(7x + 10y = -339/2)\n21x + 63y = -2205/2\n21x + 30y = -1017/2\nSubtract equations\n33y = -594\ny = -594/33\ny = -18\n\nSubstitute y\n3x + 9(-18) = -315/2\n3x = 9/2\nx = 9/2/3\nx = 3/2"} {"input": "Find x for 5x + 65/9 = 0", "output": "5x + 65/9 = 0\n5x = -65/9\nx = -65/9 / 5\nx = -13/9"} {"input": "Solve the equation 4x + 32/9 = 0", "output": "4x + 32/9 = 0\n4x = -32/9\nx = -32/9 / 4\nx = -8/9"} {"input": "Solve the system:\n2x + 5y = 11/2\n3x + 6y = 12", "output": "2x + 5y = 11/2\n3x + 6y = 12\n\nUsing elimination\n3*(2x + 5y = 11/2)\n2*(3x + 6y = 12)\n6x + 15y = 33/2\n6x + 12y = 24\nSubtract equations\n3y = -15/2\ny = -15/2/3\ny = -5/2\n\nSubstitute y\n2x + 5(-5/2) = 11/2\n2x = 18\nx = 18/2\nx = 9"} {"input": "Solve the equations:\n10x + 4y = 38/3\n2x + 5y = -26/3", "output": "10x + 4y = 38/3\n2x + 5y = -26/3\n\nUsing elimination\n2*(10x + 4y = 38/3)\n10*(2x + 5y = -26/3)\n20x + 8y = 76/3\n20x + 50y = -260/3\nSubtract equations\n-42y = 112\ny = 112/-42\ny = -8/3\n\nSubstitute y\n10x + 4(-8/3) = 38/3\n10x = 70/3\nx = 70/3/10\nx = 7/3"} {"input": "Find the solution to 7x + 63 = 0", "output": "7x + 63 = 0\n7x = -63\nx = -63 / 7\nx = -9"} {"input": "Compute the solution of x^3 + 27/10x^2 - 24/5x + 8/5 = 0", "output": "x^3 + 27/10x^2 - 24/5x + 8/5 = 0\n(x - 1/2)(x - 4/5)(x - -4) = 0\nx - 1/2 = 0\nx - 4/5 = 0\nx - -4 = 0\nx = 1/2\nx = 4/5\nx = -4"} {"input": "Solve the equation x^2 + 112/15x + 16/3 = 0", "output": "x^2 + 112/15x + 16/3 = 0\n(x - -20/3)(x - -4/5) = 0\nx - -20/3 = 0 or x - -4/5 = 0\nx = -20/3\nx = -4/5"} {"input": "Find x and y such that\n4x + 2y = 3\n2x + 5y = 3/2", "output": "4x + 2y = 3\n2x + 5y = 3/2\n\nUsing elimination\n2*(4x + 2y = 3)\n4*(2x + 5y = 3/2)\n8x + 4y = 6\n8x + 20y = 6\nSubtract equations\n-16y = 0\ny = 0/-16\ny = 0\n\nSubstitute y\n4x + 2(0) = 3\n4x = 3\nx = 3/4\nx = 3/4"} {"input": "Solve quickly: x^3 + 69/20x^2 + 27/10x = 0", "output": "x^3 + 69/20x^2 + 27/10x = 0\n(x - 0)(x - -9/4)(x - -6/5) = 0\nx - 0 = 0\nx - -9/4 = 0\nx - -6/5 = 0\nx = 0\nx = -9/4\nx = -6/5"} {"input": "Find x for x^3 + 43/36x^2 - 518/27x + 416/27 = 0", "output": "x^3 + 43/36x^2 - 518/27x + 416/27 = 0\n(x - 13/4)(x - 8/9)(x - -16/3) = 0\nx - 13/4 = 0\nx - 8/9 = 0\nx - -16/3 = 0\nx = 13/4\nx = 8/9\nx = -16/3"} {"input": "Find x and y such that\n10x + 10y = 63/2\n7x + 8y = 469/20", "output": "10x + 10y = 63/2\n7x + 8y = 469/20\n\nUsing elimination\n7*(10x + 10y = 63/2)\n10*(7x + 8y = 469/20)\n70x + 70y = 441/2\n70x + 80y = 469/2\nSubtract equations\n-10y = -14\ny = -14/-10\ny = 7/5\n\nSubstitute y\n10x + 10(7/5) = 63/2\n10x = 35/2\nx = 35/2/10\nx = 7/4"} {"input": "Solve simultaneously:\n10x + 4y = -5\n4x + 1y = -5", "output": "10x + 4y = -5\n4x + 1y = -5\n\nUsing elimination\n4*(10x + 4y = -5)\n10*(4x + 1y = -5)\n40x + 16y = -20\n40x + 10y = -50\nSubtract equations\n6y = 30\ny = 30/6\ny = 5\n\nSubstitute y\n10x + 4(5) = -5\n10x = -25\nx = -25/10\nx = -5/2"} {"input": "Find x and y such that\n2x + 1y = -40/9\n5x + 9y = -15/2", "output": "2x + 1y = -40/9\n5x + 9y = -15/2\n\nUsing elimination\n5*(2x + 1y = -40/9)\n2*(5x + 9y = -15/2)\n10x + 5y = -200/9\n10x + 18y = -15\nSubtract equations\n-13y = -65/9\ny = -65/9/-13\ny = 5/9\n\nSubstitute y\n2x + 1(5/9) = -40/9\n2x = -5\nx = -5/2\nx = -5/2"} {"input": "Find the solution to x^3 + 23/10x^2 + 13/18x - 11/45 = 0", "output": "x^3 + 23/10x^2 + 13/18x - 11/45 = 0\n(x - -11/6)(x - 1/5)(x - -2/3) = 0\nx - -11/6 = 0\nx - 1/5 = 0\nx - -2/3 = 0\nx = -11/6\nx = 1/5\nx = -2/3"} {"input": "Solve 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Solve 4x + 44/5 = 0", "output": "4x + 44/5 = 0\n4x = -44/5\nx = -44/5 / 4\nx = -11/5"} {"input": "What value of x satisfies 3x + 9/8 = 0", "output": "3x + 9/8 = 0\n3x = -9/8\nx = -9/8 / 3\nx = -3/8"} {"input": "What value of x satisfies x^2 - 5/4x - 7/8 = 0", "output": "x^2 - 5/4x - 7/8 = 0\n(x - 7/4)(x - -1/2) = 0\nx - 7/4 = 0 or x - -1/2 = 0\nx = 7/4\nx = -1/2"} {"input": "Solve the equation x^3 - 49/8x^2 + 189/16x - 117/16 = 0", "output": "x^3 - 49/8x^2 + 189/16x - 117/16 = 0\n(x - 3)(x - 13/8)(x - 3/2) = 0\nx - 3 = 0\nx - 13/8 = 0\nx - 3/2 = 0\nx = 3\nx = 13/8\nx = 3/2"} {"input": "Solve simultaneously:\n9x + 9y = -57/5\n7x + 8y = -113/15", "output": "9x + 9y = -57/5\n7x + 8y = -113/15\n\nUsing elimination\n7*(9x + 9y = -57/5)\n9*(7x + 8y = -113/15)\n63x + 63y = -399/5\n63x + 72y = -339/5\nSubtract equations\n-9y = -12\ny = -12/-9\ny = 4/3\n\nSubstitute y\n9x + 9(4/3) = -57/5\n9x = -117/5\nx = -117/5/9\nx = -13/5"} {"input": "Determine x in x^2 + 11/4x + 3/2 = 0", "output": "x^2 + 11/4x + 3/2 = 0\n(x - -2)(x - -3/4) = 0\nx - -2 = 0 or x - -3/4 = 0\nx = -2\nx = -3/4"} {"input": "Solve the equation x^2 - 23/7x + 6/7 = 0", "output": "x^2 - 23/7x + 6/7 = 0\n(x - 2/7)(x - 3) = 0\nx - 2/7 = 0 or x - 3 = 0\nx = 2/7\nx = 3"} {"input": "Solve quickly: 9x + 117/4 = 0", "output": "9x + 117/4 = 0\n9x = -117/4\nx = -117/4 / 9\nx = -13/4"} {"input": "Compute the solution of 9x - 7 = 0", "output": "9x - 7 = 0\n9x = 7\nx = 7 / 9\nx = 7/9"} {"input": "Solve the equation x^2 - 33/8x + 91/32 = 0", "output": "x^2 - 33/8x + 91/32 = 0\n(x - 13/4)(x - 7/8) = 0\nx - 13/4 = 0 or x - 7/8 = 0\nx = 13/4\nx = 7/8"} {"input": "Find x for x^2 - 16/15x - 1 = 0", "output": "x^2 - 16/15x - 1 = 0\n(x - 5/3)(x - -3/5) = 0\nx - 5/3 = 0 or x - -3/5 = 0\nx = 5/3\nx = -3/5"} {"input": "What value of x satisfies x^2 + 2x = 0", "output": "x^2 + 2x = 0\n(x - -2)(x - 0) = 0\nx - -2 = 0 or x - 0 = 0\nx = -2\nx = 0"} {"input": "Find x for 1x + 17/10 = 0", "output": "1x + 17/10 = 0\n1x = -17/10\nx = -17/10 / 1\nx = -17/10"} {"input": "Compute the solution of 8x - 12 = 0", "output": "8x - 12 = 0\n8x = 12\nx = 12 / 8\nx = 3/2"} {"input": "Find the solution to x^2 + 7x - 18 = 0", "output": "x^2 + 7x - 18 = 0\n(x - 2)(x - -9) = 0\nx - 2 = 0 or x - -9 = 0\nx = 2\nx = -9"} {"input": "Find x in 7x = 0", "output": "7x = 0\n7x = 0\nx = 0 / 7\nx = 0"} {"input": "Solve quickly: 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Compute the solution of x^2 + 22/9x - 221/27 = 0", "output": "x^2 + 22/9x - 221/27 = 0\n(x - -13/3)(x - 17/9) = 0\nx - -13/3 = 0 or x - 17/9 = 0\nx = -13/3\nx = 17/9"} {"input": "Solve x^2 - 11/4x - 5 = 0", "output": "x^2 - 11/4x - 5 = 0\n(x - -5/4)(x - 4) = 0\nx - -5/4 = 0 or x - 4 = 0\nx = -5/4\nx = 4"} {"input": "Find the solution to x^2 - 7/15x - 13/12 = 0", "output": "x^2 - 7/15x - 13/12 = 0\n(x - -5/6)(x - 13/10) = 0\nx - -5/6 = 0 or x - 13/10 = 0\nx = -5/6\nx = 13/10"} {"input": "Solve x^3 - 11/2x^2 + 15/2x = 0", "output": "x^3 - 11/2x^2 + 15/2x = 0\n(x - 3)(x - 0)(x - 5/2) = 0\nx - 3 = 0\nx - 0 = 0\nx - 5/2 = 0\nx = 3\nx = 0\nx = 5/2"} {"input": "Solve x^2 - 5x - 24 = 0", "output": "x^2 - 5x - 24 = 0\n(x - -3)(x - 8) = 0\nx - -3 = 0 or x - 8 = 0\nx = -3\nx = 8"} {"input": "Determine x in 4x - 17 = 0", "output": "4x - 17 = 0\n4x = 17\nx = 17 / 4\nx = 17/4"} {"input": "Solve the system:\n4x + 4y = 12/5\n7x + 8y = 57/10", "output": "4x + 4y = 12/5\n7x + 8y = 57/10\n\nUsing elimination\n7*(4x + 4y = 12/5)\n4*(7x + 8y = 57/10)\n28x + 28y = 84/5\n28x + 32y = 114/5\nSubtract equations\n-4y = -6\ny = -6/-4\ny = 3/2\n\nSubstitute y\n4x + 4(3/2) = 12/5\n4x = -18/5\nx = -18/5/4\nx = -9/10"} {"input": "Determine x in x^2 - 26/5x + 133/25 = 0", "output": "x^2 - 26/5x + 133/25 = 0\n(x - 7/5)(x - 19/5) = 0\nx - 7/5 = 0 or x - 19/5 = 0\nx = 7/5\nx = 19/5"} {"input": "Compute the solution of x^2 + 61/15x + 22/15 = 0", "output": "x^2 + 61/15x + 22/15 = 0\n(x - -2/5)(x - -11/3) = 0\nx - -2/5 = 0 or x - -11/3 = 0\nx = -2/5\nx = -11/3"} {"input": "Find the solution to 3x - 15/4 = 0", "output": "3x - 15/4 = 0\n3x = 15/4\nx = 15/4 / 3\nx = 5/4"} {"input": "Solve the system:\n7x + 3y = 11\n1x + 4y = -64/7", "output": "7x + 3y = 11\n1x + 4y = -64/7\n\nUsing elimination\n1*(7x + 3y = 11)\n7*(1x + 4y = -64/7)\n7x + 3y = 11\n7x + 28y = -64\nSubtract equations\n-25y = 75\ny = 75/-25\ny = -3\n\nSubstitute y\n7x + 3(-3) = 11\n7x = 20\nx = 20/7\nx = 20/7"} {"input": "Find the solution to 5x - 25/2 = 0", "output": "5x - 25/2 = 0\n5x = 25/2\nx = 25/2 / 5\nx = 5/2"} {"input": "Solve the equation x^2 - 5/4x - 63/8 = 0", "output": "x^2 - 5/4x - 63/8 = 0\n(x - -9/4)(x - 7/2) = 0\nx - -9/4 = 0 or x - 7/2 = 0\nx = -9/4\nx = 7/2"} {"input": "Determine x in 7x - 7 = 0", "output": "7x - 7 = 0\n7x = 7\nx = 7 / 7\nx = 1"} {"input": "Find the solution to x^3 - 267/35x^2 + 477/35x - 17/7 = 0", "output": "x^3 - 267/35x^2 + 477/35x - 17/7 = 0\n(x - 17/7)(x - 5)(x - 1/5) = 0\nx - 17/7 = 0\nx - 5 = 0\nx - 1/5 = 0\nx = 17/7\nx = 5\nx = 1/5"} {"input": "Solve the equation 9x + 2 = 0", "output": "9x + 2 = 0\n9x = -2\nx = -2 / 9\nx = -2/9"} {"input": "Determine x in 3x + 21/2 = 0", "output": "3x + 21/2 = 0\n3x = -21/2\nx = -21/2 / 3\nx = -7/2"} {"input": "Solve quickly: x^2 + 89/28x + 51/28 = 0", "output": "x^2 + 89/28x + 51/28 = 0\n(x - -3/4)(x - -17/7) = 0\nx - -3/4 = 0 or x - -17/7 = 0\nx = -3/4\nx = -17/7"} {"input": "Solve the system:\n8x + 7y = 11/3\n10x + 4y = 151/6", "output": "8x + 7y = 11/3\n10x + 4y = 151/6\n\nUsing elimination\n10*(8x + 7y = 11/3)\n8*(10x + 4y = 151/6)\n80x + 70y = 110/3\n80x + 32y = 604/3\nSubtract equations\n38y = -494/3\ny = -494/3/38\ny = -13/3\n\nSubstitute y\n8x + 7(-13/3) = 11/3\n8x = 34\nx = 34/8\nx = 17/4"} {"input": "What value of x satisfies x^2 - 41/12x + 13/24 = 0", "output": "x^2 - 41/12x + 13/24 = 0\n(x - 13/4)(x - 1/6) = 0\nx - 13/4 = 0 or x - 1/6 = 0\nx = 13/4\nx = 1/6"} {"input": "Solve the system:\n4x + 9y = -147/2\n3x + 5y = -42", "output": "4x + 9y = -147/2\n3x + 5y = -42\n\nUsing elimination\n3*(4x + 9y = -147/2)\n4*(3x + 5y = -42)\n12x + 27y = -441/2\n12x + 20y = -168\nSubtract equations\n7y = -105/2\ny = -105/2/7\ny = -15/2\n\nSubstitute y\n4x + 9(-15/2) = -147/2\n4x = -6\nx = -6/4\nx = -3/2"} {"input": "Compute the solution of x^2 + 29/10x + 19/10 = 0", "output": "x^2 + 29/10x + 19/10 = 0\n(x - -19/10)(x - -1) = 0\nx - -19/10 = 0 or x - -1 = 0\nx = -19/10\nx = -1"} {"input": "Solve the system:\n2x + 9y = 163/10\n6x + 2y = 7/5", "output": "2x + 9y = 163/10\n6x + 2y = 7/5\n\nUsing elimination\n6*(2x + 9y = 163/10)\n2*(6x + 2y = 7/5)\n12x + 54y = 489/5\n12x + 4y = 14/5\nSubtract equations\n50y = 95\ny = 95/50\ny = 19/10\n\nSubstitute y\n2x + 9(19/10) = 163/10\n2x = -4/5\nx = -4/5/2\nx = -2/5"} {"input": "Solve 9x - 27/4 = 0", "output": "9x - 27/4 = 0\n9x = 27/4\nx = 27/4 / 9\nx = 3/4"} {"input": "Find the solution to x^2 + 3/2x - 27/2 = 0", "output": "x^2 + 3/2x - 27/2 = 0\n(x - 3)(x - -9/2) = 0\nx - 3 = 0 or x - -9/2 = 0\nx = 3\nx = -9/2"} {"input": "Solve the equation x^3 - 11/3x^2 + 4x - 4/3 = 0", "output": "x^3 - 11/3x^2 + 4x - 4/3 = 0\n(x - 1)(x - 2/3)(x - 2) = 0\nx - 1 = 0\nx - 2/3 = 0\nx - 2 = 0\nx = 1\nx = 2/3\nx = 2"} {"input": "Solve the equation 1x - 5/4 = 0", "output": "1x - 5/4 = 0\n1x = 5/4\nx = 5/4 / 1\nx = 5/4"} {"input": "Solve x^2 + 25/12x + 1 = 0", "output": "x^2 + 25/12x + 1 = 0\n(x - -3/4)(x - -4/3) = 0\nx - -3/4 = 0 or x - -4/3 = 0\nx = -3/4\nx = -4/3"} {"input": "Find x and y such that\n10x + 10y = 105\n7x + 3y = 127/2", "output": "10x + 10y = 105\n7x + 3y = 127/2\n\nUsing elimination\n7*(10x + 10y = 105)\n10*(7x + 3y = 127/2)\n70x + 70y = 735\n70x + 30y = 635\nSubtract equations\n40y = 100\ny = 100/40\ny = 5/2\n\nSubstitute y\n10x + 10(5/2) = 105\n10x = 80\nx = 80/10\nx = 8"} {"input": "Solve 9x - 36 = 0", "output": "9x - 36 = 0\n9x = 36\nx = 36 / 9\nx = 4"} {"input": "Find the solution to x^3 + 155/21x^2 + 46/21x - 120/7 = 0", "output": "x^3 + 155/21x^2 + 46/21x - 120/7 = 0\n(x - 9/7)(x - -2)(x - -20/3) = 0\nx - 9/7 = 0\nx - -2 = 0\nx - -20/3 = 0\nx = 9/7\nx = -2\nx = -20/3"} {"input": "Solve the system:\n4x + 7y = 201/4\n10x + 5y = 415/4", "output": "4x + 7y = 201/4\n10x + 5y = 415/4\n\nUsing elimination\n10*(4x + 7y = 201/4)\n4*(10x + 5y = 415/4)\n40x + 70y = 1005/2\n40x + 20y = 415\nSubtract equations\n50y = 175/2\ny = 175/2/50\ny = 7/4\n\nSubstitute y\n4x + 7(7/4) = 201/4\n4x = 38\nx = 38/4\nx = 19/2"} {"input": "Solve simultaneously:\n1x + 2y = 46/5\n4x + 7y = 164/5", "output": "1x + 2y = 46/5\n4x + 7y = 164/5\n\nUsing elimination\n4*(1x + 2y = 46/5)\n1*(4x + 7y = 164/5)\n4x + 8y = 184/5\n4x + 7y = 164/5\nSubtract equations\n1y = 4\ny = 4/1\ny = 4\n\nSubstitute y\n1x + 2(4) = 46/5\n1x = 6/5\nx = 6/5/1\nx = 6/5"} {"input": "Find the solution to 3x - 24/5 = 0", "output": "3x - 24/5 = 0\n3x = 24/5\nx = 24/5 / 3\nx = 8/5"} {"input": "Compute the solution of x^3 - 31/10x^2 - 9/5x + 63/10 = 0", "output": "x^3 - 31/10x^2 - 9/5x + 63/10 = 0\n(x - 3/2)(x - -7/5)(x - 3) = 0\nx - 3/2 = 0\nx - -7/5 = 0\nx - 3 = 0\nx = 3/2\nx = -7/5\nx = 3"} {"input": "Solve the equations:\n3x + 4y = -11/2\n5x + 10y = -25/2", "output": "3x + 4y = -11/2\n5x + 10y = -25/2\n\nUsing elimination\n5*(3x + 4y = -11/2)\n3*(5x + 10y = -25/2)\n15x + 20y = -55/2\n15x + 30y = -75/2\nSubtract equations\n-10y = 10\ny = 10/-10\ny = -1\n\nSubstitute y\n3x + 4(-1) = -11/2\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Solve quickly: x^3 - 15/8x^2 - 63/16x + 27/16 = 0", "output": "x^3 - 15/8x^2 - 63/16x + 27/16 = 0\n(x - -3/2)(x - 3/8)(x - 3) = 0\nx - -3/2 = 0\nx - 3/8 = 0\nx - 3 = 0\nx = -3/2\nx = 3/8\nx = 3"} {"input": "Determine x in x^3 + 18/7x^2 - 165/28x - 425/28 = 0", "output": "x^3 + 18/7x^2 - 165/28x - 425/28 = 0\n(x - -5/2)(x - 17/7)(x - -5/2) = 0\nx - -5/2 = 0\nx - 17/7 = 0\nx - -5/2 = 0\nx = -5/2\nx = 17/7\nx = -5/2"} {"input": "Find x for x^2 - 1x - 10/9 = 0", "output": "x^2 - 1x - 10/9 = 0\n(x - 5/3)(x - -2/3) = 0\nx - 5/3 = 0 or x - -2/3 = 0\nx = 5/3\nx = -2/3"} {"input": "Solve the equation 2x + 5 = 0", "output": "2x + 5 = 0\n2x = -5\nx = -5 / 2\nx = -5/2"} {"input": "Find x and y such that\n10x + 9y = -135/4\n9x + 10y = -178/5", "output": "10x + 9y = -135/4\n9x + 10y = -178/5\n\nUsing elimination\n9*(10x + 9y = -135/4)\n10*(9x + 10y = -178/5)\n90x + 81y = -1215/4\n90x + 100y = -356\nSubtract equations\n-19y = 209/4\ny = 209/4/-19\ny = -11/4\n\nSubstitute y\n10x + 9(-11/4) = -135/4\n10x = -9\nx = -9/10\nx = -9/10"} {"input": "Find x and y such that\n7x + 9y = 9\n4x + 10y = 23/4", "output": "7x + 9y = 9\n4x + 10y = 23/4\n\nUsing elimination\n4*(7x + 9y = 9)\n7*(4x + 10y = 23/4)\n28x + 36y = 36\n28x + 70y = 161/4\nSubtract equations\n-34y = -17/4\ny = -17/4/-34\ny = 1/8\n\nSubstitute y\n7x + 9(1/8) = 9\n7x = 63/8\nx = 63/8/7\nx = 9/8"} {"input": "Solve quickly: x^2 - 9/2x - 209/18 = 0", "output": "x^2 - 9/2x - 209/18 = 0\n(x - -11/6)(x - 19/3) = 0\nx - -11/6 = 0 or x - 19/3 = 0\nx = -11/6\nx = 19/3"} {"input": "Determine x in 2x + 7/5 = 0", "output": "2x + 7/5 = 0\n2x = -7/5\nx = -7/5 / 2\nx = -7/10"} {"input": "Solve the system:\n3x + 2y = 14\n7x + 3y = 73/3", "output": "3x + 2y = 14\n7x + 3y = 73/3\n\nUsing elimination\n7*(3x + 2y = 14)\n3*(7x + 3y = 73/3)\n21x + 14y = 98\n21x + 9y = 73\nSubtract equations\n5y = 25\ny = 25/5\ny = 5\n\nSubstitute y\n3x + 2(5) = 14\n3x = 4\nx = 4/3\nx = 4/3"} {"input": "Find x for x^2 - 8/5x - 48/5 = 0", "output": "x^2 - 8/5x - 48/5 = 0\n(x - 4)(x - -12/5) = 0\nx - 4 = 0 or x - -12/5 = 0\nx = 4\nx = -12/5"} {"input": "Find x in x^3 + 677/84x^2 + 415/21x + 425/28 = 0", "output": "x^3 + 677/84x^2 + 415/21x + 425/28 = 0\n(x - -5/3)(x - -15/7)(x - -17/4) = 0\nx - -5/3 = 0\nx - -15/7 = 0\nx - -17/4 = 0\nx = -5/3\nx = -15/7\nx = -17/4"} {"input": "What value of x satisfies x^3 + 499/60x^2 + 1363/60x + 102/5 = 0", "output": "x^3 + 499/60x^2 + 1363/60x + 102/5 = 0\n(x - -9/4)(x - -17/5)(x - -8/3) = 0\nx - -9/4 = 0\nx - -17/5 = 0\nx - -8/3 = 0\nx = -9/4\nx = -17/5\nx = -8/3"} {"input": "Solve the equations:\n1x + 10y = 641/21\n6x + 10y = 521/21", "output": "1x + 10y = 641/21\n6x + 10y = 521/21\n\nUsing elimination\n6*(1x + 10y = 641/21)\n1*(6x + 10y = 521/21)\n6x + 60y = 1282/7\n6x + 10y = 521/21\nSubtract equations\n50y = 475/3\ny = 475/3/50\ny = 19/6\n\nSubstitute y\n1x + 10(19/6) = 641/21\n1x = -8/7\nx = -8/7/1\nx = -8/7"} {"input": "Solve the equation 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Solve x^3 + 44/21x^2 - 25/3x - 66/7 = 0", "output": "x^3 + 44/21x^2 - 25/3x - 66/7 = 0\n(x - -1)(x - -11/3)(x - 18/7) = 0\nx - -1 = 0\nx - -11/3 = 0\nx - 18/7 = 0\nx = -1\nx = -11/3\nx = 18/7"} {"input": "What value of x satisfies x^2 - 132/35x + 108/35 = 0", "output": "x^2 - 132/35x + 108/35 = 0\n(x - 18/7)(x - 6/5) = 0\nx - 18/7 = 0 or x - 6/5 = 0\nx = 18/7\nx = 6/5"} {"input": "Find x and y such that\n8x + 2y = 20/3\n2x + 10y = -52/3", "output": "8x + 2y = 20/3\n2x + 10y = -52/3\n\nUsing elimination\n2*(8x + 2y = 20/3)\n8*(2x + 10y = -52/3)\n16x + 4y = 40/3\n16x + 80y = -416/3\nSubtract equations\n-76y = 152\ny = 152/-76\ny = -2\n\nSubstitute y\n8x + 2(-2) = 20/3\n8x = 32/3\nx = 32/3/8\nx = 4/3"} {"input": "Find x in 5x - 65/7 = 0", "output": "5x - 65/7 = 0\n5x = 65/7\nx = 65/7 / 5\nx = 13/7"} {"input": "Solve the equation 9x + 171/7 = 0", "output": "9x + 171/7 = 0\n9x = -171/7\nx = -171/7 / 9\nx = -19/7"} {"input": "Solve simultaneously:\n7x + 3y = 31/3\n8x + 10y = 1618/63", "output": "7x + 3y = 31/3\n8x + 10y = 1618/63\n\nUsing elimination\n8*(7x + 3y = 31/3)\n7*(8x + 10y = 1618/63)\n56x + 24y = 248/3\n56x + 70y = 1618/9\nSubtract equations\n-46y = -874/9\ny = -874/9/-46\ny = 19/9\n\nSubstitute y\n7x + 3(19/9) = 31/3\n7x = 4\nx = 4/7\nx = 4/7"} {"input": "Solve simultaneously:\n5x + 6y = 16\n6x + 4y = 16", "output": "5x + 6y = 16\n6x + 4y = 16\n\nUsing elimination\n6*(5x + 6y = 16)\n5*(6x + 4y = 16)\n30x + 36y = 96\n30x + 20y = 80\nSubtract equations\n16y = 16\ny = 16/16\ny = 1\n\nSubstitute y\n5x + 6(1) = 16\n5x = 10\nx = 10/5\nx = 2"} {"input": "Solve quickly: 8x + 7 = 0", "output": "8x + 7 = 0\n8x = -7\nx = -7 / 8\nx = -7/8"} {"input": "Solve the equation x^2 + 77/24x + 49/24 = 0", "output": "x^2 + 77/24x + 49/24 = 0\n(x - -7/8)(x - -7/3) = 0\nx - -7/8 = 0 or x - -7/3 = 0\nx = -7/8\nx = -7/3"} {"input": "What value of x satisfies x^2 - 5x + 144/25 = 0", "output": "x^2 - 5x + 144/25 = 0\n(x - 16/5)(x - 9/5) = 0\nx - 16/5 = 0 or x - 9/5 = 0\nx = 16/5\nx = 9/5"} {"input": "Determine x in x^2 + 55/24x + 21/16 = 0", "output": "x^2 + 55/24x + 21/16 = 0\n(x - -9/8)(x - -7/6) = 0\nx - -9/8 = 0 or x - -7/6 = 0\nx = -9/8\nx = -7/6"} {"input": "Find x in 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "What value of x satisfies x^3 - 47/4x^2 - 337/4x - 85 = 0", "output": "x^3 - 47/4x^2 - 337/4x - 85 = 0\n(x - -5/4)(x - 17)(x - -4) = 0\nx - -5/4 = 0\nx - 17 = 0\nx - -4 = 0\nx = -5/4\nx = 17\nx = -4"} {"input": "Solve 8x + 16 = 0", "output": "8x + 16 = 0\n8x = -16\nx = -16 / 8\nx = -2"} {"input": "Compute the solution of x^2 + 3/2x - 9/2 = 0", "output": "x^2 + 3/2x - 9/2 = 0\n(x - 3/2)(x - -3) = 0\nx - 3/2 = 0 or x - -3 = 0\nx = 3/2\nx = -3"} {"input": "Solve the equations:\n10x + 5y = 20\n5x + 8y = 65", "output": "10x + 5y = 20\n5x + 8y = 65\n\nUsing elimination\n5*(10x + 5y = 20)\n10*(5x + 8y = 65)\n50x + 25y = 100\n50x + 80y = 650\nSubtract equations\n-55y = -550\ny = -550/-55\ny = 10\n\nSubstitute y\n10x + 5(10) = 20\n10x = -30\nx = -30/10\nx = -3"} {"input": "Find the solution to 1x + 2/7 = 0", "output": "1x + 2/7 = 0\n1x = -2/7\nx = -2/7 / 1\nx = -2/7"} {"input": "What value of x satisfies 1x - 13/3 = 0", "output": "1x - 13/3 = 0\n1x = 13/3\nx = 13/3 / 1\nx = 13/3"} {"input": "Solve quickly: x^2 - 10/9x - 200/27 = 0", "output": "x^2 - 10/9x - 200/27 = 0\n(x - -20/9)(x - 10/3) = 0\nx - -20/9 = 0 or x - 10/3 = 0\nx = -20/9\nx = 10/3"} {"input": "Solve the equation x^3 + 73/10x^2 + 18/5x - 126/5 = 0", "output": "x^3 + 73/10x^2 + 18/5x - 126/5 = 0\n(x - 3/2)(x - -14/5)(x - -6) = 0\nx - 3/2 = 0\nx - -14/5 = 0\nx - -6 = 0\nx = 3/2\nx = -14/5\nx = -6"} {"input": "Solve simultaneously:\n9x + 9y = 549/5\n8x + 9y = 504/5", "output": "9x + 9y = 549/5\n8x + 9y = 504/5\n\nUsing elimination\n8*(9x + 9y = 549/5)\n9*(8x + 9y = 504/5)\n72x + 72y = 4392/5\n72x + 81y = 4536/5\nSubtract equations\n-9y = -144/5\ny = -144/5/-9\ny = 16/5\n\nSubstitute y\n9x + 9(16/5) = 549/5\n9x = 81\nx = 81/9\nx = 9"} {"input": "Solve x^2 - 29/72x - 22/9 = 0", "output": "x^2 - 29/72x - 22/9 = 0\n(x - 16/9)(x - -11/8) = 0\nx - 16/9 = 0 or x - -11/8 = 0\nx = 16/9\nx = -11/8"} {"input": "Solve the equations:\n10x + 3y = -117/8\n2x + 1y = -131/40", "output": "10x + 3y = -117/8\n2x + 1y = -131/40\n\nUsing elimination\n2*(10x + 3y = -117/8)\n10*(2x + 1y = -131/40)\n20x + 6y = -117/4\n20x + 10y = -131/4\nSubtract equations\n-4y = 7/2\ny = 7/2/-4\ny = -7/8\n\nSubstitute y\n10x + 3(-7/8) = -117/8\n10x = -12\nx = -12/10\nx = -6/5"} {"input": "Compute the solution of x^3 - 1x^2 - 16x + 16 = 0", "output": "x^3 - 1x^2 - 16x + 16 = 0\n(x - -4)(x - 1)(x - 4) = 0\nx - -4 = 0\nx - 1 = 0\nx - 4 = 0\nx = -4\nx = 1\nx = 4"} {"input": "Find x and y such that\n1x + 8y = 58/5\n10x + 1y = -5/2", "output": "1x + 8y = 58/5\n10x + 1y = -5/2\n\nUsing elimination\n10*(1x + 8y = 58/5)\n1*(10x + 1y = -5/2)\n10x + 80y = 116\n10x + 1y = -5/2\nSubtract equations\n79y = 237/2\ny = 237/2/79\ny = 3/2\n\nSubstitute y\n1x + 8(3/2) = 58/5\n1x = -2/5\nx = -2/5/1\nx = -2/5"} {"input": "Solve the equation 8x - 24 = 0", "output": "8x - 24 = 0\n8x = 24\nx = 24 / 8\nx = 3"} {"input": "Find x for x^2 + 79/40x + 77/80 = 0", "output": "x^2 + 79/40x + 77/80 = 0\n(x - -11/10)(x - -7/8) = 0\nx - -11/10 = 0 or x - -7/8 = 0\nx = -11/10\nx = -7/8"} {"input": "What value of x satisfies 3x + 6 = 0", "output": "3x + 6 = 0\n3x = -6\nx = -6 / 3\nx = -2"} {"input": "Solve 6x - 4 = 0", "output": "6x - 4 = 0\n6x = 4\nx = 4 / 6\nx = 2/3"} {"input": "Compute the solution of x^3 - 20/3x^2 - 1517/12x + 85/4 = 0", "output": "x^3 - 20/3x^2 - 1517/12x + 85/4 = 0\n(x - -17/2)(x - 1/6)(x - 15) = 0\nx - -17/2 = 0\nx - 1/6 = 0\nx - 15 = 0\nx = -17/2\nx = 1/6\nx = 15"} {"input": "Solve quickly: 2x - 5/4 = 0", "output": "2x - 5/4 = 0\n2x = 5/4\nx = 5/4 / 2\nx = 5/8"} {"input": "Find x for x^3 + 47/10x^2 + 367/50x + 476/125 = 0", "output": "x^3 + 47/10x^2 + 367/50x + 476/125 = 0\n(x - -7/5)(x - -8/5)(x - -17/10) = 0\nx - -7/5 = 0\nx - -8/5 = 0\nx - -17/10 = 0\nx = -7/5\nx = -8/5\nx = -17/10"} {"input": "Solve the system:\n3x + 5y = 15\n3x + 7y = 13", "output": "3x + 5y = 15\n3x + 7y = 13\n\nUsing elimination\n3*(3x + 5y = 15)\n3*(3x + 7y = 13)\n9x + 15y = 45\n9x + 21y = 39\nSubtract equations\n-6y = 6\ny = 6/-6\ny = -1\n\nSubstitute y\n3x + 5(-1) = 15\n3x = 20\nx = 20/3\nx = 20/3"} {"input": "Solve the equation x^2 - 113/6x - 19/6 = 0", "output": "x^2 - 113/6x - 19/6 = 0\n(x - 19)(x - -1/6) = 0\nx - 19 = 0 or x - -1/6 = 0\nx = 19\nx = -1/6"} {"input": "Find the solution to x^3 + 625/84x^2 + 689/56x - 95/42 = 0", "output": "x^3 + 625/84x^2 + 689/56x - 95/42 = 0\n(x - 1/6)(x - -19/4)(x - -20/7) = 0\nx - 1/6 = 0\nx - -19/4 = 0\nx - -20/7 = 0\nx = 1/6\nx = -19/4\nx = -20/7"} {"input": "Solve the equation x^3 + 181/90x^2 - 9/10x - 19/9 = 0", "output": "x^3 + 181/90x^2 - 9/10x - 19/9 = 0\n(x - -10/9)(x - -19/10)(x - 1) = 0\nx - -10/9 = 0\nx - -19/10 = 0\nx - 1 = 0\nx = -10/9\nx = -19/10\nx = 1"} {"input": "Solve simultaneously:\n2x + 6y = 242/35\n8x + 7y = 849/35", "output": "2x + 6y = 242/35\n8x + 7y = 849/35\n\nUsing elimination\n8*(2x + 6y = 242/35)\n2*(8x + 7y = 849/35)\n16x + 48y = 1936/35\n16x + 14y = 1698/35\nSubtract equations\n34y = 34/5\ny = 34/5/34\ny = 1/5\n\nSubstitute y\n2x + 6(1/5) = 242/35\n2x = 40/7\nx = 40/7/2\nx = 20/7"} {"input": "Solve the system:\n3x + 4y = 15\n9x + 5y = 55/2", "output": "3x + 4y = 15\n9x + 5y = 55/2\n\nUsing elimination\n9*(3x + 4y = 15)\n3*(9x + 5y = 55/2)\n27x + 36y = 135\n27x + 15y = 165/2\nSubtract equations\n21y = 105/2\ny = 105/2/21\ny = 5/2\n\nSubstitute y\n3x + 4(5/2) = 15\n3x = 5\nx = 5/3\nx = 5/3"} {"input": "Solve quickly: x^3 - 31/40x^2 - 9/20x + 9/40 = 0", "output": "x^3 - 31/40x^2 - 9/20x + 9/40 = 0\n(x - 3/8)(x - -3/5)(x - 1) = 0\nx - 3/8 = 0\nx - -3/5 = 0\nx - 1 = 0\nx = 3/8\nx = -3/5\nx = 1"} {"input": "Solve x^2 + 3/5x - 68/5 = 0", "output": "x^2 + 3/5x - 68/5 = 0\n(x - -4)(x - 17/5) = 0\nx - -4 = 0 or x - 17/5 = 0\nx = -4\nx = 17/5"} {"input": "Solve the equation 1x - 1/2 = 0", "output": "1x - 1/2 = 0\n1x = 1/2\nx = 1/2 / 1\nx = 1/2"} {"input": "Solve quickly: x^3 + 334/35x^2 - 569/35x - 88/35 = 0", "output": "x^3 + 334/35x^2 - 569/35x - 88/35 = 0\n(x - 8/5)(x - -1/7)(x - -11) = 0\nx - 8/5 = 0\nx - -1/7 = 0\nx - -11 = 0\nx = 8/5\nx = -1/7\nx = -11"} {"input": "Find x for 9x + 27/4 = 0", "output": "9x + 27/4 = 0\n9x = -27/4\nx = -27/4 / 9\nx = -3/4"} {"input": "Solve the system:\n7x + 10y = 45\n9x + 8y = 320/7", "output": "7x + 10y = 45\n9x + 8y = 320/7\n\nUsing elimination\n9*(7x + 10y = 45)\n7*(9x + 8y = 320/7)\n63x + 90y = 405\n63x + 56y = 320\nSubtract equations\n34y = 85\ny = 85/34\ny = 5/2\n\nSubstitute y\n7x + 10(5/2) = 45\n7x = 20\nx = 20/7\nx = 20/7"} {"input": "Solve simultaneously:\n9x + 4y = 81/2\n5x + 2y = 37/2", "output": "9x + 4y = 81/2\n5x + 2y = 37/2\n\nUsing elimination\n5*(9x + 4y = 81/2)\n9*(5x + 2y = 37/2)\n45x + 20y = 405/2\n45x + 18y = 333/2\nSubtract equations\n2y = 36\ny = 36/2\ny = 18\n\nSubstitute y\n9x + 4(18) = 81/2\n9x = -63/2\nx = -63/2/9\nx = -7/2"} {"input": "Find x in x^3 - 7/20x^2 - 113/20x - 209/80 = 0", "output": "x^3 - 7/20x^2 - 113/20x - 209/80 = 0\n(x - 11/4)(x - -1/2)(x - -19/10) = 0\nx - 11/4 = 0\nx - -1/2 = 0\nx - -19/10 = 0\nx = 11/4\nx = -1/2\nx = -19/10"} {"input": "Solve the equation 10x - 55/4 = 0", "output": "10x - 55/4 = 0\n10x = 55/4\nx = 55/4 / 10\nx = 11/8"} {"input": "Solve the equation x^3 - 133/36x^2 + 917/216x - 55/36 = 0", "output": "x^3 - 133/36x^2 + 917/216x - 55/36 = 0\n(x - 3/4)(x - 10/9)(x - 11/6) = 0\nx - 3/4 = 0\nx - 10/9 = 0\nx - 11/6 = 0\nx = 3/4\nx = 10/9\nx = 11/6"} {"input": "Solve quickly: 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Solve simultaneously:\n9x + 9y = -130/7\n1x + 2y = -242/63", "output": "9x + 9y = -130/7\n1x + 2y = -242/63\n\nUsing elimination\n1*(9x + 9y = -130/7)\n9*(1x + 2y = -242/63)\n9x + 9y = -130/7\n9x + 18y = -242/7\nSubtract equations\n-9y = 16\ny = 16/-9\ny = -16/9\n\nSubstitute y\n9x + 9(-16/9) = -130/7\n9x = -18/7\nx = -18/7/9\nx = -2/7"} {"input": "Determine x in x^2 - 2x - 8 = 0", "output": "x^2 - 2x - 8 = 0\n(x - 4)(x - -2) = 0\nx - 4 = 0 or x - -2 = 0\nx = 4\nx = -2"} {"input": "Find x for x^2 + 2x - 24 = 0", "output": "x^2 + 2x - 24 = 0\n(x - 4)(x - -6) = 0\nx - 4 = 0 or x - -6 = 0\nx = 4\nx = -6"} {"input": "Find x for x^2 + 11/15x + 2/15 = 0", "output": "x^2 + 11/15x + 2/15 = 0\n(x - -2/5)(x - -1/3) = 0\nx - -2/5 = 0 or x - -1/3 = 0\nx = -2/5\nx = -1/3"} {"input": "Solve the system:\n8x + 7y = 5/3\n10x + 5y = 10/3", "output": "8x + 7y = 5/3\n10x + 5y = 10/3\n\nUsing elimination\n10*(8x + 7y = 5/3)\n8*(10x + 5y = 10/3)\n80x + 70y = 50/3\n80x + 40y = 80/3\nSubtract equations\n30y = -10\ny = -10/30\ny = -1/3\n\nSubstitute y\n8x + 7(-1/3) = 5/3\n8x = 4\nx = 4/8\nx = 1/2"} {"input": "Determine x in x^2 + 5x + 6 = 0", "output": "x^2 + 5x + 6 = 0\n(x - -3)(x - -2) = 0\nx - -3 = 0 or x - -2 = 0\nx = -3\nx = -2"} {"input": "Find x in x^3 + 25/7x^2 + 100/49x = 0", "output": "x^3 + 25/7x^2 + 100/49x = 0\n(x - -20/7)(x - -5/7)(x - 0) = 0\nx - -20/7 = 0\nx - -5/7 = 0\nx - 0 = 0\nx = -20/7\nx = -5/7\nx = 0"} {"input": "Solve the system:\n9x + 9y = -648/5\n7x + 1y = -24/5", "output": "9x + 9y = -648/5\n7x + 1y = -24/5\n\nUsing elimination\n7*(9x + 9y = -648/5)\n9*(7x + 1y = -24/5)\n63x + 63y = -4536/5\n63x + 9y = -216/5\nSubtract equations\n54y = -864\ny = -864/54\ny = -16\n\nSubstitute y\n9x + 9(-16) = -648/5\n9x = 72/5\nx = 72/5/9\nx = 8/5"} {"input": "Find x in 7x - 133/3 = 0", "output": "7x - 133/3 = 0\n7x = 133/3\nx = 133/3 / 7\nx = 19/3"} {"input": "Find x and y such that\n3x + 9y = 91/4\n1x + 4y = 37/3", "output": "3x + 9y = 91/4\n1x + 4y = 37/3\n\nUsing elimination\n1*(3x + 9y = 91/4)\n3*(1x + 4y = 37/3)\n3x + 9y = 91/4\n3x + 12y = 37\nSubtract equations\n-3y = -57/4\ny = -57/4/-3\ny = 19/4\n\nSubstitute y\n3x + 9(19/4) = 91/4\n3x = -20\nx = -20/3\nx = -20/3"} {"input": "Determine x in x^2 - 47/6x - 17/3 = 0", "output": "x^2 - 47/6x - 17/3 = 0\n(x - 17/2)(x - -2/3) = 0\nx - 17/2 = 0 or x - -2/3 = 0\nx = 17/2\nx = -2/3"} {"input": "Determine x in x^2 + 8/9x - 1/9 = 0", "output": "x^2 + 8/9x - 1/9 = 0\n(x - 1/9)(x - -1) = 0\nx - 1/9 = 0 or x - -1 = 0\nx = 1/9\nx = -1"} {"input": "Find x in x^3 + 281/70x^2 - 20/7x - 408/35 = 0", "output": "x^3 + 281/70x^2 - 20/7x - 408/35 = 0\n(x - -4)(x - 17/10)(x - -12/7) = 0\nx - -4 = 0\nx - 17/10 = 0\nx - -12/7 = 0\nx = -4\nx = 17/10\nx = -12/7"} {"input": "Solve the equations:\n5x + 7y = -63/4\n7x + 7y = -77/4", "output": "5x + 7y = -63/4\n7x + 7y = -77/4\n\nUsing elimination\n7*(5x + 7y = -63/4)\n5*(7x + 7y = -77/4)\n35x + 49y = -441/4\n35x + 35y = -385/4\nSubtract equations\n14y = -14\ny = -14/14\ny = -1\n\nSubstitute y\n5x + 7(-1) = -63/4\n5x = -35/4\nx = -35/4/5\nx = -7/4"} {"input": "What value of x satisfies 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Determine x in x^3 + 81/14x^2 + 9/14x - 162/7 = 0", "output": "x^3 + 81/14x^2 + 9/14x - 162/7 = 0\n(x - -9/2)(x - 12/7)(x - -3) = 0\nx - -9/2 = 0\nx - 12/7 = 0\nx - -3 = 0\nx = -9/2\nx = 12/7\nx = -3"} {"input": "Solve the system:\n3x + 6y = -11/3\n7x + 3y = 22/9", "output": "3x + 6y = -11/3\n7x + 3y = 22/9\n\nUsing elimination\n7*(3x + 6y = -11/3)\n3*(7x + 3y = 22/9)\n21x + 42y = -77/3\n21x + 9y = 22/3\nSubtract equations\n33y = -33\ny = -33/33\ny = -1\n\nSubstitute y\n3x + 6(-1) = -11/3\n3x = 7/3\nx = 7/3/3\nx = 7/9"} {"input": "Compute the solution of 1x + 17/2 = 0", "output": "1x + 17/2 = 0\n1x = -17/2\nx = -17/2 / 1\nx = -17/2"} {"input": "Determine x in x^2 + 9/2x - 13 = 0", "output": "x^2 + 9/2x - 13 = 0\n(x - -13/2)(x - 2) = 0\nx - -13/2 = 0 or x - 2 = 0\nx = -13/2\nx = 2"} {"input": "Solve the equation x^2 - 1/2x - 3/2 = 0", "output": "x^2 - 1/2x - 3/2 = 0\n(x - -1)(x - 3/2) = 0\nx - -1 = 0 or x - 3/2 = 0\nx = -1\nx = 3/2"} {"input": "Find the solution to x^3 - 65/72x^2 + 7/72x = 0", "output": "x^3 - 65/72x^2 + 7/72x = 0\n(x - 7/9)(x - 0)(x - 1/8) = 0\nx - 7/9 = 0\nx - 0 = 0\nx - 1/8 = 0\nx = 7/9\nx = 0\nx = 1/8"} {"input": "Determine x in x^3 + 29/9x^2 + 8/3x + 4/9 = 0", "output": "x^3 + 29/9x^2 + 8/3x + 4/9 = 0\n(x - -1)(x - -2/9)(x - -2) = 0\nx - -1 = 0\nx - -2/9 = 0\nx - -2 = 0\nx = -1\nx = -2/9\nx = -2"} {"input": "Find x for x^3 - 31/3x^2 + 29/3x + 21 = 0", "output": "x^3 - 31/3x^2 + 29/3x + 21 = 0\n(x - 9)(x - -1)(x - 7/3) = 0\nx - 9 = 0\nx - -1 = 0\nx - 7/3 = 0\nx = 9\nx = -1\nx = 7/3"} {"input": "Solve 6x - 27/2 = 0", "output": "6x - 27/2 = 0\n6x = 27/2\nx = 27/2 / 6\nx = 9/4"} {"input": "Determine x in x^2 + 65/18x - 4 = 0", "output": "x^2 + 65/18x - 4 = 0\n(x - -9/2)(x - 8/9) = 0\nx - -9/2 = 0 or x - 8/9 = 0\nx = -9/2\nx = 8/9"} {"input": "Determine x in x^2 - 25/72x - 25/6 = 0", "output": "x^2 - 25/72x - 25/6 = 0\n(x - -15/8)(x - 20/9) = 0\nx - -15/8 = 0 or x - 20/9 = 0\nx = -15/8\nx = 20/9"} {"input": "Determine x in x^3 - 73/42x^2 - 10/3x + 16/7 = 0", "output": "x^3 - 73/42x^2 - 10/3x + 16/7 = 0\n(x - 8/3)(x - 4/7)(x - -3/2) = 0\nx - 8/3 = 0\nx - 4/7 = 0\nx - -3/2 = 0\nx = 8/3\nx = 4/7\nx = -3/2"} {"input": "Compute the solution of 6x - 6/7 = 0", "output": "6x - 6/7 = 0\n6x = 6/7\nx = 6/7 / 6\nx = 1/7"} {"input": "Find the solution to x^3 + 19x^2 + 367/4x + 165/4 = 0", "output": "x^3 + 19x^2 + 367/4x + 165/4 = 0\n(x - -15/2)(x - -11)(x - -1/2) = 0\nx - -15/2 = 0\nx - -11 = 0\nx - -1/2 = 0\nx = -15/2\nx = -11\nx = -1/2"} {"input": "Solve 10x + 30 = 0", "output": "10x + 30 = 0\n10x = -30\nx = -30 / 10\nx = -3"} {"input": "Find x in 4x + 4 = 0", "output": "4x + 4 = 0\n4x = -4\nx = -4 / 4\nx = -1"} {"input": "Solve 3x + 5/3 = 0", "output": "3x + 5/3 = 0\n3x = -5/3\nx = -5/3 / 3\nx = -5/9"} {"input": "Determine x in 7x + 4 = 0", "output": "7x + 4 = 0\n7x = -4\nx = -4 / 7\nx = -4/7"} {"input": "Find the solution to 7x + 7 = 0", "output": "7x + 7 = 0\n7x = -7\nx = -7 / 7\nx = -1"} {"input": "Compute the solution of x^3 - 17/8x^2 - 725/392x + 19/28 = 0", "output": "x^3 - 17/8x^2 - 725/392x + 19/28 = 0\n(x - 2/7)(x - -7/8)(x - 19/7) = 0\nx - 2/7 = 0\nx - -7/8 = 0\nx - 19/7 = 0\nx = 2/7\nx = -7/8\nx = 19/7"} {"input": "Solve x^3 - 122/15x^2 + 43/5x + 266/15 = 0", "output": "x^3 - 122/15x^2 + 43/5x + 266/15 = 0\n(x - 19/3)(x - -1)(x - 14/5) = 0\nx - 19/3 = 0\nx - -1 = 0\nx - 14/5 = 0\nx = 19/3\nx = -1\nx = 14/5"} {"input": "Determine x in x^2 + 200/9x + 400/9 = 0", "output": "x^2 + 200/9x + 400/9 = 0\n(x - -20)(x - -20/9) = 0\nx - -20 = 0 or x - -20/9 = 0\nx = -20\nx = -20/9"} {"input": "Solve quickly: x^2 + 23/35x - 44/7 = 0", "output": "x^2 + 23/35x - 44/7 = 0\n(x - 11/5)(x - -20/7) = 0\nx - 11/5 = 0 or x - -20/7 = 0\nx = 11/5\nx = -20/7"} {"input": "Solve x^3 - 715/42x^2 - 13/42x + 85/7 = 0", "output": "x^3 - 715/42x^2 - 13/42x + 85/7 = 0\n(x - 17)(x - -5/6)(x - 6/7) = 0\nx - 17 = 0\nx - -5/6 = 0\nx - 6/7 = 0\nx = 17\nx = -5/6\nx = 6/7"} {"input": "Determine x in x^3 + 7/30x^2 - 58/5x + 208/15 = 0", "output": "x^3 + 7/30x^2 - 58/5x + 208/15 = 0\n(x - -4)(x - 8/5)(x - 13/6) = 0\nx - -4 = 0\nx - 8/5 = 0\nx - 13/6 = 0\nx = -4\nx = 8/5\nx = 13/6"} {"input": "Solve the equation x^3 + 37/30x^2 - 709/75x - 1064/75 = 0", "output": "x^3 + 37/30x^2 - 709/75x - 1064/75 = 0\n(x - -14/5)(x - -8/5)(x - 19/6) = 0\nx - -14/5 = 0\nx - -8/5 = 0\nx - 19/6 = 0\nx = -14/5\nx = -8/5\nx = 19/6"} {"input": "Solve x^3 + 169/105x^2 - 68/35x - 12/7 = 0", "output": "x^3 + 169/105x^2 - 68/35x - 12/7 = 0\n(x - -2/3)(x - 6/5)(x - -15/7) = 0\nx - -2/3 = 0\nx - 6/5 = 0\nx - -15/7 = 0\nx = -2/3\nx = 6/5\nx = -15/7"} {"input": "Find x and y such that\n7x + 10y = 143/6\n3x + 6y = 29/2", "output": "7x + 10y = 143/6\n3x + 6y = 29/2\n\nUsing elimination\n3*(7x + 10y = 143/6)\n7*(3x + 6y = 29/2)\n21x + 30y = 143/2\n21x + 42y = 203/2\nSubtract equations\n-12y = -30\ny = -30/-12\ny = 5/2\n\nSubstitute y\n7x + 10(5/2) = 143/6\n7x = -7/6\nx = -7/6/7\nx = -1/6"} {"input": "Find x and y such that\n7x + 5y = -137/6\n4x + 5y = -52/3", "output": "7x + 5y = -137/6\n4x + 5y = -52/3\n\nUsing elimination\n4*(7x + 5y = -137/6)\n7*(4x + 5y = -52/3)\n28x + 20y = -274/3\n28x + 35y = -364/3\nSubtract equations\n-15y = 30\ny = 30/-15\ny = -2\n\nSubstitute y\n7x + 5(-2) = -137/6\n7x = -77/6\nx = -77/6/7\nx = -11/6"} {"input": "Solve the equation 1x - 16 = 0", "output": "1x - 16 = 0\n1x = 16\nx = 16 / 1\nx = 16"} {"input": "Solve the equations:\n1x + 5y = 113/14\n6x + 5y = 39/7", "output": "1x + 5y = 113/14\n6x + 5y = 39/7\n\nUsing elimination\n6*(1x + 5y = 113/14)\n1*(6x + 5y = 39/7)\n6x + 30y = 339/7\n6x + 5y = 39/7\nSubtract equations\n25y = 300/7\ny = 300/7/25\ny = 12/7\n\nSubstitute y\n1x + 5(12/7) = 113/14\n1x = -1/2\nx = -1/2/1\nx = -1/2"} {"input": "Solve the equations:\n10x + 3y = 89\n1x + 3y = 25/2", "output": "10x + 3y = 89\n1x + 3y = 25/2\n\nUsing elimination\n1*(10x + 3y = 89)\n10*(1x + 3y = 25/2)\n10x + 3y = 89\n10x + 30y = 125\nSubtract equations\n-27y = -36\ny = -36/-27\ny = 4/3\n\nSubstitute y\n10x + 3(4/3) = 89\n10x = 85\nx = 85/10\nx = 17/2"} {"input": "Solve the system:\n8x + 1y = 163/7\n7x + 3y = 48", "output": "8x + 1y = 163/7\n7x + 3y = 48\n\nUsing elimination\n7*(8x + 1y = 163/7)\n8*(7x + 3y = 48)\n56x + 7y = 163\n56x + 24y = 384\nSubtract equations\n-17y = -221\ny = -221/-17\ny = 13\n\nSubstitute y\n8x + 1(13) = 163/7\n8x = 72/7\nx = 72/7/8\nx = 9/7"} {"input": "Find the solution to 6x - 20 = 0", "output": "6x - 20 = 0\n6x = 20\nx = 20 / 6\nx = 10/3"} {"input": "Solve the equations:\n5x + 5y = -55/8\n7x + 10y = -19/4", "output": "5x + 5y = -55/8\n7x + 10y = -19/4\n\nUsing elimination\n7*(5x + 5y = -55/8)\n5*(7x + 10y = -19/4)\n35x + 35y = -385/8\n35x + 50y = -95/4\nSubtract equations\n-15y = -195/8\ny = -195/8/-15\ny = 13/8\n\nSubstitute y\n5x + 5(13/8) = -55/8\n5x = -15\nx = -15/5\nx = -3"} {"input": "Determine x in x^2 - 57/10x - 91/10 = 0", "output": "x^2 - 57/10x - 91/10 = 0\n(x - -13/10)(x - 7) = 0\nx - -13/10 = 0 or x - 7 = 0\nx = -13/10\nx = 7"} {"input": "Solve the equation x^3 + 317/70x^2 + 83/14x + 15/7 = 0", "output": "x^3 + 317/70x^2 + 83/14x + 15/7 = 0\n(x - -3/5)(x - -5/2)(x - -10/7) = 0\nx - -3/5 = 0\nx - -5/2 = 0\nx - -10/7 = 0\nx = -3/5\nx = -5/2\nx = -10/7"} {"input": "Find x for x^3 - 123/70x^2 - 319/70x + 57/7 = 0", "output": "x^3 - 123/70x^2 - 319/70x + 57/7 = 0\n(x - 19/10)(x - -15/7)(x - 2) = 0\nx - 19/10 = 0\nx - -15/7 = 0\nx - 2 = 0\nx = 19/10\nx = -15/7\nx = 2"} {"input": "Find x for 3x + 20/3 = 0", "output": "3x + 20/3 = 0\n3x = -20/3\nx = -20/3 / 3\nx = -20/9"} {"input": "Solve 8x - 68 = 0", "output": "8x - 68 = 0\n8x = 68\nx = 68 / 8\nx = 17/2"} {"input": "What value of x satisfies x^3 + 43/9x^2 + 244/81x - 32/81 = 0", "output": "x^3 + 43/9x^2 + 244/81x - 32/81 = 0\n(x - -4)(x - -8/9)(x - 1/9) = 0\nx - -4 = 0\nx - -8/9 = 0\nx - 1/9 = 0\nx = -4\nx = -8/9\nx = 1/9"} {"input": "Solve the equation 10x - 170/7 = 0", "output": "10x - 170/7 = 0\n10x = 170/7\nx = 170/7 / 10\nx = 17/7"} {"input": "Find the solution to x^2 - 25/9x + 16/9 = 0", "output": "x^2 - 25/9x + 16/9 = 0\n(x - 16/9)(x - 1) = 0\nx - 16/9 = 0 or x - 1 = 0\nx = 16/9\nx = 1"} {"input": "Solve x^2 - 73/20x + 17/20 = 0", "output": "x^2 - 73/20x + 17/20 = 0\n(x - 1/4)(x - 17/5) = 0\nx - 1/4 = 0 or x - 17/5 = 0\nx = 1/4\nx = 17/5"} {"input": "Compute the solution of x^3 + 9/8x^2 - 4x - 9/2 = 0", "output": "x^3 + 9/8x^2 - 4x - 9/2 = 0\n(x - 2)(x - -2)(x - -9/8) = 0\nx - 2 = 0\nx - -2 = 0\nx - -9/8 = 0\nx = 2\nx = -2\nx = -9/8"} {"input": "Find x for x^3 + 14/9x^2 - 97/3x + 364/9 = 0", "output": "x^3 + 14/9x^2 - 97/3x + 364/9 = 0\n(x - 13/9)(x - 4)(x - -7) = 0\nx - 13/9 = 0\nx - 4 = 0\nx - -7 = 0\nx = 13/9\nx = 4\nx = -7"} {"input": "Compute the solution of x^3 + 79/20x^2 - 609/40x + 351/40 = 0", "output": "x^3 + 79/20x^2 - 609/40x + 351/40 = 0\n(x - 9/5)(x - 3/4)(x - -13/2) = 0\nx - 9/5 = 0\nx - 3/4 = 0\nx - -13/2 = 0\nx = 9/5\nx = 3/4\nx = -13/2"} {"input": "Compute the solution of x^3 - 337/36x^2 + 2417/108x - 221/27 = 0", "output": "x^3 - 337/36x^2 + 2417/108x - 221/27 = 0\n(x - 13/4)(x - 4/9)(x - 17/3) = 0\nx - 13/4 = 0\nx - 4/9 = 0\nx - 17/3 = 0\nx = 13/4\nx = 4/9\nx = 17/3"} {"input": "Solve the equation 8x - 136/3 = 0", "output": "8x - 136/3 = 0\n8x = 136/3\nx = 136/3 / 8\nx = 17/3"} {"input": "What value of x satisfies x^2 - 59/30x - 19/5 = 0", "output": "x^2 - 59/30x - 19/5 = 0\n(x - 19/6)(x - -6/5) = 0\nx - 19/6 = 0 or x - -6/5 = 0\nx = 19/6\nx = -6/5"} {"input": "Determine x in x^3 - 40/9x^2 - 269/27x + 34/9 = 0", "output": "x^3 - 40/9x^2 - 269/27x + 34/9 = 0\n(x - 6)(x - 1/3)(x - -17/9) = 0\nx - 6 = 0\nx - 1/3 = 0\nx - -17/9 = 0\nx = 6\nx = 1/3\nx = -17/9"} {"input": "Determine x in x^3 - 29/30x^2 + 14/45x - 1/30 = 0", "output": "x^3 - 29/30x^2 + 14/45x - 1/30 = 0\n(x - 1/3)(x - 1/3)(x - 3/10) = 0\nx - 1/3 = 0\nx - 1/3 = 0\nx - 3/10 = 0\nx = 1/3\nx = 1/3\nx = 3/10"} {"input": "Solve x^2 + 8/9x + 5/27 = 0", "output": "x^2 + 8/9x + 5/27 = 0\n(x - -1/3)(x - -5/9) = 0\nx - -1/3 = 0 or x - -5/9 = 0\nx = -1/3\nx = -5/9"} {"input": "Solve quickly: 3x - 42 = 0", "output": "3x - 42 = 0\n3x = 42\nx = 42 / 3\nx = 14"} {"input": "Solve quickly: x^2 + 9/7x - 36/7 = 0", "output": "x^2 + 9/7x - 36/7 = 0\n(x - -3)(x - 12/7) = 0\nx - -3 = 0 or x - 12/7 = 0\nx = -3\nx = 12/7"} {"input": "Find x and y such that\n1x + 10y = -85/3\n9x + 6y = -59", "output": "1x + 10y = -85/3\n9x + 6y = -59\n\nUsing elimination\n9*(1x + 10y = -85/3)\n1*(9x + 6y = -59)\n9x + 90y = -255\n9x + 6y = -59\nSubtract equations\n84y = -196\ny = -196/84\ny = -7/3\n\nSubstitute y\n1x + 10(-7/3) = -85/3\n1x = -5\nx = -5/1\nx = -5"} {"input": "Find x in 5x - 70/3 = 0", "output": "5x - 70/3 = 0\n5x = 70/3\nx = 70/3 / 5\nx = 14/3"} {"input": "What value of x satisfies x^2 - 19/12x - 11/24 = 0", "output": "x^2 - 19/12x - 11/24 = 0\n(x - -1/4)(x - 11/6) = 0\nx - -1/4 = 0 or x - 11/6 = 0\nx = -1/4\nx = 11/6"} {"input": "Find x in x^2 - 52/15x + 169/60 = 0", "output": "x^2 - 52/15x + 169/60 = 0\n(x - 13/10)(x - 13/6) = 0\nx - 13/10 = 0 or x - 13/6 = 0\nx = 13/10\nx = 13/6"} {"input": "Solve the equation x^3 - 131/21x^2 - 158/63x + 760/63 = 0", "output": "x^3 - 131/21x^2 - 158/63x + 760/63 = 0\n(x - 19/3)(x - -10/7)(x - 4/3) = 0\nx - 19/3 = 0\nx - -10/7 = 0\nx - 4/3 = 0\nx = 19/3\nx = -10/7\nx = 4/3"} {"input": "What value of x satisfies 7x + 140/3 = 0", "output": "7x + 140/3 = 0\n7x = -140/3\nx = -140/3 / 7\nx = -20/3"} {"input": "Solve the equations:\n7x + 10y = 29/3\n7x + 8y = 4", "output": "7x + 10y = 29/3\n7x + 8y = 4\n\nUsing elimination\n7*(7x + 10y = 29/3)\n7*(7x + 8y = 4)\n49x + 70y = 203/3\n49x + 56y = 28\nSubtract equations\n14y = 119/3\ny = 119/3/14\ny = 17/6\n\nSubstitute y\n7x + 10(17/6) = 29/3\n7x = -56/3\nx = -56/3/7\nx = -8/3"} {"input": "Find x in x^2 - 137/30x + 33/10 = 0", "output": "x^2 - 137/30x + 33/10 = 0\n(x - 11/3)(x - 9/10) = 0\nx - 11/3 = 0 or x - 9/10 = 0\nx = 11/3\nx = 9/10"} {"input": "Solve 1x - 19/3 = 0", "output": "1x - 19/3 = 0\n1x = 19/3\nx = 19/3 / 1\nx = 19/3"} {"input": "Solve the equations:\n2x + 2y = -13/18\n2x + 1y = -29/18", "output": "2x + 2y = -13/18\n2x + 1y = -29/18\n\nUsing elimination\n2*(2x + 2y = -13/18)\n2*(2x + 1y = -29/18)\n4x + 4y = -13/9\n4x + 2y = -29/9\nSubtract equations\n2y = 16/9\ny = 16/9/2\ny = 8/9\n\nSubstitute y\n2x + 2(8/9) = -13/18\n2x = -5/2\nx = -5/2/2\nx = -5/4"} {"input": "Solve x^3 + 17/9x^2 - 440/27x - 100/27 = 0", "output": "x^3 + 17/9x^2 - 440/27x - 100/27 = 0\n(x - 10/3)(x - -5)(x - -2/9) = 0\nx - 10/3 = 0\nx - -5 = 0\nx - -2/9 = 0\nx = 10/3\nx = -5\nx = -2/9"} {"input": "Determine x in 9x + 117/5 = 0", "output": "9x + 117/5 = 0\n9x = -117/5\nx = -117/5 / 9\nx = -13/5"} {"input": "Solve the equation 6x + 21 = 0", "output": "6x + 21 = 0\n6x = -21\nx = -21 / 6\nx = -7/2"} {"input": "Solve the equations:\n3x + 4y = -31/3\n9x + 7y = -26", "output": "3x + 4y = -31/3\n9x + 7y = -26\n\nUsing elimination\n9*(3x + 4y = -31/3)\n3*(9x + 7y = -26)\n27x + 36y = -93\n27x + 21y = -78\nSubtract equations\n15y = -15\ny = -15/15\ny = -1\n\nSubstitute y\n3x + 4(-1) = -31/3\n3x = -19/3\nx = -19/3/3\nx = -19/9"} {"input": "Solve x^2 - 20/3x + 25/3 = 0", "output": "x^2 - 20/3x + 25/3 = 0\n(x - 5)(x - 5/3) = 0\nx - 5 = 0 or x - 5/3 = 0\nx = 5\nx = 5/3"} {"input": "Solve the equation x^3 + 49/30x^2 + 38/45x + 2/15 = 0", "output": "x^3 + 49/30x^2 + 38/45x + 2/15 = 0\n(x - -2/3)(x - -2/3)(x - -3/10) = 0\nx - -2/3 = 0\nx - -2/3 = 0\nx - -3/10 = 0\nx = -2/3\nx = -2/3\nx = -3/10"} {"input": "Find the solution to x^2 + 175/8x + 75/2 = 0", "output": "x^2 + 175/8x + 75/2 = 0\n(x - -20)(x - -15/8) = 0\nx - -20 = 0 or x - -15/8 = 0\nx = -20\nx = -15/8"} {"input": "Solve the equations:\n2x + 3y = 78/35\n5x + 2y = 72/7", "output": "2x + 3y = 78/35\n5x + 2y = 72/7\n\nUsing elimination\n5*(2x + 3y = 78/35)\n2*(5x + 2y = 72/7)\n10x + 15y = 78/7\n10x + 4y = 144/7\nSubtract equations\n11y = -66/7\ny = -66/7/11\ny = -6/7\n\nSubstitute y\n2x + 3(-6/7) = 78/35\n2x = 24/5\nx = 24/5/2\nx = 12/5"} {"input": "Determine x in x^2 + 21/4x + 5 = 0", "output": "x^2 + 21/4x + 5 = 0\n(x - -4)(x - -5/4) = 0\nx - -4 = 0 or x - -5/4 = 0\nx = -4\nx = -5/4"} {"input": "Find the solution to x^2 + 3/5x - 2/5 = 0", "output": "x^2 + 3/5x - 2/5 = 0\n(x - -1)(x - 2/5) = 0\nx - -1 = 0 or x - 2/5 = 0\nx = -1\nx = 2/5"} {"input": "Solve simultaneously:\n1x + 9y = -52/3\n6x + 8y = -16/9", "output": "1x + 9y = -52/3\n6x + 8y = -16/9\n\nUsing elimination\n6*(1x + 9y = -52/3)\n1*(6x + 8y = -16/9)\n6x + 54y = -104\n6x + 8y = -16/9\nSubtract equations\n46y = -920/9\ny = -920/9/46\ny = -20/9\n\nSubstitute y\n1x + 9(-20/9) = -52/3\n1x = 8/3\nx = 8/3/1\nx = 8/3"} {"input": "Find x and y such that\n2x + 3y = 49/2\n10x + 9y = 203/2", "output": "2x + 3y = 49/2\n10x + 9y = 203/2\n\nUsing elimination\n10*(2x + 3y = 49/2)\n2*(10x + 9y = 203/2)\n20x + 30y = 245\n20x + 18y = 203\nSubtract equations\n12y = 42\ny = 42/12\ny = 7/2\n\nSubstitute y\n2x + 3(7/2) = 49/2\n2x = 14\nx = 14/2\nx = 7"} {"input": "Solve the equation x^2 + 37/6x + 19/2 = 0", "output": "x^2 + 37/6x + 19/2 = 0\n(x - -3)(x - -19/6) = 0\nx - -3 = 0 or x - -19/6 = 0\nx = -3\nx = -19/6"} {"input": "Compute the solution of x^3 - 29/4x^2 - 7/4x + 49/2 = 0", "output": "x^3 - 29/4x^2 - 7/4x + 49/2 = 0\n(x - 2)(x - 7)(x - -7/4) = 0\nx - 2 = 0\nx - 7 = 0\nx - -7/4 = 0\nx = 2\nx = 7\nx = -7/4"} {"input": "Determine x in 1x - 5/8 = 0", "output": "1x - 5/8 = 0\n1x = 5/8\nx = 5/8 / 1\nx = 5/8"} {"input": "Solve the system:\n6x + 3y = -39/2\n6x + 9y = -87/2", "output": "6x + 3y = -39/2\n6x + 9y = -87/2\n\nUsing elimination\n6*(6x + 3y = -39/2)\n6*(6x + 9y = -87/2)\n36x + 18y = -117\n36x + 54y = -261\nSubtract equations\n-36y = 144\ny = 144/-36\ny = -4\n\nSubstitute y\n6x + 3(-4) = -39/2\n6x = -15/2\nx = -15/2/6\nx = -5/4"} {"input": "Solve the equations:\n1x + 9y = 667/20\n8x + 6y = 193/10", "output": "1x + 9y = 667/20\n8x + 6y = 193/10\n\nUsing elimination\n8*(1x + 9y = 667/20)\n1*(8x + 6y = 193/10)\n8x + 72y = 1334/5\n8x + 6y = 193/10\nSubtract equations\n66y = 495/2\ny = 495/2/66\ny = 15/4\n\nSubstitute y\n1x + 9(15/4) = 667/20\n1x = -2/5\nx = -2/5/1\nx = -2/5"} {"input": "Compute the solution of x^3 - 2x^2 - 11x + 12 = 0", "output": "x^3 - 2x^2 - 11x + 12 = 0\n(x - 4)(x - -3)(x - 1) = 0\nx - 4 = 0\nx - -3 = 0\nx - 1 = 0\nx = 4\nx = -3\nx = 1"} {"input": "Solve x^2 + 153/7x + 260/7 = 0", "output": "x^2 + 153/7x + 260/7 = 0\n(x - -13/7)(x - -20) = 0\nx - -13/7 = 0 or x - -20 = 0\nx = -13/7\nx = -20"} {"input": "Compute the solution of x^3 + 17/12x^2 - 111/8x - 165/8 = 0", "output": "x^3 + 17/12x^2 - 111/8x - 165/8 = 0\n(x - -3/2)(x - -11/3)(x - 15/4) = 0\nx - -3/2 = 0\nx - -11/3 = 0\nx - 15/4 = 0\nx = -3/2\nx = -11/3\nx = 15/4"} {"input": "Solve the equation 5x + 50/7 = 0", "output": "5x + 50/7 = 0\n5x = -50/7\nx = -50/7 / 5\nx = -10/7"} {"input": "Solve the equations:\n6x + 5y = 73\n3x + 9y = 573/10", "output": "6x + 5y = 73\n3x + 9y = 573/10\n\nUsing elimination\n3*(6x + 5y = 73)\n6*(3x + 9y = 573/10)\n18x + 15y = 219\n18x + 54y = 1719/5\nSubtract equations\n-39y = -624/5\ny = -624/5/-39\ny = 16/5\n\nSubstitute y\n6x + 5(16/5) = 73\n6x = 57\nx = 57/6\nx = 19/2"} {"input": "Solve simultaneously:\n6x + 9y = 53/4\n6x + 8y = 11", "output": "6x + 9y = 53/4\n6x + 8y = 11\n\nUsing elimination\n6*(6x + 9y = 53/4)\n6*(6x + 8y = 11)\n36x + 54y = 159/2\n36x + 48y = 66\nSubtract equations\n6y = 27/2\ny = 27/2/6\ny = 9/4\n\nSubstitute y\n6x + 9(9/4) = 53/4\n6x = -7\nx = -7/6\nx = -7/6"} {"input": "Solve the system:\n7x + 4y = 233/9\n4x + 10y = 787/18", "output": "7x + 4y = 233/9\n4x + 10y = 787/18\n\nUsing elimination\n4*(7x + 4y = 233/9)\n7*(4x + 10y = 787/18)\n28x + 16y = 932/9\n28x + 70y = 5509/18\nSubtract equations\n-54y = -405/2\ny = -405/2/-54\ny = 15/4\n\nSubstitute y\n7x + 4(15/4) = 233/9\n7x = 98/9\nx = 98/9/7\nx = 14/9"} {"input": "Solve simultaneously:\n9x + 4y = -646/5\n9x + 10y = -134", "output": "9x + 4y = -646/5\n9x + 10y = -134\n\nUsing elimination\n9*(9x + 4y = -646/5)\n9*(9x + 10y = -134)\n81x + 36y = -5814/5\n81x + 90y = -1206\nSubtract equations\n-54y = 216/5\ny = 216/5/-54\ny = -4/5\n\nSubstitute y\n9x + 4(-4/5) = -646/5\n9x = -126\nx = -126/9\nx = -14"} {"input": "Solve simultaneously:\n10x + 7y = -32/21\n1x + 6y = -100/7", "output": "10x + 7y = -32/21\n1x + 6y = -100/7\n\nUsing elimination\n1*(10x + 7y = -32/21)\n10*(1x + 6y = -100/7)\n10x + 7y = -32/21\n10x + 60y = -1000/7\nSubtract equations\n-53y = 424/3\ny = 424/3/-53\ny = -8/3\n\nSubstitute y\n10x + 7(-8/3) = -32/21\n10x = 120/7\nx = 120/7/10\nx = 12/7"} {"input": "Solve x^2 + 23/2x + 19 = 0", "output": "x^2 + 23/2x + 19 = 0\n(x - -19/2)(x - -2) = 0\nx - -19/2 = 0 or x - -2 = 0\nx = -19/2\nx = -2"} {"input": "Solve the system:\n9x + 4y = -179/9\n2x + 1y = -41/9", "output": "9x + 4y = -179/9\n2x + 1y = -41/9\n\nUsing elimination\n2*(9x + 4y = -179/9)\n9*(2x + 1y = -41/9)\n18x + 8y = -358/9\n18x + 9y = -41\nSubtract equations\n-1y = 11/9\ny = 11/9/-1\ny = -11/9\n\nSubstitute y\n9x + 4(-11/9) = -179/9\n9x = -15\nx = -15/9\nx = -5/3"} {"input": "Compute the solution of 4x - 34/5 = 0", "output": "4x - 34/5 = 0\n4x = 34/5\nx = 34/5 / 4\nx = 17/10"} {"input": "Solve x^3 + 523/70x^2 + 177/10x + 459/35 = 0", "output": "x^3 + 523/70x^2 + 177/10x + 459/35 = 0\n(x - -3/2)(x - -18/7)(x - -17/5) = 0\nx - -3/2 = 0\nx - -18/7 = 0\nx - -17/5 = 0\nx = -3/2\nx = -18/7\nx = -17/5"} {"input": "Solve the equations:\n7x + 3y = -253/4\n10x + 10y = -295/2", "output": "7x + 3y = -253/4\n10x + 10y = -295/2\n\nUsing elimination\n10*(7x + 3y = -253/4)\n7*(10x + 10y = -295/2)\n70x + 30y = -1265/2\n70x + 70y = -2065/2\nSubtract equations\n-40y = 400\ny = 400/-40\ny = -10\n\nSubstitute y\n7x + 3(-10) = -253/4\n7x = -133/4\nx = -133/4/7\nx = -19/4"} {"input": "Solve quickly: x^2 + 4x - 13/9 = 0", "output": "x^2 + 4x - 13/9 = 0\n(x - 1/3)(x - -13/3) = 0\nx - 1/3 = 0 or x - -13/3 = 0\nx = 1/3\nx = -13/3"} {"input": "Compute the solution of 3x + 15/2 = 0", "output": "3x + 15/2 = 0\n3x = -15/2\nx = -15/2 / 3\nx = -5/2"} {"input": "Find x in 4x + 44 = 0", "output": "4x + 44 = 0\n4x = -44\nx = -44 / 4\nx = -11"} {"input": "Solve the equations:\n1x + 8y = -64/7\n2x + 9y = -23/7", "output": "1x + 8y = -64/7\n2x + 9y = -23/7\n\nUsing elimination\n2*(1x + 8y = -64/7)\n1*(2x + 9y = -23/7)\n2x + 16y = -128/7\n2x + 9y = -23/7\nSubtract equations\n7y = -15\ny = -15/7\ny = -15/7\n\nSubstitute y\n1x + 8(-15/7) = -64/7\n1x = 8\nx = 8/1\nx = 8"} {"input": "Solve the equations:\n10x + 1y = 53/3\n6x + 8y = 11/15", "output": "10x + 1y = 53/3\n6x + 8y = 11/15\n\nUsing elimination\n6*(10x + 1y = 53/3)\n10*(6x + 8y = 11/15)\n60x + 6y = 106\n60x + 80y = 22/3\nSubtract equations\n-74y = 296/3\ny = 296/3/-74\ny = -4/3\n\nSubstitute y\n10x + 1(-4/3) = 53/3\n10x = 19\nx = 19/10\nx = 19/10"} {"input": "Compute the solution of x^3 + 107/30x^2 - 94/5x - 126/5 = 0", "output": "x^3 + 107/30x^2 - 94/5x - 126/5 = 0\n(x - -7/6)(x - -6)(x - 18/5) = 0\nx - -7/6 = 0\nx - -6 = 0\nx - 18/5 = 0\nx = -7/6\nx = -6\nx = 18/5"} {"input": "Solve the equations:\n2x + 10y = 55/9\n7x + 2y = 44/9", "output": "2x + 10y = 55/9\n7x + 2y = 44/9\n\nUsing elimination\n7*(2x + 10y = 55/9)\n2*(7x + 2y = 44/9)\n14x + 70y = 385/9\n14x + 4y = 88/9\nSubtract equations\n66y = 33\ny = 33/66\ny = 1/2\n\nSubstitute y\n2x + 10(1/2) = 55/9\n2x = 10/9\nx = 10/9/2\nx = 5/9"} {"input": "Find x in x^3 + 402/35x^2 + 157/35x - 66/7 = 0", "output": "x^3 + 402/35x^2 + 157/35x - 66/7 = 0\n(x - 5/7)(x - -11)(x - -6/5) = 0\nx - 5/7 = 0\nx - -11 = 0\nx - -6/5 = 0\nx = 5/7\nx = -11\nx = -6/5"} {"input": "Determine x in x^2 - 17x + 70 = 0", "output": "x^2 - 17x + 70 = 0\n(x - 10)(x - 7) = 0\nx - 10 = 0 or x - 7 = 0\nx = 10\nx = 7"} {"input": "Solve simultaneously:\n9x + 9y = 414/7\n2x + 7y = 302/7", "output": "9x + 9y = 414/7\n2x + 7y = 302/7\n\nUsing elimination\n2*(9x + 9y = 414/7)\n9*(2x + 7y = 302/7)\n18x + 18y = 828/7\n18x + 63y = 2718/7\nSubtract equations\n-45y = -270\ny = -270/-45\ny = 6\n\nSubstitute y\n9x + 9(6) = 414/7\n9x = 36/7\nx = 36/7/9\nx = 4/7"} {"input": "Find the solution to 1x - 12/7 = 0", "output": "1x - 12/7 = 0\n1x = 12/7\nx = 12/7 / 1\nx = 12/7"} {"input": "Solve the equation x^2 + 65/18x + 7/18 = 0", "output": "x^2 + 65/18x + 7/18 = 0\n(x - -1/9)(x - -7/2) = 0\nx - -1/9 = 0 or x - -7/2 = 0\nx = -1/9\nx = -7/2"} {"input": "Find the solution to x^3 - 21/8x^2 - 905/32x - 525/32 = 0", "output": "x^3 - 21/8x^2 - 905/32x - 525/32 = 0\n(x - -5/8)(x - 7)(x - -15/4) = 0\nx - -5/8 = 0\nx - 7 = 0\nx - -15/4 = 0\nx = -5/8\nx = 7\nx = -15/4"} {"input": "Find the solution to x^2 + 22/21x - 160/21 = 0", "output": "x^2 + 22/21x - 160/21 = 0\n(x - -10/3)(x - 16/7) = 0\nx - -10/3 = 0 or x - 16/7 = 0\nx = -10/3\nx = 16/7"} {"input": "Find x for x^3 - 13/7x^2 - 8/7x + 12/7 = 0", "output": "x^3 - 13/7x^2 - 8/7x + 12/7 = 0\n(x - -1)(x - 2)(x - 6/7) = 0\nx - -1 = 0\nx - 2 = 0\nx - 6/7 = 0\nx = -1\nx = 2\nx = 6/7"} {"input": "Determine x in x^3 - 159/10x^2 - 78x - 80 = 0", "output": "x^3 - 159/10x^2 - 78x - 80 = 0\n(x - -8/5)(x - -5/2)(x - 20) = 0\nx - -8/5 = 0\nx - -5/2 = 0\nx - 20 = 0\nx = -8/5\nx = -5/2\nx = 20"} {"input": "Solve quickly: x^2 - 31/21x + 8/21 = 0", "output": "x^2 - 31/21x + 8/21 = 0\n(x - 1/3)(x - 8/7) = 0\nx - 1/3 = 0 or x - 8/7 = 0\nx = 1/3\nx = 8/7"} {"input": "Determine x in x^3 - 17/2x^2 + 23x - 20 = 0", "output": "x^3 - 17/2x^2 + 23x - 20 = 0\n(x - 2)(x - 5/2)(x - 4) = 0\nx - 2 = 0\nx - 5/2 = 0\nx - 4 = 0\nx = 2\nx = 5/2\nx = 4"} {"input": "What value of x satisfies 6x + 36/5 = 0", "output": "6x + 36/5 = 0\n6x = -36/5\nx = -36/5 / 6\nx = -6/5"} {"input": "Solve 5x - 35 = 0", "output": "5x - 35 = 0\n5x = 35\nx = 35 / 5\nx = 7"} {"input": "Solve quickly: 10x - 30 = 0", "output": "10x - 30 = 0\n10x = 30\nx = 30 / 10\nx = 3"} {"input": "Find x in 2x + 7/5 = 0", "output": "2x + 7/5 = 0\n2x = -7/5\nx = -7/5 / 2\nx = -7/10"} {"input": "Find x for 6x + 9 = 0", "output": "6x + 9 = 0\n6x = -9\nx = -9 / 6\nx = -3/2"} {"input": "Solve the system:\n3x + 3y = 30\n3x + 6y = 66", "output": "3x + 3y = 30\n3x + 6y = 66\n\nUsing elimination\n3*(3x + 3y = 30)\n3*(3x + 6y = 66)\n9x + 9y = 90\n9x + 18y = 198\nSubtract equations\n-9y = -108\ny = -108/-9\ny = 12\n\nSubstitute y\n3x + 3(12) = 30\n3x = -6\nx = -6/3\nx = -2"} {"input": "Determine x in x^3 - 11/9x^2 - 1334/441x - 8/7 = 0", "output": "x^3 - 11/9x^2 - 1334/441x - 8/7 = 0\n(x - -4/7)(x - 18/7)(x - -7/9) = 0\nx - -4/7 = 0\nx - 18/7 = 0\nx - -7/9 = 0\nx = -4/7\nx = 18/7\nx = -7/9"} {"input": "What value of x satisfies x^2 + 29/6x + 35/6 = 0", "output": "x^2 + 29/6x + 35/6 = 0\n(x - -5/2)(x - -7/3) = 0\nx - -5/2 = 0 or x - -7/3 = 0\nx = -5/2\nx = -7/3"} {"input": "Determine x in x^2 - 33/5x + 8 = 0", "output": "x^2 - 33/5x + 8 = 0\n(x - 8/5)(x - 5) = 0\nx - 8/5 = 0 or x - 5 = 0\nx = 8/5\nx = 5"} {"input": "Solve x^2 - 10/3x - 11/9 = 0", "output": "x^2 - 10/3x - 11/9 = 0\n(x - -1/3)(x - 11/3) = 0\nx - -1/3 = 0 or x - 11/3 = 0\nx = -1/3\nx = 11/3"} {"input": "Solve the equations:\n8x + 4y = 80/3\n9x + 5y = 65/2", "output": "8x + 4y = 80/3\n9x + 5y = 65/2\n\nUsing elimination\n9*(8x + 4y = 80/3)\n8*(9x + 5y = 65/2)\n72x + 36y = 240\n72x + 40y = 260\nSubtract equations\n-4y = -20\ny = -20/-4\ny = 5\n\nSubstitute y\n8x + 4(5) = 80/3\n8x = 20/3\nx = 20/3/8\nx = 5/6"} {"input": "Solve simultaneously:\n4x + 7y = -78/5\n2x + 6y = -64/5", "output": "4x + 7y = -78/5\n2x + 6y = -64/5\n\nUsing elimination\n2*(4x + 7y = -78/5)\n4*(2x + 6y = -64/5)\n8x + 14y = -156/5\n8x + 24y = -256/5\nSubtract equations\n-10y = 20\ny = 20/-10\ny = -2\n\nSubstitute y\n4x + 7(-2) = -78/5\n4x = -8/5\nx = -8/5/4\nx = -2/5"} {"input": "Find x in x^2 + 25/4x - 13/8 = 0", "output": "x^2 + 25/4x - 13/8 = 0\n(x - 1/4)(x - -13/2) = 0\nx - 1/4 = 0 or x - -13/2 = 0\nx = 1/4\nx = -13/2"} {"input": "Solve simultaneously:\n7x + 5y = 33\n3x + 10y = -33", "output": "7x + 5y = 33\n3x + 10y = -33\n\nUsing elimination\n3*(7x + 5y = 33)\n7*(3x + 10y = -33)\n21x + 15y = 99\n21x + 70y = -231\nSubtract equations\n-55y = 330\ny = 330/-55\ny = -6\n\nSubstitute y\n7x + 5(-6) = 33\n7x = 63\nx = 63/7\nx = 9"} {"input": "Solve the equation 9x + 18/7 = 0", "output": "9x + 18/7 = 0\n9x = -18/7\nx = -18/7 / 9\nx = -2/7"} {"input": "Solve quickly: x^2 - 67/70x + 3/35 = 0", "output": "x^2 - 67/70x + 3/35 = 0\n(x - 1/10)(x - 6/7) = 0\nx - 1/10 = 0 or x - 6/7 = 0\nx = 1/10\nx = 6/7"} {"input": "Find x for x^3 - 331/90x^2 + 16/75x + 6/25 = 0", "output": "x^3 - 331/90x^2 + 16/75x + 6/25 = 0\n(x - -2/9)(x - 3/10)(x - 18/5) = 0\nx - -2/9 = 0\nx - 3/10 = 0\nx - 18/5 = 0\nx = -2/9\nx = 3/10\nx = 18/5"} {"input": "Solve x^3 + 157/30x^2 + 5x - 51/10 = 0", "output": "x^3 + 157/30x^2 + 5x - 51/10 = 0\n(x - -3)(x - 3/5)(x - -17/6) = 0\nx - -3 = 0\nx - 3/5 = 0\nx - -17/6 = 0\nx = -3\nx = 3/5\nx = -17/6"} {"input": "Solve x^2 - 7x + 45/4 = 0", "output": "x^2 - 7x + 45/4 = 0\n(x - 9/2)(x - 5/2) = 0\nx - 9/2 = 0 or x - 5/2 = 0\nx = 9/2\nx = 5/2"} {"input": "Solve x^3 + 286/35x^2 - 289/35x - 36/5 = 0", "output": "x^3 + 286/35x^2 - 289/35x - 36/5 = 0\n(x - -9)(x - -4/7)(x - 7/5) = 0\nx - -9 = 0\nx - -4/7 = 0\nx - 7/5 = 0\nx = -9\nx = -4/7\nx = 7/5"} {"input": "Solve quickly: 10x + 24 = 0", "output": "10x + 24 = 0\n10x = -24\nx = -24 / 10\nx = -12/5"} {"input": "Determine x in 2x + 10 = 0", "output": "2x + 10 = 0\n2x = -10\nx = -10 / 2\nx = -5"} {"input": "Find x in x^3 + 837/140x^2 + 1501/140x + 51/10 = 0", "output": "x^3 + 837/140x^2 + 1501/140x + 51/10 = 0\n(x - -17/7)(x - -14/5)(x - -3/4) = 0\nx - -17/7 = 0\nx - -14/5 = 0\nx - -3/4 = 0\nx = -17/7\nx = -14/5\nx = -3/4"} {"input": "Find x for x^2 - 7/9x - 2/9 = 0", "output": "x^2 - 7/9x - 2/9 = 0\n(x - 1)(x - -2/9) = 0\nx - 1 = 0 or x - -2/9 = 0\nx = 1\nx = -2/9"} {"input": "Solve simultaneously:\n1x + 9y = -99/5\n5x + 10y = -52/3", "output": "1x + 9y = -99/5\n5x + 10y = -52/3\n\nUsing elimination\n5*(1x + 9y = -99/5)\n1*(5x + 10y = -52/3)\n5x + 45y = -99\n5x + 10y = -52/3\nSubtract equations\n35y = -245/3\ny = -245/3/35\ny = -7/3\n\nSubstitute y\n1x + 9(-7/3) = -99/5\n1x = 6/5\nx = 6/5/1\nx = 6/5"} {"input": "Find x and y such that\n3x + 4y = 4\n1x + 9y = 131/12", "output": "3x + 4y = 4\n1x + 9y = 131/12\n\nUsing elimination\n1*(3x + 4y = 4)\n3*(1x + 9y = 131/12)\n3x + 4y = 4\n3x + 27y = 131/4\nSubtract equations\n-23y = -115/4\ny = -115/4/-23\ny = 5/4\n\nSubstitute y\n3x + 4(5/4) = 4\n3x = -1\nx = -1/3\nx = -1/3"} {"input": "Solve the equations:\n7x + 2y = 158/9\n5x + 4y = 136/9", "output": "7x + 2y = 158/9\n5x + 4y = 136/9\n\nUsing elimination\n5*(7x + 2y = 158/9)\n7*(5x + 4y = 136/9)\n35x + 10y = 790/9\n35x + 28y = 952/9\nSubtract equations\n-18y = -18\ny = -18/-18\ny = 1\n\nSubstitute y\n7x + 2(1) = 158/9\n7x = 140/9\nx = 140/9/7\nx = 20/9"} {"input": "Find x and y such that\n5x + 3y = 211/21\n6x + 3y = 235/21", "output": "5x + 3y = 211/21\n6x + 3y = 235/21\n\nUsing elimination\n6*(5x + 3y = 211/21)\n5*(6x + 3y = 235/21)\n30x + 18y = 422/7\n30x + 15y = 1175/21\nSubtract equations\n3y = 13/3\ny = 13/3/3\ny = 13/9\n\nSubstitute y\n5x + 3(13/9) = 211/21\n5x = 40/7\nx = 40/7/5\nx = 8/7"} {"input": "Find x in 8x + 32/3 = 0", "output": "8x + 32/3 = 0\n8x = -32/3\nx = -32/3 / 8\nx = -4/3"} {"input": "Solve x^3 + 3/5x^2 - 2066/405x - 136/27 = 0", "output": "x^3 + 3/5x^2 - 2066/405x - 136/27 = 0\n(x - 12/5)(x - -10/9)(x - -17/9) = 0\nx - 12/5 = 0\nx - -10/9 = 0\nx - -17/9 = 0\nx = 12/5\nx = -10/9\nx = -17/9"} {"input": "Find the solution to x^2 - 11/2x - 13/2 = 0", "output": "x^2 - 11/2x - 13/2 = 0\n(x - -1)(x - 13/2) = 0\nx - -1 = 0 or x - 13/2 = 0\nx = -1\nx = 13/2"} {"input": "Solve the equation x^2 + 79/18x + 119/27 = 0", "output": "x^2 + 79/18x + 119/27 = 0\n(x - -17/6)(x - -14/9) = 0\nx - -17/6 = 0 or x - -14/9 = 0\nx = -17/6\nx = -14/9"} {"input": "What value of x satisfies x^3 + 75/14x^2 + 79/14x - 30/7 = 0", "output": "x^3 + 75/14x^2 + 79/14x - 30/7 = 0\n(x - -20/7)(x - 1/2)(x - -3) = 0\nx - -20/7 = 0\nx - 1/2 = 0\nx - -3 = 0\nx = -20/7\nx = 1/2\nx = -3"} {"input": "Compute the solution of 2x - 32/9 = 0", "output": "2x - 32/9 = 0\n2x = 32/9\nx = 32/9 / 2\nx = 16/9"} {"input": "Determine x in x^2 + 20x + 36 = 0", "output": "x^2 + 20x + 36 = 0\n(x - -18)(x - -2) = 0\nx - -18 = 0 or x - -2 = 0\nx = -18\nx = -2"} {"input": "Compute the solution of x^3 - 47/5x^2 + 134/5x - 24 = 0", "output": "x^3 - 47/5x^2 + 134/5x - 24 = 0\n(x - 2)(x - 12/5)(x - 5) = 0\nx - 2 = 0\nx - 12/5 = 0\nx - 5 = 0\nx = 2\nx = 12/5\nx = 5"} {"input": "Find x in x^3 - 297/14x^2 + 283/14x + 570/7 = 0", "output": "x^3 - 297/14x^2 + 283/14x + 570/7 = 0\n(x - -3/2)(x - 20)(x - 19/7) = 0\nx - -3/2 = 0\nx - 20 = 0\nx - 19/7 = 0\nx = -3/2\nx = 20\nx = 19/7"} {"input": "Solve the equations:\n10x + 2y = 23\n5x + 8y = 22", "output": "10x + 2y = 23\n5x + 8y = 22\n\nUsing elimination\n5*(10x + 2y = 23)\n10*(5x + 8y = 22)\n50x + 10y = 115\n50x + 80y = 220\nSubtract equations\n-70y = -105\ny = -105/-70\ny = 3/2\n\nSubstitute y\n10x + 2(3/2) = 23\n10x = 20\nx = 20/10\nx = 2"} {"input": "Solve simultaneously:\n8x + 1y = -81/7\n3x + 7y = -3/2", "output": "8x + 1y = -81/7\n3x + 7y = -3/2\n\nUsing elimination\n3*(8x + 1y = -81/7)\n8*(3x + 7y = -3/2)\n24x + 3y = -243/7\n24x + 56y = -12\nSubtract equations\n-53y = -159/7\ny = -159/7/-53\ny = 3/7\n\nSubstitute y\n8x + 1(3/7) = -81/7\n8x = -12\nx = -12/8\nx = -3/2"} {"input": "Find x and y such that\n1x + 9y = -45/8\n10x + 4y = -91/2", "output": "1x + 9y = -45/8\n10x + 4y = -91/2\n\nUsing elimination\n10*(1x + 9y = -45/8)\n1*(10x + 4y = -91/2)\n10x + 90y = -225/4\n10x + 4y = -91/2\nSubtract equations\n86y = -43/4\ny = -43/4/86\ny = -1/8\n\nSubstitute y\n1x + 9(-1/8) = -45/8\n1x = -9/2\nx = -9/2/1\nx = -9/2"} {"input": "Find x and y such that\n1x + 5y = 49/4\n7x + 1y = 71/4", "output": "1x + 5y = 49/4\n7x + 1y = 71/4\n\nUsing elimination\n7*(1x + 5y = 49/4)\n1*(7x + 1y = 71/4)\n7x + 35y = 343/4\n7x + 1y = 71/4\nSubtract equations\n34y = 68\ny = 68/34\ny = 2\n\nSubstitute y\n1x + 5(2) = 49/4\n1x = 9/4\nx = 9/4/1\nx = 9/4"} {"input": "Find x and y such that\n10x + 9y = 23/3\n4x + 3y = 11/3", "output": "10x + 9y = 23/3\n4x + 3y = 11/3\n\nUsing elimination\n4*(10x + 9y = 23/3)\n10*(4x + 3y = 11/3)\n40x + 36y = 92/3\n40x + 30y = 110/3\nSubtract equations\n6y = -6\ny = -6/6\ny = -1\n\nSubstitute y\n10x + 9(-1) = 23/3\n10x = 50/3\nx = 50/3/10\nx = 5/3"} {"input": "What value of x satisfies x^3 - 9x = 0", "output": "x^3 - 9x = 0\n(x - 0)(x - 3)(x - -3) = 0\nx - 0 = 0\nx - 3 = 0\nx - -3 = 0\nx = 0\nx = 3\nx = -3"} {"input": "Solve quickly: 8x + 72 = 0", "output": "8x + 72 = 0\n8x = -72\nx = -72 / 8\nx = -9"} {"input": "Find x and y such that\n2x + 6y = -47/5\n1x + 4y = -51/10", "output": "2x + 6y = -47/5\n1x + 4y = -51/10\n\nUsing elimination\n1*(2x + 6y = -47/5)\n2*(1x + 4y = -51/10)\n2x + 6y = -47/5\n2x + 8y = -51/5\nSubtract equations\n-2y = 4/5\ny = 4/5/-2\ny = -2/5\n\nSubstitute y\n2x + 6(-2/5) = -47/5\n2x = -7\nx = -7/2\nx = -7/2"} {"input": "What value of x satisfies x^3 - 29/6x^2 - 281/18x + 1045/27 = 0", "output": "x^3 - 29/6x^2 - 281/18x + 1045/27 = 0\n(x - -10/3)(x - 11/6)(x - 19/3) = 0\nx - -10/3 = 0\nx - 11/6 = 0\nx - 19/3 = 0\nx = -10/3\nx = 11/6\nx = 19/3"} {"input": "Solve the equation 8x + 36 = 0", "output": "8x + 36 = 0\n8x = -36\nx = -36 / 8\nx = -9/2"} {"input": "Solve quickly: x^3 + 191/35x^2 - 1177/140x - 741/70 = 0", "output": "x^3 + 191/35x^2 - 1177/140x - 741/70 = 0\n(x - 19/10)(x - -13/2)(x - -6/7) = 0\nx - 19/10 = 0\nx - -13/2 = 0\nx - -6/7 = 0\nx = 19/10\nx = -13/2\nx = -6/7"} {"input": "Solve simultaneously:\n10x + 6y = -139/4\n2x + 5y = -67/8", "output": "10x + 6y = -139/4\n2x + 5y = -67/8\n\nUsing elimination\n2*(10x + 6y = -139/4)\n10*(2x + 5y = -67/8)\n20x + 12y = -139/2\n20x + 50y = -335/4\nSubtract equations\n-38y = 57/4\ny = 57/4/-38\ny = -3/8\n\nSubstitute y\n10x + 6(-3/8) = -139/4\n10x = -65/2\nx = -65/2/10\nx = -13/4"} {"input": "Solve simultaneously:\n1x + 6y = 127/6\n9x + 9y = 21/2", "output": "1x + 6y = 127/6\n9x + 9y = 21/2\n\nUsing elimination\n9*(1x + 6y = 127/6)\n1*(9x + 9y = 21/2)\n9x + 54y = 381/2\n9x + 9y = 21/2\nSubtract equations\n45y = 180\ny = 180/45\ny = 4\n\nSubstitute y\n1x + 6(4) = 127/6\n1x = -17/6\nx = -17/6/1\nx = -17/6"} {"input": "Find x and y such that\n4x + 7y = 76/3\n6x + 4y = 10/3", "output": "4x + 7y = 76/3\n6x + 4y = 10/3\n\nUsing elimination\n6*(4x + 7y = 76/3)\n4*(6x + 4y = 10/3)\n24x + 42y = 152\n24x + 16y = 40/3\nSubtract equations\n26y = 416/3\ny = 416/3/26\ny = 16/3\n\nSubstitute y\n4x + 7(16/3) = 76/3\n4x = -12\nx = -12/4\nx = -3"} {"input": "Solve quickly: 4x - 9 = 0", "output": "4x - 9 = 0\n4x = 9\nx = 9 / 4\nx = 9/4"} {"input": "Compute the solution of x^3 + 9/2x^2 + 313/50x + 63/25 = 0", "output": "x^3 + 9/2x^2 + 313/50x + 63/25 = 0\n(x - -7/10)(x - -2)(x - -9/5) = 0\nx - -7/10 = 0\nx - -2 = 0\nx - -9/5 = 0\nx = -7/10\nx = -2\nx = -9/5"} {"input": "What value of x satisfies 6x - 114 = 0", "output": "6x - 114 = 0\n6x = 114\nx = 114 / 6\nx = 19"} {"input": "Solve x^2 - 119/15x + 152/15 = 0", "output": "x^2 - 119/15x + 152/15 = 0\n(x - 19/3)(x - 8/5) = 0\nx - 19/3 = 0 or x - 8/5 = 0\nx = 19/3\nx = 8/5"} {"input": "Solve the equation x^3 - 212/21x^2 + 1159/84x - 85/42 = 0", "output": "x^3 - 212/21x^2 + 1159/84x - 85/42 = 0\n(x - 10/7)(x - 1/6)(x - 17/2) = 0\nx - 10/7 = 0\nx - 1/6 = 0\nx - 17/2 = 0\nx = 10/7\nx = 1/6\nx = 17/2"} {"input": "Solve quickly: x^2 - 2/5x - 63/25 = 0", "output": "x^2 - 2/5x - 63/25 = 0\n(x - 9/5)(x - -7/5) = 0\nx - 9/5 = 0 or x - -7/5 = 0\nx = 9/5\nx = -7/5"} {"input": "Find the solution to x^2 - 4/3x - 7/3 = 0", "output": "x^2 - 4/3x - 7/3 = 0\n(x - 7/3)(x - -1) = 0\nx - 7/3 = 0 or x - -1 = 0\nx = 7/3\nx = -1"} {"input": "Compute the solution of x^3 + 37/14x^2 - 1585/14x + 1950/7 = 0", "output": "x^3 + 37/14x^2 - 1585/14x + 1950/7 = 0\n(x - -13)(x - 20/7)(x - 15/2) = 0\nx - -13 = 0\nx - 20/7 = 0\nx - 15/2 = 0\nx = -13\nx = 20/7\nx = 15/2"} {"input": "Solve the equation 10x + 85/2 = 0", "output": "10x + 85/2 = 0\n10x = -85/2\nx = -85/2 / 10\nx = -17/4"} {"input": "Compute the solution of x^3 - 5/4x^2 - 3/2x = 0", "output": "x^3 - 5/4x^2 - 3/2x = 0\n(x - 0)(x - 2)(x - -3/4) = 0\nx - 0 = 0\nx - 2 = 0\nx - -3/4 = 0\nx = 0\nx = 2\nx = -3/4"} {"input": "What value of x satisfies x^2 + 5x + 44/9 = 0", "output": "x^2 + 5x + 44/9 = 0\n(x - -11/3)(x - -4/3) = 0\nx - -11/3 = 0 or x - -4/3 = 0\nx = -11/3\nx = -4/3"} {"input": "What value of x satisfies x^2 - 49/6x + 85/6 = 0", "output": "x^2 - 49/6x + 85/6 = 0\n(x - 17/3)(x - 5/2) = 0\nx - 17/3 = 0 or x - 5/2 = 0\nx = 17/3\nx = 5/2"} {"input": "Solve quickly: x^2 + 17/2x + 18 = 0", "output": "x^2 + 17/2x + 18 = 0\n(x - -9/2)(x - -4) = 0\nx - -9/2 = 0 or x - -4 = 0\nx = -9/2\nx = -4"} {"input": "Find x in 6x + 54/5 = 0", "output": "6x + 54/5 = 0\n6x = -54/5\nx = -54/5 / 6\nx = -9/5"} {"input": "Solve quickly: 10x = 0", "output": "10x = 0\n10x = 0\nx = 0 / 10\nx = 0"} {"input": "Solve quickly: x^2 + 19/4x + 11/2 = 0", "output": "x^2 + 19/4x + 11/2 = 0\n(x - -2)(x - -11/4) = 0\nx - -2 = 0 or x - -11/4 = 0\nx = -2\nx = -11/4"} {"input": "Solve quickly: x^2 - 23/4x + 45/8 = 0", "output": "x^2 - 23/4x + 45/8 = 0\n(x - 9/2)(x - 5/4) = 0\nx - 9/2 = 0 or x - 5/4 = 0\nx = 9/2\nx = 5/4"} {"input": "Solve the system:\n2x + 1y = -2\n10x + 3y = -11", "output": "2x + 1y = -2\n10x + 3y = -11\n\nUsing elimination\n10*(2x + 1y = -2)\n2*(10x + 3y = -11)\n20x + 10y = -20\n20x + 6y = -22\nSubtract equations\n4y = 2\ny = 2/4\ny = 1/2\n\nSubstitute y\n2x + 1(1/2) = -2\n2x = -5/2\nx = -5/2/2\nx = -5/4"} {"input": "Find the solution to x^2 - 13/18x - 35/27 = 0", "output": "x^2 - 13/18x - 35/27 = 0\n(x - -5/6)(x - 14/9) = 0\nx - -5/6 = 0 or x - 14/9 = 0\nx = -5/6\nx = 14/9"} {"input": "Solve the equations:\n2x + 7y = -193/3\n3x + 10y = -92", "output": "2x + 7y = -193/3\n3x + 10y = -92\n\nUsing elimination\n3*(2x + 7y = -193/3)\n2*(3x + 10y = -92)\n6x + 21y = -193\n6x + 20y = -184\nSubtract equations\n1y = -9\ny = -9/1\ny = -9\n\nSubstitute y\n2x + 7(-9) = -193/3\n2x = -4/3\nx = -4/3/2\nx = -2/3"} {"input": "Solve the system:\n6x + 6y = 372/7\n10x + 5y = 340/7", "output": "6x + 6y = 372/7\n10x + 5y = 340/7\n\nUsing elimination\n10*(6x + 6y = 372/7)\n6*(10x + 5y = 340/7)\n60x + 60y = 3720/7\n60x + 30y = 2040/7\nSubtract equations\n30y = 240\ny = 240/30\ny = 8\n\nSubstitute y\n6x + 6(8) = 372/7\n6x = 36/7\nx = 36/7/6\nx = 6/7"} {"input": "Solve the equations:\n2x + 10y = -5/12\n2x + 7y = -19/24", "output": "2x + 10y = -5/12\n2x + 7y = -19/24\n\nUsing elimination\n2*(2x + 10y = -5/12)\n2*(2x + 7y = -19/24)\n4x + 20y = -5/6\n4x + 14y = -19/12\nSubtract equations\n6y = 3/4\ny = 3/4/6\ny = 1/8\n\nSubstitute y\n2x + 10(1/8) = -5/12\n2x = -5/3\nx = -5/3/2\nx = -5/6"} {"input": "Find x for x^3 - 188/15x^2 + 41/15x + 44 = 0", "output": "x^3 - 188/15x^2 + 41/15x + 44 = 0\n(x - -5/3)(x - 12)(x - 11/5) = 0\nx - -5/3 = 0\nx - 12 = 0\nx - 11/5 = 0\nx = -5/3\nx = 12\nx = 11/5"} {"input": "Compute the solution of x^3 + 72/7x^2 - 460/7x - 192 = 0", "output": "x^3 + 72/7x^2 - 460/7x - 192 = 0\n(x - 6)(x - -16/7)(x - -14) = 0\nx - 6 = 0\nx - -16/7 = 0\nx - -14 = 0\nx = 6\nx = -16/7\nx = -14"} {"input": "What value of x satisfies 9x - 72/5 = 0", "output": "9x - 72/5 = 0\n9x = 72/5\nx = 72/5 / 9\nx = 8/5"} {"input": "Solve the system:\n7x + 5y = 75/4\n4x + 10y = 425/14", "output": "7x + 5y = 75/4\n4x + 10y = 425/14\n\nUsing elimination\n4*(7x + 5y = 75/4)\n7*(4x + 10y = 425/14)\n28x + 20y = 75\n28x + 70y = 425/2\nSubtract equations\n-50y = -275/2\ny = -275/2/-50\ny = 11/4\n\nSubstitute y\n7x + 5(11/4) = 75/4\n7x = 5\nx = 5/7\nx = 5/7"} {"input": "Find x in 2x - 14/5 = 0", "output": "2x - 14/5 = 0\n2x = 14/5\nx = 14/5 / 2\nx = 7/5"} {"input": "Find the solution to x^2 - 10/9x - 32/27 = 0", "output": "x^2 - 10/9x - 32/27 = 0\n(x - 16/9)(x - -2/3) = 0\nx - 16/9 = 0 or x - -2/3 = 0\nx = 16/9\nx = -2/3"} {"input": "Find x for x^2 - 1x + 12/49 = 0", "output": "x^2 - 1x + 12/49 = 0\n(x - 3/7)(x - 4/7) = 0\nx - 3/7 = 0 or x - 4/7 = 0\nx = 3/7\nx = 4/7"} {"input": "Determine x in 7x + 63/2 = 0", "output": "7x + 63/2 = 0\n7x = -63/2\nx = -63/2 / 7\nx = -9/2"} {"input": "Compute the solution of x^3 + 391/72x^2 - 961/144x + 65/36 = 0", "output": "x^3 + 391/72x^2 - 961/144x + 65/36 = 0\n(x - -13/2)(x - 4/9)(x - 5/8) = 0\nx - -13/2 = 0\nx - 4/9 = 0\nx - 5/8 = 0\nx = -13/2\nx = 4/9\nx = 5/8"} {"input": "Solve x^2 - 107/35x + 78/35 = 0", "output": "x^2 - 107/35x + 78/35 = 0\n(x - 6/5)(x - 13/7) = 0\nx - 6/5 = 0 or x - 13/7 = 0\nx = 6/5\nx = 13/7"} {"input": "Determine x in x^2 + 2x + 24/25 = 0", "output": "x^2 + 2x + 24/25 = 0\n(x - -4/5)(x - -6/5) = 0\nx - -4/5 = 0 or x - -6/5 = 0\nx = -4/5\nx = -6/5"} {"input": "Find the solution to 6x + 11 = 0", "output": "6x + 11 = 0\n6x = -11\nx = -11 / 6\nx = -11/6"} {"input": "Find x and y such that\n3x + 9y = 405/56\n2x + 10y = 183/28", "output": "3x + 9y = 405/56\n2x + 10y = 183/28\n\nUsing elimination\n2*(3x + 9y = 405/56)\n3*(2x + 10y = 183/28)\n6x + 18y = 405/28\n6x + 30y = 549/28\nSubtract equations\n-12y = -36/7\ny = -36/7/-12\ny = 3/7\n\nSubstitute y\n3x + 9(3/7) = 405/56\n3x = 27/8\nx = 27/8/3\nx = 9/8"} {"input": "Determine x in x^2 + 9/2x - 28 = 0", "output": "x^2 + 9/2x - 28 = 0\n(x - -8)(x - 7/2) = 0\nx - -8 = 0 or x - 7/2 = 0\nx = -8\nx = 7/2"} {"input": "Find the solution to x^3 - 23/10x^2 - 243/80x + 567/80 = 0", "output": "x^3 - 23/10x^2 - 243/80x + 567/80 = 0\n(x - 9/4)(x - 9/5)(x - -7/4) = 0\nx - 9/4 = 0\nx - 9/5 = 0\nx - -7/4 = 0\nx = 9/4\nx = 9/5\nx = -7/4"} {"input": "Find x for x^3 + 31/70x^2 - 52/7x - 40/7 = 0", "output": "x^3 + 31/70x^2 - 52/7x - 40/7 = 0\n(x - -4/5)(x - 20/7)(x - -5/2) = 0\nx - -4/5 = 0\nx - 20/7 = 0\nx - -5/2 = 0\nx = -4/5\nx = 20/7\nx = -5/2"} {"input": "Find the solution to x^3 + 4x^2 - 21/4x - 27/2 = 0", "output": "x^3 + 4x^2 - 21/4x - 27/2 = 0\n(x - -9/2)(x - -3/2)(x - 2) = 0\nx - -9/2 = 0\nx - -3/2 = 0\nx - 2 = 0\nx = -9/2\nx = -3/2\nx = 2"} {"input": "Find x in x^3 - 81/5x^2 + 68x - 60 = 0", "output": "x^3 - 81/5x^2 + 68x - 60 = 0\n(x - 5)(x - 10)(x - 6/5) = 0\nx - 5 = 0\nx - 10 = 0\nx - 6/5 = 0\nx = 5\nx = 10\nx = 6/5"} {"input": "Find x and y such that\n3x + 1y = 79/40\n5x + 10y = 133/8", "output": "3x + 1y = 79/40\n5x + 10y = 133/8\n\nUsing elimination\n5*(3x + 1y = 79/40)\n3*(5x + 10y = 133/8)\n15x + 5y = 79/8\n15x + 30y = 399/8\nSubtract equations\n-25y = -40\ny = -40/-25\ny = 8/5\n\nSubstitute y\n3x + 1(8/5) = 79/40\n3x = 3/8\nx = 3/8/3\nx = 1/8"} {"input": "Solve the equation 4x + 13/2 = 0", "output": "4x + 13/2 = 0\n4x = -13/2\nx = -13/2 / 4\nx = -13/8"} {"input": "Find x and y such that\n10x + 2y = -68/5\n8x + 5y = 0", "output": "10x + 2y = -68/5\n8x + 5y = 0\n\nUsing elimination\n8*(10x + 2y = -68/5)\n10*(8x + 5y = 0)\n80x + 16y = -544/5\n80x + 50y = 0\nSubtract equations\n-34y = -544/5\ny = -544/5/-34\ny = 16/5\n\nSubstitute y\n10x + 2(16/5) = -68/5\n10x = -20\nx = -20/10\nx = -2"} {"input": "Solve the equation x^3 - 11/2x^2 - 41/4x + 195/8 = 0", "output": "x^3 - 11/2x^2 - 41/4x + 195/8 = 0\n(x - 3/2)(x - -5/2)(x - 13/2) = 0\nx - 3/2 = 0\nx - -5/2 = 0\nx - 13/2 = 0\nx = 3/2\nx = -5/2\nx = 13/2"} {"input": "Solve simultaneously:\n3x + 8y = 753/40\n5x + 8y = 743/40", "output": "3x + 8y = 753/40\n5x + 8y = 743/40\n\nUsing elimination\n5*(3x + 8y = 753/40)\n3*(5x + 8y = 743/40)\n15x + 40y = 753/8\n15x + 24y = 2229/40\nSubtract equations\n16y = 192/5\ny = 192/5/16\ny = 12/5\n\nSubstitute y\n3x + 8(12/5) = 753/40\n3x = -3/8\nx = -3/8/3\nx = -1/8"} {"input": "Solve quickly: 5x + 15/2 = 0", "output": "5x + 15/2 = 0\n5x = -15/2\nx = -15/2 / 5\nx = -3/2"} {"input": "Solve x^2 + 63/8x - 1 = 0", "output": "x^2 + 63/8x - 1 = 0\n(x - -8)(x - 1/8) = 0\nx - -8 = 0 or x - 1/8 = 0\nx = -8\nx = 1/8"} {"input": "Solve x^3 - 479/168x^2 - 205/84x + 475/56 = 0", "output": "x^3 - 479/168x^2 - 205/84x + 475/56 = 0\n(x - 15/7)(x - -5/3)(x - 19/8) = 0\nx - 15/7 = 0\nx - -5/3 = 0\nx - 19/8 = 0\nx = 15/7\nx = -5/3\nx = 19/8"} {"input": "Solve the system:\n10x + 7y = 8\n8x + 5y = 32/5", "output": "10x + 7y = 8\n8x + 5y = 32/5\n\nUsing elimination\n8*(10x + 7y = 8)\n10*(8x + 5y = 32/5)\n80x + 56y = 64\n80x + 50y = 64\nSubtract equations\n6y = 0\ny = 0/6\ny = 0\n\nSubstitute y\n10x + 7(0) = 8\n10x = 8\nx = 8/10\nx = 4/5"} {"input": "Solve x^2 - 33/20x - 119/20 = 0", "output": "x^2 - 33/20x - 119/20 = 0\n(x - -7/4)(x - 17/5) = 0\nx - -7/4 = 0 or x - 17/5 = 0\nx = -7/4\nx = 17/5"} {"input": "Find the solution to x^3 - 131/10x^2 + 373/10x - 18/5 = 0", "output": "x^3 - 131/10x^2 + 373/10x - 18/5 = 0\n(x - 1/10)(x - 4)(x - 9) = 0\nx - 1/10 = 0\nx - 4 = 0\nx - 9 = 0\nx = 1/10\nx = 4\nx = 9"} {"input": "Determine x in x^2 + 107/30x + 19/15 = 0", "output": "x^2 + 107/30x + 19/15 = 0\n(x - -2/5)(x - -19/6) = 0\nx - -2/5 = 0 or x - -19/6 = 0\nx = -2/5\nx = -19/6"} {"input": "Solve x^3 - 67/20x^2 - 227/40x + 39/2 = 0", "output": "x^3 - 67/20x^2 - 227/40x + 39/2 = 0\n(x - 5/2)(x - -12/5)(x - 13/4) = 0\nx - 5/2 = 0\nx - -12/5 = 0\nx - 13/4 = 0\nx = 5/2\nx = -12/5\nx = 13/4"} {"input": "Determine x in x^2 + 7/10x = 0", "output": "x^2 + 7/10x = 0\n(x - -7/10)(x - 0) = 0\nx - -7/10 = 0 or x - 0 = 0\nx = -7/10\nx = 0"} {"input": "Determine x in x^2 + 19/10x - 361/50 = 0", "output": "x^2 + 19/10x - 361/50 = 0\n(x - 19/10)(x - -19/5) = 0\nx - 19/10 = 0 or x - -19/5 = 0\nx = 19/10\nx = -19/5"} {"input": "What value of x satisfies 5x + 35/2 = 0", "output": "5x + 35/2 = 0\n5x = -35/2\nx = -35/2 / 5\nx = -7/2"} {"input": "Compute the solution of x^2 + 1/3x - 44/3 = 0", "output": "x^2 + 1/3x - 44/3 = 0\n(x - -4)(x - 11/3) = 0\nx - -4 = 0 or x - 11/3 = 0\nx = -4\nx = 11/3"} {"input": "What value of x satisfies x^2 - 120/7x - 400/7 = 0", "output": "x^2 - 120/7x - 400/7 = 0\n(x - 20)(x - -20/7) = 0\nx - 20 = 0 or x - -20/7 = 0\nx = 20\nx = -20/7"} {"input": "Solve the system:\n6x + 1y = -139/4\n3x + 3y = -97/4", "output": "6x + 1y = -139/4\n3x + 3y = -97/4\n\nUsing elimination\n3*(6x + 1y = -139/4)\n6*(3x + 3y = -97/4)\n18x + 3y = -417/4\n18x + 18y = -291/2\nSubtract equations\n-15y = 165/4\ny = 165/4/-15\ny = -11/4\n\nSubstitute y\n6x + 1(-11/4) = -139/4\n6x = -32\nx = -32/6\nx = -16/3"} {"input": "Determine x in x^3 + 145/18x^2 + 52/9x - 169/6 = 0", "output": "x^3 + 145/18x^2 + 52/9x - 169/6 = 0\n(x - 13/9)(x - -3)(x - -13/2) = 0\nx - 13/9 = 0\nx - -3 = 0\nx - -13/2 = 0\nx = 13/9\nx = -3\nx = -13/2"} {"input": "Find the solution to x^2 + 43/24x - 209/48 = 0", "output": "x^2 + 43/24x - 209/48 = 0\n(x - 11/8)(x - -19/6) = 0\nx - 11/8 = 0 or x - -19/6 = 0\nx = 11/8\nx = -19/6"} {"input": "Compute the solution of 3x + 57/10 = 0", "output": "3x + 57/10 = 0\n3x = -57/10\nx = -57/10 / 3\nx = -19/10"} {"input": "Find x for x^2 + 23/6x + 11/3 = 0", "output": "x^2 + 23/6x + 11/3 = 0\n(x - -2)(x - -11/6) = 0\nx - -2 = 0 or x - -11/6 = 0\nx = -2\nx = -11/6"} {"input": "Find x in x^3 - 167/6x^2 + 423/2x - 1064/3 = 0", "output": "x^3 - 167/6x^2 + 423/2x - 1064/3 = 0\n(x - 19/2)(x - 16)(x - 7/3) = 0\nx - 19/2 = 0\nx - 16 = 0\nx - 7/3 = 0\nx = 19/2\nx = 16\nx = 7/3"} {"input": "Find x for x^2 + 111/35x + 88/35 = 0", "output": "x^2 + 111/35x + 88/35 = 0\n(x - -8/5)(x - -11/7) = 0\nx - -8/5 = 0 or x - -11/7 = 0\nx = -8/5\nx = -11/7"} {"input": "Solve x^2 + 10x + 21 = 0", "output": "x^2 + 10x + 21 = 0\n(x - -7)(x - -3) = 0\nx - -7 = 0 or x - -3 = 0\nx = -7\nx = -3"} {"input": "What value of x satisfies x^3 - 449/45x^2 - 1396/45x + 1216/15 = 0", "output": "x^3 - 449/45x^2 - 1396/45x + 1216/15 = 0\n(x - -19/5)(x - 16/9)(x - 12) = 0\nx - -19/5 = 0\nx - 16/9 = 0\nx - 12 = 0\nx = -19/5\nx = 16/9\nx = 12"} {"input": "Solve quickly: 10x - 17 = 0", "output": "10x - 17 = 0\n10x = 17\nx = 17 / 10\nx = 17/10"} {"input": "Find x in x^2 + 39/4x + 135/8 = 0", "output": "x^2 + 39/4x + 135/8 = 0\n(x - -9/4)(x - -15/2) = 0\nx - -9/4 = 0 or x - -15/2 = 0\nx = -9/4\nx = -15/2"} {"input": "Find x in x^2 - 5/7x - 2/7 = 0", "output": "x^2 - 5/7x - 2/7 = 0\n(x - 1)(x - -2/7) = 0\nx - 1 = 0 or x - -2/7 = 0\nx = 1\nx = -2/7"} {"input": "Solve quickly: 5x - 25/6 = 0", "output": "5x - 25/6 = 0\n5x = 25/6\nx = 25/6 / 5\nx = 5/6"} {"input": "Solve the system:\n4x + 8y = -206/5\n10x + 8y = -37", "output": "4x + 8y = -206/5\n10x + 8y = -37\n\nUsing elimination\n10*(4x + 8y = -206/5)\n4*(10x + 8y = -37)\n40x + 80y = -412\n40x + 32y = -148\nSubtract equations\n48y = -264\ny = -264/48\ny = -11/2\n\nSubstitute y\n4x + 8(-11/2) = -206/5\n4x = 14/5\nx = 14/5/4\nx = 7/10"} {"input": "Find the solution to 5x + 80 = 0", "output": "5x + 80 = 0\n5x = -80\nx = -80 / 5\nx = -16"} {"input": "Find x and y such that\n8x + 9y = -144/7\n1x + 1y = -16/7", "output": "8x + 9y = -144/7\n1x + 1y = -16/7\n\nUsing elimination\n1*(8x + 9y = -144/7)\n8*(1x + 1y = -16/7)\n8x + 9y = -144/7\n8x + 8y = -128/7\nSubtract equations\n1y = -16/7\ny = -16/7/1\ny = -16/7\n\nSubstitute y\n8x + 9(-16/7) = -144/7\n8x = 0\nx = 0/8\nx = 0"} {"input": "What value of x satisfies x^2 + 33/10x + 8/25 = 0", "output": "x^2 + 33/10x + 8/25 = 0\n(x - -1/10)(x - -16/5) = 0\nx - -1/10 = 0 or x - -16/5 = 0\nx = -1/10\nx = -16/5"} {"input": "Find the solution to 9x + 153/4 = 0", "output": "9x + 153/4 = 0\n9x = -153/4\nx = -153/4 / 9\nx = -17/4"} {"input": "Solve the equations:\n3x + 5y = 43/9\n1x + 7y = 89/9", "output": "3x + 5y = 43/9\n1x + 7y = 89/9\n\nUsing elimination\n1*(3x + 5y = 43/9)\n3*(1x + 7y = 89/9)\n3x + 5y = 43/9\n3x + 21y = 89/3\nSubtract equations\n-16y = -224/9\ny = -224/9/-16\ny = 14/9\n\nSubstitute y\n3x + 5(14/9) = 43/9\n3x = -3\nx = -3/3\nx = -1"} {"input": "Solve the equations:\n1x + 6y = 339/8\n3x + 1y = 331/24", "output": "1x + 6y = 339/8\n3x + 1y = 331/24\n\nUsing elimination\n3*(1x + 6y = 339/8)\n1*(3x + 1y = 331/24)\n3x + 18y = 1017/8\n3x + 1y = 331/24\nSubtract equations\n17y = 340/3\ny = 340/3/17\ny = 20/3\n\nSubstitute y\n1x + 6(20/3) = 339/8\n1x = 19/8\nx = 19/8/1\nx = 19/8"} {"input": "What value of x satisfies 3x - 17/2 = 0", "output": "3x - 17/2 = 0\n3x = 17/2\nx = 17/2 / 3\nx = 17/6"} {"input": "Find x for 4x - 8/3 = 0", "output": "4x - 8/3 = 0\n4x = 8/3\nx = 8/3 / 4\nx = 2/3"} {"input": "Solve quickly: x^3 + 29/5x^2 + 42/5x = 0", "output": "x^3 + 29/5x^2 + 42/5x = 0\n(x - -14/5)(x - -3)(x - 0) = 0\nx - -14/5 = 0\nx - -3 = 0\nx - 0 = 0\nx = -14/5\nx = -3\nx = 0"} {"input": "Solve simultaneously:\n4x + 7y = -58\n8x + 1y = -142", "output": "4x + 7y = -58\n8x + 1y = -142\n\nUsing elimination\n8*(4x + 7y = -58)\n4*(8x + 1y = -142)\n32x + 56y = -464\n32x + 4y = -568\nSubtract equations\n52y = 104\ny = 104/52\ny = 2\n\nSubstitute y\n4x + 7(2) = -58\n4x = -72\nx = -72/4\nx = -18"} {"input": "Compute the solution of x^2 + 7/6x - 1/2 = 0", "output": "x^2 + 7/6x - 1/2 = 0\n(x - 1/3)(x - -3/2) = 0\nx - 1/3 = 0 or x - -3/2 = 0\nx = 1/3\nx = -3/2"} {"input": "Compute the solution of 2x + 4/3 = 0", "output": "2x + 4/3 = 0\n2x = -4/3\nx = -4/3 / 2\nx = -2/3"} {"input": "Solve the system:\n6x + 5y = 29/5\n7x + 7y = 63/10", "output": "6x + 5y = 29/5\n7x + 7y = 63/10\n\nUsing elimination\n7*(6x + 5y = 29/5)\n6*(7x + 7y = 63/10)\n42x + 35y = 203/5\n42x + 42y = 189/5\nSubtract equations\n-7y = 14/5\ny = 14/5/-7\ny = -2/5\n\nSubstitute y\n6x + 5(-2/5) = 29/5\n6x = 39/5\nx = 39/5/6\nx = 13/10"} {"input": "Find x in x^3 + 5/2x^2 - 303/16x + 99/8 = 0", "output": "x^3 + 5/2x^2 - 303/16x + 99/8 = 0\n(x - -6)(x - 11/4)(x - 3/4) = 0\nx - -6 = 0\nx - 11/4 = 0\nx - 3/4 = 0\nx = -6\nx = 11/4\nx = 3/4"} {"input": "Compute the solution of x^2 - 7/18x - 95/18 = 0", "output": "x^2 - 7/18x - 95/18 = 0\n(x - -19/9)(x - 5/2) = 0\nx - -19/9 = 0 or x - 5/2 = 0\nx = -19/9\nx = 5/2"} {"input": "Find x and y such that\n4x + 1y = 3/2\n3x + 2y = -3/4", "output": "4x + 1y = 3/2\n3x + 2y = -3/4\n\nUsing elimination\n3*(4x + 1y = 3/2)\n4*(3x + 2y = -3/4)\n12x + 3y = 9/2\n12x + 8y = -3\nSubtract equations\n-5y = 15/2\ny = 15/2/-5\ny = -3/2\n\nSubstitute y\n4x + 1(-3/2) = 3/2\n4x = 3\nx = 3/4\nx = 3/4"} {"input": "Solve x^2 + 7x + 6 = 0", "output": "x^2 + 7x + 6 = 0\n(x - -1)(x - -6) = 0\nx - -1 = 0 or x - -6 = 0\nx = -1\nx = -6"} {"input": "Solve the equation x^2 - 39/8x - 169/16 = 0", "output": "x^2 - 39/8x - 169/16 = 0\n(x - 13/2)(x - -13/8) = 0\nx - 13/2 = 0 or x - -13/8 = 0\nx = 13/2\nx = -13/8"} {"input": "Solve quickly: x^3 + 277/120x^2 + 89/60x + 11/40 = 0", "output": "x^3 + 277/120x^2 + 89/60x + 11/40 = 0\n(x - -11/8)(x - -1/3)(x - -3/5) = 0\nx - -11/8 = 0\nx - -1/3 = 0\nx - -3/5 = 0\nx = -11/8\nx = -1/3\nx = -3/5"} {"input": "Solve x^3 + 23/3x^2 - 142/3x + 56 = 0", "output": "x^3 + 23/3x^2 - 142/3x + 56 = 0\n(x - 7/3)(x - 2)(x - -12) = 0\nx - 7/3 = 0\nx - 2 = 0\nx - -12 = 0\nx = 7/3\nx = 2\nx = -12"} {"input": "Find x for 2x + 32 = 0", "output": "2x + 32 = 0\n2x = -32\nx = -32 / 2\nx = -16"} {"input": "Find x in x^3 + 56/45x^2 - 13/9x - 4/5 = 0", "output": "x^3 + 56/45x^2 - 13/9x - 4/5 = 0\n(x - -9/5)(x - -4/9)(x - 1) = 0\nx - -9/5 = 0\nx - -4/9 = 0\nx - 1 = 0\nx = -9/5\nx = -4/9\nx = 1"} {"input": "Solve simultaneously:\n2x + 2y = 19/4\n6x + 9y = 147/8", "output": "2x + 2y = 19/4\n6x + 9y = 147/8\n\nUsing elimination\n6*(2x + 2y = 19/4)\n2*(6x + 9y = 147/8)\n12x + 12y = 57/2\n12x + 18y = 147/4\nSubtract equations\n-6y = -33/4\ny = -33/4/-6\ny = 11/8\n\nSubstitute y\n2x + 2(11/8) = 19/4\n2x = 2\nx = 2/2\nx = 1"} {"input": "Find x for 3x - 9/4 = 0", "output": "3x - 9/4 = 0\n3x = 9/4\nx = 9/4 / 3\nx = 3/4"} {"input": "What value of x satisfies 7x - 112/3 = 0", "output": "7x - 112/3 = 0\n7x = 112/3\nx = 112/3 / 7\nx = 16/3"} {"input": "Solve the equations:\n5x + 1y = -374/63\n9x + 1y = -82/7", "output": "5x + 1y = -374/63\n9x + 1y = -82/7\n\nUsing elimination\n9*(5x + 1y = -374/63)\n5*(9x + 1y = -82/7)\n45x + 9y = -374/7\n45x + 5y = -410/7\nSubtract equations\n4y = 36/7\ny = 36/7/4\ny = 9/7\n\nSubstitute y\n5x + 1(9/7) = -374/63\n5x = -65/9\nx = -65/9/5\nx = -13/9"} {"input": "Determine x in x^2 + 6x = 0", "output": "x^2 + 6x = 0\n(x - -6)(x - 0) = 0\nx - -6 = 0 or x - 0 = 0\nx = -6\nx = 0"} {"input": "What value of x satisfies x^3 + 1063/180x^2 + 679/60x + 637/90 = 0", "output": "x^3 + 1063/180x^2 + 679/60x + 637/90 = 0\n(x - -7/4)(x - -13/5)(x - -14/9) = 0\nx - -7/4 = 0\nx - -13/5 = 0\nx - -14/9 = 0\nx = -7/4\nx = -13/5\nx = -14/9"} {"input": "Determine x in x^2 + 67/5x - 24 = 0", "output": "x^2 + 67/5x - 24 = 0\n(x - 8/5)(x - -15) = 0\nx - 8/5 = 0 or x - -15 = 0\nx = 8/5\nx = -15"} {"input": "Solve the equation 8x - 6 = 0", "output": "8x - 6 = 0\n8x = 6\nx = 6 / 8\nx = 3/4"} {"input": "What value of x satisfies x^3 + 59/6x^2 + 57/2x + 77/3 = 0", "output": "x^3 + 59/6x^2 + 57/2x + 77/3 = 0\n(x - -11/2)(x - -7/3)(x - -2) = 0\nx - -11/2 = 0\nx - -7/3 = 0\nx - -2 = 0\nx = -11/2\nx = -7/3\nx = -2"} {"input": "Compute the solution of x^3 - 7/4x^2 - 4x + 7 = 0", "output": "x^3 - 7/4x^2 - 4x + 7 = 0\n(x - 7/4)(x - -2)(x - 2) = 0\nx - 7/4 = 0\nx - -2 = 0\nx - 2 = 0\nx = 7/4\nx = -2\nx = 2"} {"input": "Determine x in x^2 - 3/2x = 0", "output": "x^2 - 3/2x = 0\n(x - 0)(x - 3/2) = 0\nx - 0 = 0 or x - 3/2 = 0\nx = 0\nx = 3/2"} {"input": "Determine x in 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Determine x in x^2 + 45/7x - 4 = 0", "output": "x^2 + 45/7x - 4 = 0\n(x - -7)(x - 4/7) = 0\nx - -7 = 0 or x - 4/7 = 0\nx = -7\nx = 4/7"} {"input": "What value of x satisfies x^3 - 35/3x^2 + 326/9x - 520/27 = 0", "output": "x^3 - 35/3x^2 + 326/9x - 520/27 = 0\n(x - 2/3)(x - 20/3)(x - 13/3) = 0\nx - 2/3 = 0\nx - 20/3 = 0\nx - 13/3 = 0\nx = 2/3\nx = 20/3\nx = 13/3"} {"input": "Determine x in x^2 - 21/8x - 11/2 = 0", "output": "x^2 - 21/8x - 11/2 = 0\n(x - 4)(x - -11/8) = 0\nx - 4 = 0 or x - -11/8 = 0\nx = 4\nx = -11/8"} {"input": "Determine x in 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Determine x in x^2 - 11/3x = 0", "output": "x^2 - 11/3x = 0\n(x - 0)(x - 11/3) = 0\nx - 0 = 0 or x - 11/3 = 0\nx = 0\nx = 11/3"} {"input": "What value of x satisfies x^3 - 40/9x^2 + 197/108x + 140/27 = 0", "output": "x^3 - 40/9x^2 + 197/108x + 140/27 = 0\n(x - 7/2)(x - -5/6)(x - 16/9) = 0\nx - 7/2 = 0\nx - -5/6 = 0\nx - 16/9 = 0\nx = 7/2\nx = -5/6\nx = 16/9"} {"input": "Determine x in x^3 - 25/2x^2 + 51x - 135/2 = 0", "output": "x^3 - 25/2x^2 + 51x - 135/2 = 0\n(x - 9/2)(x - 5)(x - 3) = 0\nx - 9/2 = 0\nx - 5 = 0\nx - 3 = 0\nx = 9/2\nx = 5\nx = 3"} {"input": "Solve the system:\n4x + 8y = -151/3\n9x + 10y = -719/12", "output": "4x + 8y = -151/3\n9x + 10y = -719/12\n\nUsing elimination\n9*(4x + 8y = -151/3)\n4*(9x + 10y = -719/12)\n36x + 72y = -453\n36x + 40y = -719/3\nSubtract equations\n32y = -640/3\ny = -640/3/32\ny = -20/3\n\nSubstitute y\n4x + 8(-20/3) = -151/3\n4x = 3\nx = 3/4\nx = 3/4"} {"input": "Compute the solution of x^2 + 73/9x - 170/9 = 0", "output": "x^2 + 73/9x - 170/9 = 0\n(x - 17/9)(x - -10) = 0\nx - 17/9 = 0 or x - -10 = 0\nx = 17/9\nx = -10"} {"input": "Find x for 9x + 72/5 = 0", "output": "9x + 72/5 = 0\n9x = -72/5\nx = -72/5 / 9\nx = -8/5"} {"input": "Find x in x^2 - 149/24x + 65/8 = 0", "output": "x^2 - 149/24x + 65/8 = 0\n(x - 15/8)(x - 13/3) = 0\nx - 15/8 = 0 or x - 13/3 = 0\nx = 15/8\nx = 13/3"} {"input": "Solve the equation 4x + 32/9 = 0", "output": "4x + 32/9 = 0\n4x = -32/9\nx = -32/9 / 4\nx = -8/9"} {"input": "Determine x in x^2 - 1/2x - 3/2 = 0", "output": "x^2 - 1/2x - 3/2 = 0\n(x - 3/2)(x - -1) = 0\nx - 3/2 = 0 or x - -1 = 0\nx = 3/2\nx = -1"} {"input": "Solve x^3 - 7/6x^2 - 13/18x + 1/3 = 0", "output": "x^3 - 7/6x^2 - 13/18x + 1/3 = 0\n(x - -2/3)(x - 3/2)(x - 1/3) = 0\nx - -2/3 = 0\nx - 3/2 = 0\nx - 1/3 = 0\nx = -2/3\nx = 3/2\nx = 1/3"} {"input": "Solve the system:\n3x + 5y = 76/7\n3x + 9y = 120/7", "output": "3x + 5y = 76/7\n3x + 9y = 120/7\n\nUsing elimination\n3*(3x + 5y = 76/7)\n3*(3x + 9y = 120/7)\n9x + 15y = 228/7\n9x + 27y = 360/7\nSubtract equations\n-12y = -132/7\ny = -132/7/-12\ny = 11/7\n\nSubstitute y\n3x + 5(11/7) = 76/7\n3x = 3\nx = 3/3\nx = 1"} {"input": "Find x for 10x - 85/2 = 0", "output": "10x - 85/2 = 0\n10x = 85/2\nx = 85/2 / 10\nx = 17/4"} {"input": "Compute the solution of 4x - 8/5 = 0", "output": "4x - 8/5 = 0\n4x = 8/5\nx = 8/5 / 4\nx = 2/5"} {"input": "Compute the solution of x^3 - 181/360x^2 - 229/120x + 11/45 = 0", "output": "x^3 - 181/360x^2 - 229/120x + 11/45 = 0\n(x - 1/8)(x - 8/5)(x - -11/9) = 0\nx - 1/8 = 0\nx - 8/5 = 0\nx - -11/9 = 0\nx = 1/8\nx = 8/5\nx = -11/9"} {"input": "Find the solution to x^2 - 3/5x - 8/5 = 0", "output": "x^2 - 3/5x - 8/5 = 0\n(x - -1)(x - 8/5) = 0\nx - -1 = 0 or x - 8/5 = 0\nx = -1\nx = 8/5"} {"input": "Solve the equation 6x + 20 = 0", "output": "6x + 20 = 0\n6x = -20\nx = -20 / 6\nx = -10/3"} {"input": "Solve the equations:\n1x + 3y = -41/4\n2x + 4y = -25", "output": "1x + 3y = -41/4\n2x + 4y = -25\n\nUsing elimination\n2*(1x + 3y = -41/4)\n1*(2x + 4y = -25)\n2x + 6y = -41/2\n2x + 4y = -25\nSubtract equations\n2y = 9/2\ny = 9/2/2\ny = 9/4\n\nSubstitute y\n1x + 3(9/4) = -41/4\n1x = -17\nx = -17/1\nx = -17"} {"input": "Solve simultaneously:\n1x + 9y = 321/7\n10x + 5y = 235/7", "output": "1x + 9y = 321/7\n10x + 5y = 235/7\n\nUsing elimination\n10*(1x + 9y = 321/7)\n1*(10x + 5y = 235/7)\n10x + 90y = 3210/7\n10x + 5y = 235/7\nSubtract equations\n85y = 425\ny = 425/85\ny = 5\n\nSubstitute y\n1x + 9(5) = 321/7\n1x = 6/7\nx = 6/7/1\nx = 6/7"} {"input": "Find x in 9x - 45/2 = 0", "output": "9x - 45/2 = 0\n9x = 45/2\nx = 45/2 / 9\nx = 5/2"} {"input": "Find x and y such that\n2x + 6y = 34\n2x + 9y = 49", "output": "2x + 6y = 34\n2x + 9y = 49\n\nUsing elimination\n2*(2x + 6y = 34)\n2*(2x + 9y = 49)\n4x + 12y = 68\n4x + 18y = 98\nSubtract equations\n-6y = -30\ny = -30/-6\ny = 5\n\nSubstitute y\n2x + 6(5) = 34\n2x = 4\nx = 4/2\nx = 2"} {"input": "Solve the equation 1x - 3/2 = 0", "output": "1x - 3/2 = 0\n1x = 3/2\nx = 3/2 / 1\nx = 3/2"} {"input": "Find x for x^3 - 197/90x^2 - 2/15x + 119/90 = 0", "output": "x^3 - 197/90x^2 - 2/15x + 119/90 = 0\n(x - 17/9)(x - -7/10)(x - 1) = 0\nx - 17/9 = 0\nx - -7/10 = 0\nx - 1 = 0\nx = 17/9\nx = -7/10\nx = 1"} {"input": "Determine x in x^2 - 5/56x - 25/56 = 0", "output": "x^2 - 5/56x - 25/56 = 0\n(x - -5/8)(x - 5/7) = 0\nx - -5/8 = 0 or x - 5/7 = 0\nx = -5/8\nx = 5/7"} {"input": "Find x in 6x - 36 = 0", "output": "6x - 36 = 0\n6x = 36\nx = 36 / 6\nx = 6"} {"input": "Solve x^3 - 731/70x^2 + 933/70x - 108/35 = 0", "output": "x^3 - 731/70x^2 + 933/70x - 108/35 = 0\n(x - 8/7)(x - 9)(x - 3/10) = 0\nx - 8/7 = 0\nx - 9 = 0\nx - 3/10 = 0\nx = 8/7\nx = 9\nx = 3/10"} {"input": "Solve the equation x^2 - 23x + 76 = 0", "output": "x^2 - 23x + 76 = 0\n(x - 19)(x - 4) = 0\nx - 19 = 0 or x - 4 = 0\nx = 19\nx = 4"} {"input": "Solve the equation x^3 - 869/36x^2 + 2963/36x + 85/9 = 0", "output": "x^3 - 869/36x^2 + 2963/36x + 85/9 = 0\n(x - 20)(x - -1/9)(x - 17/4) = 0\nx - 20 = 0\nx - -1/9 = 0\nx - 17/4 = 0\nx = 20\nx = -1/9\nx = 17/4"} {"input": "Solve quickly: 5x - 85/6 = 0", "output": "5x - 85/6 = 0\n5x = 85/6\nx = 85/6 / 5\nx = 17/6"} {"input": "Solve the system:\n5x + 5y = 225/14\n10x + 5y = 415/14", "output": "5x + 5y = 225/14\n10x + 5y = 415/14\n\nUsing elimination\n10*(5x + 5y = 225/14)\n5*(10x + 5y = 415/14)\n50x + 50y = 1125/7\n50x + 25y = 2075/14\nSubtract equations\n25y = 25/2\ny = 25/2/25\ny = 1/2\n\nSubstitute y\n5x + 5(1/2) = 225/14\n5x = 95/7\nx = 95/7/5\nx = 19/7"} {"input": "Solve simultaneously:\n5x + 5y = -215/72\n9x + 3y = -73/8", "output": "5x + 5y = -215/72\n9x + 3y = -73/8\n\nUsing elimination\n9*(5x + 5y = -215/72)\n5*(9x + 3y = -73/8)\n45x + 45y = -215/8\n45x + 15y = -365/8\nSubtract equations\n30y = 75/4\ny = 75/4/30\ny = 5/8\n\nSubstitute y\n5x + 5(5/8) = -215/72\n5x = -55/9\nx = -55/9/5\nx = -11/9"} {"input": "Find x in x^3 - 112/45x^2 - 221/45x + 152/15 = 0", "output": "x^3 - 112/45x^2 - 221/45x + 152/15 = 0\n(x - 3)(x - 8/5)(x - -19/9) = 0\nx - 3 = 0\nx - 8/5 = 0\nx - -19/9 = 0\nx = 3\nx = 8/5\nx = -19/9"} {"input": "Solve x^3 - 283/21x^2 + 380/21x - 32/7 = 0", "output": "x^3 - 283/21x^2 + 380/21x - 32/7 = 0\n(x - 1/3)(x - 8/7)(x - 12) = 0\nx - 1/3 = 0\nx - 8/7 = 0\nx - 12 = 0\nx = 1/3\nx = 8/7\nx = 12"} {"input": "What value of x satisfies x^2 + 53/30x + 4/15 = 0", "output": "x^2 + 53/30x + 4/15 = 0\n(x - -8/5)(x - -1/6) = 0\nx - -8/5 = 0 or x - -1/6 = 0\nx = -8/5\nx = -1/6"} {"input": "Solve quickly: x^3 + 3/2x^2 + 2/9x - 5/18 = 0", "output": "x^3 + 3/2x^2 + 2/9x - 5/18 = 0\n(x - -1)(x - -5/6)(x - 1/3) = 0\nx - -1 = 0\nx - -5/6 = 0\nx - 1/3 = 0\nx = -1\nx = -5/6\nx = 1/3"} {"input": "Find x and y such that\n8x + 8y = 432/5\n4x + 7y = 381/5", "output": "8x + 8y = 432/5\n4x + 7y = 381/5\n\nUsing elimination\n4*(8x + 8y = 432/5)\n8*(4x + 7y = 381/5)\n32x + 32y = 1728/5\n32x + 56y = 3048/5\nSubtract equations\n-24y = -264\ny = -264/-24\ny = 11\n\nSubstitute y\n8x + 8(11) = 432/5\n8x = -8/5\nx = -8/5/8\nx = -1/5"} {"input": "Solve 2x - 1 = 0", "output": "2x - 1 = 0\n2x = 1\nx = 1 / 2\nx = 1/2"} {"input": "What value of x satisfies x^2 - 11/2x + 9/2 = 0", "output": "x^2 - 11/2x + 9/2 = 0\n(x - 1)(x - 9/2) = 0\nx - 1 = 0 or x - 9/2 = 0\nx = 1\nx = 9/2"} {"input": "Find x for x^2 - 26/15x - 17/3 = 0", "output": "x^2 - 26/15x - 17/3 = 0\n(x - -5/3)(x - 17/5) = 0\nx - -5/3 = 0 or x - 17/5 = 0\nx = -5/3\nx = 17/5"} {"input": "Find x and y such that\n3x + 2y = 43/20\n1x + 9y = -513/40", "output": "3x + 2y = 43/20\n1x + 9y = -513/40\n\nUsing elimination\n1*(3x + 2y = 43/20)\n3*(1x + 9y = -513/40)\n3x + 2y = 43/20\n3x + 27y = -1539/40\nSubtract equations\n-25y = 325/8\ny = 325/8/-25\ny = -13/8\n\nSubstitute y\n3x + 2(-13/8) = 43/20\n3x = 27/5\nx = 27/5/3\nx = 9/5"} {"input": "Find the solution to 1x - 3 = 0", "output": "1x - 3 = 0\n1x = 3\nx = 3 / 1\nx = 3"} {"input": "What value of x satisfies x^2 - 29/8x + 13/4 = 0", "output": "x^2 - 29/8x + 13/4 = 0\n(x - 2)(x - 13/8) = 0\nx - 2 = 0 or x - 13/8 = 0\nx = 2\nx = 13/8"} {"input": "Find x for x^3 + 73/30x^2 + 9/5x + 11/30 = 0", "output": "x^3 + 73/30x^2 + 9/5x + 11/30 = 0\n(x - -1/3)(x - -1)(x - -11/10) = 0\nx - -1/3 = 0\nx - -1 = 0\nx - -11/10 = 0\nx = -1/3\nx = -1\nx = -11/10"} {"input": "Solve the equation 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "Find x in x^3 - 61/15x^2 + 76/15x - 28/15 = 0", "output": "x^3 - 61/15x^2 + 76/15x - 28/15 = 0\n(x - 7/5)(x - 2/3)(x - 2) = 0\nx - 7/5 = 0\nx - 2/3 = 0\nx - 2 = 0\nx = 7/5\nx = 2/3\nx = 2"} {"input": "Solve the equations:\n6x + 8y = -622/21\n3x + 2y = -241/21", "output": "6x + 8y = -622/21\n3x + 2y = -241/21\n\nUsing elimination\n3*(6x + 8y = -622/21)\n6*(3x + 2y = -241/21)\n18x + 24y = -622/7\n18x + 12y = -482/7\nSubtract equations\n12y = -20\ny = -20/12\ny = -5/3\n\nSubstitute y\n6x + 8(-5/3) = -622/21\n6x = -114/7\nx = -114/7/6\nx = -19/7"} {"input": "Compute the solution of 10x + 10/3 = 0", "output": "10x + 10/3 = 0\n10x = -10/3\nx = -10/3 / 10\nx = -1/3"} {"input": "What value of x satisfies x^2 + 21/10x - 27/10 = 0", "output": "x^2 + 21/10x - 27/10 = 0\n(x - 9/10)(x - -3) = 0\nx - 9/10 = 0 or x - -3 = 0\nx = 9/10\nx = -3"} {"input": "Solve 9x - 45 = 0", "output": "9x - 45 = 0\n9x = 45\nx = 45 / 9\nx = 5"} {"input": "Solve the system:\n6x + 3y = 43\n5x + 2y = 88/3", "output": "6x + 3y = 43\n5x + 2y = 88/3\n\nUsing elimination\n5*(6x + 3y = 43)\n6*(5x + 2y = 88/3)\n30x + 15y = 215\n30x + 12y = 176\nSubtract equations\n3y = 39\ny = 39/3\ny = 13\n\nSubstitute y\n6x + 3(13) = 43\n6x = 4\nx = 4/6\nx = 2/3"} {"input": "Solve the equations:\n10x + 2y = 9\n2x + 4y = -63/5", "output": "10x + 2y = 9\n2x + 4y = -63/5\n\nUsing elimination\n2*(10x + 2y = 9)\n10*(2x + 4y = -63/5)\n20x + 4y = 18\n20x + 40y = -126\nSubtract equations\n-36y = 144\ny = 144/-36\ny = -4\n\nSubstitute y\n10x + 2(-4) = 9\n10x = 17\nx = 17/10\nx = 17/10"} {"input": "Find x in 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Compute the solution of 2x - 2/5 = 0", "output": "2x - 2/5 = 0\n2x = 2/5\nx = 2/5 / 2\nx = 1/5"} {"input": "Solve simultaneously:\n5x + 2y = -53/15\n4x + 6y = -49/15", "output": "5x + 2y = -53/15\n4x + 6y = -49/15\n\nUsing elimination\n4*(5x + 2y = -53/15)\n5*(4x + 6y = -49/15)\n20x + 8y = -212/15\n20x + 30y = -49/3\nSubtract equations\n-22y = 11/5\ny = 11/5/-22\ny = -1/10\n\nSubstitute y\n5x + 2(-1/10) = -53/15\n5x = -10/3\nx = -10/3/5\nx = -2/3"} {"input": "Find the solution to x^2 + 47/9x - 190/27 = 0", "output": "x^2 + 47/9x - 190/27 = 0\n(x - -19/3)(x - 10/9) = 0\nx - -19/3 = 0 or x - 10/9 = 0\nx = -19/3\nx = 10/9"} {"input": "Find x and y such that\n6x + 8y = 184/3\n3x + 6y = 44", "output": "6x + 8y = 184/3\n3x + 6y = 44\n\nUsing elimination\n3*(6x + 8y = 184/3)\n6*(3x + 6y = 44)\n18x + 24y = 184\n18x + 36y = 264\nSubtract equations\n-12y = -80\ny = -80/-12\ny = 20/3\n\nSubstitute y\n6x + 8(20/3) = 184/3\n6x = 8\nx = 8/6\nx = 4/3"} {"input": "Solve quickly: x^3 + 113/7x^2 + 15x - 225/7 = 0", "output": "x^3 + 113/7x^2 + 15x - 225/7 = 0\n(x - 1)(x - -15)(x - -15/7) = 0\nx - 1 = 0\nx - -15 = 0\nx - -15/7 = 0\nx = 1\nx = -15\nx = -15/7"} {"input": "Find x for x^2 - 53/10x - 39/5 = 0", "output": "x^2 - 53/10x - 39/5 = 0\n(x - -6/5)(x - 13/2) = 0\nx - -6/5 = 0 or x - 13/2 = 0\nx = -6/5\nx = 13/2"} {"input": "Determine x in x^2 + 87/20x + 143/40 = 0", "output": "x^2 + 87/20x + 143/40 = 0\n(x - -13/4)(x - -11/10) = 0\nx - -13/4 = 0 or x - -11/10 = 0\nx = -13/4\nx = -11/10"} {"input": "Solve quickly: x^3 + 71/24x^2 + 163/96x - 5/8 = 0", "output": "x^3 + 71/24x^2 + 163/96x - 5/8 = 0\n(x - 1/4)(x - -4/3)(x - -15/8) = 0\nx - 1/4 = 0\nx - -4/3 = 0\nx - -15/8 = 0\nx = 1/4\nx = -4/3\nx = -15/8"} {"input": "Solve the equation x^3 - 25/6x^2 - 68/3x + 40 = 0", "output": "x^3 - 25/6x^2 - 68/3x + 40 = 0\n(x - -4)(x - 3/2)(x - 20/3) = 0\nx - -4 = 0\nx - 3/2 = 0\nx - 20/3 = 0\nx = -4\nx = 3/2\nx = 20/3"} {"input": "Find x in 1x + 12 = 0", "output": "1x + 12 = 0\n1x = -12\nx = -12 / 1\nx = -12"} {"input": "Find x and y such that\n7x + 7y = -49/5\n8x + 6y = -47/5", "output": "7x + 7y = -49/5\n8x + 6y = -47/5\n\nUsing elimination\n8*(7x + 7y = -49/5)\n7*(8x + 6y = -47/5)\n56x + 56y = -392/5\n56x + 42y = -329/5\nSubtract equations\n14y = -63/5\ny = -63/5/14\ny = -9/10\n\nSubstitute y\n7x + 7(-9/10) = -49/5\n7x = -7/2\nx = -7/2/7\nx = -1/2"} {"input": "Find the solution to 4x + 32/3 = 0", "output": "4x + 32/3 = 0\n4x = -32/3\nx = -32/3 / 4\nx = -8/3"} {"input": "Solve quickly: x^2 + 52/9x + 169/27 = 0", "output": "x^2 + 52/9x + 169/27 = 0\n(x - -13/3)(x - -13/9) = 0\nx - -13/3 = 0 or x - -13/9 = 0\nx = -13/3\nx = -13/9"} {"input": "Find the solution to x^3 + 9/5x^2 - 38/5x + 24/5 = 0", "output": "x^3 + 9/5x^2 - 38/5x + 24/5 = 0\n(x - 6/5)(x - -4)(x - 1) = 0\nx - 6/5 = 0\nx - -4 = 0\nx - 1 = 0\nx = 6/5\nx = -4\nx = 1"} {"input": "What value of x satisfies 1x + 5/9 = 0", "output": "1x + 5/9 = 0\n1x = -5/9\nx = -5/9 / 1\nx = -5/9"} {"input": "Find x and y such that\n1x + 4y = 46/3\n5x + 4y = 42", "output": "1x + 4y = 46/3\n5x + 4y = 42\n\nUsing elimination\n5*(1x + 4y = 46/3)\n1*(5x + 4y = 42)\n5x + 20y = 230/3\n5x + 4y = 42\nSubtract equations\n16y = 104/3\ny = 104/3/16\ny = 13/6\n\nSubstitute y\n1x + 4(13/6) = 46/3\n1x = 20/3\nx = 20/3/1\nx = 20/3"} {"input": "Solve quickly: x^2 + 35/3x + 304/9 = 0", "output": "x^2 + 35/3x + 304/9 = 0\n(x - -19/3)(x - -16/3) = 0\nx - -19/3 = 0 or x - -16/3 = 0\nx = -19/3\nx = -16/3"} {"input": "Determine x in x^2 + 15/2x + 9 = 0", "output": "x^2 + 15/2x + 9 = 0\n(x - -6)(x - -3/2) = 0\nx - -6 = 0 or x - -3/2 = 0\nx = -6\nx = -3/2"} {"input": "Determine x in x^2 - 77/20x + 13/4 = 0", "output": "x^2 - 77/20x + 13/4 = 0\n(x - 13/5)(x - 5/4) = 0\nx - 13/5 = 0 or x - 5/4 = 0\nx = 13/5\nx = 5/4"} {"input": "Solve the equations:\n8x + 1y = -1205/8\n8x + 6y = -575/4", "output": "8x + 1y = -1205/8\n8x + 6y = -575/4\n\nUsing elimination\n8*(8x + 1y = -1205/8)\n8*(8x + 6y = -575/4)\n64x + 8y = -1205\n64x + 48y = -1150\nSubtract equations\n-40y = -55\ny = -55/-40\ny = 11/8\n\nSubstitute y\n8x + 1(11/8) = -1205/8\n8x = -152\nx = -152/8\nx = -19"} {"input": "Find x for x^3 - 4x^2 - 433/36x + 187/9 = 0", "output": "x^3 - 4x^2 - 433/36x + 187/9 = 0\n(x - 4/3)(x - -17/6)(x - 11/2) = 0\nx - 4/3 = 0\nx - -17/6 = 0\nx - 11/2 = 0\nx = 4/3\nx = -17/6\nx = 11/2"} {"input": "Solve the equation x^2 + 1/2x - 3/50 = 0", "output": "x^2 + 1/2x - 3/50 = 0\n(x - 1/10)(x - -3/5) = 0\nx - 1/10 = 0 or x - -3/5 = 0\nx = 1/10\nx = -3/5"} {"input": "What value of x satisfies 8x + 64/3 = 0", "output": "8x + 64/3 = 0\n8x = -64/3\nx = -64/3 / 8\nx = -8/3"} {"input": "Solve simultaneously:\n7x + 3y = -499/8\n2x + 5y = -353/4", "output": "7x + 3y = -499/8\n2x + 5y = -353/4\n\nUsing elimination\n2*(7x + 3y = -499/8)\n7*(2x + 5y = -353/4)\n14x + 6y = -499/4\n14x + 35y = -2471/4\nSubtract equations\n-29y = 493\ny = 493/-29\ny = -17\n\nSubstitute y\n7x + 3(-17) = -499/8\n7x = -91/8\nx = -91/8/7\nx = -13/8"} {"input": "Find x for x^2 + 137/28x + 19/28 = 0", "output": "x^2 + 137/28x + 19/28 = 0\n(x - -1/7)(x - -19/4) = 0\nx - -1/7 = 0 or x - -19/4 = 0\nx = -1/7\nx = -19/4"} {"input": "Solve simultaneously:\n3x + 2y = -35/2\n7x + 5y = -85/2", "output": "3x + 2y = -35/2\n7x + 5y = -85/2\n\nUsing elimination\n7*(3x + 2y = -35/2)\n3*(7x + 5y = -85/2)\n21x + 14y = -245/2\n21x + 15y = -255/2\nSubtract equations\n-1y = 5\ny = 5/-1\ny = -5\n\nSubstitute y\n3x + 2(-5) = -35/2\n3x = -15/2\nx = -15/2/3\nx = -5/2"} {"input": "Solve the equations:\n2x + 5y = -7/3\n2x + 10y = 88/3", "output": "2x + 5y = -7/3\n2x + 10y = 88/3\n\nUsing elimination\n2*(2x + 5y = -7/3)\n2*(2x + 10y = 88/3)\n4x + 10y = -14/3\n4x + 20y = 176/3\nSubtract equations\n-10y = -190/3\ny = -190/3/-10\ny = 19/3\n\nSubstitute y\n2x + 5(19/3) = -7/3\n2x = -34\nx = -34/2\nx = -17"} {"input": "Solve the equation 7x + 133/4 = 0", "output": "7x + 133/4 = 0\n7x = -133/4\nx = -133/4 / 7\nx = -19/4"} {"input": "Solve the equation x^3 + 51/5x^2 + 11x + 9/5 = 0", "output": "x^3 + 51/5x^2 + 11x + 9/5 = 0\n(x - -1/5)(x - -1)(x - -9) = 0\nx - -1/5 = 0\nx - -1 = 0\nx - -9 = 0\nx = -1/5\nx = -1\nx = -9"} {"input": "Solve the equations:\n9x + 4y = -65/2\n6x + 1y = -15", "output": "9x + 4y = -65/2\n6x + 1y = -15\n\nUsing elimination\n6*(9x + 4y = -65/2)\n9*(6x + 1y = -15)\n54x + 24y = -195\n54x + 9y = -135\nSubtract equations\n15y = -60\ny = -60/15\ny = -4\n\nSubstitute y\n9x + 4(-4) = -65/2\n9x = -33/2\nx = -33/2/9\nx = -11/6"} {"input": "Solve x^3 - 19/2x^2 + 37/2x - 7 = 0", "output": "x^3 - 19/2x^2 + 37/2x - 7 = 0\n(x - 1/2)(x - 7)(x - 2) = 0\nx - 1/2 = 0\nx - 7 = 0\nx - 2 = 0\nx = 1/2\nx = 7\nx = 2"} {"input": "Solve the system:\n9x + 2y = 401/10\n4x + 8y = 82/5", "output": "9x + 2y = 401/10\n4x + 8y = 82/5\n\nUsing elimination\n4*(9x + 2y = 401/10)\n9*(4x + 8y = 82/5)\n36x + 8y = 802/5\n36x + 72y = 738/5\nSubtract equations\n-64y = 64/5\ny = 64/5/-64\ny = -1/5\n\nSubstitute y\n9x + 2(-1/5) = 401/10\n9x = 81/2\nx = 81/2/9\nx = 9/2"} {"input": "Solve the system:\n1x + 4y = 269/8\n4x + 1y = 7", "output": "1x + 4y = 269/8\n4x + 1y = 7\n\nUsing elimination\n4*(1x + 4y = 269/8)\n1*(4x + 1y = 7)\n4x + 16y = 269/2\n4x + 1y = 7\nSubtract equations\n15y = 255/2\ny = 255/2/15\ny = 17/2\n\nSubstitute y\n1x + 4(17/2) = 269/8\n1x = -3/8\nx = -3/8/1\nx = -3/8"} {"input": "Find x for x^3 + 391/28x^2 + 479/14x + 495/28 = 0", "output": "x^3 + 391/28x^2 + 479/14x + 495/28 = 0\n(x - -11)(x - -5/7)(x - -9/4) = 0\nx - -11 = 0\nx - -5/7 = 0\nx - -9/4 = 0\nx = -11\nx = -5/7\nx = -9/4"} {"input": "Find the solution to x^3 + 21/4x^2 + 73/8x + 21/4 = 0", "output": "x^3 + 21/4x^2 + 73/8x + 21/4 = 0\n(x - -7/4)(x - -3/2)(x - -2) = 0\nx - -7/4 = 0\nx - -3/2 = 0\nx - -2 = 0\nx = -7/4\nx = -3/2\nx = -2"} {"input": "What value of x satisfies x^3 - 43/10x^2 + 201/50x - 9/25 = 0", "output": "x^3 - 43/10x^2 + 201/50x - 9/25 = 0\n(x - 3)(x - 6/5)(x - 1/10) = 0\nx - 3 = 0\nx - 6/5 = 0\nx - 1/10 = 0\nx = 3\nx = 6/5\nx = 1/10"} {"input": "Solve simultaneously:\n10x + 5y = -1\n7x + 3y = -7/5", "output": "10x + 5y = -1\n7x + 3y = -7/5\n\nUsing elimination\n7*(10x + 5y = -1)\n10*(7x + 3y = -7/5)\n70x + 35y = -7\n70x + 30y = -14\nSubtract equations\n5y = 7\ny = 7/5\ny = 7/5\n\nSubstitute y\n10x + 5(7/5) = -1\n10x = -8\nx = -8/10\nx = -4/5"} {"input": "What value of x satisfies x^3 + 9/2x^2 - 9x = 0", "output": "x^3 + 9/2x^2 - 9x = 0\n(x - 0)(x - 3/2)(x - -6) = 0\nx - 0 = 0\nx - 3/2 = 0\nx - -6 = 0\nx = 0\nx = 3/2\nx = -6"} {"input": "Find x for x^2 - 9x + 20 = 0", "output": "x^2 - 9x + 20 = 0\n(x - 5)(x - 4) = 0\nx - 5 = 0 or x - 4 = 0\nx = 5\nx = 4"} {"input": "Solve the equation x^2 - 4/3x - 32/3 = 0", "output": "x^2 - 4/3x - 32/3 = 0\n(x - 4)(x - -8/3) = 0\nx - 4 = 0 or x - -8/3 = 0\nx = 4\nx = -8/3"} {"input": "Solve simultaneously:\n1x + 9y = -95/4\n5x + 1y = -79/4", "output": "1x + 9y = -95/4\n5x + 1y = -79/4\n\nUsing elimination\n5*(1x + 9y = -95/4)\n1*(5x + 1y = -79/4)\n5x + 45y = -475/4\n5x + 1y = -79/4\nSubtract equations\n44y = -99\ny = -99/44\ny = -9/4\n\nSubstitute y\n1x + 9(-9/4) = -95/4\n1x = -7/2\nx = -7/2/1\nx = -7/2"} {"input": "Solve simultaneously:\n4x + 9y = 247/5\n8x + 4y = 242/5", "output": "4x + 9y = 247/5\n8x + 4y = 242/5\n\nUsing elimination\n8*(4x + 9y = 247/5)\n4*(8x + 4y = 242/5)\n32x + 72y = 1976/5\n32x + 16y = 968/5\nSubtract equations\n56y = 1008/5\ny = 1008/5/56\ny = 18/5\n\nSubstitute y\n4x + 9(18/5) = 247/5\n4x = 17\nx = 17/4\nx = 17/4"} {"input": "Find the solution to x^3 - 122/45x^2 - 244/45x + 8 = 0", "output": "x^3 - 122/45x^2 - 244/45x + 8 = 0\n(x - 18/5)(x - 10/9)(x - -2) = 0\nx - 18/5 = 0\nx - 10/9 = 0\nx - -2 = 0\nx = 18/5\nx = 10/9\nx = -2"} {"input": "Find x and y such that\n7x + 6y = -327/10\n10x + 6y = -87/2", "output": "7x + 6y = -327/10\n10x + 6y = -87/2\n\nUsing elimination\n10*(7x + 6y = -327/10)\n7*(10x + 6y = -87/2)\n70x + 60y = -327\n70x + 42y = -609/2\nSubtract equations\n18y = -45/2\ny = -45/2/18\ny = -5/4\n\nSubstitute y\n7x + 6(-5/4) = -327/10\n7x = -126/5\nx = -126/5/7\nx = -18/5"} {"input": "Find x and y such that\n9x + 8y = 156/35\n2x + 4y = -132/35", "output": "9x + 8y = 156/35\n2x + 4y = -132/35\n\nUsing elimination\n2*(9x + 8y = 156/35)\n9*(2x + 4y = -132/35)\n18x + 16y = 312/35\n18x + 36y = -1188/35\nSubtract equations\n-20y = 300/7\ny = 300/7/-20\ny = -15/7\n\nSubstitute y\n9x + 8(-15/7) = 156/35\n9x = 108/5\nx = 108/5/9\nx = 12/5"} {"input": "Solve quickly: x^2 + 12x - 28 = 0", "output": "x^2 + 12x - 28 = 0\n(x - -14)(x - 2) = 0\nx - -14 = 0 or x - 2 = 0\nx = -14\nx = 2"} {"input": "Find x in 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "Solve simultaneously:\n4x + 7y = -81/10\n6x + 5y = -21/2", "output": "4x + 7y = -81/10\n6x + 5y = -21/2\n\nUsing elimination\n6*(4x + 7y = -81/10)\n4*(6x + 5y = -21/2)\n24x + 42y = -243/5\n24x + 20y = -42\nSubtract equations\n22y = -33/5\ny = -33/5/22\ny = -3/10\n\nSubstitute y\n4x + 7(-3/10) = -81/10\n4x = -6\nx = -6/4\nx = -3/2"} {"input": "Find x and y such that\n10x + 2y = 710/7\n7x + 6y = 520/7", "output": "10x + 2y = 710/7\n7x + 6y = 520/7\n\nUsing elimination\n7*(10x + 2y = 710/7)\n10*(7x + 6y = 520/7)\n70x + 14y = 710\n70x + 60y = 5200/7\nSubtract equations\n-46y = -230/7\ny = -230/7/-46\ny = 5/7\n\nSubstitute y\n10x + 2(5/7) = 710/7\n10x = 100\nx = 100/10\nx = 10"} {"input": "Solve the equation x^3 - 15/2x^2 - 9x + 40 = 0", "output": "x^3 - 15/2x^2 - 9x + 40 = 0\n(x - 2)(x - -5/2)(x - 8) = 0\nx - 2 = 0\nx - -5/2 = 0\nx - 8 = 0\nx = 2\nx = -5/2\nx = 8"} {"input": "What value of x satisfies 5x - 25 = 0", "output": "5x - 25 = 0\n5x = 25\nx = 25 / 5\nx = 5"} {"input": "Find the solution to x^3 - 141/8x^2 - 109/16x + 9/8 = 0", "output": "x^3 - 141/8x^2 - 109/16x + 9/8 = 0\n(x - -1/2)(x - 1/8)(x - 18) = 0\nx - -1/2 = 0\nx - 1/8 = 0\nx - 18 = 0\nx = -1/2\nx = 1/8\nx = 18"} {"input": "Find x and y such that\n5x + 4y = -71/3\n5x + 5y = -625/24", "output": "5x + 4y = -71/3\n5x + 5y = -625/24\n\nUsing elimination\n5*(5x + 4y = -71/3)\n5*(5x + 5y = -625/24)\n25x + 20y = -355/3\n25x + 25y = -3125/24\nSubtract equations\n-5y = 95/8\ny = 95/8/-5\ny = -19/8\n\nSubstitute y\n5x + 4(-19/8) = -71/3\n5x = -85/6\nx = -85/6/5\nx = -17/6"} {"input": "Find x and y such that\n2x + 8y = 158/63\n5x + 7y = -242/63", "output": "2x + 8y = 158/63\n5x + 7y = -242/63\n\nUsing elimination\n5*(2x + 8y = 158/63)\n2*(5x + 7y = -242/63)\n10x + 40y = 790/63\n10x + 14y = -484/63\nSubtract equations\n26y = 182/9\ny = 182/9/26\ny = 7/9\n\nSubstitute y\n2x + 8(7/9) = 158/63\n2x = -26/7\nx = -26/7/2\nx = -13/7"} {"input": "Compute the solution of 10x - 14 = 0", "output": "10x - 14 = 0\n10x = 14\nx = 14 / 10\nx = 7/5"} {"input": "Solve quickly: 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Solve simultaneously:\n9x + 6y = 375/2\n7x + 6y = 299/2", "output": "9x + 6y = 375/2\n7x + 6y = 299/2\n\nUsing elimination\n7*(9x + 6y = 375/2)\n9*(7x + 6y = 299/2)\n63x + 42y = 2625/2\n63x + 54y = 2691/2\nSubtract equations\n-12y = -33\ny = -33/-12\ny = 11/4\n\nSubstitute y\n9x + 6(11/4) = 375/2\n9x = 171\nx = 171/9\nx = 19"} {"input": "What value of x satisfies 7x + 133/4 = 0", "output": "7x + 133/4 = 0\n7x = -133/4\nx = -133/4 / 7\nx = -19/4"} {"input": "Find x and y such that\n6x + 10y = -25/2\n7x + 6y = -49/2", "output": "6x + 10y = -25/2\n7x + 6y = -49/2\n\nUsing elimination\n7*(6x + 10y = -25/2)\n6*(7x + 6y = -49/2)\n42x + 70y = -175/2\n42x + 36y = -147\nSubtract equations\n34y = 119/2\ny = 119/2/34\ny = 7/4\n\nSubstitute y\n6x + 10(7/4) = -25/2\n6x = -30\nx = -30/6\nx = -5"} {"input": "Solve x^3 - 77/15x^2 - 82/15x + 352/15 = 0", "output": "x^3 - 77/15x^2 - 82/15x + 352/15 = 0\n(x - -11/5)(x - 2)(x - 16/3) = 0\nx - -11/5 = 0\nx - 2 = 0\nx - 16/3 = 0\nx = -11/5\nx = 2\nx = 16/3"} {"input": "Find the solution to x^3 + 3/14x^2 - 27/14x = 0", "output": "x^3 + 3/14x^2 - 27/14x = 0\n(x - -3/2)(x - 0)(x - 9/7) = 0\nx - -3/2 = 0\nx - 0 = 0\nx - 9/7 = 0\nx = -3/2\nx = 0\nx = 9/7"} {"input": "Find x in 2x - 4 = 0", "output": "2x - 4 = 0\n2x = 4\nx = 4 / 2\nx = 2"} {"input": "What value of x satisfies 5x + 25/3 = 0", "output": "5x + 25/3 = 0\n5x = -25/3\nx = -25/3 / 5\nx = -5/3"} {"input": "Solve the equations:\n7x + 3y = 157/4\n7x + 6y = 181/4", "output": "7x + 3y = 157/4\n7x + 6y = 181/4\n\nUsing elimination\n7*(7x + 3y = 157/4)\n7*(7x + 6y = 181/4)\n49x + 21y = 1099/4\n49x + 42y = 1267/4\nSubtract equations\n-21y = -42\ny = -42/-21\ny = 2\n\nSubstitute y\n7x + 3(2) = 157/4\n7x = 133/4\nx = 133/4/7\nx = 19/4"} {"input": "Solve 10x + 50/3 = 0", "output": "10x + 50/3 = 0\n10x = -50/3\nx = -50/3 / 10\nx = -5/3"} {"input": "Determine x in x^3 + 627/35x^2 + 496/35x - 816/35 = 0", "output": "x^3 + 627/35x^2 + 496/35x - 816/35 = 0\n(x - 4/5)(x - -12/7)(x - -17) = 0\nx - 4/5 = 0\nx - -12/7 = 0\nx - -17 = 0\nx = 4/5\nx = -12/7\nx = -17"} {"input": "Find x and y such that\n9x + 7y = -249/5\n4x + 9y = -93/5", "output": "9x + 7y = -249/5\n4x + 9y = -93/5\n\nUsing elimination\n4*(9x + 7y = -249/5)\n9*(4x + 9y = -93/5)\n36x + 28y = -996/5\n36x + 81y = -837/5\nSubtract equations\n-53y = -159/5\ny = -159/5/-53\ny = 3/5\n\nSubstitute y\n9x + 7(3/5) = -249/5\n9x = -54\nx = -54/9\nx = -6"} {"input": "Find x in x^2 + 11/2x + 6 = 0", "output": "x^2 + 11/2x + 6 = 0\n(x - -3/2)(x - -4) = 0\nx - -3/2 = 0 or x - -4 = 0\nx = -3/2\nx = -4"} {"input": "Solve x^2 - 7/40x - 1/2 = 0", "output": "x^2 - 7/40x - 1/2 = 0\n(x - 4/5)(x - -5/8) = 0\nx - 4/5 = 0 or x - -5/8 = 0\nx = 4/5\nx = -5/8"} {"input": "Solve quickly: 4x - 12 = 0", "output": "4x - 12 = 0\n4x = 12\nx = 12 / 4\nx = 3"} {"input": "Solve the equation 5x + 15/2 = 0", "output": "5x + 15/2 = 0\n5x = -15/2\nx = -15/2 / 5\nx = -3/2"} {"input": "Compute the solution of x^2 + 16/9x - 4/9 = 0", "output": "x^2 + 16/9x - 4/9 = 0\n(x - 2/9)(x - -2) = 0\nx - 2/9 = 0 or x - -2 = 0\nx = 2/9\nx = -2"} {"input": "Find x for x^2 + 13/2x + 3 = 0", "output": "x^2 + 13/2x + 3 = 0\n(x - -1/2)(x - -6) = 0\nx - -1/2 = 0 or x - -6 = 0\nx = -1/2\nx = -6"} {"input": "Solve 1x - 5/3 = 0", "output": "1x - 5/3 = 0\n1x = 5/3\nx = 5/3 / 1\nx = 5/3"} {"input": "Solve the equation x^2 + 26/9x - 40/9 = 0", "output": "x^2 + 26/9x - 40/9 = 0\n(x - 10/9)(x - -4) = 0\nx - 10/9 = 0 or x - -4 = 0\nx = 10/9\nx = -4"} {"input": "Solve simultaneously:\n1x + 6y = -99/20\n9x + 5y = -557/40", "output": "1x + 6y = -99/20\n9x + 5y = -557/40\n\nUsing elimination\n9*(1x + 6y = -99/20)\n1*(9x + 5y = -557/40)\n9x + 54y = -891/20\n9x + 5y = -557/40\nSubtract equations\n49y = -245/8\ny = -245/8/49\ny = -5/8\n\nSubstitute y\n1x + 6(-5/8) = -99/20\n1x = -6/5\nx = -6/5/1\nx = -6/5"} {"input": "Solve the equation 7x + 7 = 0", "output": "7x + 7 = 0\n7x = -7\nx = -7 / 7\nx = -1"} {"input": "Determine x in 1x + 18/7 = 0", "output": "1x + 18/7 = 0\n1x = -18/7\nx = -18/7 / 1\nx = -18/7"} {"input": "Find x in x^2 - 7/5x - 52/5 = 0", "output": "x^2 - 7/5x - 52/5 = 0\n(x - -13/5)(x - 4) = 0\nx - -13/5 = 0 or x - 4 = 0\nx = -13/5\nx = 4"} {"input": "Find the solution to x^2 - 13/7x - 24/7 = 0", "output": "x^2 - 13/7x - 24/7 = 0\n(x - 3)(x - -8/7) = 0\nx - 3 = 0 or x - -8/7 = 0\nx = 3\nx = -8/7"} {"input": "Compute the solution of x^3 - 26/35x^2 - 471/245x + 216/245 = 0", "output": "x^3 - 26/35x^2 - 471/245x + 216/245 = 0\n(x - 8/5)(x - 3/7)(x - -9/7) = 0\nx - 8/5 = 0\nx - 3/7 = 0\nx - -9/7 = 0\nx = 8/5\nx = 3/7\nx = -9/7"} {"input": "Solve x^3 + 389/140x^2 + 5/14x - 39/140 = 0", "output": "x^3 + 389/140x^2 + 5/14x - 39/140 = 0\n(x - -3/7)(x - 1/4)(x - -13/5) = 0\nx - -3/7 = 0\nx - 1/4 = 0\nx - -13/5 = 0\nx = -3/7\nx = 1/4\nx = -13/5"} {"input": "Solve the system:\n4x + 8y = -77/2\n9x + 9y = -333/8", "output": "4x + 8y = -77/2\n9x + 9y = -333/8\n\nUsing elimination\n9*(4x + 8y = -77/2)\n4*(9x + 9y = -333/8)\n36x + 72y = -693/2\n36x + 36y = -333/2\nSubtract equations\n36y = -180\ny = -180/36\ny = -5\n\nSubstitute y\n4x + 8(-5) = -77/2\n4x = 3/2\nx = 3/2/4\nx = 3/8"} {"input": "Find x and y such that\n8x + 7y = -64/7\n6x + 1y = -48/7", "output": "8x + 7y = -64/7\n6x + 1y = -48/7\n\nUsing elimination\n6*(8x + 7y = -64/7)\n8*(6x + 1y = -48/7)\n48x + 42y = -384/7\n48x + 8y = -384/7\nSubtract equations\n34y = 0\ny = 0/34\ny = 0\n\nSubstitute y\n8x + 7(0) = -64/7\n8x = -64/7\nx = -64/7/8\nx = -8/7"} {"input": "Solve x^2 + 9/20x - 91/40 = 0", "output": "x^2 + 9/20x - 91/40 = 0\n(x - 13/10)(x - -7/4) = 0\nx - 13/10 = 0 or x - -7/4 = 0\nx = 13/10\nx = -7/4"} {"input": "Solve x^3 + 34/7x^2 + 359/49x + 170/49 = 0", "output": "x^3 + 34/7x^2 + 359/49x + 170/49 = 0\n(x - -10/7)(x - -17/7)(x - -1) = 0\nx - -10/7 = 0\nx - -17/7 = 0\nx - -1 = 0\nx = -10/7\nx = -17/7\nx = -1"} {"input": "Solve x^3 + 37/12x^2 - 461/24x + 209/24 = 0", "output": "x^3 + 37/12x^2 - 461/24x + 209/24 = 0\n(x - -19/3)(x - 11/4)(x - 1/2) = 0\nx - -19/3 = 0\nx - 11/4 = 0\nx - 1/2 = 0\nx = -19/3\nx = 11/4\nx = 1/2"} {"input": "Solve the equations:\n10x + 7y = 227/6\n1x + 6y = 67/3", "output": "10x + 7y = 227/6\n1x + 6y = 67/3\n\nUsing elimination\n1*(10x + 7y = 227/6)\n10*(1x + 6y = 67/3)\n10x + 7y = 227/6\n10x + 60y = 670/3\nSubtract equations\n-53y = -371/2\ny = -371/2/-53\ny = 7/2\n\nSubstitute y\n10x + 7(7/2) = 227/6\n10x = 40/3\nx = 40/3/10\nx = 4/3"} {"input": "Solve the system:\n9x + 8y = -87/2\n1x + 10y = -39", "output": "9x + 8y = -87/2\n1x + 10y = -39\n\nUsing elimination\n1*(9x + 8y = -87/2)\n9*(1x + 10y = -39)\n9x + 8y = -87/2\n9x + 90y = -351\nSubtract equations\n-82y = 615/2\ny = 615/2/-82\ny = -15/4\n\nSubstitute y\n9x + 8(-15/4) = -87/2\n9x = -27/2\nx = -27/2/9\nx = -3/2"} {"input": "Solve the equations:\n4x + 3y = 335/14\n2x + 5y = 437/14", "output": "4x + 3y = 335/14\n2x + 5y = 437/14\n\nUsing elimination\n2*(4x + 3y = 335/14)\n4*(2x + 5y = 437/14)\n8x + 6y = 335/7\n8x + 20y = 874/7\nSubtract equations\n-14y = -77\ny = -77/-14\ny = 11/2\n\nSubstitute y\n4x + 3(11/2) = 335/14\n4x = 52/7\nx = 52/7/4\nx = 13/7"} {"input": "Solve the equations:\n9x + 7y = 5\n10x + 8y = 27/5", "output": "9x + 7y = 5\n10x + 8y = 27/5\n\nUsing elimination\n10*(9x + 7y = 5)\n9*(10x + 8y = 27/5)\n90x + 70y = 50\n90x + 72y = 243/5\nSubtract equations\n-2y = 7/5\ny = 7/5/-2\ny = -7/10\n\nSubstitute y\n9x + 7(-7/10) = 5\n9x = 99/10\nx = 99/10/9\nx = 11/10"} {"input": "Solve the system:\n3x + 1y = 165/56\n6x + 3y = 153/28", "output": "3x + 1y = 165/56\n6x + 3y = 153/28\n\nUsing elimination\n6*(3x + 1y = 165/56)\n3*(6x + 3y = 153/28)\n18x + 6y = 495/28\n18x + 9y = 459/28\nSubtract equations\n-3y = 9/7\ny = 9/7/-3\ny = -3/7\n\nSubstitute y\n3x + 1(-3/7) = 165/56\n3x = 27/8\nx = 27/8/3\nx = 9/8"} {"input": "Determine x in 1x + 8/7 = 0", "output": "1x + 8/7 = 0\n1x = -8/7\nx = -8/7 / 1\nx = -8/7"} {"input": "Solve the system:\n2x + 1y = 15\n2x + 5y = 87", "output": "2x + 1y = 15\n2x + 5y = 87\n\nUsing elimination\n2*(2x + 1y = 15)\n2*(2x + 5y = 87)\n4x + 2y = 30\n4x + 10y = 174\nSubtract equations\n-8y = -144\ny = -144/-8\ny = 18\n\nSubstitute y\n2x + 1(18) = 15\n2x = -3\nx = -3/2\nx = -3/2"} {"input": "Solve simultaneously:\n7x + 5y = 18/7\n7x + 6y = 37/7", "output": "7x + 5y = 18/7\n7x + 6y = 37/7\n\nUsing elimination\n7*(7x + 5y = 18/7)\n7*(7x + 6y = 37/7)\n49x + 35y = 18\n49x + 42y = 37\nSubtract equations\n-7y = -19\ny = -19/-7\ny = 19/7\n\nSubstitute y\n7x + 5(19/7) = 18/7\n7x = -11\nx = -11/7\nx = -11/7"} {"input": "Find x and y such that\n9x + 10y = -265/8\n8x + 6y = -127/5", "output": "9x + 10y = -265/8\n8x + 6y = -127/5\n\nUsing elimination\n8*(9x + 10y = -265/8)\n9*(8x + 6y = -127/5)\n72x + 80y = -265\n72x + 54y = -1143/5\nSubtract equations\n26y = -182/5\ny = -182/5/26\ny = -7/5\n\nSubstitute y\n9x + 10(-7/5) = -265/8\n9x = -153/8\nx = -153/8/9\nx = -17/8"} {"input": "What value of x satisfies x^3 + 34/5x^2 + 69/5x + 36/5 = 0", "output": "x^3 + 34/5x^2 + 69/5x + 36/5 = 0\n(x - -4/5)(x - -3)(x - -3) = 0\nx - -4/5 = 0\nx - -3 = 0\nx - -3 = 0\nx = -4/5\nx = -3\nx = -3"} {"input": "Solve simultaneously:\n8x + 7y = -467/35\n10x + 5y = -101/7", "output": "8x + 7y = -467/35\n10x + 5y = -101/7\n\nUsing elimination\n10*(8x + 7y = -467/35)\n8*(10x + 5y = -101/7)\n80x + 70y = -934/7\n80x + 40y = -808/7\nSubtract equations\n30y = -18\ny = -18/30\ny = -3/5\n\nSubstitute y\n8x + 7(-3/5) = -467/35\n8x = -64/7\nx = -64/7/8\nx = -8/7"} {"input": "Find the solution to x^2 - 9/5x = 0", "output": "x^2 - 9/5x = 0\n(x - 0)(x - 9/5) = 0\nx - 0 = 0 or x - 9/5 = 0\nx = 0\nx = 9/5"} {"input": "Determine x in x^3 - 395/72x^2 + 139/18x - 19/24 = 0", "output": "x^3 - 395/72x^2 + 139/18x - 19/24 = 0\n(x - 3)(x - 1/9)(x - 19/8) = 0\nx - 3 = 0\nx - 1/9 = 0\nx - 19/8 = 0\nx = 3\nx = 1/9\nx = 19/8"} {"input": "What value of x satisfies 10x - 130 = 0", "output": "10x - 130 = 0\n10x = 130\nx = 130 / 10\nx = 13"} {"input": "Solve x^2 - 47/20x + 21/20 = 0", "output": "x^2 - 47/20x + 21/20 = 0\n(x - 7/4)(x - 3/5) = 0\nx - 7/4 = 0 or x - 3/5 = 0\nx = 7/4\nx = 3/5"} {"input": "Solve 5x - 20 = 0", "output": "5x - 20 = 0\n5x = 20\nx = 20 / 5\nx = 4"} {"input": "Solve quickly: x^2 + 113/63x + 22/63 = 0", "output": "x^2 + 113/63x + 22/63 = 0\n(x - -2/9)(x - -11/7) = 0\nx - -2/9 = 0 or x - -11/7 = 0\nx = -2/9\nx = -11/7"} {"input": "Solve x^2 - 29/18x - 19/18 = 0", "output": "x^2 - 29/18x - 19/18 = 0\n(x - 19/9)(x - -1/2) = 0\nx - 19/9 = 0 or x - -1/2 = 0\nx = 19/9\nx = -1/2"} {"input": "Find the solution to 8x - 20 = 0", "output": "8x - 20 = 0\n8x = 20\nx = 20 / 8\nx = 5/2"} {"input": "Solve the equation x^3 - 41/24x^2 - 229/24x + 55/4 = 0", "output": "x^3 - 41/24x^2 - 229/24x + 55/4 = 0\n(x - 11/8)(x - -3)(x - 10/3) = 0\nx - 11/8 = 0\nx - -3 = 0\nx - 10/3 = 0\nx = 11/8\nx = -3\nx = 10/3"} {"input": "Solve 10x + 25 = 0", "output": "10x + 25 = 0\n10x = -25\nx = -25 / 10\nx = -5/2"} {"input": "Find the solution to x^3 - 251/10x^2 + 912/5x - 378 = 0", "output": "x^3 - 251/10x^2 + 912/5x - 378 = 0\n(x - 15/2)(x - 14)(x - 18/5) = 0\nx - 15/2 = 0\nx - 14 = 0\nx - 18/5 = 0\nx = 15/2\nx = 14\nx = 18/5"} {"input": "Find x for 4x + 8 = 0", "output": "4x + 8 = 0\n4x = -8\nx = -8 / 4\nx = -2"} {"input": "Solve the equation x^3 - 55/6x^2 - 39/2x - 22/3 = 0", "output": "x^3 - 55/6x^2 - 39/2x - 22/3 = 0\n(x - 11)(x - -1/2)(x - -4/3) = 0\nx - 11 = 0\nx - -1/2 = 0\nx - -4/3 = 0\nx = 11\nx = -1/2\nx = -4/3"} {"input": "Find x for x^2 + 43/5x + 17/20 = 0", "output": "x^2 + 43/5x + 17/20 = 0\n(x - -17/2)(x - -1/10) = 0\nx - -17/2 = 0 or x - -1/10 = 0\nx = -17/2\nx = -1/10"} {"input": "Solve simultaneously:\n4x + 9y = 65/12\n2x + 3y = 19/12", "output": "4x + 9y = 65/12\n2x + 3y = 19/12\n\nUsing elimination\n2*(4x + 9y = 65/12)\n4*(2x + 3y = 19/12)\n8x + 18y = 65/6\n8x + 12y = 19/3\nSubtract equations\n6y = 9/2\ny = 9/2/6\ny = 3/4\n\nSubstitute y\n4x + 9(3/4) = 65/12\n4x = -4/3\nx = -4/3/4\nx = -1/3"} {"input": "Solve the system:\n1x + 3y = -10\n6x + 3y = 75/2", "output": "1x + 3y = -10\n6x + 3y = 75/2\n\nUsing elimination\n6*(1x + 3y = -10)\n1*(6x + 3y = 75/2)\n6x + 18y = -60\n6x + 3y = 75/2\nSubtract equations\n15y = -195/2\ny = -195/2/15\ny = -13/2\n\nSubstitute y\n1x + 3(-13/2) = -10\n1x = 19/2\nx = 19/2/1\nx = 19/2"} {"input": "Solve the equations:\n5x + 5y = -375/28\n7x + 6y = -29/2", "output": "5x + 5y = -375/28\n7x + 6y = -29/2\n\nUsing elimination\n7*(5x + 5y = -375/28)\n5*(7x + 6y = -29/2)\n35x + 35y = -375/4\n35x + 30y = -145/2\nSubtract equations\n5y = -85/4\ny = -85/4/5\ny = -17/4\n\nSubstitute y\n5x + 5(-17/4) = -375/28\n5x = 55/7\nx = 55/7/5\nx = 11/7"} {"input": "Solve quickly: 8x - 16/5 = 0", "output": "8x - 16/5 = 0\n8x = 16/5\nx = 16/5 / 8\nx = 2/5"} {"input": "Compute the solution of 5x + 5/9 = 0", "output": "5x + 5/9 = 0\n5x = -5/9\nx = -5/9 / 5\nx = -1/9"} {"input": "Solve quickly: x^3 + 9/8x^2 - 7/4x = 0", "output": "x^3 + 9/8x^2 - 7/4x = 0\n(x - 7/8)(x - -2)(x - 0) = 0\nx - 7/8 = 0\nx - -2 = 0\nx - 0 = 0\nx = 7/8\nx = -2\nx = 0"} {"input": "Find x and y such that\n6x + 6y = 12/5\n1x + 8y = 137/10", "output": "6x + 6y = 12/5\n1x + 8y = 137/10\n\nUsing elimination\n1*(6x + 6y = 12/5)\n6*(1x + 8y = 137/10)\n6x + 6y = 12/5\n6x + 48y = 411/5\nSubtract equations\n-42y = -399/5\ny = -399/5/-42\ny = 19/10\n\nSubstitute y\n6x + 6(19/10) = 12/5\n6x = -9\nx = -9/6\nx = -3/2"} {"input": "Find x in x^2 + 19/3x + 26/3 = 0", "output": "x^2 + 19/3x + 26/3 = 0\n(x - -2)(x - -13/3) = 0\nx - -2 = 0 or x - -13/3 = 0\nx = -2\nx = -13/3"} {"input": "What value of x satisfies x^3 + 473/42x^2 + 148/7x + 99/14 = 0", "output": "x^3 + 473/42x^2 + 148/7x + 99/14 = 0\n(x - -3/7)(x - -9)(x - -11/6) = 0\nx - -3/7 = 0\nx - -9 = 0\nx - -11/6 = 0\nx = -3/7\nx = -9\nx = -11/6"} {"input": "Solve the system:\n8x + 7y = 178/5\n7x + 8y = 212/5", "output": "8x + 7y = 178/5\n7x + 8y = 212/5\n\nUsing elimination\n7*(8x + 7y = 178/5)\n8*(7x + 8y = 212/5)\n56x + 49y = 1246/5\n56x + 64y = 1696/5\nSubtract equations\n-15y = -90\ny = -90/-15\ny = 6\n\nSubstitute y\n8x + 7(6) = 178/5\n8x = -32/5\nx = -32/5/8\nx = -4/5"} {"input": "Solve the system:\n7x + 3y = 87/4\n5x + 7y = 135/4", "output": "7x + 3y = 87/4\n5x + 7y = 135/4\n\nUsing elimination\n5*(7x + 3y = 87/4)\n7*(5x + 7y = 135/4)\n35x + 15y = 435/4\n35x + 49y = 945/4\nSubtract equations\n-34y = -255/2\ny = -255/2/-34\ny = 15/4\n\nSubstitute y\n7x + 3(15/4) = 87/4\n7x = 21/2\nx = 21/2/7\nx = 3/2"} {"input": "Determine x in 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Solve x^2 + 23/3x + 10 = 0", "output": "x^2 + 23/3x + 10 = 0\n(x - -6)(x - -5/3) = 0\nx - -6 = 0 or x - -5/3 = 0\nx = -6\nx = -5/3"} {"input": "Find the solution to x^2 + 185/24x + 38/3 = 0", "output": "x^2 + 185/24x + 38/3 = 0\n(x - -19/8)(x - -16/3) = 0\nx - -19/8 = 0 or x - -16/3 = 0\nx = -19/8\nx = -16/3"} {"input": "Solve x^2 + 64/9x + 95/9 = 0", "output": "x^2 + 64/9x + 95/9 = 0\n(x - -19/9)(x - -5) = 0\nx - -19/9 = 0 or x - -5 = 0\nx = -19/9\nx = -5"} {"input": "Solve the equations:\n2x + 9y = 4\n9x + 9y = 113/2", "output": "2x + 9y = 4\n9x + 9y = 113/2\n\nUsing elimination\n9*(2x + 9y = 4)\n2*(9x + 9y = 113/2)\n18x + 81y = 36\n18x + 18y = 113\nSubtract equations\n63y = -77\ny = -77/63\ny = -11/9\n\nSubstitute y\n2x + 9(-11/9) = 4\n2x = 15\nx = 15/2\nx = 15/2"} {"input": "Solve simultaneously:\n4x + 3y = -93/7\n8x + 10y = -170/7", "output": "4x + 3y = -93/7\n8x + 10y = -170/7\n\nUsing elimination\n8*(4x + 3y = -93/7)\n4*(8x + 10y = -170/7)\n32x + 24y = -744/7\n32x + 40y = -680/7\nSubtract equations\n-16y = -64/7\ny = -64/7/-16\ny = 4/7\n\nSubstitute y\n4x + 3(4/7) = -93/7\n4x = -15\nx = -15/4\nx = -15/4"} {"input": "Solve 8x - 52 = 0", "output": "8x - 52 = 0\n8x = 52\nx = 52 / 8\nx = 13/2"} {"input": "Compute the solution of x^2 + 29/40x + 3/40 = 0", "output": "x^2 + 29/40x + 3/40 = 0\n(x - -3/5)(x - -1/8) = 0\nx - -3/5 = 0 or x - -1/8 = 0\nx = -3/5\nx = -1/8"} {"input": "What value of x satisfies x^2 - 13/14x - 5/7 = 0", "output": "x^2 - 13/14x - 5/7 = 0\n(x - -1/2)(x - 10/7) = 0\nx - -1/2 = 0 or x - 10/7 = 0\nx = -1/2\nx = 10/7"} {"input": "Determine x in x^3 - 271/45x^2 - 214/45x + 88/3 = 0", "output": "x^3 - 271/45x^2 - 214/45x + 88/3 = 0\n(x - -11/5)(x - 6)(x - 20/9) = 0\nx - -11/5 = 0\nx - 6 = 0\nx - 20/9 = 0\nx = -11/5\nx = 6\nx = 20/9"} {"input": "Solve the equation x^2 + 44/9x + 17/3 = 0", "output": "x^2 + 44/9x + 17/3 = 0\n(x - -3)(x - -17/9) = 0\nx - -3 = 0 or x - -17/9 = 0\nx = -3\nx = -17/9"} {"input": "Find x in x^2 + 41/4x - 33/4 = 0", "output": "x^2 + 41/4x - 33/4 = 0\n(x - 3/4)(x - -11) = 0\nx - 3/4 = 0 or x - -11 = 0\nx = 3/4\nx = -11"} {"input": "Solve the equation x^2 + 41/56x - 117/56 = 0", "output": "x^2 + 41/56x - 117/56 = 0\n(x - -13/7)(x - 9/8) = 0\nx - -13/7 = 0 or x - 9/8 = 0\nx = -13/7\nx = 9/8"} {"input": "Find x for x^2 + 103/10x + 21 = 0", "output": "x^2 + 103/10x + 21 = 0\n(x - -14/5)(x - -15/2) = 0\nx - -14/5 = 0 or x - -15/2 = 0\nx = -14/5\nx = -15/2"} {"input": "Solve quickly: 6x - 3 = 0", "output": "6x - 3 = 0\n6x = 3\nx = 3 / 6\nx = 1/2"} {"input": "Find x for 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "Find x in x^2 - 19/42x - 88/21 = 0", "output": "x^2 - 19/42x - 88/21 = 0\n(x - -11/6)(x - 16/7) = 0\nx - -11/6 = 0 or x - 16/7 = 0\nx = -11/6\nx = 16/7"} {"input": "Solve 3x + 21 = 0", "output": "3x + 21 = 0\n3x = -21\nx = -21 / 3\nx = -7"} {"input": "Find x for x^3 + 103/21x^2 + 20/3x + 12/7 = 0", "output": "x^3 + 103/21x^2 + 20/3x + 12/7 = 0\n(x - -1/3)(x - -2)(x - -18/7) = 0\nx - -1/3 = 0\nx - -2 = 0\nx - -18/7 = 0\nx = -1/3\nx = -2\nx = -18/7"} {"input": "Solve x^2 + 4x - 28/9 = 0", "output": "x^2 + 4x - 28/9 = 0\n(x - 2/3)(x - -14/3) = 0\nx - 2/3 = 0 or x - -14/3 = 0\nx = 2/3\nx = -14/3"} {"input": "Solve quickly: x^3 - 11/5x^2 - 38/5x + 8/5 = 0", "output": "x^3 - 11/5x^2 - 38/5x + 8/5 = 0\n(x - -2)(x - 4)(x - 1/5) = 0\nx - -2 = 0\nx - 4 = 0\nx - 1/5 = 0\nx = -2\nx = 4\nx = 1/5"} {"input": "Solve the system:\n8x + 6y = 64/9\n10x + 7y = 80/9", "output": "8x + 6y = 64/9\n10x + 7y = 80/9\n\nUsing elimination\n10*(8x + 6y = 64/9)\n8*(10x + 7y = 80/9)\n80x + 60y = 640/9\n80x + 56y = 640/9\nSubtract equations\n4y = 0\ny = 0/4\ny = 0\n\nSubstitute y\n8x + 6(0) = 64/9\n8x = 64/9\nx = 64/9/8\nx = 8/9"} {"input": "Find x and y such that\n7x + 7y = 483/10\n7x + 6y = 247/5", "output": "7x + 7y = 483/10\n7x + 6y = 247/5\n\nUsing elimination\n7*(7x + 7y = 483/10)\n7*(7x + 6y = 247/5)\n49x + 49y = 3381/10\n49x + 42y = 1729/5\nSubtract equations\n7y = -77/10\ny = -77/10/7\ny = -11/10\n\nSubstitute y\n7x + 7(-11/10) = 483/10\n7x = 56\nx = 56/7\nx = 8"} {"input": "Determine x in 7x - 2 = 0", "output": "7x - 2 = 0\n7x = 2\nx = 2 / 7\nx = 2/7"} {"input": "Solve 5x - 15/2 = 0", "output": "5x - 15/2 = 0\n5x = 15/2\nx = 15/2 / 5\nx = 3/2"} {"input": "Find the solution to x^2 - 12/7x - 64/7 = 0", "output": "x^2 - 12/7x - 64/7 = 0\n(x - 4)(x - -16/7) = 0\nx - 4 = 0 or x - -16/7 = 0\nx = 4\nx = -16/7"} {"input": "Solve simultaneously:\n5x + 10y = 33\n4x + 6y = 104/5", "output": "5x + 10y = 33\n4x + 6y = 104/5\n\nUsing elimination\n4*(5x + 10y = 33)\n5*(4x + 6y = 104/5)\n20x + 40y = 132\n20x + 30y = 104\nSubtract equations\n10y = 28\ny = 28/10\ny = 14/5\n\nSubstitute y\n5x + 10(14/5) = 33\n5x = 5\nx = 5/5\nx = 1"} {"input": "Solve the equation x^2 - 5x + 6 = 0", "output": "x^2 - 5x + 6 = 0\n(x - 3)(x - 2) = 0\nx - 3 = 0 or x - 2 = 0\nx = 3\nx = 2"} {"input": "Determine x in x^2 + 17/8x - 15/16 = 0", "output": "x^2 + 17/8x - 15/16 = 0\n(x - -5/2)(x - 3/8) = 0\nx - -5/2 = 0 or x - 3/8 = 0\nx = -5/2\nx = 3/8"} {"input": "Solve the system:\n10x + 3y = -1/5\n10x + 2y = 6/5", "output": "10x + 3y = -1/5\n10x + 2y = 6/5\n\nUsing elimination\n10*(10x + 3y = -1/5)\n10*(10x + 2y = 6/5)\n100x + 30y = -2\n100x + 20y = 12\nSubtract equations\n10y = -14\ny = -14/10\ny = -7/5\n\nSubstitute y\n10x + 3(-7/5) = -1/5\n10x = 4\nx = 4/10\nx = 2/5"} {"input": "Solve x^2 + 101/45x + 52/45 = 0", "output": "x^2 + 101/45x + 52/45 = 0\n(x - -13/9)(x - -4/5) = 0\nx - -13/9 = 0 or x - -4/5 = 0\nx = -13/9\nx = -4/5"} {"input": "Find the solution to x^3 + 145/56x^2 - 41/28x - 171/56 = 0", "output": "x^3 + 145/56x^2 - 41/28x - 171/56 = 0\n(x - -19/7)(x - 9/8)(x - -1) = 0\nx - -19/7 = 0\nx - 9/8 = 0\nx - -1 = 0\nx = -19/7\nx = 9/8\nx = -1"} {"input": "Solve the equation x^3 - 131/10x^2 - 1401/50x - 36/5 = 0", "output": "x^3 - 131/10x^2 - 1401/50x - 36/5 = 0\n(x - -3/10)(x - -8/5)(x - 15) = 0\nx - -3/10 = 0\nx - -8/5 = 0\nx - 15 = 0\nx = -3/10\nx = -8/5\nx = 15"} {"input": "Determine x in x^3 - 41/18x^2 - 10/27x + 50/27 = 0", "output": "x^3 - 41/18x^2 - 10/27x + 50/27 = 0\n(x - -5/6)(x - 10/9)(x - 2) = 0\nx - -5/6 = 0\nx - 10/9 = 0\nx - 2 = 0\nx = -5/6\nx = 10/9\nx = 2"} {"input": "Find x for x^2 + 3/4x - 85/4 = 0", "output": "x^2 + 3/4x - 85/4 = 0\n(x - -5)(x - 17/4) = 0\nx - -5 = 0 or x - 17/4 = 0\nx = -5\nx = 17/4"} {"input": "Solve quickly: 4x + 17 = 0", "output": "4x + 17 = 0\n4x = -17\nx = -17 / 4\nx = -17/4"} {"input": "Find x for x^3 + 2x^2 - 11/4x - 15/4 = 0", "output": "x^3 + 2x^2 - 11/4x - 15/4 = 0\n(x - 3/2)(x - -1)(x - -5/2) = 0\nx - 3/2 = 0\nx - -1 = 0\nx - -5/2 = 0\nx = 3/2\nx = -1\nx = -5/2"} {"input": "Solve the equations:\n1x + 7y = 23/5\n10x + 1y = -23", "output": "1x + 7y = 23/5\n10x + 1y = -23\n\nUsing elimination\n10*(1x + 7y = 23/5)\n1*(10x + 1y = -23)\n10x + 70y = 46\n10x + 1y = -23\nSubtract equations\n69y = 69\ny = 69/69\ny = 1\n\nSubstitute y\n1x + 7(1) = 23/5\n1x = -12/5\nx = -12/5/1\nx = -12/5"} {"input": "Solve simultaneously:\n10x + 4y = -44\n5x + 10y = -40", "output": "10x + 4y = -44\n5x + 10y = -40\n\nUsing elimination\n5*(10x + 4y = -44)\n10*(5x + 10y = -40)\n50x + 20y = -220\n50x + 100y = -400\nSubtract equations\n-80y = 180\ny = 180/-80\ny = -9/4\n\nSubstitute y\n10x + 4(-9/4) = -44\n10x = -35\nx = -35/10\nx = -7/2"} {"input": "Find the solution to 2x - 17/5 = 0", "output": "2x - 17/5 = 0\n2x = 17/5\nx = 17/5 / 2\nx = 17/10"} {"input": "Solve the equations:\n10x + 7y = -739/30\n7x + 5y = -52/3", "output": "10x + 7y = -739/30\n7x + 5y = -52/3\n\nUsing elimination\n7*(10x + 7y = -739/30)\n10*(7x + 5y = -52/3)\n70x + 49y = -5173/30\n70x + 50y = -520/3\nSubtract equations\n-1y = 9/10\ny = 9/10/-1\ny = -9/10\n\nSubstitute y\n10x + 7(-9/10) = -739/30\n10x = -55/3\nx = -55/3/10\nx = -11/6"} {"input": "What value of x satisfies x^2 - 117/14x + 110/7 = 0", "output": "x^2 - 117/14x + 110/7 = 0\n(x - 20/7)(x - 11/2) = 0\nx - 20/7 = 0 or x - 11/2 = 0\nx = 20/7\nx = 11/2"} {"input": "Determine x in x^2 - 37/30x - 14/5 = 0", "output": "x^2 - 37/30x - 14/5 = 0\n(x - -7/6)(x - 12/5) = 0\nx - -7/6 = 0 or x - 12/5 = 0\nx = -7/6\nx = 12/5"} {"input": "Find the solution to 7x + 7 = 0", "output": "7x + 7 = 0\n7x = -7\nx = -7 / 7\nx = -1"} {"input": "Find x for x^2 - 137/24x + 143/24 = 0", "output": "x^2 - 137/24x + 143/24 = 0\n(x - 11/8)(x - 13/3) = 0\nx - 11/8 = 0 or x - 13/3 = 0\nx = 11/8\nx = 13/3"} {"input": "Find x and y such that\n9x + 6y = 57/5\n7x + 8y = 203/15", "output": "9x + 6y = 57/5\n7x + 8y = 203/15\n\nUsing elimination\n7*(9x + 6y = 57/5)\n9*(7x + 8y = 203/15)\n63x + 42y = 399/5\n63x + 72y = 609/5\nSubtract equations\n-30y = -42\ny = -42/-30\ny = 7/5\n\nSubstitute y\n9x + 6(7/5) = 57/5\n9x = 3\nx = 3/9\nx = 1/3"} {"input": "Find x for x^2 - 62/5x - 112/5 = 0", "output": "x^2 - 62/5x - 112/5 = 0\n(x - -8/5)(x - 14) = 0\nx - -8/5 = 0 or x - 14 = 0\nx = -8/5\nx = 14"} {"input": "Find x and y such that\n4x + 6y = 47/2\n10x + 9y = 169/4", "output": "4x + 6y = 47/2\n10x + 9y = 169/4\n\nUsing elimination\n10*(4x + 6y = 47/2)\n4*(10x + 9y = 169/4)\n40x + 60y = 235\n40x + 36y = 169\nSubtract equations\n24y = 66\ny = 66/24\ny = 11/4\n\nSubstitute y\n4x + 6(11/4) = 47/2\n4x = 7\nx = 7/4\nx = 7/4"} {"input": "Compute the solution of x^2 - 8/3x - 11/3 = 0", "output": "x^2 - 8/3x - 11/3 = 0\n(x - 11/3)(x - -1) = 0\nx - 11/3 = 0 or x - -1 = 0\nx = 11/3\nx = -1"} {"input": "What value of x satisfies x^2 - 52/9x - 95/27 = 0", "output": "x^2 - 52/9x - 95/27 = 0\n(x - -5/9)(x - 19/3) = 0\nx - -5/9 = 0 or x - 19/3 = 0\nx = -5/9\nx = 19/3"} {"input": "Find x in 4x - 64 = 0", "output": "4x - 64 = 0\n4x = 64\nx = 64 / 4\nx = 16"} {"input": "Determine x in x^3 + 8/5x^2 - 11/5x - 14/5 = 0", "output": "x^3 + 8/5x^2 - 11/5x - 14/5 = 0\n(x - -1)(x - -2)(x - 7/5) = 0\nx - -1 = 0\nx - -2 = 0\nx - 7/5 = 0\nx = -1\nx = -2\nx = 7/5"} {"input": "Solve the equation x^3 + 1/5x^2 - 152/25x + 84/25 = 0", "output": "x^3 + 1/5x^2 - 152/25x + 84/25 = 0\n(x - 2)(x - -14/5)(x - 3/5) = 0\nx - 2 = 0\nx - -14/5 = 0\nx - 3/5 = 0\nx = 2\nx = -14/5\nx = 3/5"} {"input": "Find x for x^3 + 27/4x^2 + 1669/162x + 1235/324 = 0", "output": "x^3 + 27/4x^2 + 1669/162x + 1235/324 = 0\n(x - -5/9)(x - -13/9)(x - -19/4) = 0\nx - -5/9 = 0\nx - -13/9 = 0\nx - -19/4 = 0\nx = -5/9\nx = -13/9\nx = -19/4"} {"input": "Compute the solution of 1x + 14/3 = 0", "output": "1x + 14/3 = 0\n1x = -14/3\nx = -14/3 / 1\nx = -14/3"} {"input": "Solve the equation 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Solve quickly: x^3 + 8x^2 - 67/9x - 910/9 = 0", "output": "x^3 + 8x^2 - 67/9x - 910/9 = 0\n(x - 10/3)(x - -7)(x - -13/3) = 0\nx - 10/3 = 0\nx - -7 = 0\nx - -13/3 = 0\nx = 10/3\nx = -7\nx = -13/3"} {"input": "Find the solution to 7x - 35 = 0", "output": "7x - 35 = 0\n7x = 35\nx = 35 / 7\nx = 5"} {"input": "Solve x^2 + 115/24x - 25/2 = 0", "output": "x^2 + 115/24x - 25/2 = 0\n(x - -20/3)(x - 15/8) = 0\nx - -20/3 = 0 or x - 15/8 = 0\nx = -20/3\nx = 15/8"} {"input": "Determine x in 10x - 160/3 = 0", "output": "10x - 160/3 = 0\n10x = 160/3\nx = 160/3 / 10\nx = 16/3"} {"input": "Solve the equation x^2 + 20/7x + 64/49 = 0", "output": "x^2 + 20/7x + 64/49 = 0\n(x - -16/7)(x - -4/7) = 0\nx - -16/7 = 0 or x - -4/7 = 0\nx = -16/7\nx = -4/7"} {"input": "What value of x satisfies 2x + 12/5 = 0", "output": "2x + 12/5 = 0\n2x = -12/5\nx = -12/5 / 2\nx = -6/5"} {"input": "Find x and y such that\n4x + 1y = -44/3\n6x + 7y = -187/6", "output": "4x + 1y = -44/3\n6x + 7y = -187/6\n\nUsing elimination\n6*(4x + 1y = -44/3)\n4*(6x + 7y = -187/6)\n24x + 6y = -88\n24x + 28y = -374/3\nSubtract equations\n-22y = 110/3\ny = 110/3/-22\ny = -5/3\n\nSubstitute y\n4x + 1(-5/3) = -44/3\n4x = -13\nx = -13/4\nx = -13/4"} {"input": "Solve the equations:\n6x + 9y = -3\n1x + 2y = -1/9", "output": "6x + 9y = -3\n1x + 2y = -1/9\n\nUsing elimination\n1*(6x + 9y = -3)\n6*(1x + 2y = -1/9)\n6x + 9y = -3\n6x + 12y = -2/3\nSubtract equations\n-3y = -7/3\ny = -7/3/-3\ny = 7/9\n\nSubstitute y\n6x + 9(7/9) = -3\n6x = -10\nx = -10/6\nx = -5/3"} {"input": "Determine x in x^2 + 1/28x - 209/28 = 0", "output": "x^2 + 1/28x - 209/28 = 0\n(x - -11/4)(x - 19/7) = 0\nx - -11/4 = 0 or x - 19/7 = 0\nx = -11/4\nx = 19/7"} {"input": "What value of x satisfies x^3 - 43/3x^2 - 119/12x - 5/4 = 0", "output": "x^3 - 43/3x^2 - 119/12x - 5/4 = 0\n(x - -1/6)(x - 15)(x - -1/2) = 0\nx - -1/6 = 0\nx - 15 = 0\nx - -1/2 = 0\nx = -1/6\nx = 15\nx = -1/2"} {"input": "Solve simultaneously:\n9x + 10y = 105/4\n1x + 9y = 59/4", "output": "9x + 10y = 105/4\n1x + 9y = 59/4\n\nUsing elimination\n1*(9x + 10y = 105/4)\n9*(1x + 9y = 59/4)\n9x + 10y = 105/4\n9x + 81y = 531/4\nSubtract equations\n-71y = -213/2\ny = -213/2/-71\ny = 3/2\n\nSubstitute y\n9x + 10(3/2) = 105/4\n9x = 45/4\nx = 45/4/9\nx = 5/4"} {"input": "Solve quickly: 1x + 13/10 = 0", "output": "1x + 13/10 = 0\n1x = -13/10\nx = -13/10 / 1\nx = -13/10"} {"input": "Find x in x^2 + 32/3x + 15 = 0", "output": "x^2 + 32/3x + 15 = 0\n(x - -5/3)(x - -9) = 0\nx - -5/3 = 0 or x - -9 = 0\nx = -5/3\nx = -9"} {"input": "Find x and y such that\n4x + 1y = 64/3\n10x + 1y = 115/3", "output": "4x + 1y = 64/3\n10x + 1y = 115/3\n\nUsing elimination\n10*(4x + 1y = 64/3)\n4*(10x + 1y = 115/3)\n40x + 10y = 640/3\n40x + 4y = 460/3\nSubtract equations\n6y = 60\ny = 60/6\ny = 10\n\nSubstitute y\n4x + 1(10) = 64/3\n4x = 34/3\nx = 34/3/4\nx = 17/6"} {"input": "Find x for 8x - 4 = 0", "output": "8x - 4 = 0\n8x = 4\nx = 4 / 8\nx = 1/2"} {"input": "Solve the system:\n8x + 5y = -167/4\n6x + 2y = -30", "output": "8x + 5y = -167/4\n6x + 2y = -30\n\nUsing elimination\n6*(8x + 5y = -167/4)\n8*(6x + 2y = -30)\n48x + 30y = -501/2\n48x + 16y = -240\nSubtract equations\n14y = -21/2\ny = -21/2/14\ny = -3/4\n\nSubstitute y\n8x + 5(-3/4) = -167/4\n8x = -38\nx = -38/8\nx = -19/4"} {"input": "Find x for 10x - 50 = 0", "output": "10x - 50 = 0\n10x = 50\nx = 50 / 10\nx = 5"} {"input": "Find x for x^3 - 3x^2 - 1/25x + 99/25 = 0", "output": "x^3 - 3x^2 - 1/25x + 99/25 = 0\n(x - 11/5)(x - 9/5)(x - -1) = 0\nx - 11/5 = 0\nx - 9/5 = 0\nx - -1 = 0\nx = 11/5\nx = 9/5\nx = -1"} {"input": "What value of x satisfies x^3 + 2/3x^2 - 144/25x - 96/25 = 0", "output": "x^3 + 2/3x^2 - 144/25x - 96/25 = 0\n(x - 12/5)(x - -2/3)(x - -12/5) = 0\nx - 12/5 = 0\nx - -2/3 = 0\nx - -12/5 = 0\nx = 12/5\nx = -2/3\nx = -12/5"} {"input": "Solve quickly: x^3 + 85/24x^2 + 59/24x - 5/4 = 0", "output": "x^3 + 85/24x^2 + 59/24x - 5/4 = 0\n(x - -15/8)(x - -2)(x - 1/3) = 0\nx - -15/8 = 0\nx - -2 = 0\nx - 1/3 = 0\nx = -15/8\nx = -2\nx = 1/3"} {"input": "Solve the equation x^2 - 7/8x = 0", "output": "x^2 - 7/8x = 0\n(x - 7/8)(x - 0) = 0\nx - 7/8 = 0 or x - 0 = 0\nx = 7/8\nx = 0"} {"input": "Find x for x^3 - 11/8x^2 - 2467/8x + 2907/4 = 0", "output": "x^3 - 11/8x^2 - 2467/8x + 2907/4 = 0\n(x - 19/8)(x - -18)(x - 17) = 0\nx - 19/8 = 0\nx - -18 = 0\nx - 17 = 0\nx = 19/8\nx = -18\nx = 17"} {"input": "Determine x in x^2 + 43/8x + 15/8 = 0", "output": "x^2 + 43/8x + 15/8 = 0\n(x - -3/8)(x - -5) = 0\nx - -3/8 = 0 or x - -5 = 0\nx = -3/8\nx = -5"} {"input": "Determine x in 8x - 76 = 0", "output": "8x - 76 = 0\n8x = 76\nx = 76 / 8\nx = 19/2"} {"input": "Solve the equation x^2 - 92/45x + 13/15 = 0", "output": "x^2 - 92/45x + 13/15 = 0\n(x - 3/5)(x - 13/9) = 0\nx - 3/5 = 0 or x - 13/9 = 0\nx = 3/5\nx = 13/9"} {"input": "Find x for x^3 - 35/8x^2 + 203/36x - 19/9 = 0", "output": "x^3 - 35/8x^2 + 203/36x - 19/9 = 0\n(x - 4/3)(x - 2/3)(x - 19/8) = 0\nx - 4/3 = 0\nx - 2/3 = 0\nx - 19/8 = 0\nx = 4/3\nx = 2/3\nx = 19/8"} {"input": "Find x for x^2 + 17/2x + 15 = 0", "output": "x^2 + 17/2x + 15 = 0\n(x - -5/2)(x - -6) = 0\nx - -5/2 = 0 or x - -6 = 0\nx = -5/2\nx = -6"} {"input": "Solve the equation 10x + 130/3 = 0", "output": "10x + 130/3 = 0\n10x = -130/3\nx = -130/3 / 10\nx = -13/3"} {"input": "What value of x satisfies x^3 - 313/30x^2 + 448/15x - 247/10 = 0", "output": "x^3 - 313/30x^2 + 448/15x - 247/10 = 0\n(x - 13/5)(x - 3/2)(x - 19/3) = 0\nx - 13/5 = 0\nx - 3/2 = 0\nx - 19/3 = 0\nx = 13/5\nx = 3/2\nx = 19/3"} {"input": "Find x in x^3 + 30x^2 + 209x - 240 = 0", "output": "x^3 + 30x^2 + 209x - 240 = 0\n(x - 1)(x - -16)(x - -15) = 0\nx - 1 = 0\nx - -16 = 0\nx - -15 = 0\nx = 1\nx = -16\nx = -15"} {"input": "Solve quickly: x^3 + 142/15x^2 + 57/5x - 8/3 = 0", "output": "x^3 + 142/15x^2 + 57/5x - 8/3 = 0\n(x - -8)(x - -5/3)(x - 1/5) = 0\nx - -8 = 0\nx - -5/3 = 0\nx - 1/5 = 0\nx = -8\nx = -5/3\nx = 1/5"} {"input": "Compute the solution of x^2 - 83/24x - 91/24 = 0", "output": "x^2 - 83/24x - 91/24 = 0\n(x - 13/3)(x - -7/8) = 0\nx - 13/3 = 0 or x - -7/8 = 0\nx = 13/3\nx = -7/8"} {"input": "Find x for x^3 + 43/28x^2 - 53/28x - 9/14 = 0", "output": "x^3 + 43/28x^2 - 53/28x - 9/14 = 0\n(x - 1)(x - -2/7)(x - -9/4) = 0\nx - 1 = 0\nx - -2/7 = 0\nx - -9/4 = 0\nx = 1\nx = -2/7\nx = -9/4"} {"input": "What value of x satisfies 10x + 19 = 0", "output": "10x + 19 = 0\n10x = -19\nx = -19 / 10\nx = -19/10"} {"input": "What value of x satisfies x^3 + 2/3x^2 - 365/9x + 238/9 = 0", "output": "x^3 + 2/3x^2 - 365/9x + 238/9 = 0\n(x - 2/3)(x - 17/3)(x - -7) = 0\nx - 2/3 = 0\nx - 17/3 = 0\nx - -7 = 0\nx = 2/3\nx = 17/3\nx = -7"} {"input": "Solve quickly: 3x - 39/5 = 0", "output": "3x - 39/5 = 0\n3x = 39/5\nx = 39/5 / 3\nx = 13/5"} {"input": "What value of x satisfies x^2 - 60/7x - 100/7 = 0", "output": "x^2 - 60/7x - 100/7 = 0\n(x - 10)(x - -10/7) = 0\nx - 10 = 0 or x - -10/7 = 0\nx = 10\nx = -10/7"} {"input": "Solve the equation x^2 - 13/6x - 55/3 = 0", "output": "x^2 - 13/6x - 55/3 = 0\n(x - 11/2)(x - -10/3) = 0\nx - 11/2 = 0 or x - -10/3 = 0\nx = 11/2\nx = -10/3"} {"input": "Determine x in x^3 + 97/10x^2 + 7/10x - 57/5 = 0", "output": "x^3 + 97/10x^2 + 7/10x - 57/5 = 0\n(x - -6/5)(x - 1)(x - -19/2) = 0\nx - -6/5 = 0\nx - 1 = 0\nx - -19/2 = 0\nx = -6/5\nx = 1\nx = -19/2"} {"input": "Find x and y such that\n6x + 7y = -629/30\n6x + 6y = -89/5", "output": "6x + 7y = -629/30\n6x + 6y = -89/5\n\nUsing elimination\n6*(6x + 7y = -629/30)\n6*(6x + 6y = -89/5)\n36x + 42y = -629/5\n36x + 36y = -534/5\nSubtract equations\n6y = -19\ny = -19/6\ny = -19/6\n\nSubstitute y\n6x + 7(-19/6) = -629/30\n6x = 6/5\nx = 6/5/6\nx = 1/5"} {"input": "Solve the system:\n2x + 6y = 63/5\n5x + 5y = 31/2", "output": "2x + 6y = 63/5\n5x + 5y = 31/2\n\nUsing elimination\n5*(2x + 6y = 63/5)\n2*(5x + 5y = 31/2)\n10x + 30y = 63\n10x + 10y = 31\nSubtract equations\n20y = 32\ny = 32/20\ny = 8/5\n\nSubstitute y\n2x + 6(8/5) = 63/5\n2x = 3\nx = 3/2\nx = 3/2"} {"input": "Compute the solution of x^3 + 7/12x^2 - 473/24x + 30 = 0", "output": "x^3 + 7/12x^2 - 473/24x + 30 = 0\n(x - 9/4)(x - -16/3)(x - 5/2) = 0\nx - 9/4 = 0\nx - -16/3 = 0\nx - 5/2 = 0\nx = 9/4\nx = -16/3\nx = 5/2"} {"input": "Find x for 5x - 2 = 0", "output": "5x - 2 = 0\n5x = 2\nx = 2 / 5\nx = 2/5"} {"input": "Solve x^2 + 14x + 45 = 0", "output": "x^2 + 14x + 45 = 0\n(x - -9)(x - -5) = 0\nx - -9 = 0 or x - -5 = 0\nx = -9\nx = -5"} {"input": "Solve simultaneously:\n1x + 4y = 118/15\n7x + 6y = 147/5", "output": "1x + 4y = 118/15\n7x + 6y = 147/5\n\nUsing elimination\n7*(1x + 4y = 118/15)\n1*(7x + 6y = 147/5)\n7x + 28y = 826/15\n7x + 6y = 147/5\nSubtract equations\n22y = 77/3\ny = 77/3/22\ny = 7/6\n\nSubstitute y\n1x + 4(7/6) = 118/15\n1x = 16/5\nx = 16/5/1\nx = 16/5"} {"input": "Solve x^2 - 9/2x + 81/16 = 0", "output": "x^2 - 9/2x + 81/16 = 0\n(x - 9/4)(x - 9/4) = 0\nx - 9/4 = 0 or x - 9/4 = 0\nx = 9/4\nx = 9/4"} {"input": "What value of x satisfies 10x - 85/3 = 0", "output": "10x - 85/3 = 0\n10x = 85/3\nx = 85/3 / 10\nx = 17/6"} {"input": "Solve the equation 4x - 3 = 0", "output": "4x - 3 = 0\n4x = 3\nx = 3 / 4\nx = 3/4"} {"input": "Find x in x^2 - 1/18x - 13/6 = 0", "output": "x^2 - 1/18x - 13/6 = 0\n(x - 3/2)(x - -13/9) = 0\nx - 3/2 = 0 or x - -13/9 = 0\nx = 3/2\nx = -13/9"} {"input": "Solve x^3 + 113/15x^2 + 116/15x - 44/5 = 0", "output": "x^3 + 113/15x^2 + 116/15x - 44/5 = 0\n(x - -11/5)(x - 2/3)(x - -6) = 0\nx - -11/5 = 0\nx - 2/3 = 0\nx - -6 = 0\nx = -11/5\nx = 2/3\nx = -6"} {"input": "Solve the equation x^2 + 14/3x - 8 = 0", "output": "x^2 + 14/3x - 8 = 0\n(x - 4/3)(x - -6) = 0\nx - 4/3 = 0 or x - -6 = 0\nx = 4/3\nx = -6"} {"input": "Solve quickly: 3x + 12 = 0", "output": "3x + 12 = 0\n3x = -12\nx = -12 / 3\nx = -4"} {"input": "Determine x in x^3 - 113/105x^2 - 268/35x - 36/7 = 0", "output": "x^3 - 113/105x^2 - 268/35x - 36/7 = 0\n(x - -6/7)(x - 18/5)(x - -5/3) = 0\nx - -6/7 = 0\nx - 18/5 = 0\nx - -5/3 = 0\nx = -6/7\nx = 18/5\nx = -5/3"} {"input": "Find x for 9x - 81/2 = 0", "output": "9x - 81/2 = 0\n9x = 81/2\nx = 81/2 / 9\nx = 9/2"} {"input": "Compute the solution of x^3 + 27/8x^2 + 3/2x - 5/2 = 0", "output": "x^3 + 27/8x^2 + 3/2x - 5/2 = 0\n(x - -2)(x - 5/8)(x - -2) = 0\nx - -2 = 0\nx - 5/8 = 0\nx - -2 = 0\nx = -2\nx = 5/8\nx = -2"} {"input": "Solve x^3 + 73/4x^2 + 491/8x + 105/4 = 0", "output": "x^3 + 73/4x^2 + 491/8x + 105/4 = 0\n(x - -14)(x - -15/4)(x - -1/2) = 0\nx - -14 = 0\nx - -15/4 = 0\nx - -1/2 = 0\nx = -14\nx = -15/4\nx = -1/2"} {"input": "Solve x^2 + 17/6x - 5/3 = 0", "output": "x^2 + 17/6x - 5/3 = 0\n(x - -10/3)(x - 1/2) = 0\nx - -10/3 = 0 or x - 1/2 = 0\nx = -10/3\nx = 1/2"} {"input": "Compute the solution of x^3 - 43/2x^2 + 213/2x - 135 = 0", "output": "x^3 - 43/2x^2 + 213/2x - 135 = 0\n(x - 2)(x - 9/2)(x - 15) = 0\nx - 2 = 0\nx - 9/2 = 0\nx - 15 = 0\nx = 2\nx = 9/2\nx = 15"} {"input": "Find x and y such that\n8x + 4y = -688/5\n8x + 5y = -134", "output": "8x + 4y = -688/5\n8x + 5y = -134\n\nUsing elimination\n8*(8x + 4y = -688/5)\n8*(8x + 5y = -134)\n64x + 32y = -5504/5\n64x + 40y = -1072\nSubtract equations\n-8y = -144/5\ny = -144/5/-8\ny = 18/5\n\nSubstitute y\n8x + 4(18/5) = -688/5\n8x = -152\nx = -152/8\nx = -19"} {"input": "Find x for x^3 - 3/2x^2 - 107/18x + 13/3 = 0", "output": "x^3 - 3/2x^2 - 107/18x + 13/3 = 0\n(x - -13/6)(x - 3)(x - 2/3) = 0\nx - -13/6 = 0\nx - 3 = 0\nx - 2/3 = 0\nx = -13/6\nx = 3\nx = 2/3"} {"input": "Find the solution to x^2 - 20/3x - 21 = 0", "output": "x^2 - 20/3x - 21 = 0\n(x - -7/3)(x - 9) = 0\nx - -7/3 = 0 or x - 9 = 0\nx = -7/3\nx = 9"} {"input": "Solve the system:\n7x + 1y = -223/10\n5x + 2y = -88/5", "output": "7x + 1y = -223/10\n5x + 2y = -88/5\n\nUsing elimination\n5*(7x + 1y = -223/10)\n7*(5x + 2y = -88/5)\n35x + 5y = -223/2\n35x + 14y = -616/5\nSubtract equations\n-9y = 117/10\ny = 117/10/-9\ny = -13/10\n\nSubstitute y\n7x + 1(-13/10) = -223/10\n7x = -21\nx = -21/7\nx = -3"} {"input": "Solve the equation 10x - 45/4 = 0", "output": "10x - 45/4 = 0\n10x = 45/4\nx = 45/4 / 10\nx = 9/8"} {"input": "Solve the system:\n2x + 7y = -64/15\n4x + 6y = -32/15", "output": "2x + 7y = -64/15\n4x + 6y = -32/15\n\nUsing elimination\n4*(2x + 7y = -64/15)\n2*(4x + 6y = -32/15)\n8x + 28y = -256/15\n8x + 12y = -64/15\nSubtract equations\n16y = -64/5\ny = -64/5/16\ny = -4/5\n\nSubstitute y\n2x + 7(-4/5) = -64/15\n2x = 4/3\nx = 4/3/2\nx = 2/3"} {"input": "Solve quickly: x^2 + 101/30x + 77/30 = 0", "output": "x^2 + 101/30x + 77/30 = 0\n(x - -11/5)(x - -7/6) = 0\nx - -11/5 = 0 or x - -7/6 = 0\nx = -11/5\nx = -7/6"} {"input": "Determine x in x^3 + 148/9x^2 + 1793/27x + 1936/27 = 0", "output": "x^3 + 148/9x^2 + 1793/27x + 1936/27 = 0\n(x - -11/3)(x - -11)(x - -16/9) = 0\nx - -11/3 = 0\nx - -11 = 0\nx - -16/9 = 0\nx = -11/3\nx = -11\nx = -16/9"} {"input": "Solve quickly: x^3 - 91/10x^2 + 67/5x + 91/10 = 0", "output": "x^3 - 91/10x^2 + 67/5x + 91/10 = 0\n(x - 13/5)(x - 7)(x - -1/2) = 0\nx - 13/5 = 0\nx - 7 = 0\nx - -1/2 = 0\nx = 13/5\nx = 7\nx = -1/2"} {"input": "Find x in x^2 - 2/7x - 24/7 = 0", "output": "x^2 - 2/7x - 24/7 = 0\n(x - 2)(x - -12/7) = 0\nx - 2 = 0 or x - -12/7 = 0\nx = 2\nx = -12/7"} {"input": "Solve 8x + 88/5 = 0", "output": "8x + 88/5 = 0\n8x = -88/5\nx = -88/5 / 8\nx = -11/5"} {"input": "Determine x in x^3 - 3x^2 - 532/9x - 980/9 = 0", "output": "x^3 - 3x^2 - 532/9x - 980/9 = 0\n(x - 10)(x - -14/3)(x - -7/3) = 0\nx - 10 = 0\nx - -14/3 = 0\nx - -7/3 = 0\nx = 10\nx = -14/3\nx = -7/3"} {"input": "What value of x satisfies 5x - 2 = 0", "output": "5x - 2 = 0\n5x = 2\nx = 2 / 5\nx = 2/5"} {"input": "Determine x in 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x for x^3 - 37/10x^2 + 7/10x = 0", "output": "x^3 - 37/10x^2 + 7/10x = 0\n(x - 0)(x - 1/5)(x - 7/2) = 0\nx - 0 = 0\nx - 1/5 = 0\nx - 7/2 = 0\nx = 0\nx = 1/5\nx = 7/2"} {"input": "Find x in x^3 - 53/30x^2 - 21x - 132/5 = 0", "output": "x^3 - 53/30x^2 - 21x - 132/5 = 0\n(x - -12/5)(x - -11/6)(x - 6) = 0\nx - -12/5 = 0\nx - -11/6 = 0\nx - 6 = 0\nx = -12/5\nx = -11/6\nx = 6"} {"input": "Solve simultaneously:\n1x + 10y = -1772/63\n7x + 6y = -884/63", "output": "1x + 10y = -1772/63\n7x + 6y = -884/63\n\nUsing elimination\n7*(1x + 10y = -1772/63)\n1*(7x + 6y = -884/63)\n7x + 70y = -1772/9\n7x + 6y = -884/63\nSubtract equations\n64y = -1280/7\ny = -1280/7/64\ny = -20/7\n\nSubstitute y\n1x + 10(-20/7) = -1772/63\n1x = 4/9\nx = 4/9/1\nx = 4/9"} {"input": "Solve simultaneously:\n7x + 1y = 166/3\n9x + 9y = 210", "output": "7x + 1y = 166/3\n9x + 9y = 210\n\nUsing elimination\n9*(7x + 1y = 166/3)\n7*(9x + 9y = 210)\n63x + 9y = 498\n63x + 63y = 1470\nSubtract equations\n-54y = -972\ny = -972/-54\ny = 18\n\nSubstitute y\n7x + 1(18) = 166/3\n7x = 112/3\nx = 112/3/7\nx = 16/3"} {"input": "Solve x^2 + 38/15x + 77/60 = 0", "output": "x^2 + 38/15x + 77/60 = 0\n(x - -11/6)(x - -7/10) = 0\nx - -11/6 = 0 or x - -7/10 = 0\nx = -11/6\nx = -7/10"} {"input": "Find x in x^2 + 4/3x + 1/3 = 0", "output": "x^2 + 4/3x + 1/3 = 0\n(x - -1)(x - -1/3) = 0\nx - -1 = 0 or x - -1/3 = 0\nx = -1\nx = -1/3"} {"input": "Determine x in 6x - 8/3 = 0", "output": "6x - 8/3 = 0\n6x = 8/3\nx = 8/3 / 6\nx = 4/9"} {"input": "Solve the equation x^3 + 401/315x^2 - 24/7x - 68/45 = 0", "output": "x^3 + 401/315x^2 - 24/7x - 68/45 = 0\n(x - -17/7)(x - 14/9)(x - -2/5) = 0\nx - -17/7 = 0\nx - 14/9 = 0\nx - -2/5 = 0\nx = -17/7\nx = 14/9\nx = -2/5"} {"input": "Find x and y such that\n8x + 3y = 406/15\n7x + 8y = 581/15", "output": "8x + 3y = 406/15\n7x + 8y = 581/15\n\nUsing elimination\n7*(8x + 3y = 406/15)\n8*(7x + 8y = 581/15)\n56x + 21y = 2842/15\n56x + 64y = 4648/15\nSubtract equations\n-43y = -602/5\ny = -602/5/-43\ny = 14/5\n\nSubstitute y\n8x + 3(14/5) = 406/15\n8x = 56/3\nx = 56/3/8\nx = 7/3"} {"input": "Solve quickly: 3x - 3 = 0", "output": "3x - 3 = 0\n3x = 3\nx = 3 / 3\nx = 1"} {"input": "Find x for x^2 + 5x + 4 = 0", "output": "x^2 + 5x + 4 = 0\n(x - -4)(x - -1) = 0\nx - -4 = 0 or x - -1 = 0\nx = -4\nx = -1"} {"input": "What value of x satisfies x^3 - 49/2x^2 + 114x + 459/2 = 0", "output": "x^3 - 49/2x^2 + 114x + 459/2 = 0\n(x - 17)(x - -3/2)(x - 9) = 0\nx - 17 = 0\nx - -3/2 = 0\nx - 9 = 0\nx = 17\nx = -3/2\nx = 9"} {"input": "Find x for x^2 - 86/35x + 48/35 = 0", "output": "x^2 - 86/35x + 48/35 = 0\n(x - 6/7)(x - 8/5) = 0\nx - 6/7 = 0 or x - 8/5 = 0\nx = 6/7\nx = 8/5"} {"input": "Solve the equation x^3 - 295/18x^2 + 509/9x + 760/9 = 0", "output": "x^3 - 295/18x^2 + 509/9x + 760/9 = 0\n(x - 8)(x - -10/9)(x - 19/2) = 0\nx - 8 = 0\nx - -10/9 = 0\nx - 19/2 = 0\nx = 8\nx = -10/9\nx = 19/2"} {"input": "Solve quickly: 7x - 91/5 = 0", "output": "7x - 91/5 = 0\n7x = 91/5\nx = 91/5 / 7\nx = 13/5"} {"input": "Find x for x^3 + 197/90x^2 - 268/45x + 19/30 = 0", "output": "x^3 + 197/90x^2 - 268/45x + 19/30 = 0\n(x - 3/2)(x - 1/9)(x - -19/5) = 0\nx - 3/2 = 0\nx - 1/9 = 0\nx - -19/5 = 0\nx = 3/2\nx = 1/9\nx = -19/5"} {"input": "Solve the equation x^2 + 7x = 0", "output": "x^2 + 7x = 0\n(x - -7)(x - 0) = 0\nx - -7 = 0 or x - 0 = 0\nx = -7\nx = 0"} {"input": "Solve x^2 - 49/9x + 130/27 = 0", "output": "x^2 - 49/9x + 130/27 = 0\n(x - 10/9)(x - 13/3) = 0\nx - 10/9 = 0 or x - 13/3 = 0\nx = 10/9\nx = 13/3"} {"input": "Determine x in x^2 + 7x + 6 = 0", "output": "x^2 + 7x + 6 = 0\n(x - -6)(x - -1) = 0\nx - -6 = 0 or x - -1 = 0\nx = -6\nx = -1"} {"input": "Solve the system:\n5x + 3y = 48/7\n8x + 7y = 123/7", "output": "5x + 3y = 48/7\n8x + 7y = 123/7\n\nUsing elimination\n8*(5x + 3y = 48/7)\n5*(8x + 7y = 123/7)\n40x + 24y = 384/7\n40x + 35y = 615/7\nSubtract equations\n-11y = -33\ny = -33/-11\ny = 3\n\nSubstitute y\n5x + 3(3) = 48/7\n5x = -15/7\nx = -15/7/5\nx = -3/7"} {"input": "Find x and y such that\n6x + 6y = 267/20\n1x + 9y = 289/40", "output": "6x + 6y = 267/20\n1x + 9y = 289/40\n\nUsing elimination\n1*(6x + 6y = 267/20)\n6*(1x + 9y = 289/40)\n6x + 6y = 267/20\n6x + 54y = 867/20\nSubtract equations\n-48y = -30\ny = -30/-48\ny = 5/8\n\nSubstitute y\n6x + 6(5/8) = 267/20\n6x = 48/5\nx = 48/5/6\nx = 8/5"} {"input": "Solve quickly: x^3 - 1/8x^2 - 145/16x - 77/8 = 0", "output": "x^3 - 1/8x^2 - 145/16x - 77/8 = 0\n(x - 7/2)(x - -11/8)(x - -2) = 0\nx - 7/2 = 0\nx - -11/8 = 0\nx - -2 = 0\nx = 7/2\nx = -11/8\nx = -2"} {"input": "Find the solution to x^3 + 337/70x^2 + 13/2x + 76/35 = 0", "output": "x^3 + 337/70x^2 + 13/2x + 76/35 = 0\n(x - -8/5)(x - -1/2)(x - -19/7) = 0\nx - -8/5 = 0\nx - -1/2 = 0\nx - -19/7 = 0\nx = -8/5\nx = -1/2\nx = -19/7"} {"input": "Solve quickly: x^2 + 11x + 10 = 0", "output": "x^2 + 11x + 10 = 0\n(x - -1)(x - -10) = 0\nx - -1 = 0 or x - -10 = 0\nx = -1\nx = -10"} {"input": "Find the solution to x^2 + 23/24x - 95/12 = 0", "output": "x^2 + 23/24x - 95/12 = 0\n(x - 19/8)(x - -10/3) = 0\nx - 19/8 = 0 or x - -10/3 = 0\nx = 19/8\nx = -10/3"} {"input": "Find x and y such that\n8x + 4y = -6/5\n3x + 1y = -7/10", "output": "8x + 4y = -6/5\n3x + 1y = -7/10\n\nUsing elimination\n3*(8x + 4y = -6/5)\n8*(3x + 1y = -7/10)\n24x + 12y = -18/5\n24x + 8y = -28/5\nSubtract equations\n4y = 2\ny = 2/4\ny = 1/2\n\nSubstitute y\n8x + 4(1/2) = -6/5\n8x = -16/5\nx = -16/5/8\nx = -2/5"} {"input": "Find the solution to x^2 - 64/5x + 48/5 = 0", "output": "x^2 - 64/5x + 48/5 = 0\n(x - 12)(x - 4/5) = 0\nx - 12 = 0 or x - 4/5 = 0\nx = 12\nx = 4/5"} {"input": "Determine x in x^2 + 166/35x + 144/35 = 0", "output": "x^2 + 166/35x + 144/35 = 0\n(x - -18/5)(x - -8/7) = 0\nx - -18/5 = 0 or x - -8/7 = 0\nx = -18/5\nx = -8/7"} {"input": "Find x for 2x + 34/7 = 0", "output": "2x + 34/7 = 0\n2x = -34/7\nx = -34/7 / 2\nx = -17/7"} {"input": "Determine x in x^2 + 5/2x = 0", "output": "x^2 + 5/2x = 0\n(x - -5/2)(x - 0) = 0\nx - -5/2 = 0 or x - 0 = 0\nx = -5/2\nx = 0"} {"input": "Solve the system:\n1x + 3y = 3/2\n4x + 6y = -6", "output": "1x + 3y = 3/2\n4x + 6y = -6\n\nUsing elimination\n4*(1x + 3y = 3/2)\n1*(4x + 6y = -6)\n4x + 12y = 6\n4x + 6y = -6\nSubtract equations\n6y = 12\ny = 12/6\ny = 2\n\nSubstitute y\n1x + 3(2) = 3/2\n1x = -9/2\nx = -9/2/1\nx = -9/2"} {"input": "Find x in x^2 + 157/9x - 266/9 = 0", "output": "x^2 + 157/9x - 266/9 = 0\n(x - -19)(x - 14/9) = 0\nx - -19 = 0 or x - 14/9 = 0\nx = -19\nx = 14/9"} {"input": "Determine x in x^2 - 56/9x + 221/27 = 0", "output": "x^2 - 56/9x + 221/27 = 0\n(x - 13/3)(x - 17/9) = 0\nx - 13/3 = 0 or x - 17/9 = 0\nx = 13/3\nx = 17/9"} {"input": "Find x for x^2 - 45/28x - 13/28 = 0", "output": "x^2 - 45/28x - 13/28 = 0\n(x - 13/7)(x - -1/4) = 0\nx - 13/7 = 0 or x - -1/4 = 0\nx = 13/7\nx = -1/4"} {"input": "Find x for x^3 + 22x^2 + 83/4x - 385 = 0", "output": "x^3 + 22x^2 + 83/4x - 385 = 0\n(x - 7/2)(x - -20)(x - -11/2) = 0\nx - 7/2 = 0\nx - -20 = 0\nx - -11/2 = 0\nx = 7/2\nx = -20\nx = -11/2"} {"input": "Solve simultaneously:\n10x + 4y = 122/5\n4x + 3y = 113/10", "output": "10x + 4y = 122/5\n4x + 3y = 113/10\n\nUsing elimination\n4*(10x + 4y = 122/5)\n10*(4x + 3y = 113/10)\n40x + 16y = 488/5\n40x + 30y = 113\nSubtract equations\n-14y = -77/5\ny = -77/5/-14\ny = 11/10\n\nSubstitute y\n10x + 4(11/10) = 122/5\n10x = 20\nx = 20/10\nx = 2"} {"input": "Compute the solution of x^3 + 121/45x^2 - 37/9x + 19/45 = 0", "output": "x^3 + 121/45x^2 - 37/9x + 19/45 = 0\n(x - 1/9)(x - 1)(x - -19/5) = 0\nx - 1/9 = 0\nx - 1 = 0\nx - -19/5 = 0\nx = 1/9\nx = 1\nx = -19/5"} {"input": "Solve simultaneously:\n1x + 7y = -8/3\n10x + 2y = 460/21", "output": "1x + 7y = -8/3\n10x + 2y = 460/21\n\nUsing elimination\n10*(1x + 7y = -8/3)\n1*(10x + 2y = 460/21)\n10x + 70y = -80/3\n10x + 2y = 460/21\nSubtract equations\n68y = -340/7\ny = -340/7/68\ny = -5/7\n\nSubstitute y\n1x + 7(-5/7) = -8/3\n1x = 7/3\nx = 7/3/1\nx = 7/3"} {"input": "Determine x in x^2 - 1/6x - 17/2 = 0", "output": "x^2 - 1/6x - 17/2 = 0\n(x - -17/6)(x - 3) = 0\nx - -17/6 = 0 or x - 3 = 0\nx = -17/6\nx = 3"} {"input": "Determine x in x^2 - 4/3x - 160/81 = 0", "output": "x^2 - 4/3x - 160/81 = 0\n(x - 20/9)(x - -8/9) = 0\nx - 20/9 = 0 or x - -8/9 = 0\nx = 20/9\nx = -8/9"} {"input": "Solve quickly: x^3 + 97/6x^2 + 319/6x + 38 = 0", "output": "x^3 + 97/6x^2 + 319/6x + 38 = 0\n(x - -19/6)(x - -12)(x - -1) = 0\nx - -19/6 = 0\nx - -12 = 0\nx - -1 = 0\nx = -19/6\nx = -12\nx = -1"} {"input": "Solve simultaneously:\n7x + 5y = 32\n9x + 3y = 48", "output": "7x + 5y = 32\n9x + 3y = 48\n\nUsing elimination\n9*(7x + 5y = 32)\n7*(9x + 3y = 48)\n63x + 45y = 288\n63x + 21y = 336\nSubtract equations\n24y = -48\ny = -48/24\ny = -2\n\nSubstitute y\n7x + 5(-2) = 32\n7x = 42\nx = 42/7\nx = 6"} {"input": "Find x for 10x - 50/9 = 0", "output": "10x - 50/9 = 0\n10x = 50/9\nx = 50/9 / 10\nx = 5/9"} {"input": "Solve 10x + 30 = 0", "output": "10x + 30 = 0\n10x = -30\nx = -30 / 10\nx = -3"} {"input": "Find x and y such that\n7x + 8y = -102/5\n8x + 9y = -116/5", "output": "7x + 8y = -102/5\n8x + 9y = -116/5\n\nUsing elimination\n8*(7x + 8y = -102/5)\n7*(8x + 9y = -116/5)\n56x + 64y = -816/5\n56x + 63y = -812/5\nSubtract equations\n1y = -4/5\ny = -4/5/1\ny = -4/5\n\nSubstitute y\n7x + 8(-4/5) = -102/5\n7x = -14\nx = -14/7\nx = -2"} {"input": "Solve the equations:\n10x + 9y = 47\n6x + 1y = 67/3", "output": "10x + 9y = 47\n6x + 1y = 67/3\n\nUsing elimination\n6*(10x + 9y = 47)\n10*(6x + 1y = 67/3)\n60x + 54y = 282\n60x + 10y = 670/3\nSubtract equations\n44y = 176/3\ny = 176/3/44\ny = 4/3\n\nSubstitute y\n10x + 9(4/3) = 47\n10x = 35\nx = 35/10\nx = 7/2"} {"input": "Solve x^3 - 91/40x^2 + 1/160x + 273/160 = 0", "output": "x^3 - 91/40x^2 + 1/160x + 273/160 = 0\n(x - -3/4)(x - 13/8)(x - 7/5) = 0\nx - -3/4 = 0\nx - 13/8 = 0\nx - 7/5 = 0\nx = -3/4\nx = 13/8\nx = 7/5"} {"input": "Solve quickly: x^2 - 35/4x - 39 = 0", "output": "x^2 - 35/4x - 39 = 0\n(x - -13/4)(x - 12) = 0\nx - -13/4 = 0 or x - 12 = 0\nx = -13/4\nx = 12"} {"input": "Determine x in x^3 + 19/15x^2 - 178/25x - 224/75 = 0", "output": "x^3 + 19/15x^2 - 178/25x - 224/75 = 0\n(x - -2/5)(x - -16/5)(x - 7/3) = 0\nx - -2/5 = 0\nx - -16/5 = 0\nx - 7/3 = 0\nx = -2/5\nx = -16/5\nx = 7/3"} {"input": "Find x for 1x - 20/3 = 0", "output": "1x - 20/3 = 0\n1x = 20/3\nx = 20/3 / 1\nx = 20/3"} {"input": "Solve 6x - 18 = 0", "output": "6x - 18 = 0\n6x = 18\nx = 18 / 6\nx = 3"} {"input": "Find x in x^2 - 17/6x - 1/2 = 0", "output": "x^2 - 17/6x - 1/2 = 0\n(x - -1/6)(x - 3) = 0\nx - -1/6 = 0 or x - 3 = 0\nx = -1/6\nx = 3"} {"input": "Compute the solution of x^3 - 75/4x^2 + 883/8x - 195 = 0", "output": "x^3 - 75/4x^2 + 883/8x - 195 = 0\n(x - 15/2)(x - 13/4)(x - 8) = 0\nx - 15/2 = 0\nx - 13/4 = 0\nx - 8 = 0\nx = 15/2\nx = 13/4\nx = 8"} {"input": "Solve quickly: x^3 + 135/56x^2 - 13/7x - 15/56 = 0", "output": "x^3 + 135/56x^2 - 13/7x - 15/56 = 0\n(x - 5/7)(x - -3)(x - -1/8) = 0\nx - 5/7 = 0\nx - -3 = 0\nx - -1/8 = 0\nx = 5/7\nx = -3\nx = -1/8"} {"input": "Solve the system:\n9x + 9y = 72\n10x + 5y = 90", "output": "9x + 9y = 72\n10x + 5y = 90\n\nUsing elimination\n10*(9x + 9y = 72)\n9*(10x + 5y = 90)\n90x + 90y = 720\n90x + 45y = 810\nSubtract equations\n45y = -90\ny = -90/45\ny = -2\n\nSubstitute y\n9x + 9(-2) = 72\n9x = 90\nx = 90/9\nx = 10"} {"input": "Determine x in 10x - 25/2 = 0", "output": "10x - 25/2 = 0\n10x = 25/2\nx = 25/2 / 10\nx = 5/4"} {"input": "What value of x satisfies x^3 - 23/4x^2 + 811/196x + 285/98 = 0", "output": "x^3 - 23/4x^2 + 811/196x + 285/98 = 0\n(x - -3/7)(x - 19/4)(x - 10/7) = 0\nx - -3/7 = 0\nx - 19/4 = 0\nx - 10/7 = 0\nx = -3/7\nx = 19/4\nx = 10/7"} {"input": "Determine x in x^3 + 4x^2 + 3x = 0", "output": "x^3 + 4x^2 + 3x = 0\n(x - 0)(x - -3)(x - -1) = 0\nx - 0 = 0\nx - -3 = 0\nx - -1 = 0\nx = 0\nx = -3\nx = -1"} {"input": "Solve simultaneously:\n8x + 9y = 9\n7x + 5y = 17/8", "output": "8x + 9y = 9\n7x + 5y = 17/8\n\nUsing elimination\n7*(8x + 9y = 9)\n8*(7x + 5y = 17/8)\n56x + 63y = 63\n56x + 40y = 17\nSubtract equations\n23y = 46\ny = 46/23\ny = 2\n\nSubstitute y\n8x + 9(2) = 9\n8x = -9\nx = -9/8\nx = -9/8"} {"input": "Find x for x^2 + 33/10x + 2 = 0", "output": "x^2 + 33/10x + 2 = 0\n(x - -4/5)(x - -5/2) = 0\nx - -4/5 = 0 or x - -5/2 = 0\nx = -4/5\nx = -5/2"} {"input": "Solve the equations:\n1x + 5y = -5\n8x + 5y = -5", "output": "1x + 5y = -5\n8x + 5y = -5\n\nUsing elimination\n8*(1x + 5y = -5)\n1*(8x + 5y = -5)\n8x + 40y = -40\n8x + 5y = -5\nSubtract equations\n35y = -35\ny = -35/35\ny = -1\n\nSubstitute y\n1x + 5(-1) = -5\n1x = 0\nx = 0/1\nx = 0"} {"input": "Solve the equation 7x + 18 = 0", "output": "7x + 18 = 0\n7x = -18\nx = -18 / 7\nx = -18/7"} {"input": "Find x in x^3 - 59/90x^2 + 17/162x - 2/405 = 0", "output": "x^3 - 59/90x^2 + 17/162x - 2/405 = 0\n(x - 1/9)(x - 4/9)(x - 1/10) = 0\nx - 1/9 = 0\nx - 4/9 = 0\nx - 1/10 = 0\nx = 1/9\nx = 4/9\nx = 1/10"} {"input": "Solve 1x - 16/3 = 0", "output": "1x - 16/3 = 0\n1x = 16/3\nx = 16/3 / 1\nx = 16/3"} {"input": "Solve simultaneously:\n7x + 4y = 128/9\n3x + 6y = 44/3", "output": "7x + 4y = 128/9\n3x + 6y = 44/3\n\nUsing elimination\n3*(7x + 4y = 128/9)\n7*(3x + 6y = 44/3)\n21x + 12y = 128/3\n21x + 42y = 308/3\nSubtract equations\n-30y = -60\ny = -60/-30\ny = 2\n\nSubstitute y\n7x + 4(2) = 128/9\n7x = 56/9\nx = 56/9/7\nx = 8/9"} {"input": "Solve the equations:\n9x + 10y = -81\n9x + 8y = -63", "output": "9x + 10y = -81\n9x + 8y = -63\n\nUsing elimination\n9*(9x + 10y = -81)\n9*(9x + 8y = -63)\n81x + 90y = -729\n81x + 72y = -567\nSubtract equations\n18y = -162\ny = -162/18\ny = -9\n\nSubstitute y\n9x + 10(-9) = -81\n9x = 9\nx = 9/9\nx = 1"} {"input": "What value of x satisfies 1x + 13/7 = 0", "output": "1x + 13/7 = 0\n1x = -13/7\nx = -13/7 / 1\nx = -13/7"} {"input": "What value of x satisfies x^3 - 115/9x^2 - 143/27x + 845/27 = 0", "output": "x^3 - 115/9x^2 - 143/27x + 845/27 = 0\n(x - 13/9)(x - 13)(x - -5/3) = 0\nx - 13/9 = 0\nx - 13 = 0\nx - -5/3 = 0\nx = 13/9\nx = 13\nx = -5/3"} {"input": "Solve the equations:\n3x + 4y = 21/5\n10x + 7y = 51/5", "output": "3x + 4y = 21/5\n10x + 7y = 51/5\n\nUsing elimination\n10*(3x + 4y = 21/5)\n3*(10x + 7y = 51/5)\n30x + 40y = 42\n30x + 21y = 153/5\nSubtract equations\n19y = 57/5\ny = 57/5/19\ny = 3/5\n\nSubstitute y\n3x + 4(3/5) = 21/5\n3x = 9/5\nx = 9/5/3\nx = 3/5"} {"input": "Solve the equation x^3 + 271/42x^2 + 559/42x + 60/7 = 0", "output": "x^3 + 271/42x^2 + 559/42x + 60/7 = 0\n(x - -8/3)(x - -9/7)(x - -5/2) = 0\nx - -8/3 = 0\nx - -9/7 = 0\nx - -5/2 = 0\nx = -8/3\nx = -9/7\nx = -5/2"} {"input": "Solve quickly: 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "What value of x satisfies 7x - 35/4 = 0", "output": "7x - 35/4 = 0\n7x = 35/4\nx = 35/4 / 7\nx = 5/4"} {"input": "Solve the equation x^3 + 31/10x^2 + 3/10x = 0", "output": "x^3 + 31/10x^2 + 3/10x = 0\n(x - 0)(x - -3)(x - -1/10) = 0\nx - 0 = 0\nx - -3 = 0\nx - -1/10 = 0\nx = 0\nx = -3\nx = -1/10"} {"input": "Compute the solution of x^2 - 7/3x - 40/3 = 0", "output": "x^2 - 7/3x - 40/3 = 0\n(x - 5)(x - -8/3) = 0\nx - 5 = 0 or x - -8/3 = 0\nx = 5\nx = -8/3"} {"input": "Compute the solution of 4x - 80/7 = 0", "output": "4x - 80/7 = 0\n4x = 80/7\nx = 80/7 / 4\nx = 20/7"} {"input": "Find the solution to 8x - 64 = 0", "output": "8x - 64 = 0\n8x = 64\nx = 64 / 8\nx = 8"} {"input": "Find x for 9x + 54 = 0", "output": "9x + 54 = 0\n9x = -54\nx = -54 / 9\nx = -6"} {"input": "Solve the equations:\n6x + 3y = -237/10\n7x + 10y = -27", "output": "6x + 3y = -237/10\n7x + 10y = -27\n\nUsing elimination\n7*(6x + 3y = -237/10)\n6*(7x + 10y = -27)\n42x + 21y = -1659/10\n42x + 60y = -162\nSubtract equations\n-39y = -39/10\ny = -39/10/-39\ny = 1/10\n\nSubstitute y\n6x + 3(1/10) = -237/10\n6x = -24\nx = -24/6\nx = -4"} {"input": "Determine x in 5x - 5/4 = 0", "output": "5x - 5/4 = 0\n5x = 5/4\nx = 5/4 / 5\nx = 1/4"} {"input": "Find x in x^3 + 10x^2 - 4x - 40 = 0", "output": "x^3 + 10x^2 - 4x - 40 = 0\n(x - 2)(x - -10)(x - -2) = 0\nx - 2 = 0\nx - -10 = 0\nx - -2 = 0\nx = 2\nx = -10\nx = -2"} {"input": "Solve the equation 9x - 99 = 0", "output": "9x - 99 = 0\n9x = 99\nx = 99 / 9\nx = 11"} {"input": "Find x in x^2 - 6x + 8 = 0", "output": "x^2 - 6x + 8 = 0\n(x - 2)(x - 4) = 0\nx - 2 = 0 or x - 4 = 0\nx = 2\nx = 4"} {"input": "Find x in x^2 - 13/2x - 35 = 0", "output": "x^2 - 13/2x - 35 = 0\n(x - 10)(x - -7/2) = 0\nx - 10 = 0 or x - -7/2 = 0\nx = 10\nx = -7/2"} {"input": "Find x for x^3 + 18x^2 + 89x + 132 = 0", "output": "x^3 + 18x^2 + 89x + 132 = 0\n(x - -4)(x - -3)(x - -11) = 0\nx - -4 = 0\nx - -3 = 0\nx - -11 = 0\nx = -4\nx = -3\nx = -11"} {"input": "Compute the solution of x^3 + 34/21x^2 - 667/567x - 130/63 = 0", "output": "x^3 + 34/21x^2 - 667/567x - 130/63 = 0\n(x - -9/7)(x - 10/9)(x - -13/9) = 0\nx - -9/7 = 0\nx - 10/9 = 0\nx - -13/9 = 0\nx = -9/7\nx = 10/9\nx = -13/9"} {"input": "Find x in 8x + 1 = 0", "output": "8x + 1 = 0\n8x = -1\nx = -1 / 8\nx = -1/8"} {"input": "Find x and y such that\n5x + 3y = 35/2\n1x + 1y = 5/2", "output": "5x + 3y = 35/2\n1x + 1y = 5/2\n\nUsing elimination\n1*(5x + 3y = 35/2)\n5*(1x + 1y = 5/2)\n5x + 3y = 35/2\n5x + 5y = 25/2\nSubtract equations\n-2y = 5\ny = 5/-2\ny = -5/2\n\nSubstitute y\n5x + 3(-5/2) = 35/2\n5x = 25\nx = 25/5\nx = 5"} {"input": "Solve the system:\n3x + 7y = -17/9\n8x + 4y = 116/9", "output": "3x + 7y = -17/9\n8x + 4y = 116/9\n\nUsing elimination\n8*(3x + 7y = -17/9)\n3*(8x + 4y = 116/9)\n24x + 56y = -136/9\n24x + 12y = 116/3\nSubtract equations\n44y = -484/9\ny = -484/9/44\ny = -11/9\n\nSubstitute y\n3x + 7(-11/9) = -17/9\n3x = 20/3\nx = 20/3/3\nx = 20/9"} {"input": "Solve 7x - 63/5 = 0", "output": "7x - 63/5 = 0\n7x = 63/5\nx = 63/5 / 7\nx = 9/5"} {"input": "Compute the solution of x^2 + 116/5x + 64 = 0", "output": "x^2 + 116/5x + 64 = 0\n(x - -16/5)(x - -20) = 0\nx - -16/5 = 0 or x - -20 = 0\nx = -16/5\nx = -20"} {"input": "Determine x in x^2 - 31/21x + 8/21 = 0", "output": "x^2 - 31/21x + 8/21 = 0\n(x - 1/3)(x - 8/7) = 0\nx - 1/3 = 0 or x - 8/7 = 0\nx = 1/3\nx = 8/7"} {"input": "Solve quickly: x^2 + 83/10x - 17/10 = 0", "output": "x^2 + 83/10x - 17/10 = 0\n(x - 1/5)(x - -17/2) = 0\nx - 1/5 = 0 or x - -17/2 = 0\nx = 1/5\nx = -17/2"} {"input": "Find x in 2x + 4/3 = 0", "output": "2x + 4/3 = 0\n2x = -4/3\nx = -4/3 / 2\nx = -2/3"} {"input": "Solve quickly: x^3 - 8/35x^2 - 27/5x + 162/35 = 0", "output": "x^3 - 8/35x^2 - 27/5x + 162/35 = 0\n(x - -18/7)(x - 1)(x - 9/5) = 0\nx - -18/7 = 0\nx - 1 = 0\nx - 9/5 = 0\nx = -18/7\nx = 1\nx = 9/5"} {"input": "Find the solution to 10x - 14 = 0", "output": "10x - 14 = 0\n10x = 14\nx = 14 / 10\nx = 7/5"} {"input": "Solve the equation x^3 + 220/9x^2 + 3379/27x + 494/3 = 0", "output": "x^3 + 220/9x^2 + 3379/27x + 494/3 = 0\n(x - -13/3)(x - -18)(x - -19/9) = 0\nx - -13/3 = 0\nx - -18 = 0\nx - -19/9 = 0\nx = -13/3\nx = -18\nx = -19/9"} {"input": "Find x for x^2 - 9/14x - 65/14 = 0", "output": "x^2 - 9/14x - 65/14 = 0\n(x - 5/2)(x - -13/7) = 0\nx - 5/2 = 0 or x - -13/7 = 0\nx = 5/2\nx = -13/7"} {"input": "Find x for x^3 - 221/40x^2 + 1589/160x - 931/160 = 0", "output": "x^3 - 221/40x^2 + 1589/160x - 931/160 = 0\n(x - 19/8)(x - 7/4)(x - 7/5) = 0\nx - 19/8 = 0\nx - 7/4 = 0\nx - 7/5 = 0\nx = 19/8\nx = 7/4\nx = 7/5"} {"input": "Solve the equations:\n7x + 10y = -281/18\n10x + 3y = -97/3", "output": "7x + 10y = -281/18\n10x + 3y = -97/3\n\nUsing elimination\n10*(7x + 10y = -281/18)\n7*(10x + 3y = -97/3)\n70x + 100y = -1405/9\n70x + 21y = -679/3\nSubtract equations\n79y = 632/9\ny = 632/9/79\ny = 8/9\n\nSubstitute y\n7x + 10(8/9) = -281/18\n7x = -49/2\nx = -49/2/7\nx = -7/2"} {"input": "Find x in 7x + 77/3 = 0", "output": "7x + 77/3 = 0\n7x = -77/3\nx = -77/3 / 7\nx = -11/3"} {"input": "Solve quickly: x^3 - 104/45x^2 + 19/45x = 0", "output": "x^3 - 104/45x^2 + 19/45x = 0\n(x - 0)(x - 1/5)(x - 19/9) = 0\nx - 0 = 0\nx - 1/5 = 0\nx - 19/9 = 0\nx = 0\nx = 1/5\nx = 19/9"} {"input": "Find x in 9x + 144/5 = 0", "output": "9x + 144/5 = 0\n9x = -144/5\nx = -144/5 / 9\nx = -16/5"} {"input": "Find x in 8x + 120/7 = 0", "output": "8x + 120/7 = 0\n8x = -120/7\nx = -120/7 / 8\nx = -15/7"} {"input": "Solve the equation x^3 + 17/15x^2 - 8/5x + 4/15 = 0", "output": "x^3 + 17/15x^2 - 8/5x + 4/15 = 0\n(x - 2/3)(x - -2)(x - 1/5) = 0\nx - 2/3 = 0\nx - -2 = 0\nx - 1/5 = 0\nx = 2/3\nx = -2\nx = 1/5"} {"input": "Solve quickly: x^3 - 3/28x^2 - 99/28x - 1/2 = 0", "output": "x^3 - 3/28x^2 - 99/28x - 1/2 = 0\n(x - -7/4)(x - 2)(x - -1/7) = 0\nx - -7/4 = 0\nx - 2 = 0\nx - -1/7 = 0\nx = -7/4\nx = 2\nx = -1/7"} {"input": "What value of x satisfies x^3 + 9x^2 - 10x = 0", "output": "x^3 + 9x^2 - 10x = 0\n(x - 1)(x - 0)(x - -10) = 0\nx - 1 = 0\nx - 0 = 0\nx - -10 = 0\nx = 1\nx = 0\nx = -10"} {"input": "Solve the system:\n7x + 8y = 7/9\n10x + 2y = -122/9", "output": "7x + 8y = 7/9\n10x + 2y = -122/9\n\nUsing elimination\n10*(7x + 8y = 7/9)\n7*(10x + 2y = -122/9)\n70x + 80y = 70/9\n70x + 14y = -854/9\nSubtract equations\n66y = 308/3\ny = 308/3/66\ny = 14/9\n\nSubstitute y\n7x + 8(14/9) = 7/9\n7x = -35/3\nx = -35/3/7\nx = -5/3"} {"input": "What value of x satisfies x^3 + 83/10x^2 + 229/10x + 21 = 0", "output": "x^3 + 83/10x^2 + 229/10x + 21 = 0\n(x - -5/2)(x - -14/5)(x - -3) = 0\nx - -5/2 = 0\nx - -14/5 = 0\nx - -3 = 0\nx = -5/2\nx = -14/5\nx = -3"} {"input": "Compute the solution of 9x + 5 = 0", "output": "9x + 5 = 0\n9x = -5\nx = -5 / 9\nx = -5/9"} {"input": "Find the solution to x^2 - 19/9x - 154/27 = 0", "output": "x^2 - 19/9x - 154/27 = 0\n(x - -14/9)(x - 11/3) = 0\nx - -14/9 = 0 or x - 11/3 = 0\nx = -14/9\nx = 11/3"} {"input": "Compute the solution of x^3 - 1327/210x^2 - 62/105x + 19/6 = 0", "output": "x^3 - 1327/210x^2 - 62/105x + 19/6 = 0\n(x - 19/3)(x - -5/7)(x - 7/10) = 0\nx - 19/3 = 0\nx - -5/7 = 0\nx - 7/10 = 0\nx = 19/3\nx = -5/7\nx = 7/10"} {"input": "Compute the solution of x^3 + 52/15x^2 + 89/60x - 26/15 = 0", "output": "x^3 + 52/15x^2 + 89/60x - 26/15 = 0\n(x - -8/3)(x - 1/2)(x - -13/10) = 0\nx - -8/3 = 0\nx - 1/2 = 0\nx - -13/10 = 0\nx = -8/3\nx = 1/2\nx = -13/10"} {"input": "Find x and y such that\n4x + 1y = -152/9\n4x + 8y = -208/9", "output": "4x + 1y = -152/9\n4x + 8y = -208/9\n\nUsing elimination\n4*(4x + 1y = -152/9)\n4*(4x + 8y = -208/9)\n16x + 4y = -608/9\n16x + 32y = -832/9\nSubtract equations\n-28y = 224/9\ny = 224/9/-28\ny = -8/9\n\nSubstitute y\n4x + 1(-8/9) = -152/9\n4x = -16\nx = -16/4\nx = -4"} {"input": "Find the solution to x^3 + 7/2x^2 - 119x + 117/2 = 0", "output": "x^3 + 7/2x^2 - 119x + 117/2 = 0\n(x - 9)(x - 1/2)(x - -13) = 0\nx - 9 = 0\nx - 1/2 = 0\nx - -13 = 0\nx = 9\nx = 1/2\nx = -13"} {"input": "Find x and y such that\n1x + 6y = 41/4\n10x + 7y = 191/6", "output": "1x + 6y = 41/4\n10x + 7y = 191/6\n\nUsing elimination\n10*(1x + 6y = 41/4)\n1*(10x + 7y = 191/6)\n10x + 60y = 205/2\n10x + 7y = 191/6\nSubtract equations\n53y = 212/3\ny = 212/3/53\ny = 4/3\n\nSubstitute y\n1x + 6(4/3) = 41/4\n1x = 9/4\nx = 9/4/1\nx = 9/4"} {"input": "Solve the equation x^2 + 159/28x + 85/14 = 0", "output": "x^2 + 159/28x + 85/14 = 0\n(x - -17/4)(x - -10/7) = 0\nx - -17/4 = 0 or x - -10/7 = 0\nx = -17/4\nx = -10/7"} {"input": "Solve the equation x^2 - 15/2x - 19 = 0", "output": "x^2 - 15/2x - 19 = 0\n(x - 19/2)(x - -2) = 0\nx - 19/2 = 0 or x - -2 = 0\nx = 19/2\nx = -2"} {"input": "Find x and y such that\n10x + 1y = -533/12\n2x + 8y = 26/3", "output": "10x + 1y = -533/12\n2x + 8y = 26/3\n\nUsing elimination\n2*(10x + 1y = -533/12)\n10*(2x + 8y = 26/3)\n20x + 2y = -533/6\n20x + 80y = 260/3\nSubtract equations\n-78y = -351/2\ny = -351/2/-78\ny = 9/4\n\nSubstitute y\n10x + 1(9/4) = -533/12\n10x = -140/3\nx = -140/3/10\nx = -14/3"} {"input": "Solve the system:\n6x + 1y = 13\n9x + 6y = 42", "output": "6x + 1y = 13\n9x + 6y = 42\n\nUsing elimination\n9*(6x + 1y = 13)\n6*(9x + 6y = 42)\n54x + 9y = 117\n54x + 36y = 252\nSubtract equations\n-27y = -135\ny = -135/-27\ny = 5\n\nSubstitute y\n6x + 1(5) = 13\n6x = 8\nx = 8/6\nx = 4/3"} {"input": "Solve the equation x^3 + 83/36x^2 - 1163/108x + 7/6 = 0", "output": "x^3 + 83/36x^2 - 1163/108x + 7/6 = 0\n(x - 9/4)(x - 1/9)(x - -14/3) = 0\nx - 9/4 = 0\nx - 1/9 = 0\nx - -14/3 = 0\nx = 9/4\nx = 1/9\nx = -14/3"} {"input": "Solve the equation 7x - 91/10 = 0", "output": "7x - 91/10 = 0\n7x = 91/10\nx = 91/10 / 7\nx = 13/10"} {"input": "Find x and y such that\n10x + 7y = -145/12\n3x + 10y = -27/2", "output": "10x + 7y = -145/12\n3x + 10y = -27/2\n\nUsing elimination\n3*(10x + 7y = -145/12)\n10*(3x + 10y = -27/2)\n30x + 21y = -145/4\n30x + 100y = -135\nSubtract equations\n-79y = 395/4\ny = 395/4/-79\ny = -5/4\n\nSubstitute y\n10x + 7(-5/4) = -145/12\n10x = -10/3\nx = -10/3/10\nx = -1/3"} {"input": "Solve the system:\n6x + 10y = -37/6\n2x + 8y = -8/9", "output": "6x + 10y = -37/6\n2x + 8y = -8/9\n\nUsing elimination\n2*(6x + 10y = -37/6)\n6*(2x + 8y = -8/9)\n12x + 20y = -37/3\n12x + 48y = -16/3\nSubtract equations\n-28y = -7\ny = -7/-28\ny = 1/4\n\nSubstitute y\n6x + 10(1/4) = -37/6\n6x = -26/3\nx = -26/3/6\nx = -13/9"} {"input": "Determine x in x^3 + 3/8x^2 - 19/16x - 9/16 = 0", "output": "x^3 + 3/8x^2 - 19/16x - 9/16 = 0\n(x - 9/8)(x - -1/2)(x - -1) = 0\nx - 9/8 = 0\nx - -1/2 = 0\nx - -1 = 0\nx = 9/8\nx = -1/2\nx = -1"} {"input": "Determine x in x^2 - 7/5x = 0", "output": "x^2 - 7/5x = 0\n(x - 0)(x - 7/5) = 0\nx - 0 = 0 or x - 7/5 = 0\nx = 0\nx = 7/5"} {"input": "Solve the equation x^2 + 21/10x + 4/5 = 0", "output": "x^2 + 21/10x + 4/5 = 0\n(x - -1/2)(x - -8/5) = 0\nx - -1/2 = 0 or x - -8/5 = 0\nx = -1/2\nx = -8/5"} {"input": "What value of x satisfies x^2 + 17/8x + 15/32 = 0", "output": "x^2 + 17/8x + 15/32 = 0\n(x - -1/4)(x - -15/8) = 0\nx - -1/4 = 0 or x - -15/8 = 0\nx = -1/4\nx = -15/8"} {"input": "Find x for x^2 - 19/6x - 11/6 = 0", "output": "x^2 - 19/6x - 11/6 = 0\n(x - 11/3)(x - -1/2) = 0\nx - 11/3 = 0 or x - -1/2 = 0\nx = 11/3\nx = -1/2"} {"input": "Determine x in x^3 - 101/84x^2 - 289/42x + 285/28 = 0", "output": "x^3 - 101/84x^2 - 289/42x + 285/28 = 0\n(x - -19/7)(x - 5/3)(x - 9/4) = 0\nx - -19/7 = 0\nx - 5/3 = 0\nx - 9/4 = 0\nx = -19/7\nx = 5/3\nx = 9/4"} {"input": "Solve quickly: 10x + 50 = 0", "output": "10x + 50 = 0\n10x = -50\nx = -50 / 10\nx = -5"} {"input": "Find x in x^3 - 57/28x^2 - 247/28x + 132/7 = 0", "output": "x^3 - 57/28x^2 - 247/28x + 132/7 = 0\n(x - -3)(x - 11/4)(x - 16/7) = 0\nx - -3 = 0\nx - 11/4 = 0\nx - 16/7 = 0\nx = -3\nx = 11/4\nx = 16/7"} {"input": "Compute the solution of 2x + 2 = 0", "output": "2x + 2 = 0\n2x = -2\nx = -2 / 2\nx = -1"} {"input": "Solve x^3 + 251/90x^2 + 4/5x - 17/10 = 0", "output": "x^3 + 251/90x^2 + 4/5x - 17/10 = 0\n(x - -17/9)(x - 3/5)(x - -3/2) = 0\nx - -17/9 = 0\nx - 3/5 = 0\nx - -3/2 = 0\nx = -17/9\nx = 3/5\nx = -3/2"} {"input": "Determine x in x^2 + 6/5x - 7/25 = 0", "output": "x^2 + 6/5x - 7/25 = 0\n(x - -7/5)(x - 1/5) = 0\nx - -7/5 = 0 or x - 1/5 = 0\nx = -7/5\nx = 1/5"} {"input": "Solve x^2 + 2x + 3/4 = 0", "output": "x^2 + 2x + 3/4 = 0\n(x - -1/2)(x - -3/2) = 0\nx - -1/2 = 0 or x - -3/2 = 0\nx = -1/2\nx = -3/2"} {"input": "Solve the equations:\n2x + 4y = 148/9\n3x + 10y = 110/3", "output": "2x + 4y = 148/9\n3x + 10y = 110/3\n\nUsing elimination\n3*(2x + 4y = 148/9)\n2*(3x + 10y = 110/3)\n6x + 12y = 148/3\n6x + 20y = 220/3\nSubtract equations\n-8y = -24\ny = -24/-8\ny = 3\n\nSubstitute y\n2x + 4(3) = 148/9\n2x = 40/9\nx = 40/9/2\nx = 20/9"} {"input": "Solve the equation x^3 + 3/5x^2 - 49/25x + 9/25 = 0", "output": "x^3 + 3/5x^2 - 49/25x + 9/25 = 0\n(x - 1/5)(x - 1)(x - -9/5) = 0\nx - 1/5 = 0\nx - 1 = 0\nx - -9/5 = 0\nx = 1/5\nx = 1\nx = -9/5"} {"input": "Find x in x^2 + 41/10x + 33/10 = 0", "output": "x^2 + 41/10x + 33/10 = 0\n(x - -3)(x - -11/10) = 0\nx - -3 = 0 or x - -11/10 = 0\nx = -3\nx = -11/10"} {"input": "Find the solution to 5x - 10/3 = 0", "output": "5x - 10/3 = 0\n5x = 10/3\nx = 10/3 / 5\nx = 2/3"} {"input": "Solve the system:\n1x + 9y = -47/2\n2x + 3y = -46/3", "output": "1x + 9y = -47/2\n2x + 3y = -46/3\n\nUsing elimination\n2*(1x + 9y = -47/2)\n1*(2x + 3y = -46/3)\n2x + 18y = -47\n2x + 3y = -46/3\nSubtract equations\n15y = -95/3\ny = -95/3/15\ny = -19/9\n\nSubstitute y\n1x + 9(-19/9) = -47/2\n1x = -9/2\nx = -9/2/1\nx = -9/2"} {"input": "Compute the solution of x^3 - 14x^2 + 275/9x + 242/9 = 0", "output": "x^3 - 14x^2 + 275/9x + 242/9 = 0\n(x - 11)(x - -2/3)(x - 11/3) = 0\nx - 11 = 0\nx - -2/3 = 0\nx - 11/3 = 0\nx = 11\nx = -2/3\nx = 11/3"} {"input": "Solve x^2 - 185/42x + 33/7 = 0", "output": "x^2 - 185/42x + 33/7 = 0\n(x - 11/6)(x - 18/7) = 0\nx - 11/6 = 0 or x - 18/7 = 0\nx = 11/6\nx = 18/7"} {"input": "Solve quickly: x^2 + 90/7x - 16 = 0", "output": "x^2 + 90/7x - 16 = 0\n(x - -14)(x - 8/7) = 0\nx - -14 = 0 or x - 8/7 = 0\nx = -14\nx = 8/7"} {"input": "Solve the equation 5x + 85/7 = 0", "output": "5x + 85/7 = 0\n5x = -85/7\nx = -85/7 / 5\nx = -17/7"} {"input": "Solve the equation x^2 + 125/18x + 26/9 = 0", "output": "x^2 + 125/18x + 26/9 = 0\n(x - -4/9)(x - -13/2) = 0\nx - -4/9 = 0 or x - -13/2 = 0\nx = -4/9\nx = -13/2"} {"input": "Find x in 7x - 63 = 0", "output": "7x - 63 = 0\n7x = 63\nx = 63 / 7\nx = 9"} {"input": "Solve x^3 + 17/18x^2 - 317/6x + 260/9 = 0", "output": "x^3 + 17/18x^2 - 317/6x + 260/9 = 0\n(x - 5/9)(x - -8)(x - 13/2) = 0\nx - 5/9 = 0\nx - -8 = 0\nx - 13/2 = 0\nx = 5/9\nx = -8\nx = 13/2"} {"input": "Find x in x^3 + 68/5x^2 - 439/20x - 57/4 = 0", "output": "x^3 + 68/5x^2 - 439/20x - 57/4 = 0\n(x - 19/10)(x - -15)(x - -1/2) = 0\nx - 19/10 = 0\nx - -15 = 0\nx - -1/2 = 0\nx = 19/10\nx = -15\nx = -1/2"} {"input": "Solve x^3 - 2x^2 - 49/36x + 49/18 = 0", "output": "x^3 - 2x^2 - 49/36x + 49/18 = 0\n(x - 7/6)(x - -7/6)(x - 2) = 0\nx - 7/6 = 0\nx - -7/6 = 0\nx - 2 = 0\nx = 7/6\nx = -7/6\nx = 2"} {"input": "Solve x^3 + 73/24x^2 + 65/96x - 169/64 = 0", "output": "x^3 + 73/24x^2 + 65/96x - 169/64 = 0\n(x - -13/8)(x - -13/6)(x - 3/4) = 0\nx - -13/8 = 0\nx - -13/6 = 0\nx - 3/4 = 0\nx = -13/8\nx = -13/6\nx = 3/4"} {"input": "Solve the equations:\n3x + 5y = -32\n6x + 2y = -304/5", "output": "3x + 5y = -32\n6x + 2y = -304/5\n\nUsing elimination\n6*(3x + 5y = -32)\n3*(6x + 2y = -304/5)\n18x + 30y = -192\n18x + 6y = -912/5\nSubtract equations\n24y = -48/5\ny = -48/5/24\ny = -2/5\n\nSubstitute y\n3x + 5(-2/5) = -32\n3x = -30\nx = -30/3\nx = -10"} {"input": "Find x and y such that\n8x + 7y = 45/7\n8x + 1y = 75/7", "output": "8x + 7y = 45/7\n8x + 1y = 75/7\n\nUsing elimination\n8*(8x + 7y = 45/7)\n8*(8x + 1y = 75/7)\n64x + 56y = 360/7\n64x + 8y = 600/7\nSubtract equations\n48y = -240/7\ny = -240/7/48\ny = -5/7\n\nSubstitute y\n8x + 7(-5/7) = 45/7\n8x = 80/7\nx = 80/7/8\nx = 10/7"} {"input": "What value of x satisfies x^3 - 47/12x^2 + 113/24x - 7/4 = 0", "output": "x^3 - 47/12x^2 + 113/24x - 7/4 = 0\n(x - 2)(x - 3/4)(x - 7/6) = 0\nx - 2 = 0\nx - 3/4 = 0\nx - 7/6 = 0\nx = 2\nx = 3/4\nx = 7/6"} {"input": "Find x and y such that\n1x + 8y = 64/3\n2x + 5y = 29/3", "output": "1x + 8y = 64/3\n2x + 5y = 29/3\n\nUsing elimination\n2*(1x + 8y = 64/3)\n1*(2x + 5y = 29/3)\n2x + 16y = 128/3\n2x + 5y = 29/3\nSubtract equations\n11y = 33\ny = 33/11\ny = 3\n\nSubstitute y\n1x + 8(3) = 64/3\n1x = -8/3\nx = -8/3/1\nx = -8/3"} {"input": "Find x in 5x - 35/8 = 0", "output": "5x - 35/8 = 0\n5x = 35/8\nx = 35/8 / 5\nx = 7/8"} {"input": "Determine x in 2x - 10 = 0", "output": "2x - 10 = 0\n2x = 10\nx = 10 / 2\nx = 5"} {"input": "Solve the system:\n2x + 9y = 223/9\n9x + 8y = 14", "output": "2x + 9y = 223/9\n9x + 8y = 14\n\nUsing elimination\n9*(2x + 9y = 223/9)\n2*(9x + 8y = 14)\n18x + 81y = 223\n18x + 16y = 28\nSubtract equations\n65y = 195\ny = 195/65\ny = 3\n\nSubstitute y\n2x + 9(3) = 223/9\n2x = -20/9\nx = -20/9/2\nx = -10/9"} {"input": "Determine x in x^2 - 11/18x - 85/18 = 0", "output": "x^2 - 11/18x - 85/18 = 0\n(x - 5/2)(x - -17/9) = 0\nx - 5/2 = 0 or x - -17/9 = 0\nx = 5/2\nx = -17/9"} {"input": "Solve the equation x^2 + 3/8x - 1/16 = 0", "output": "x^2 + 3/8x - 1/16 = 0\n(x - 1/8)(x - -1/2) = 0\nx - 1/8 = 0 or x - -1/2 = 0\nx = 1/8\nx = -1/2"} {"input": "Solve quickly: x^3 + 7/9x^2 - 86/27x - 40/27 = 0", "output": "x^3 + 7/9x^2 - 86/27x - 40/27 = 0\n(x - 5/3)(x - -4/9)(x - -2) = 0\nx - 5/3 = 0\nx - -4/9 = 0\nx - -2 = 0\nx = 5/3\nx = -4/9\nx = -2"} {"input": "Compute the solution of x^2 + 5/2x - 7/2 = 0", "output": "x^2 + 5/2x - 7/2 = 0\n(x - -7/2)(x - 1) = 0\nx - -7/2 = 0 or x - 1 = 0\nx = -7/2\nx = 1"} {"input": "Solve simultaneously:\n9x + 2y = -20\n6x + 6y = -18", "output": "9x + 2y = -20\n6x + 6y = -18\n\nUsing elimination\n6*(9x + 2y = -20)\n9*(6x + 6y = -18)\n54x + 12y = -120\n54x + 54y = -162\nSubtract equations\n-42y = 42\ny = 42/-42\ny = -1\n\nSubstitute y\n9x + 2(-1) = -20\n9x = -18\nx = -18/9\nx = -2"} {"input": "Find x in x^2 + 18/35x - 32/5 = 0", "output": "x^2 + 18/35x - 32/5 = 0\n(x - 16/7)(x - -14/5) = 0\nx - 16/7 = 0 or x - -14/5 = 0\nx = 16/7\nx = -14/5"} {"input": "Compute the solution of x^2 + 15x + 26 = 0", "output": "x^2 + 15x + 26 = 0\n(x - -2)(x - -13) = 0\nx - -2 = 0 or x - -13 = 0\nx = -2\nx = -13"} {"input": "Compute the solution of x^2 - 19/9x + 2/9 = 0", "output": "x^2 - 19/9x + 2/9 = 0\n(x - 1/9)(x - 2) = 0\nx - 1/9 = 0 or x - 2 = 0\nx = 1/9\nx = 2"} {"input": "Solve the equation x^2 - 10/9x + 1/9 = 0", "output": "x^2 - 10/9x + 1/9 = 0\n(x - 1)(x - 1/9) = 0\nx - 1 = 0 or x - 1/9 = 0\nx = 1\nx = 1/9"} {"input": "Solve the equations:\n7x + 9y = -40\n3x + 4y = -35/2", "output": "7x + 9y = -40\n3x + 4y = -35/2\n\nUsing elimination\n3*(7x + 9y = -40)\n7*(3x + 4y = -35/2)\n21x + 27y = -120\n21x + 28y = -245/2\nSubtract equations\n-1y = 5/2\ny = 5/2/-1\ny = -5/2\n\nSubstitute y\n7x + 9(-5/2) = -40\n7x = -35/2\nx = -35/2/7\nx = -5/2"} {"input": "Solve x^2 - 18/7x - 9/7 = 0", "output": "x^2 - 18/7x - 9/7 = 0\n(x - -3/7)(x - 3) = 0\nx - -3/7 = 0 or x - 3 = 0\nx = -3/7\nx = 3"} {"input": "Find x for x^3 + 5/2x^2 - 4x - 10 = 0", "output": "x^3 + 5/2x^2 - 4x - 10 = 0\n(x - -2)(x - -5/2)(x - 2) = 0\nx - -2 = 0\nx - -5/2 = 0\nx - 2 = 0\nx = -2\nx = -5/2\nx = 2"} {"input": "Find x in 3x - 20 = 0", "output": "3x - 20 = 0\n3x = 20\nx = 20 / 3\nx = 20/3"} {"input": "Solve the equation x^3 + 23/10x^2 - 337/50x - 78/5 = 0", "output": "x^3 + 23/10x^2 - 337/50x - 78/5 = 0\n(x - -12/5)(x - 13/5)(x - -5/2) = 0\nx - -12/5 = 0\nx - 13/5 = 0\nx - -5/2 = 0\nx = -12/5\nx = 13/5\nx = -5/2"} {"input": "Solve the equation x^3 - 44/5x^2 + 92/5x - 48/5 = 0", "output": "x^3 - 44/5x^2 + 92/5x - 48/5 = 0\n(x - 6)(x - 2)(x - 4/5) = 0\nx - 6 = 0\nx - 2 = 0\nx - 4/5 = 0\nx = 6\nx = 2\nx = 4/5"} {"input": "Determine x in 5x + 65/2 = 0", "output": "5x + 65/2 = 0\n5x = -65/2\nx = -65/2 / 5\nx = -13/2"} {"input": "Solve quickly: x^2 + 15x + 14 = 0", "output": "x^2 + 15x + 14 = 0\n(x - -14)(x - -1) = 0\nx - -14 = 0 or x - -1 = 0\nx = -14\nx = -1"} {"input": "Solve simultaneously:\n6x + 1y = 21/2\n2x + 9y = 85/2", "output": "6x + 1y = 21/2\n2x + 9y = 85/2\n\nUsing elimination\n2*(6x + 1y = 21/2)\n6*(2x + 9y = 85/2)\n12x + 2y = 21\n12x + 54y = 255\nSubtract equations\n-52y = -234\ny = -234/-52\ny = 9/2\n\nSubstitute y\n6x + 1(9/2) = 21/2\n6x = 6\nx = 6/6\nx = 1"} {"input": "Determine x in 6x + 12/5 = 0", "output": "6x + 12/5 = 0\n6x = -12/5\nx = -12/5 / 6\nx = -2/5"} {"input": "Solve simultaneously:\n10x + 5y = -205/3\n10x + 9y = -75", "output": "10x + 5y = -205/3\n10x + 9y = -75\n\nUsing elimination\n10*(10x + 5y = -205/3)\n10*(10x + 9y = -75)\n100x + 50y = -2050/3\n100x + 90y = -750\nSubtract equations\n-40y = 200/3\ny = 200/3/-40\ny = -5/3\n\nSubstitute y\n10x + 5(-5/3) = -205/3\n10x = -60\nx = -60/10\nx = -6"} {"input": "Find x in x^2 + 27/10x + 1/2 = 0", "output": "x^2 + 27/10x + 1/2 = 0\n(x - -5/2)(x - -1/5) = 0\nx - -5/2 = 0 or x - -1/5 = 0\nx = -5/2\nx = -1/5"} {"input": "Solve the equations:\n5x + 6y = 36/5\n6x + 1y = -5", "output": "5x + 6y = 36/5\n6x + 1y = -5\n\nUsing elimination\n6*(5x + 6y = 36/5)\n5*(6x + 1y = -5)\n30x + 36y = 216/5\n30x + 5y = -25\nSubtract equations\n31y = 341/5\ny = 341/5/31\ny = 11/5\n\nSubstitute y\n5x + 6(11/5) = 36/5\n5x = -6\nx = -6/5\nx = -6/5"} {"input": "Solve the equations:\n4x + 2y = 116/5\n1x + 8y = 733/10", "output": "4x + 2y = 116/5\n1x + 8y = 733/10\n\nUsing elimination\n1*(4x + 2y = 116/5)\n4*(1x + 8y = 733/10)\n4x + 2y = 116/5\n4x + 32y = 1466/5\nSubtract equations\n-30y = -270\ny = -270/-30\ny = 9\n\nSubstitute y\n4x + 2(9) = 116/5\n4x = 26/5\nx = 26/5/4\nx = 13/10"} {"input": "Compute the solution of 2x + 20 = 0", "output": "2x + 20 = 0\n2x = -20\nx = -20 / 2\nx = -10"} {"input": "Solve quickly: x^3 + 78/5x^2 + 153/20x - 81/4 = 0", "output": "x^3 + 78/5x^2 + 153/20x - 81/4 = 0\n(x - 9/10)(x - -15)(x - -3/2) = 0\nx - 9/10 = 0\nx - -15 = 0\nx - -3/2 = 0\nx = 9/10\nx = -15\nx = -3/2"} {"input": "Solve simultaneously:\n6x + 4y = -22/35\n7x + 8y = -9/35", "output": "6x + 4y = -22/35\n7x + 8y = -9/35\n\nUsing elimination\n7*(6x + 4y = -22/35)\n6*(7x + 8y = -9/35)\n42x + 28y = -22/5\n42x + 48y = -54/35\nSubtract equations\n-20y = -20/7\ny = -20/7/-20\ny = 1/7\n\nSubstitute y\n6x + 4(1/7) = -22/35\n6x = -6/5\nx = -6/5/6\nx = -1/5"} {"input": "Solve quickly: x^2 - 68/35x + 32/35 = 0", "output": "x^2 - 68/35x + 32/35 = 0\n(x - 4/5)(x - 8/7) = 0\nx - 4/5 = 0 or x - 8/7 = 0\nx = 4/5\nx = 8/7"} {"input": "What value of x satisfies x^3 + 104/45x^2 - 128/45x = 0", "output": "x^3 + 104/45x^2 - 128/45x = 0\n(x - -16/5)(x - 0)(x - 8/9) = 0\nx - -16/5 = 0\nx - 0 = 0\nx - 8/9 = 0\nx = -16/5\nx = 0\nx = 8/9"} {"input": "Determine x in x^3 + 3x^2 - 13/16x - 45/8 = 0", "output": "x^3 + 3x^2 - 13/16x - 45/8 = 0\n(x - 5/4)(x - -2)(x - -9/4) = 0\nx - 5/4 = 0\nx - -2 = 0\nx - -9/4 = 0\nx = 5/4\nx = -2\nx = -9/4"} {"input": "What value of x satisfies x^3 - 29/5x^2 - 31/20x + 21/10 = 0", "output": "x^3 - 29/5x^2 - 31/20x + 21/10 = 0\n(x - 1/2)(x - 6)(x - -7/10) = 0\nx - 1/2 = 0\nx - 6 = 0\nx - -7/10 = 0\nx = 1/2\nx = 6\nx = -7/10"} {"input": "Find x for x^2 - 55/18x - 14/9 = 0", "output": "x^2 - 55/18x - 14/9 = 0\n(x - -4/9)(x - 7/2) = 0\nx - -4/9 = 0 or x - 7/2 = 0\nx = -4/9\nx = 7/2"} {"input": "Solve simultaneously:\n1x + 10y = -51\n10x + 8y = -50", "output": "1x + 10y = -51\n10x + 8y = -50\n\nUsing elimination\n10*(1x + 10y = -51)\n1*(10x + 8y = -50)\n10x + 100y = -510\n10x + 8y = -50\nSubtract equations\n92y = -460\ny = -460/92\ny = -5\n\nSubstitute y\n1x + 10(-5) = -51\n1x = -1\nx = -1/1\nx = -1"} {"input": "Solve the system:\n8x + 3y = 31/3\n2x + 1y = 10/3", "output": "8x + 3y = 31/3\n2x + 1y = 10/3\n\nUsing elimination\n2*(8x + 3y = 31/3)\n8*(2x + 1y = 10/3)\n16x + 6y = 62/3\n16x + 8y = 80/3\nSubtract equations\n-2y = -6\ny = -6/-2\ny = 3\n\nSubstitute y\n8x + 3(3) = 31/3\n8x = 4/3\nx = 4/3/8\nx = 1/6"} {"input": "Solve the equations:\n9x + 5y = -800/21\n6x + 2y = -356/21", "output": "9x + 5y = -800/21\n6x + 2y = -356/21\n\nUsing elimination\n6*(9x + 5y = -800/21)\n9*(6x + 2y = -356/21)\n54x + 30y = -1600/7\n54x + 18y = -1068/7\nSubtract equations\n12y = -76\ny = -76/12\ny = -19/3\n\nSubstitute y\n9x + 5(-19/3) = -800/21\n9x = -45/7\nx = -45/7/9\nx = -5/7"} {"input": "What value of x satisfies x^3 - 197/18x^2 + 326/9x - 65/2 = 0", "output": "x^3 - 197/18x^2 + 326/9x - 65/2 = 0\n(x - 9/2)(x - 5)(x - 13/9) = 0\nx - 9/2 = 0\nx - 5 = 0\nx - 13/9 = 0\nx = 9/2\nx = 5\nx = 13/9"} {"input": "Find the solution to 2x - 2/7 = 0", "output": "2x - 2/7 = 0\n2x = 2/7\nx = 2/7 / 2\nx = 1/7"} {"input": "Solve the equations:\n7x + 5y = 215/24\n8x + 10y = 20/3", "output": "7x + 5y = 215/24\n8x + 10y = 20/3\n\nUsing elimination\n8*(7x + 5y = 215/24)\n7*(8x + 10y = 20/3)\n56x + 40y = 215/3\n56x + 70y = 140/3\nSubtract equations\n-30y = 25\ny = 25/-30\ny = -5/6\n\nSubstitute y\n7x + 5(-5/6) = 215/24\n7x = 105/8\nx = 105/8/7\nx = 15/8"} {"input": "Find x in x^3 + 17/5x^2 - 37/5x + 3 = 0", "output": "x^3 + 17/5x^2 - 37/5x + 3 = 0\n(x - 3/5)(x - 1)(x - -5) = 0\nx - 3/5 = 0\nx - 1 = 0\nx - -5 = 0\nx = 3/5\nx = 1\nx = -5"} {"input": "What value of x satisfies x^3 - 5/2x^2 - 2x + 3/2 = 0", "output": "x^3 - 5/2x^2 - 2x + 3/2 = 0\n(x - 1/2)(x - -1)(x - 3) = 0\nx - 1/2 = 0\nx - -1 = 0\nx - 3 = 0\nx = 1/2\nx = -1\nx = 3"} {"input": "Find x in 3x - 9 = 0", "output": "3x - 9 = 0\n3x = 9\nx = 9 / 3\nx = 3"} {"input": "Solve the system:\n9x + 9y = 486/7\n6x + 8y = 334/7", "output": "9x + 9y = 486/7\n6x + 8y = 334/7\n\nUsing elimination\n6*(9x + 9y = 486/7)\n9*(6x + 8y = 334/7)\n54x + 54y = 2916/7\n54x + 72y = 3006/7\nSubtract equations\n-18y = -90/7\ny = -90/7/-18\ny = 5/7\n\nSubstitute y\n9x + 9(5/7) = 486/7\n9x = 63\nx = 63/9\nx = 7"} {"input": "Compute the solution of x^3 + 67/6x^2 + 10x - 50/3 = 0", "output": "x^3 + 67/6x^2 + 10x - 50/3 = 0\n(x - 5/6)(x - -10)(x - -2) = 0\nx - 5/6 = 0\nx - -10 = 0\nx - -2 = 0\nx = 5/6\nx = -10\nx = -2"} {"input": "Compute the solution of 5x = 0", "output": "5x = 0\n5x = 0\nx = 0 / 5\nx = 0"} {"input": "Solve the equation x^2 - 5x - 36 = 0", "output": "x^2 - 5x - 36 = 0\n(x - 9)(x - -4) = 0\nx - 9 = 0 or x - -4 = 0\nx = 9\nx = -4"} {"input": "Solve the system:\n9x + 7y = -5/3\n8x + 3y = -52/9", "output": "9x + 7y = -5/3\n8x + 3y = -52/9\n\nUsing elimination\n8*(9x + 7y = -5/3)\n9*(8x + 3y = -52/9)\n72x + 56y = -40/3\n72x + 27y = -52\nSubtract equations\n29y = 116/3\ny = 116/3/29\ny = 4/3\n\nSubstitute y\n9x + 7(4/3) = -5/3\n9x = -11\nx = -11/9\nx = -11/9"} {"input": "Determine x in x^3 + 89/10x^2 - 64/5x - 18 = 0", "output": "x^3 + 89/10x^2 - 64/5x - 18 = 0\n(x - -9/10)(x - 2)(x - -10) = 0\nx - -9/10 = 0\nx - 2 = 0\nx - -10 = 0\nx = -9/10\nx = 2\nx = -10"} {"input": "Solve quickly: x^2 - 49/4x + 285/8 = 0", "output": "x^2 - 49/4x + 285/8 = 0\n(x - 15/2)(x - 19/4) = 0\nx - 15/2 = 0 or x - 19/4 = 0\nx = 15/2\nx = 19/4"} {"input": "Find x in x^3 + 7/4x^2 - 607/8x - 765/8 = 0", "output": "x^3 + 7/4x^2 - 607/8x - 765/8 = 0\n(x - 17/2)(x - -9)(x - -5/4) = 0\nx - 17/2 = 0\nx - -9 = 0\nx - -5/4 = 0\nx = 17/2\nx = -9\nx = -5/4"} {"input": "Find x and y such that\n7x + 2y = 0\n6x + 7y = 37/7", "output": "7x + 2y = 0\n6x + 7y = 37/7\n\nUsing elimination\n6*(7x + 2y = 0)\n7*(6x + 7y = 37/7)\n42x + 12y = 0\n42x + 49y = 37\nSubtract equations\n-37y = -37\ny = -37/-37\ny = 1\n\nSubstitute y\n7x + 2(1) = 0\n7x = -2\nx = -2/7\nx = -2/7"} {"input": "Solve the equations:\n8x + 6y = -25\n8x + 8y = -27", "output": "8x + 6y = -25\n8x + 8y = -27\n\nUsing elimination\n8*(8x + 6y = -25)\n8*(8x + 8y = -27)\n64x + 48y = -200\n64x + 64y = -216\nSubtract equations\n-16y = 16\ny = 16/-16\ny = -1\n\nSubstitute y\n8x + 6(-1) = -25\n8x = -19\nx = -19/8\nx = -19/8"} {"input": "Solve simultaneously:\n9x + 4y = -177/5\n6x + 9y = -213/5", "output": "9x + 4y = -177/5\n6x + 9y = -213/5\n\nUsing elimination\n6*(9x + 4y = -177/5)\n9*(6x + 9y = -213/5)\n54x + 24y = -1062/5\n54x + 81y = -1917/5\nSubtract equations\n-57y = 171\ny = 171/-57\ny = -3\n\nSubstitute y\n9x + 4(-3) = -177/5\n9x = -117/5\nx = -117/5/9\nx = -13/5"} {"input": "Find the solution to x^2 - 221/70x + 169/70 = 0", "output": "x^2 - 221/70x + 169/70 = 0\n(x - 13/7)(x - 13/10) = 0\nx - 13/7 = 0 or x - 13/10 = 0\nx = 13/7\nx = 13/10"} {"input": "Solve x^3 + 5/6x^2 - 493/3x + 1445/2 = 0", "output": "x^3 + 5/6x^2 - 493/3x + 1445/2 = 0\n(x - -15)(x - 17/2)(x - 17/3) = 0\nx - -15 = 0\nx - 17/2 = 0\nx - 17/3 = 0\nx = -15\nx = 17/2\nx = 17/3"} {"input": "Find x for x^2 - 115/12x + 68/3 = 0", "output": "x^2 - 115/12x + 68/3 = 0\n(x - 17/4)(x - 16/3) = 0\nx - 17/4 = 0 or x - 16/3 = 0\nx = 17/4\nx = 16/3"} {"input": "Solve simultaneously:\n6x + 9y = -142/5\n4x + 7y = -922/45", "output": "6x + 9y = -142/5\n4x + 7y = -922/45\n\nUsing elimination\n4*(6x + 9y = -142/5)\n6*(4x + 7y = -922/45)\n24x + 36y = -568/5\n24x + 42y = -1844/15\nSubtract equations\n-6y = 28/3\ny = 28/3/-6\ny = -14/9\n\nSubstitute y\n6x + 9(-14/9) = -142/5\n6x = -72/5\nx = -72/5/6\nx = -12/5"} {"input": "Find x and y such that\n6x + 10y = -58/3\n1x + 7y = 17/3", "output": "6x + 10y = -58/3\n1x + 7y = 17/3\n\nUsing elimination\n1*(6x + 10y = -58/3)\n6*(1x + 7y = 17/3)\n6x + 10y = -58/3\n6x + 42y = 34\nSubtract equations\n-32y = -160/3\ny = -160/3/-32\ny = 5/3\n\nSubstitute y\n6x + 10(5/3) = -58/3\n6x = -36\nx = -36/6\nx = -6"} {"input": "Solve the system:\n10x + 9y = 88\n4x + 8y = 77", "output": "10x + 9y = 88\n4x + 8y = 77\n\nUsing elimination\n4*(10x + 9y = 88)\n10*(4x + 8y = 77)\n40x + 36y = 352\n40x + 80y = 770\nSubtract equations\n-44y = -418\ny = -418/-44\ny = 19/2\n\nSubstitute y\n10x + 9(19/2) = 88\n10x = 5/2\nx = 5/2/10\nx = 1/4"} {"input": "Solve quickly: 8x - 112/9 = 0", "output": "8x - 112/9 = 0\n8x = 112/9\nx = 112/9 / 8\nx = 14/9"} {"input": "Solve the system:\n1x + 1y = 11/3\n7x + 2y = 67/3", "output": "1x + 1y = 11/3\n7x + 2y = 67/3\n\nUsing elimination\n7*(1x + 1y = 11/3)\n1*(7x + 2y = 67/3)\n7x + 7y = 77/3\n7x + 2y = 67/3\nSubtract equations\n5y = 10/3\ny = 10/3/5\ny = 2/3\n\nSubstitute y\n1x + 1(2/3) = 11/3\n1x = 3\nx = 3/1\nx = 3"} {"input": "Solve simultaneously:\n1x + 8y = 129\n4x + 7y = 116", "output": "1x + 8y = 129\n4x + 7y = 116\n\nUsing elimination\n4*(1x + 8y = 129)\n1*(4x + 7y = 116)\n4x + 32y = 516\n4x + 7y = 116\nSubtract equations\n25y = 400\ny = 400/25\ny = 16\n\nSubstitute y\n1x + 8(16) = 129\n1x = 1\nx = 1/1\nx = 1"} {"input": "Compute the solution of x^2 - 11/3x - 48 = 0", "output": "x^2 - 11/3x - 48 = 0\n(x - -16/3)(x - 9) = 0\nx - -16/3 = 0 or x - 9 = 0\nx = -16/3\nx = 9"} {"input": "Determine x in 9x + 20 = 0", "output": "9x + 20 = 0\n9x = -20\nx = -20 / 9\nx = -20/9"} {"input": "Compute the solution of 9x + 108/5 = 0", "output": "9x + 108/5 = 0\n9x = -108/5\nx = -108/5 / 9\nx = -12/5"} {"input": "Determine x in x^2 - 112/15x + 196/15 = 0", "output": "x^2 - 112/15x + 196/15 = 0\n(x - 14/3)(x - 14/5) = 0\nx - 14/3 = 0 or x - 14/5 = 0\nx = 14/3\nx = 14/5"} {"input": "Compute the solution of 6x - 48/5 = 0", "output": "6x - 48/5 = 0\n6x = 48/5\nx = 48/5 / 6\nx = 8/5"} {"input": "Solve the system:\n1x + 3y = -43/10\n7x + 10y = -191/10", "output": "1x + 3y = -43/10\n7x + 10y = -191/10\n\nUsing elimination\n7*(1x + 3y = -43/10)\n1*(7x + 10y = -191/10)\n7x + 21y = -301/10\n7x + 10y = -191/10\nSubtract equations\n11y = -11\ny = -11/11\ny = -1\n\nSubstitute y\n1x + 3(-1) = -43/10\n1x = -13/10\nx = -13/10/1\nx = -13/10"} {"input": "Find the solution to x^2 - 47/9x + 44/9 = 0", "output": "x^2 - 47/9x + 44/9 = 0\n(x - 11/9)(x - 4) = 0\nx - 11/9 = 0 or x - 4 = 0\nx = 11/9\nx = 4"} {"input": "Solve x^2 + 15/4x - 17/8 = 0", "output": "x^2 + 15/4x - 17/8 = 0\n(x - -17/4)(x - 1/2) = 0\nx - -17/4 = 0 or x - 1/2 = 0\nx = -17/4\nx = 1/2"} {"input": "Solve the equations:\n8x + 9y = -871/14\n4x + 5y = -467/14", "output": "8x + 9y = -871/14\n4x + 5y = -467/14\n\nUsing elimination\n4*(8x + 9y = -871/14)\n8*(4x + 5y = -467/14)\n32x + 36y = -1742/7\n32x + 40y = -1868/7\nSubtract equations\n-4y = 18\ny = 18/-4\ny = -9/2\n\nSubstitute y\n8x + 9(-9/2) = -871/14\n8x = -152/7\nx = -152/7/8\nx = -19/7"} {"input": "Find the solution to 5x + 15/2 = 0", "output": "5x + 15/2 = 0\n5x = -15/2\nx = -15/2 / 5\nx = -3/2"} {"input": "Solve quickly: x^3 + 11/7x^2 = 0", "output": "x^3 + 11/7x^2 = 0\n(x - 0)(x - 0)(x - -11/7) = 0\nx - 0 = 0\nx - 0 = 0\nx - -11/7 = 0\nx = 0\nx = 0\nx = -11/7"} {"input": "Find the solution to x^3 - 38/5x^2 - 19/5x + 24/5 = 0", "output": "x^3 - 38/5x^2 - 19/5x + 24/5 = 0\n(x - 3/5)(x - 8)(x - -1) = 0\nx - 3/5 = 0\nx - 8 = 0\nx - -1 = 0\nx = 3/5\nx = 8\nx = -1"} {"input": "Solve the equations:\n10x + 10y = 185/3\n8x + 7y = 133/3", "output": "10x + 10y = 185/3\n8x + 7y = 133/3\n\nUsing elimination\n8*(10x + 10y = 185/3)\n10*(8x + 7y = 133/3)\n80x + 80y = 1480/3\n80x + 70y = 1330/3\nSubtract equations\n10y = 50\ny = 50/10\ny = 5\n\nSubstitute y\n10x + 10(5) = 185/3\n10x = 35/3\nx = 35/3/10\nx = 7/6"} {"input": "Find the solution to x^3 - 37/6x^2 + 97/12x - 21/8 = 0", "output": "x^3 - 37/6x^2 + 97/12x - 21/8 = 0\n(x - 7/6)(x - 9/2)(x - 1/2) = 0\nx - 7/6 = 0\nx - 9/2 = 0\nx - 1/2 = 0\nx = 7/6\nx = 9/2\nx = 1/2"} {"input": "Find x in x^2 - 12/7x - 19/7 = 0", "output": "x^2 - 12/7x - 19/7 = 0\n(x - 19/7)(x - -1) = 0\nx - 19/7 = 0 or x - -1 = 0\nx = 19/7\nx = -1"} {"input": "What value of x satisfies 9x + 3/2 = 0", "output": "9x + 3/2 = 0\n9x = -3/2\nx = -3/2 / 9\nx = -1/6"} {"input": "Solve the equation 3x - 1 = 0", "output": "3x - 1 = 0\n3x = 1\nx = 1 / 3\nx = 1/3"} {"input": "Solve the system:\n4x + 7y = -29\n6x + 8y = -67/2", "output": "4x + 7y = -29\n6x + 8y = -67/2\n\nUsing elimination\n6*(4x + 7y = -29)\n4*(6x + 8y = -67/2)\n24x + 42y = -174\n24x + 32y = -134\nSubtract equations\n10y = -40\ny = -40/10\ny = -4\n\nSubstitute y\n4x + 7(-4) = -29\n4x = -1\nx = -1/4\nx = -1/4"} {"input": "Find x in x^2 - 31/8x + 15/32 = 0", "output": "x^2 - 31/8x + 15/32 = 0\n(x - 15/4)(x - 1/8) = 0\nx - 15/4 = 0 or x - 1/8 = 0\nx = 15/4\nx = 1/8"} {"input": "What value of x satisfies x^2 + 27/2x + 81/2 = 0", "output": "x^2 + 27/2x + 81/2 = 0\n(x - -9/2)(x - -9) = 0\nx - -9/2 = 0 or x - -9 = 0\nx = -9/2\nx = -9"} {"input": "Determine x in x^3 - 61/20x^2 - 235/8x - 30 = 0", "output": "x^3 - 61/20x^2 - 235/8x - 30 = 0\n(x - 15/2)(x - -5/4)(x - -16/5) = 0\nx - 15/2 = 0\nx - -5/4 = 0\nx - -16/5 = 0\nx = 15/2\nx = -5/4\nx = -16/5"} {"input": "Determine x in x^3 - 203/180x^2 - 2537/180x - 133/9 = 0", "output": "x^3 - 203/180x^2 - 2537/180x - 133/9 = 0\n(x - -7/5)(x - 19/4)(x - -20/9) = 0\nx - -7/5 = 0\nx - 19/4 = 0\nx - -20/9 = 0\nx = -7/5\nx = 19/4\nx = -20/9"} {"input": "Solve 8x - 144/7 = 0", "output": "8x - 144/7 = 0\n8x = 144/7\nx = 144/7 / 8\nx = 18/7"} {"input": "Solve the equation x^3 + 18/5x^2 - 1563/20x - 4199/20 = 0", "output": "x^3 + 18/5x^2 - 1563/20x - 4199/20 = 0\n(x - -13/5)(x - 17/2)(x - -19/2) = 0\nx - -13/5 = 0\nx - 17/2 = 0\nx - -19/2 = 0\nx = -13/5\nx = 17/2\nx = -19/2"} {"input": "Solve 4x - 12 = 0", "output": "4x - 12 = 0\n4x = 12\nx = 12 / 4\nx = 3"} {"input": "Solve the equations:\n4x + 3y = -195/2\n2x + 1y = -89/2", "output": "4x + 3y = -195/2\n2x + 1y = -89/2\n\nUsing elimination\n2*(4x + 3y = -195/2)\n4*(2x + 1y = -89/2)\n8x + 6y = -195\n8x + 4y = -178\nSubtract equations\n2y = -17\ny = -17/2\ny = -17/2\n\nSubstitute y\n4x + 3(-17/2) = -195/2\n4x = -72\nx = -72/4\nx = -18"} {"input": "Find x and y such that\n2x + 5y = -199/12\n10x + 1y = -347/12", "output": "2x + 5y = -199/12\n10x + 1y = -347/12\n\nUsing elimination\n10*(2x + 5y = -199/12)\n2*(10x + 1y = -347/12)\n20x + 50y = -995/6\n20x + 2y = -347/6\nSubtract equations\n48y = -108\ny = -108/48\ny = -9/4\n\nSubstitute y\n2x + 5(-9/4) = -199/12\n2x = -16/3\nx = -16/3/2\nx = -8/3"} {"input": "Compute the solution of 7x - 56/3 = 0", "output": "7x - 56/3 = 0\n7x = 56/3\nx = 56/3 / 7\nx = 8/3"} {"input": "Solve quickly: 9x + 99/10 = 0", "output": "9x + 99/10 = 0\n9x = -99/10\nx = -99/10 / 9\nx = -11/10"} {"input": "Solve the equations:\n10x + 9y = 211/7\n2x + 3y = 319/35", "output": "10x + 9y = 211/7\n2x + 3y = 319/35\n\nUsing elimination\n2*(10x + 9y = 211/7)\n10*(2x + 3y = 319/35)\n20x + 18y = 422/7\n20x + 30y = 638/7\nSubtract equations\n-12y = -216/7\ny = -216/7/-12\ny = 18/7\n\nSubstitute y\n10x + 9(18/7) = 211/7\n10x = 7\nx = 7/10\nx = 7/10"} {"input": "Find x for 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve x^3 + 25/18x^2 - 2443/450x - 931/225 = 0", "output": "x^3 + 25/18x^2 - 2443/450x - 931/225 = 0\n(x - -14/5)(x - -7/10)(x - 19/9) = 0\nx - -14/5 = 0\nx - -7/10 = 0\nx - 19/9 = 0\nx = -14/5\nx = -7/10\nx = 19/9"} {"input": "Solve the system:\n8x + 9y = 146/7\n2x + 4y = 54/7", "output": "8x + 9y = 146/7\n2x + 4y = 54/7\n\nUsing elimination\n2*(8x + 9y = 146/7)\n8*(2x + 4y = 54/7)\n16x + 18y = 292/7\n16x + 32y = 432/7\nSubtract equations\n-14y = -20\ny = -20/-14\ny = 10/7\n\nSubstitute y\n8x + 9(10/7) = 146/7\n8x = 8\nx = 8/8\nx = 1"} {"input": "Solve x^2 - 20/3x + 25/3 = 0", "output": "x^2 - 20/3x + 25/3 = 0\n(x - 5/3)(x - 5) = 0\nx - 5/3 = 0 or x - 5 = 0\nx = 5/3\nx = 5"} {"input": "Solve the system:\n8x + 10y = 160/9\n10x + 6y = 200/9", "output": "8x + 10y = 160/9\n10x + 6y = 200/9\n\nUsing elimination\n10*(8x + 10y = 160/9)\n8*(10x + 6y = 200/9)\n80x + 100y = 1600/9\n80x + 48y = 1600/9\nSubtract equations\n52y = 0\ny = 0/52\ny = 0\n\nSubstitute y\n8x + 10(0) = 160/9\n8x = 160/9\nx = 160/9/8\nx = 20/9"} {"input": "Solve the system:\n5x + 3y = 71/3\n8x + 2y = 352/9", "output": "5x + 3y = 71/3\n8x + 2y = 352/9\n\nUsing elimination\n8*(5x + 3y = 71/3)\n5*(8x + 2y = 352/9)\n40x + 24y = 568/3\n40x + 10y = 1760/9\nSubtract equations\n14y = -56/9\ny = -56/9/14\ny = -4/9\n\nSubstitute y\n5x + 3(-4/9) = 71/3\n5x = 25\nx = 25/5\nx = 5"} {"input": "Find x and y such that\n5x + 10y = 118/7\n2x + 10y = 506/35", "output": "5x + 10y = 118/7\n2x + 10y = 506/35\n\nUsing elimination\n2*(5x + 10y = 118/7)\n5*(2x + 10y = 506/35)\n10x + 20y = 236/7\n10x + 50y = 506/7\nSubtract equations\n-30y = -270/7\ny = -270/7/-30\ny = 9/7\n\nSubstitute y\n5x + 10(9/7) = 118/7\n5x = 4\nx = 4/5\nx = 4/5"} {"input": "Compute the solution of 3x - 1 = 0", "output": "3x - 1 = 0\n3x = 1\nx = 1 / 3\nx = 1/3"} {"input": "Solve the equation x^2 + 1/10x - 91/50 = 0", "output": "x^2 + 1/10x - 91/50 = 0\n(x - -7/5)(x - 13/10) = 0\nx - -7/5 = 0 or x - 13/10 = 0\nx = -7/5\nx = 13/10"} {"input": "Find x for x^2 - 37/9x + 104/27 = 0", "output": "x^2 - 37/9x + 104/27 = 0\n(x - 13/9)(x - 8/3) = 0\nx - 13/9 = 0 or x - 8/3 = 0\nx = 13/9\nx = 8/3"} {"input": "Find the solution to 1x - 10/9 = 0", "output": "1x - 10/9 = 0\n1x = 10/9\nx = 10/9 / 1\nx = 10/9"} {"input": "Solve quickly: x^2 + 89/30x - 77/30 = 0", "output": "x^2 + 89/30x - 77/30 = 0\n(x - -11/3)(x - 7/10) = 0\nx - -11/3 = 0 or x - 7/10 = 0\nx = -11/3\nx = 7/10"} {"input": "Compute the solution of x^2 + 10/3x + 1 = 0", "output": "x^2 + 10/3x + 1 = 0\n(x - -1/3)(x - -3) = 0\nx - -1/3 = 0 or x - -3 = 0\nx = -1/3\nx = -3"} {"input": "Find x and y such that\n7x + 1y = -65/4\n9x + 7y = -135/4", "output": "7x + 1y = -65/4\n9x + 7y = -135/4\n\nUsing elimination\n9*(7x + 1y = -65/4)\n7*(9x + 7y = -135/4)\n63x + 9y = -585/4\n63x + 49y = -945/4\nSubtract equations\n-40y = 90\ny = 90/-40\ny = -9/4\n\nSubstitute y\n7x + 1(-9/4) = -65/4\n7x = -14\nx = -14/7\nx = -2"} {"input": "Solve 5x + 75/8 = 0", "output": "5x + 75/8 = 0\n5x = -75/8\nx = -75/8 / 5\nx = -15/8"} {"input": "Solve the equation 9x - 5 = 0", "output": "9x - 5 = 0\n9x = 5\nx = 5 / 9\nx = 5/9"} {"input": "Find the solution to x^2 + 26/9x - 95/9 = 0", "output": "x^2 + 26/9x - 95/9 = 0\n(x - 19/9)(x - -5) = 0\nx - 19/9 = 0 or x - -5 = 0\nx = 19/9\nx = -5"} {"input": "Solve x^3 + 3/2x^2 - 199/16x - 51/16 = 0", "output": "x^3 + 3/2x^2 - 199/16x - 51/16 = 0\n(x - -1/4)(x - -17/4)(x - 3) = 0\nx - -1/4 = 0\nx - -17/4 = 0\nx - 3 = 0\nx = -1/4\nx = -17/4\nx = 3"} {"input": "Solve x^2 + 15/4x + 13/8 = 0", "output": "x^2 + 15/4x + 13/8 = 0\n(x - -13/4)(x - -1/2) = 0\nx - -13/4 = 0 or x - -1/2 = 0\nx = -13/4\nx = -1/2"} {"input": "Solve simultaneously:\n4x + 6y = -252/5\n4x + 3y = -117/5", "output": "4x + 6y = -252/5\n4x + 3y = -117/5\n\nUsing elimination\n4*(4x + 6y = -252/5)\n4*(4x + 3y = -117/5)\n16x + 24y = -1008/5\n16x + 12y = -468/5\nSubtract equations\n12y = -108\ny = -108/12\ny = -9\n\nSubstitute y\n4x + 6(-9) = -252/5\n4x = 18/5\nx = 18/5/4\nx = 9/10"} {"input": "Determine x in x^2 + 49/18x + 49/27 = 0", "output": "x^2 + 49/18x + 49/27 = 0\n(x - -7/6)(x - -14/9) = 0\nx - -7/6 = 0 or x - -14/9 = 0\nx = -7/6\nx = -14/9"} {"input": "Find x for 8x - 160 = 0", "output": "8x - 160 = 0\n8x = 160\nx = 160 / 8\nx = 20"} {"input": "Solve quickly: x^2 + 5/2x - 25/2 = 0", "output": "x^2 + 5/2x - 25/2 = 0\n(x - -5)(x - 5/2) = 0\nx - -5 = 0 or x - 5/2 = 0\nx = -5\nx = 5/2"} {"input": "Determine x in x^3 + 362/63x^2 + 1247/189x + 130/63 = 0", "output": "x^3 + 362/63x^2 + 1247/189x + 130/63 = 0\n(x - -5/9)(x - -13/3)(x - -6/7) = 0\nx - -5/9 = 0\nx - -13/3 = 0\nx - -6/7 = 0\nx = -5/9\nx = -13/3\nx = -6/7"} {"input": "Solve quickly: x^3 - 415/72x^2 + 1549/144x - 935/144 = 0", "output": "x^3 - 415/72x^2 + 1549/144x - 935/144 = 0\n(x - 11/8)(x - 5/2)(x - 17/9) = 0\nx - 11/8 = 0\nx - 5/2 = 0\nx - 17/9 = 0\nx = 11/8\nx = 5/2\nx = 17/9"} {"input": "Solve the system:\n10x + 5y = 30\n5x + 2y = 31/2", "output": "10x + 5y = 30\n5x + 2y = 31/2\n\nUsing elimination\n5*(10x + 5y = 30)\n10*(5x + 2y = 31/2)\n50x + 25y = 150\n50x + 20y = 155\nSubtract equations\n5y = -5\ny = -5/5\ny = -1\n\nSubstitute y\n10x + 5(-1) = 30\n10x = 35\nx = 35/10\nx = 7/2"} {"input": "Find x and y such that\n2x + 8y = -44/3\n2x + 5y = -61/6", "output": "2x + 8y = -44/3\n2x + 5y = -61/6\n\nUsing elimination\n2*(2x + 8y = -44/3)\n2*(2x + 5y = -61/6)\n4x + 16y = -88/3\n4x + 10y = -61/3\nSubtract equations\n6y = -9\ny = -9/6\ny = -3/2\n\nSubstitute y\n2x + 8(-3/2) = -44/3\n2x = -8/3\nx = -8/3/2\nx = -4/3"} {"input": "Solve the equations:\n6x + 1y = -217/15\n1x + 9y = 91/5", "output": "6x + 1y = -217/15\n1x + 9y = 91/5\n\nUsing elimination\n1*(6x + 1y = -217/15)\n6*(1x + 9y = 91/5)\n6x + 1y = -217/15\n6x + 54y = 546/5\nSubtract equations\n-53y = -371/3\ny = -371/3/-53\ny = 7/3\n\nSubstitute y\n6x + 1(7/3) = -217/15\n6x = -84/5\nx = -84/5/6\nx = -14/5"} {"input": "Determine x in 3x - 12/7 = 0", "output": "3x - 12/7 = 0\n3x = 12/7\nx = 12/7 / 3\nx = 4/7"} {"input": "Find the solution to 10x - 10 = 0", "output": "10x - 10 = 0\n10x = 10\nx = 10 / 10\nx = 1"} {"input": "Solve x^3 - 19/10x^2 + 73/80x - 1/8 = 0", "output": "x^3 - 19/10x^2 + 73/80x - 1/8 = 0\n(x - 2/5)(x - 1/4)(x - 5/4) = 0\nx - 2/5 = 0\nx - 1/4 = 0\nx - 5/4 = 0\nx = 2/5\nx = 1/4\nx = 5/4"} {"input": "What value of x satisfies x^3 + 983/280x^2 + 11/5x - 48/35 = 0", "output": "x^3 + 983/280x^2 + 11/5x - 48/35 = 0\n(x - 3/8)(x - -8/5)(x - -16/7) = 0\nx - 3/8 = 0\nx - -8/5 = 0\nx - -16/7 = 0\nx = 3/8\nx = -8/5\nx = -16/7"} {"input": "Find x in x^3 + 37/3x^2 - 140x + 800/3 = 0", "output": "x^3 + 37/3x^2 - 140x + 800/3 = 0\n(x - 5)(x - 8/3)(x - -20) = 0\nx - 5 = 0\nx - 8/3 = 0\nx - -20 = 0\nx = 5\nx = 8/3\nx = -20"} {"input": "Find the solution to 8x - 40/3 = 0", "output": "8x - 40/3 = 0\n8x = 40/3\nx = 40/3 / 8\nx = 5/3"} {"input": "Find the solution to x^2 - 37/14x + 15/14 = 0", "output": "x^2 - 37/14x + 15/14 = 0\n(x - 1/2)(x - 15/7) = 0\nx - 1/2 = 0 or x - 15/7 = 0\nx = 1/2\nx = 15/7"} {"input": "Find x for 9x - 54 = 0", "output": "9x - 54 = 0\n9x = 54\nx = 54 / 9\nx = 6"} {"input": "Solve the equations:\n6x + 3y = 12\n8x + 2y = 66/5", "output": "6x + 3y = 12\n8x + 2y = 66/5\n\nUsing elimination\n8*(6x + 3y = 12)\n6*(8x + 2y = 66/5)\n48x + 24y = 96\n48x + 12y = 396/5\nSubtract equations\n12y = 84/5\ny = 84/5/12\ny = 7/5\n\nSubstitute y\n6x + 3(7/5) = 12\n6x = 39/5\nx = 39/5/6\nx = 13/10"} {"input": "Find x for x^3 - 581/72x^2 - 917/144x + 1105/48 = 0", "output": "x^3 - 581/72x^2 - 917/144x + 1105/48 = 0\n(x - -15/8)(x - 13/9)(x - 17/2) = 0\nx - -15/8 = 0\nx - 13/9 = 0\nx - 17/2 = 0\nx = -15/8\nx = 13/9\nx = 17/2"} {"input": "Solve simultaneously:\n1x + 5y = -29/6\n5x + 8y = -82/15", "output": "1x + 5y = -29/6\n5x + 8y = -82/15\n\nUsing elimination\n5*(1x + 5y = -29/6)\n1*(5x + 8y = -82/15)\n5x + 25y = -145/6\n5x + 8y = -82/15\nSubtract equations\n17y = -187/10\ny = -187/10/17\ny = -11/10\n\nSubstitute y\n1x + 5(-11/10) = -29/6\n1x = 2/3\nx = 2/3/1\nx = 2/3"} {"input": "Compute the solution of x^2 + 23/15x + 2/5 = 0", "output": "x^2 + 23/15x + 2/5 = 0\n(x - -6/5)(x - -1/3) = 0\nx - -6/5 = 0 or x - -1/3 = 0\nx = -6/5\nx = -1/3"} {"input": "Solve the equation 5x - 5/8 = 0", "output": "5x - 5/8 = 0\n5x = 5/8\nx = 5/8 / 5\nx = 1/8"} {"input": "Find the solution to x^3 + 10/3x^2 + 28/9x + 8/9 = 0", "output": "x^3 + 10/3x^2 + 28/9x + 8/9 = 0\n(x - -2/3)(x - -2)(x - -2/3) = 0\nx - -2/3 = 0\nx - -2 = 0\nx - -2/3 = 0\nx = -2/3\nx = -2\nx = -2/3"} {"input": "Find the solution to x^3 - 377/105x^2 + 4/5x + 4/21 = 0", "output": "x^3 - 377/105x^2 + 4/5x + 4/21 = 0\n(x - -1/7)(x - 10/3)(x - 2/5) = 0\nx - -1/7 = 0\nx - 10/3 = 0\nx - 2/5 = 0\nx = -1/7\nx = 10/3\nx = 2/5"} {"input": "Compute the solution of 8x + 40/7 = 0", "output": "8x + 40/7 = 0\n8x = -40/7\nx = -40/7 / 8\nx = -5/7"} {"input": "Solve quickly: x^2 + 7/5x - 51/100 = 0", "output": "x^2 + 7/5x - 51/100 = 0\n(x - 3/10)(x - -17/10) = 0\nx - 3/10 = 0 or x - -17/10 = 0\nx = 3/10\nx = -17/10"} {"input": "Solve x^2 - 32/21x - 64/21 = 0", "output": "x^2 - 32/21x - 64/21 = 0\n(x - 8/3)(x - -8/7) = 0\nx - 8/3 = 0 or x - -8/7 = 0\nx = 8/3\nx = -8/7"} {"input": "Determine x in x^3 - 37/10x^2 - 31/5x - 3/2 = 0", "output": "x^3 - 37/10x^2 - 31/5x - 3/2 = 0\n(x - -1)(x - -3/10)(x - 5) = 0\nx - -1 = 0\nx - -3/10 = 0\nx - 5 = 0\nx = -1\nx = -3/10\nx = 5"} {"input": "Solve x^2 + 23/6x - 3 = 0", "output": "x^2 + 23/6x - 3 = 0\n(x - -9/2)(x - 2/3) = 0\nx - -9/2 = 0 or x - 2/3 = 0\nx = -9/2\nx = 2/3"} {"input": "Solve x^2 - 7/4x - 11/4 = 0", "output": "x^2 - 7/4x - 11/4 = 0\n(x - 11/4)(x - -1) = 0\nx - 11/4 = 0 or x - -1 = 0\nx = 11/4\nx = -1"} {"input": "Find x for x^3 - 74/315x^2 - 141/35x + 16/7 = 0", "output": "x^3 - 74/315x^2 - 141/35x + 16/7 = 0\n(x - -15/7)(x - 3/5)(x - 16/9) = 0\nx - -15/7 = 0\nx - 3/5 = 0\nx - 16/9 = 0\nx = -15/7\nx = 3/5\nx = 16/9"} {"input": "What value of x satisfies x^2 - 47/3x - 16/3 = 0", "output": "x^2 - 47/3x - 16/3 = 0\n(x - 16)(x - -1/3) = 0\nx - 16 = 0 or x - -1/3 = 0\nx = 16\nx = -1/3"} {"input": "What value of x satisfies 4x + 4/5 = 0", "output": "4x + 4/5 = 0\n4x = -4/5\nx = -4/5 / 4\nx = -1/5"} {"input": "Solve simultaneously:\n4x + 10y = 0\n2x + 4y = -1", "output": "4x + 10y = 0\n2x + 4y = -1\n\nUsing elimination\n2*(4x + 10y = 0)\n4*(2x + 4y = -1)\n8x + 20y = 0\n8x + 16y = -4\nSubtract equations\n4y = 4\ny = 4/4\ny = 1\n\nSubstitute y\n4x + 10(1) = 0\n4x = -10\nx = -10/4\nx = -5/2"} {"input": "Find x for 10x + 20 = 0", "output": "10x + 20 = 0\n10x = -20\nx = -20 / 10\nx = -2"} {"input": "Find x in x^2 + 11/15x - 26/3 = 0", "output": "x^2 + 11/15x - 26/3 = 0\n(x - -10/3)(x - 13/5) = 0\nx - -10/3 = 0 or x - 13/5 = 0\nx = -10/3\nx = 13/5"} {"input": "Solve x^3 - 31/6x^2 + 64/9x - 11/6 = 0", "output": "x^3 - 31/6x^2 + 64/9x - 11/6 = 0\n(x - 11/6)(x - 3)(x - 1/3) = 0\nx - 11/6 = 0\nx - 3 = 0\nx - 1/3 = 0\nx = 11/6\nx = 3\nx = 1/3"} {"input": "Solve the equations:\n8x + 2y = -32\n1x + 6y = -27", "output": "8x + 2y = -32\n1x + 6y = -27\n\nUsing elimination\n1*(8x + 2y = -32)\n8*(1x + 6y = -27)\n8x + 2y = -32\n8x + 48y = -216\nSubtract equations\n-46y = 184\ny = 184/-46\ny = -4\n\nSubstitute y\n8x + 2(-4) = -32\n8x = -24\nx = -24/8\nx = -3"} {"input": "What value of x satisfies x^2 - 8x + 12 = 0", "output": "x^2 - 8x + 12 = 0\n(x - 2)(x - 6) = 0\nx - 2 = 0 or x - 6 = 0\nx = 2\nx = 6"} {"input": "Compute the solution of x^2 - 17/5x + 14/5 = 0", "output": "x^2 - 17/5x + 14/5 = 0\n(x - 7/5)(x - 2) = 0\nx - 7/5 = 0 or x - 2 = 0\nx = 7/5\nx = 2"} {"input": "Find x for x^3 - 183/14x^2 - 885/14x - 425/7 = 0", "output": "x^3 - 183/14x^2 - 885/14x - 425/7 = 0\n(x - -10/7)(x - -5/2)(x - 17) = 0\nx - -10/7 = 0\nx - -5/2 = 0\nx - 17 = 0\nx = -10/7\nx = -5/2\nx = 17"} {"input": "Compute the solution of 8x - 64/3 = 0", "output": "8x - 64/3 = 0\n8x = 64/3\nx = 64/3 / 8\nx = 8/3"} {"input": "Solve 6x - 18 = 0", "output": "6x - 18 = 0\n6x = 18\nx = 18 / 6\nx = 3"} {"input": "Compute the solution of 2x - 17/2 = 0", "output": "2x - 17/2 = 0\n2x = 17/2\nx = 17/2 / 2\nx = 17/4"} {"input": "Solve simultaneously:\n4x + 2y = -26/21\n7x + 10y = -52/3", "output": "4x + 2y = -26/21\n7x + 10y = -52/3\n\nUsing elimination\n7*(4x + 2y = -26/21)\n4*(7x + 10y = -52/3)\n28x + 14y = -26/3\n28x + 40y = -208/3\nSubtract equations\n-26y = 182/3\ny = 182/3/-26\ny = -7/3\n\nSubstitute y\n4x + 2(-7/3) = -26/21\n4x = 24/7\nx = 24/7/4\nx = 6/7"} {"input": "Find x in x^3 - 16/3x^2 - 212/9x + 160/9 = 0", "output": "x^3 - 16/3x^2 - 212/9x + 160/9 = 0\n(x - -10/3)(x - 2/3)(x - 8) = 0\nx - -10/3 = 0\nx - 2/3 = 0\nx - 8 = 0\nx = -10/3\nx = 2/3\nx = 8"} {"input": "Find x and y such that\n9x + 8y = 103/3\n8x + 4y = 76/3", "output": "9x + 8y = 103/3\n8x + 4y = 76/3\n\nUsing elimination\n8*(9x + 8y = 103/3)\n9*(8x + 4y = 76/3)\n72x + 64y = 824/3\n72x + 36y = 228\nSubtract equations\n28y = 140/3\ny = 140/3/28\ny = 5/3\n\nSubstitute y\n9x + 8(5/3) = 103/3\n9x = 21\nx = 21/9\nx = 7/3"} {"input": "Solve quickly: 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Find x in 9x + 117/8 = 0", "output": "9x + 117/8 = 0\n9x = -117/8\nx = -117/8 / 9\nx = -13/8"} {"input": "Solve the equation x^3 + 133/90x^2 - 247/135x + 7/18 = 0", "output": "x^3 + 133/90x^2 - 247/135x + 7/18 = 0\n(x - 3/10)(x - -7/3)(x - 5/9) = 0\nx - 3/10 = 0\nx - -7/3 = 0\nx - 5/9 = 0\nx = 3/10\nx = -7/3\nx = 5/9"} {"input": "Find x in x^3 + 1/3x^2 - 95/48x + 7/8 = 0", "output": "x^3 + 1/3x^2 - 95/48x + 7/8 = 0\n(x - 3/4)(x - 2/3)(x - -7/4) = 0\nx - 3/4 = 0\nx - 2/3 = 0\nx - -7/4 = 0\nx = 3/4\nx = 2/3\nx = -7/4"} {"input": "What value of x satisfies x^3 + 13/3x^2 + 4/9x - 32/3 = 0", "output": "x^3 + 13/3x^2 + 4/9x - 32/3 = 0\n(x - -3)(x - -8/3)(x - 4/3) = 0\nx - -3 = 0\nx - -8/3 = 0\nx - 4/3 = 0\nx = -3\nx = -8/3\nx = 4/3"} {"input": "What value of x satisfies 2x - 40/3 = 0", "output": "2x - 40/3 = 0\n2x = 40/3\nx = 40/3 / 2\nx = 20/3"} {"input": "Solve the equations:\n8x + 7y = 15\n7x + 4y = 11", "output": "8x + 7y = 15\n7x + 4y = 11\n\nUsing elimination\n7*(8x + 7y = 15)\n8*(7x + 4y = 11)\n56x + 49y = 105\n56x + 32y = 88\nSubtract equations\n17y = 17\ny = 17/17\ny = 1\n\nSubstitute y\n8x + 7(1) = 15\n8x = 8\nx = 8/8\nx = 1"} {"input": "Compute the solution of 3x + 17/2 = 0", "output": "3x + 17/2 = 0\n3x = -17/2\nx = -17/2 / 3\nx = -17/6"} {"input": "Solve the equation x^3 + 14/3x^2 - 835/48x - 325/12 = 0", "output": "x^3 + 14/3x^2 - 835/48x - 325/12 = 0\n(x - 13/4)(x - -5/4)(x - -20/3) = 0\nx - 13/4 = 0\nx - -5/4 = 0\nx - -20/3 = 0\nx = 13/4\nx = -5/4\nx = -20/3"} {"input": "Solve x^3 - 21/5x^2 - 101/20x + 21/4 = 0", "output": "x^3 - 21/5x^2 - 101/20x + 21/4 = 0\n(x - 7/10)(x - -3/2)(x - 5) = 0\nx - 7/10 = 0\nx - -3/2 = 0\nx - 5 = 0\nx = 7/10\nx = -3/2\nx = 5"} {"input": "Solve quickly: 8x + 24/5 = 0", "output": "8x + 24/5 = 0\n8x = -24/5\nx = -24/5 / 8\nx = -3/5"} {"input": "What value of x satisfies 8x + 18 = 0", "output": "8x + 18 = 0\n8x = -18\nx = -18 / 8\nx = -9/4"} {"input": "Solve x^3 + 31/2x^2 + 153/2x + 117 = 0", "output": "x^3 + 31/2x^2 + 153/2x + 117 = 0\n(x - -13/2)(x - -6)(x - -3) = 0\nx - -13/2 = 0\nx - -6 = 0\nx - -3 = 0\nx = -13/2\nx = -6\nx = -3"} {"input": "Solve simultaneously:\n9x + 3y = 53\n9x + 2y = 166/3", "output": "9x + 3y = 53\n9x + 2y = 166/3\n\nUsing elimination\n9*(9x + 3y = 53)\n9*(9x + 2y = 166/3)\n81x + 27y = 477\n81x + 18y = 498\nSubtract equations\n9y = -21\ny = -21/9\ny = -7/3\n\nSubstitute y\n9x + 3(-7/3) = 53\n9x = 60\nx = 60/9\nx = 20/3"} {"input": "Find x in x^2 + 71/4x + 247/4 = 0", "output": "x^2 + 71/4x + 247/4 = 0\n(x - -13)(x - -19/4) = 0\nx - -13 = 0 or x - -19/4 = 0\nx = -13\nx = -19/4"} {"input": "Solve the equation x^3 - 185/24x^2 + 43/3x - 95/24 = 0", "output": "x^3 - 185/24x^2 + 43/3x - 95/24 = 0\n(x - 1/3)(x - 5)(x - 19/8) = 0\nx - 1/3 = 0\nx - 5 = 0\nx - 19/8 = 0\nx = 1/3\nx = 5\nx = 19/8"} {"input": "Solve quickly: 10x - 95 = 0", "output": "10x - 95 = 0\n10x = 95\nx = 95 / 10\nx = 19/2"} {"input": "Find x and y such that\n9x + 9y = 75/7\n3x + 8y = 125/7", "output": "9x + 9y = 75/7\n3x + 8y = 125/7\n\nUsing elimination\n3*(9x + 9y = 75/7)\n9*(3x + 8y = 125/7)\n27x + 27y = 225/7\n27x + 72y = 1125/7\nSubtract equations\n-45y = -900/7\ny = -900/7/-45\ny = 20/7\n\nSubstitute y\n9x + 9(20/7) = 75/7\n9x = -15\nx = -15/9\nx = -5/3"} {"input": "Find x for 1x + 7/9 = 0", "output": "1x + 7/9 = 0\n1x = -7/9\nx = -7/9 / 1\nx = -7/9"} {"input": "Solve the system:\n7x + 3y = -136/5\n8x + 10y = -254/5", "output": "7x + 3y = -136/5\n8x + 10y = -254/5\n\nUsing elimination\n8*(7x + 3y = -136/5)\n7*(8x + 10y = -254/5)\n56x + 24y = -1088/5\n56x + 70y = -1778/5\nSubtract equations\n-46y = 138\ny = 138/-46\ny = -3\n\nSubstitute y\n7x + 3(-3) = -136/5\n7x = -91/5\nx = -91/5/7\nx = -13/5"} {"input": "Solve quickly: x^2 - 39/4x - 55/4 = 0", "output": "x^2 - 39/4x - 55/4 = 0\n(x - -5/4)(x - 11) = 0\nx - -5/4 = 0 or x - 11 = 0\nx = -5/4\nx = 11"} {"input": "Solve the system:\n10x + 9y = -1/2\n6x + 5y = 3/2", "output": "10x + 9y = -1/2\n6x + 5y = 3/2\n\nUsing elimination\n6*(10x + 9y = -1/2)\n10*(6x + 5y = 3/2)\n60x + 54y = -3\n60x + 50y = 15\nSubtract equations\n4y = -18\ny = -18/4\ny = -9/2\n\nSubstitute y\n10x + 9(-9/2) = -1/2\n10x = 40\nx = 40/10\nx = 4"} {"input": "Compute the solution of 5x + 5/9 = 0", "output": "5x + 5/9 = 0\n5x = -5/9\nx = -5/9 / 5\nx = -1/9"} {"input": "Solve the equation x^2 - 187/9x + 304/9 = 0", "output": "x^2 - 187/9x + 304/9 = 0\n(x - 19)(x - 16/9) = 0\nx - 19 = 0 or x - 16/9 = 0\nx = 19\nx = 16/9"} {"input": "Find x for x^3 + 52/3x^2 + 251/81x - 3536/81 = 0", "output": "x^3 + 52/3x^2 + 251/81x - 3536/81 = 0\n(x - 13/9)(x - -16/9)(x - -17) = 0\nx - 13/9 = 0\nx - -16/9 = 0\nx - -17 = 0\nx = 13/9\nx = -16/9\nx = -17"} {"input": "Find x in x^2 + 11/3x - 14/3 = 0", "output": "x^2 + 11/3x - 14/3 = 0\n(x - 1)(x - -14/3) = 0\nx - 1 = 0 or x - -14/3 = 0\nx = 1\nx = -14/3"} {"input": "Solve simultaneously:\n5x + 7y = 38/9\n10x + 1y = -145/9", "output": "5x + 7y = 38/9\n10x + 1y = -145/9\n\nUsing elimination\n10*(5x + 7y = 38/9)\n5*(10x + 1y = -145/9)\n50x + 70y = 380/9\n50x + 5y = -725/9\nSubtract equations\n65y = 1105/9\ny = 1105/9/65\ny = 17/9\n\nSubstitute y\n5x + 7(17/9) = 38/9\n5x = -9\nx = -9/5\nx = -9/5"} {"input": "Find the solution to 10x + 65/3 = 0", "output": "10x + 65/3 = 0\n10x = -65/3\nx = -65/3 / 10\nx = -13/6"} {"input": "Solve 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "Determine x in 6x - 60 = 0", "output": "6x - 60 = 0\n6x = 60\nx = 60 / 6\nx = 10"} {"input": "Solve the equation x^2 - 4/9x - 5/9 = 0", "output": "x^2 - 4/9x - 5/9 = 0\n(x - -5/9)(x - 1) = 0\nx - -5/9 = 0 or x - 1 = 0\nx = -5/9\nx = 1"} {"input": "Find the solution to x^3 + 77/15x^2 + 70/9x + 16/5 = 0", "output": "x^3 + 77/15x^2 + 70/9x + 16/5 = 0\n(x - -2/3)(x - -9/5)(x - -8/3) = 0\nx - -2/3 = 0\nx - -9/5 = 0\nx - -8/3 = 0\nx = -2/3\nx = -9/5\nx = -8/3"} {"input": "Find x for x^2 + 8/15x - 28/3 = 0", "output": "x^2 + 8/15x - 28/3 = 0\n(x - 14/5)(x - -10/3) = 0\nx - 14/5 = 0 or x - -10/3 = 0\nx = 14/5\nx = -10/3"} {"input": "Find x and y such that\n5x + 9y = 23/3\n6x + 2y = -4", "output": "5x + 9y = 23/3\n6x + 2y = -4\n\nUsing elimination\n6*(5x + 9y = 23/3)\n5*(6x + 2y = -4)\n30x + 54y = 46\n30x + 10y = -20\nSubtract equations\n44y = 66\ny = 66/44\ny = 3/2\n\nSubstitute y\n5x + 9(3/2) = 23/3\n5x = -35/6\nx = -35/6/5\nx = -7/6"} {"input": "Solve quickly: x^3 - 27/4x^2 + 41/64x + 819/128 = 0", "output": "x^3 - 27/4x^2 + 41/64x + 819/128 = 0\n(x - 9/8)(x - -7/8)(x - 13/2) = 0\nx - 9/8 = 0\nx - -7/8 = 0\nx - 13/2 = 0\nx = 9/8\nx = -7/8\nx = 13/2"} {"input": "Determine x in x^2 - 164/63x + 32/21 = 0", "output": "x^2 - 164/63x + 32/21 = 0\n(x - 8/9)(x - 12/7) = 0\nx - 8/9 = 0 or x - 12/7 = 0\nx = 8/9\nx = 12/7"} {"input": "Find x in x^3 - 59/18x^2 - 29/27x + 28/27 = 0", "output": "x^3 - 59/18x^2 - 29/27x + 28/27 = 0\n(x - 7/2)(x - -2/3)(x - 4/9) = 0\nx - 7/2 = 0\nx - -2/3 = 0\nx - 4/9 = 0\nx = 7/2\nx = -2/3\nx = 4/9"} {"input": "What value of x satisfies 6x - 15 = 0", "output": "6x - 15 = 0\n6x = 15\nx = 15 / 6\nx = 5/2"} {"input": "Determine x in 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve the equation x^3 - 25/21x^2 - 192/7x + 1360/21 = 0", "output": "x^3 - 25/21x^2 - 192/7x + 1360/21 = 0\n(x - 4)(x - -17/3)(x - 20/7) = 0\nx - 4 = 0\nx - -17/3 = 0\nx - 20/7 = 0\nx = 4\nx = -17/3\nx = 20/7"} {"input": "Find x and y such that\n2x + 7y = -14\n3x + 9y = -24", "output": "2x + 7y = -14\n3x + 9y = -24\n\nUsing elimination\n3*(2x + 7y = -14)\n2*(3x + 9y = -24)\n6x + 21y = -42\n6x + 18y = -48\nSubtract equations\n3y = 6\ny = 6/3\ny = 2\n\nSubstitute y\n2x + 7(2) = -14\n2x = -28\nx = -28/2\nx = -14"} {"input": "Solve the system:\n2x + 1y = -37/20\n5x + 3y = -217/40", "output": "2x + 1y = -37/20\n5x + 3y = -217/40\n\nUsing elimination\n5*(2x + 1y = -37/20)\n2*(5x + 3y = -217/40)\n10x + 5y = -37/4\n10x + 6y = -217/20\nSubtract equations\n-1y = 8/5\ny = 8/5/-1\ny = -8/5\n\nSubstitute y\n2x + 1(-8/5) = -37/20\n2x = -1/4\nx = -1/4/2\nx = -1/8"} {"input": "Find x for x^2 + 69/10x - 68/5 = 0", "output": "x^2 + 69/10x - 68/5 = 0\n(x - -17/2)(x - 8/5) = 0\nx - -17/2 = 0 or x - 8/5 = 0\nx = -17/2\nx = 8/5"} {"input": "Find x in x^2 + 109/45x + 22/45 = 0", "output": "x^2 + 109/45x + 22/45 = 0\n(x - -11/5)(x - -2/9) = 0\nx - -11/5 = 0 or x - -2/9 = 0\nx = -11/5\nx = -2/9"} {"input": "Solve simultaneously:\n6x + 3y = -259/3\n9x + 4y = -1162/9", "output": "6x + 3y = -259/3\n9x + 4y = -1162/9\n\nUsing elimination\n9*(6x + 3y = -259/3)\n6*(9x + 4y = -1162/9)\n54x + 27y = -777\n54x + 24y = -2324/3\nSubtract equations\n3y = -7/3\ny = -7/3/3\ny = -7/9\n\nSubstitute y\n6x + 3(-7/9) = -259/3\n6x = -84\nx = -84/6\nx = -14"} {"input": "Determine x in x^2 + 247/63x + 80/21 = 0", "output": "x^2 + 247/63x + 80/21 = 0\n(x - -16/9)(x - -15/7) = 0\nx - -16/9 = 0 or x - -15/7 = 0\nx = -16/9\nx = -15/7"} {"input": "Find x for 4x - 34 = 0", "output": "4x - 34 = 0\n4x = 34\nx = 34 / 4\nx = 17/2"} {"input": "Determine x in x^3 - 161/20x^2 + 389/40x + 91/40 = 0", "output": "x^3 - 161/20x^2 + 389/40x + 91/40 = 0\n(x - -1/5)(x - 7/4)(x - 13/2) = 0\nx - -1/5 = 0\nx - 7/4 = 0\nx - 13/2 = 0\nx = -1/5\nx = 7/4\nx = 13/2"} {"input": "Find x in x^3 - 3/8x^2 - 117/32x + 35/16 = 0", "output": "x^3 - 3/8x^2 - 117/32x + 35/16 = 0\n(x - 5/8)(x - -2)(x - 7/4) = 0\nx - 5/8 = 0\nx - -2 = 0\nx - 7/4 = 0\nx = 5/8\nx = -2\nx = 7/4"} {"input": "Solve the equation x^2 + 17/14x - 6/7 = 0", "output": "x^2 + 17/14x - 6/7 = 0\n(x - 1/2)(x - -12/7) = 0\nx - 1/2 = 0 or x - -12/7 = 0\nx = 1/2\nx = -12/7"} {"input": "Solve the equations:\n4x + 6y = -91/10\n7x + 3y = -131/20", "output": "4x + 6y = -91/10\n7x + 3y = -131/20\n\nUsing elimination\n7*(4x + 6y = -91/10)\n4*(7x + 3y = -131/20)\n28x + 42y = -637/10\n28x + 12y = -131/5\nSubtract equations\n30y = -75/2\ny = -75/2/30\ny = -5/4\n\nSubstitute y\n4x + 6(-5/4) = -91/10\n4x = -8/5\nx = -8/5/4\nx = -2/5"} {"input": "Solve the equation 6x + 108/7 = 0", "output": "6x + 108/7 = 0\n6x = -108/7\nx = -108/7 / 6\nx = -18/7"} {"input": "Solve x^2 + 97/10x + 63/10 = 0", "output": "x^2 + 97/10x + 63/10 = 0\n(x - -9)(x - -7/10) = 0\nx - -9 = 0 or x - -7/10 = 0\nx = -9\nx = -7/10"} {"input": "Compute the solution of 7x + 4 = 0", "output": "7x + 4 = 0\n7x = -4\nx = -4 / 7\nx = -4/7"} {"input": "Solve x^2 - 16x - 17 = 0", "output": "x^2 - 16x - 17 = 0\n(x - -1)(x - 17) = 0\nx - -1 = 0 or x - 17 = 0\nx = -1\nx = 17"} {"input": "Find the solution to x^3 + 13/28x^2 - 59/7x - 165/28 = 0", "output": "x^3 + 13/28x^2 - 59/7x - 165/28 = 0\n(x - -5/7)(x - 3)(x - -11/4) = 0\nx - -5/7 = 0\nx - 3 = 0\nx - -11/4 = 0\nx = -5/7\nx = 3\nx = -11/4"} {"input": "Find x and y such that\n10x + 6y = 147\n7x + 10y = 403/2", "output": "10x + 6y = 147\n7x + 10y = 403/2\n\nUsing elimination\n7*(10x + 6y = 147)\n10*(7x + 10y = 403/2)\n70x + 42y = 1029\n70x + 100y = 2015\nSubtract equations\n-58y = -986\ny = -986/-58\ny = 17\n\nSubstitute y\n10x + 6(17) = 147\n10x = 45\nx = 45/10\nx = 9/2"} {"input": "Solve the system:\n5x + 10y = 255/14\n6x + 5y = 125/7", "output": "5x + 10y = 255/14\n6x + 5y = 125/7\n\nUsing elimination\n6*(5x + 10y = 255/14)\n5*(6x + 5y = 125/7)\n30x + 60y = 765/7\n30x + 25y = 625/7\nSubtract equations\n35y = 20\ny = 20/35\ny = 4/7\n\nSubstitute y\n5x + 10(4/7) = 255/14\n5x = 25/2\nx = 25/2/5\nx = 5/2"} {"input": "Find x for x^3 - 26/3x^2 - 317/3x - 560/3 = 0", "output": "x^3 - 26/3x^2 - 317/3x - 560/3 = 0\n(x - 16)(x - -5)(x - -7/3) = 0\nx - 16 = 0\nx - -5 = 0\nx - -7/3 = 0\nx = 16\nx = -5\nx = -7/3"} {"input": "Find the solution to x^3 + 3/8x^2 - 99/32x + 85/64 = 0", "output": "x^3 + 3/8x^2 - 99/32x + 85/64 = 0\n(x - -17/8)(x - 5/4)(x - 1/2) = 0\nx - -17/8 = 0\nx - 5/4 = 0\nx - 1/2 = 0\nx = -17/8\nx = 5/4\nx = 1/2"} {"input": "Solve the equation x^2 - 127/72x - 5/24 = 0", "output": "x^2 - 127/72x - 5/24 = 0\n(x - 15/8)(x - -1/9) = 0\nx - 15/8 = 0 or x - -1/9 = 0\nx = 15/8\nx = -1/9"} {"input": "Solve the equation 3x + 3 = 0", "output": "3x + 3 = 0\n3x = -3\nx = -3 / 3\nx = -1"} {"input": "Compute the solution of x^2 + 136/21x + 19/21 = 0", "output": "x^2 + 136/21x + 19/21 = 0\n(x - -1/7)(x - -19/3) = 0\nx - -1/7 = 0 or x - -19/3 = 0\nx = -1/7\nx = -19/3"} {"input": "Solve quickly: 6x - 18/5 = 0", "output": "6x - 18/5 = 0\n6x = 18/5\nx = 18/5 / 6\nx = 3/5"} {"input": "What value of x satisfies x^3 - 43/9x^2 + 4/3x + 64/9 = 0", "output": "x^3 - 43/9x^2 + 4/3x + 64/9 = 0\n(x - -1)(x - 4)(x - 16/9) = 0\nx - -1 = 0\nx - 4 = 0\nx - 16/9 = 0\nx = -1\nx = 4\nx = 16/9"} {"input": "Find x in x^2 - 19/56x - 15/56 = 0", "output": "x^2 - 19/56x - 15/56 = 0\n(x - 5/7)(x - -3/8) = 0\nx - 5/7 = 0 or x - -3/8 = 0\nx = 5/7\nx = -3/8"} {"input": "Determine x in x^2 + 19/3x + 26/3 = 0", "output": "x^2 + 19/3x + 26/3 = 0\n(x - -2)(x - -13/3) = 0\nx - -2 = 0 or x - -13/3 = 0\nx = -2\nx = -13/3"} {"input": "Solve quickly: x^3 - 251/45x^2 + 31/45x + 11 = 0", "output": "x^3 - 251/45x^2 + 31/45x + 11 = 0\n(x - 9/5)(x - -11/9)(x - 5) = 0\nx - 9/5 = 0\nx - -11/9 = 0\nx - 5 = 0\nx = 9/5\nx = -11/9\nx = 5"} {"input": "Solve x^2 + 56/15x - 128/15 = 0", "output": "x^2 + 56/15x - 128/15 = 0\n(x - 8/5)(x - -16/3) = 0\nx - 8/5 = 0 or x - -16/3 = 0\nx = 8/5\nx = -16/3"} {"input": "What value of x satisfies x^3 - 24/5x^2 + 37/5x - 18/5 = 0", "output": "x^3 - 24/5x^2 + 37/5x - 18/5 = 0\n(x - 9/5)(x - 2)(x - 1) = 0\nx - 9/5 = 0\nx - 2 = 0\nx - 1 = 0\nx = 9/5\nx = 2\nx = 1"} {"input": "Solve the system:\n5x + 9y = -23/21\n9x + 2y = -241/7", "output": "5x + 9y = -23/21\n9x + 2y = -241/7\n\nUsing elimination\n9*(5x + 9y = -23/21)\n5*(9x + 2y = -241/7)\n45x + 81y = -69/7\n45x + 10y = -1205/7\nSubtract equations\n71y = 1136/7\ny = 1136/7/71\ny = 16/7\n\nSubstitute y\n5x + 9(16/7) = -23/21\n5x = -65/3\nx = -65/3/5\nx = -13/3"} {"input": "Solve quickly: 2x - 3 = 0", "output": "2x - 3 = 0\n2x = 3\nx = 3 / 2\nx = 3/2"} {"input": "Solve simultaneously:\n2x + 1y = -45/8\n10x + 1y = -173/8", "output": "2x + 1y = -45/8\n10x + 1y = -173/8\n\nUsing elimination\n10*(2x + 1y = -45/8)\n2*(10x + 1y = -173/8)\n20x + 10y = -225/4\n20x + 2y = -173/4\nSubtract equations\n8y = -13\ny = -13/8\ny = -13/8\n\nSubstitute y\n2x + 1(-13/8) = -45/8\n2x = -4\nx = -4/2\nx = -2"} {"input": "What value of x satisfies 9x - 54 = 0", "output": "9x - 54 = 0\n9x = 54\nx = 54 / 9\nx = 6"} {"input": "What value of x satisfies x^3 + 37/20x^2 - 673/40x - 1547/40 = 0", "output": "x^3 + 37/20x^2 - 673/40x - 1547/40 = 0\n(x - 17/4)(x - -13/5)(x - -7/2) = 0\nx - 17/4 = 0\nx - -13/5 = 0\nx - -7/2 = 0\nx = 17/4\nx = -13/5\nx = -7/2"} {"input": "Determine x in x^2 - 3/10x - 2/5 = 0", "output": "x^2 - 3/10x - 2/5 = 0\n(x - -1/2)(x - 4/5) = 0\nx - -1/2 = 0 or x - 4/5 = 0\nx = -1/2\nx = 4/5"} {"input": "Solve the equation x^2 + 35/8x - 25/8 = 0", "output": "x^2 + 35/8x - 25/8 = 0\n(x - 5/8)(x - -5) = 0\nx - 5/8 = 0 or x - -5 = 0\nx = 5/8\nx = -5"} {"input": "Determine x in 8x - 16/5 = 0", "output": "8x - 16/5 = 0\n8x = 16/5\nx = 16/5 / 8\nx = 2/5"} {"input": "Find x for 4x + 8/9 = 0", "output": "4x + 8/9 = 0\n4x = -8/9\nx = -8/9 / 4\nx = -2/9"} {"input": "Determine x in 3x + 21/10 = 0", "output": "3x + 21/10 = 0\n3x = -21/10\nx = -21/10 / 3\nx = -7/10"} {"input": "Find the solution to 6x - 15 = 0", "output": "6x - 15 = 0\n6x = 15\nx = 15 / 6\nx = 5/2"} {"input": "Find the solution to 5x + 35/4 = 0", "output": "5x + 35/4 = 0\n5x = -35/4\nx = -35/4 / 5\nx = -7/4"} {"input": "Find the solution to x^3 + 13/4x^2 + 9/4x = 0", "output": "x^3 + 13/4x^2 + 9/4x = 0\n(x - 0)(x - -9/4)(x - -1) = 0\nx - 0 = 0\nx - -9/4 = 0\nx - -1 = 0\nx = 0\nx = -9/4\nx = -1"} {"input": "Solve the system:\n10x + 1y = 11/4\n3x + 3y = -213/20", "output": "10x + 1y = 11/4\n3x + 3y = -213/20\n\nUsing elimination\n3*(10x + 1y = 11/4)\n10*(3x + 3y = -213/20)\n30x + 3y = 33/4\n30x + 30y = -213/2\nSubtract equations\n-27y = 459/4\ny = 459/4/-27\ny = -17/4\n\nSubstitute y\n10x + 1(-17/4) = 11/4\n10x = 7\nx = 7/10\nx = 7/10"} {"input": "Find x for x^3 - 2/5x^2 - 57/5x + 54/5 = 0", "output": "x^3 - 2/5x^2 - 57/5x + 54/5 = 0\n(x - -18/5)(x - 3)(x - 1) = 0\nx - -18/5 = 0\nx - 3 = 0\nx - 1 = 0\nx = -18/5\nx = 3\nx = 1"} {"input": "Find x for 10x + 36 = 0", "output": "10x + 36 = 0\n10x = -36\nx = -36 / 10\nx = -18/5"} {"input": "Solve simultaneously:\n10x + 6y = 247/10\n10x + 2y = 199/10", "output": "10x + 6y = 247/10\n10x + 2y = 199/10\n\nUsing elimination\n10*(10x + 6y = 247/10)\n10*(10x + 2y = 199/10)\n100x + 60y = 247\n100x + 20y = 199\nSubtract equations\n40y = 48\ny = 48/40\ny = 6/5\n\nSubstitute y\n10x + 6(6/5) = 247/10\n10x = 35/2\nx = 35/2/10\nx = 7/4"} {"input": "Find x in x^3 + 6/7x^2 - 211/28x + 6 = 0", "output": "x^3 + 6/7x^2 - 211/28x + 6 = 0\n(x - -7/2)(x - 8/7)(x - 3/2) = 0\nx - -7/2 = 0\nx - 8/7 = 0\nx - 3/2 = 0\nx = -7/2\nx = 8/7\nx = 3/2"} {"input": "Solve the equations:\n4x + 4y = -39\n8x + 9y = -331/4", "output": "4x + 4y = -39\n8x + 9y = -331/4\n\nUsing elimination\n8*(4x + 4y = -39)\n4*(8x + 9y = -331/4)\n32x + 32y = -312\n32x + 36y = -331\nSubtract equations\n-4y = 19\ny = 19/-4\ny = -19/4\n\nSubstitute y\n4x + 4(-19/4) = -39\n4x = -20\nx = -20/4\nx = -5"} {"input": "Find x in 4x - 12/7 = 0", "output": "4x - 12/7 = 0\n4x = 12/7\nx = 12/7 / 4\nx = 3/7"} {"input": "Solve quickly: x^3 - 36/7x^2 + 96/49x + 512/49 = 0", "output": "x^3 - 36/7x^2 + 96/49x + 512/49 = 0\n(x - -8/7)(x - 4)(x - 16/7) = 0\nx - -8/7 = 0\nx - 4 = 0\nx - 16/7 = 0\nx = -8/7\nx = 4\nx = 16/7"} {"input": "Find x and y such that\n6x + 3y = 219/4\n9x + 6y = 81", "output": "6x + 3y = 219/4\n9x + 6y = 81\n\nUsing elimination\n9*(6x + 3y = 219/4)\n6*(9x + 6y = 81)\n54x + 27y = 1971/4\n54x + 36y = 486\nSubtract equations\n-9y = 27/4\ny = 27/4/-9\ny = -3/4\n\nSubstitute y\n6x + 3(-3/4) = 219/4\n6x = 57\nx = 57/6\nx = 19/2"} {"input": "Solve the equation 1x - 2/9 = 0", "output": "1x - 2/9 = 0\n1x = 2/9\nx = 2/9 / 1\nx = 2/9"} {"input": "Find the solution to x^2 - 73/24x + 19/12 = 0", "output": "x^2 - 73/24x + 19/12 = 0\n(x - 2/3)(x - 19/8) = 0\nx - 2/3 = 0 or x - 19/8 = 0\nx = 2/3\nx = 19/8"} {"input": "Find x in x^2 - 48/35x - 108/35 = 0", "output": "x^2 - 48/35x - 108/35 = 0\n(x - -6/5)(x - 18/7) = 0\nx - -6/5 = 0 or x - 18/7 = 0\nx = -6/5\nx = 18/7"} {"input": "Solve x^2 - 29/10x - 3/10 = 0", "output": "x^2 - 29/10x - 3/10 = 0\n(x - -1/10)(x - 3) = 0\nx - -1/10 = 0 or x - 3 = 0\nx = -1/10\nx = 3"} {"input": "Find x for x^3 + 3/8x^2 - 207/32x - 187/32 = 0", "output": "x^3 + 3/8x^2 - 207/32x - 187/32 = 0\n(x - 11/4)(x - -1)(x - -17/8) = 0\nx - 11/4 = 0\nx - -1 = 0\nx - -17/8 = 0\nx = 11/4\nx = -1\nx = -17/8"} {"input": "Find x in 6x - 12/7 = 0", "output": "6x - 12/7 = 0\n6x = 12/7\nx = 12/7 / 6\nx = 2/7"} {"input": "Solve the equation x^3 + 49/4x^2 - 95/4x + 21/2 = 0", "output": "x^3 + 49/4x^2 - 95/4x + 21/2 = 0\n(x - -14)(x - 3/4)(x - 1) = 0\nx - -14 = 0\nx - 3/4 = 0\nx - 1 = 0\nx = -14\nx = 3/4\nx = 1"} {"input": "What value of x satisfies 8x - 136/7 = 0", "output": "8x - 136/7 = 0\n8x = 136/7\nx = 136/7 / 8\nx = 17/7"} {"input": "Solve the equation 4x + 26/3 = 0", "output": "4x + 26/3 = 0\n4x = -26/3\nx = -26/3 / 4\nx = -13/6"} {"input": "Find the solution to 9x + 21/2 = 0", "output": "9x + 21/2 = 0\n9x = -21/2\nx = -21/2 / 9\nx = -7/6"} {"input": "Find the solution to x^3 - 16/3x^2 - 11/36x + 847/36 = 0", "output": "x^3 - 16/3x^2 - 11/36x + 847/36 = 0\n(x - 11/3)(x - 7/2)(x - -11/6) = 0\nx - 11/3 = 0\nx - 7/2 = 0\nx - -11/6 = 0\nx = 11/3\nx = 7/2\nx = -11/6"} {"input": "Find the solution to 5x + 25/2 = 0", "output": "5x + 25/2 = 0\n5x = -25/2\nx = -25/2 / 5\nx = -5/2"} {"input": "Find the solution to 2x + 19/3 = 0", "output": "2x + 19/3 = 0\n2x = -19/3\nx = -19/3 / 2\nx = -19/6"} {"input": "Compute the solution of x^3 + 1/42x^2 - 7/2x + 52/21 = 0", "output": "x^3 + 1/42x^2 - 7/2x + 52/21 = 0\n(x - -13/6)(x - 8/7)(x - 1) = 0\nx - -13/6 = 0\nx - 8/7 = 0\nx - 1 = 0\nx = -13/6\nx = 8/7\nx = 1"} {"input": "Solve quickly: x^2 - 15x + 36 = 0", "output": "x^2 - 15x + 36 = 0\n(x - 12)(x - 3) = 0\nx - 12 = 0 or x - 3 = 0\nx = 12\nx = 3"} {"input": "Find x and y such that\n9x + 8y = -1139/90\n2x + 2y = -121/45", "output": "9x + 8y = -1139/90\n2x + 2y = -121/45\n\nUsing elimination\n2*(9x + 8y = -1139/90)\n9*(2x + 2y = -121/45)\n18x + 16y = -1139/45\n18x + 18y = -121/5\nSubtract equations\n-2y = -10/9\ny = -10/9/-2\ny = 5/9\n\nSubstitute y\n9x + 8(5/9) = -1139/90\n9x = -171/10\nx = -171/10/9\nx = -19/10"} {"input": "Find the solution to 6x + 38/3 = 0", "output": "6x + 38/3 = 0\n6x = -38/3\nx = -38/3 / 6\nx = -19/9"} {"input": "Solve quickly: x^2 - 9/7x = 0", "output": "x^2 - 9/7x = 0\n(x - 0)(x - 9/7) = 0\nx - 0 = 0 or x - 9/7 = 0\nx = 0\nx = 9/7"} {"input": "Solve quickly: x^2 + 11/7x - 18/7 = 0", "output": "x^2 + 11/7x - 18/7 = 0\n(x - -18/7)(x - 1) = 0\nx - -18/7 = 0 or x - 1 = 0\nx = -18/7\nx = 1"} {"input": "Compute the solution of x^3 - 172/63x^2 - 3/7x + 208/63 = 0", "output": "x^3 - 172/63x^2 - 3/7x + 208/63 = 0\n(x - 13/9)(x - 16/7)(x - -1) = 0\nx - 13/9 = 0\nx - 16/7 = 0\nx - -1 = 0\nx = 13/9\nx = 16/7\nx = -1"} {"input": "Solve the system:\n9x + 4y = 665/18\n4x + 4y = 130/9", "output": "9x + 4y = 665/18\n4x + 4y = 130/9\n\nUsing elimination\n4*(9x + 4y = 665/18)\n9*(4x + 4y = 130/9)\n36x + 16y = 1330/9\n36x + 36y = 130\nSubtract equations\n-20y = 160/9\ny = 160/9/-20\ny = -8/9\n\nSubstitute y\n9x + 4(-8/9) = 665/18\n9x = 81/2\nx = 81/2/9\nx = 9/2"} {"input": "What value of x satisfies x^2 - 5/12x - 25/12 = 0", "output": "x^2 - 5/12x - 25/12 = 0\n(x - -5/4)(x - 5/3) = 0\nx - -5/4 = 0 or x - 5/3 = 0\nx = -5/4\nx = 5/3"} {"input": "Find x in 9x - 60 = 0", "output": "9x - 60 = 0\n9x = 60\nx = 60 / 9\nx = 20/3"} {"input": "Compute the solution of x^3 - 169/14x^2 + 173/7x + 440/7 = 0", "output": "x^3 - 169/14x^2 + 173/7x + 440/7 = 0\n(x - 8)(x - -10/7)(x - 11/2) = 0\nx - 8 = 0\nx - -10/7 = 0\nx - 11/2 = 0\nx = 8\nx = -10/7\nx = 11/2"} {"input": "Solve the equations:\n10x + 3y = -9/4\n6x + 6y = -39/4", "output": "10x + 3y = -9/4\n6x + 6y = -39/4\n\nUsing elimination\n6*(10x + 3y = -9/4)\n10*(6x + 6y = -39/4)\n60x + 18y = -27/2\n60x + 60y = -195/2\nSubtract equations\n-42y = 84\ny = 84/-42\ny = -2\n\nSubstitute y\n10x + 3(-2) = -9/4\n10x = 15/4\nx = 15/4/10\nx = 3/8"} {"input": "Solve the equation 10x - 45/2 = 0", "output": "10x - 45/2 = 0\n10x = 45/2\nx = 45/2 / 10\nx = 9/4"} {"input": "Determine x in x^3 + 65/3x^2 + 178/3x - 120 = 0", "output": "x^3 + 65/3x^2 + 178/3x - 120 = 0\n(x - -18)(x - -5)(x - 4/3) = 0\nx - -18 = 0\nx - -5 = 0\nx - 4/3 = 0\nx = -18\nx = -5\nx = 4/3"} {"input": "Solve quickly: x^2 + 191/10x - 18 = 0", "output": "x^2 + 191/10x - 18 = 0\n(x - 9/10)(x - -20) = 0\nx - 9/10 = 0 or x - -20 = 0\nx = 9/10\nx = -20"} {"input": "Find x for 3x + 2/3 = 0", "output": "3x + 2/3 = 0\n3x = -2/3\nx = -2/3 / 3\nx = -2/9"} {"input": "Solve simultaneously:\n6x + 9y = -8/3\n10x + 3y = -112/9", "output": "6x + 9y = -8/3\n10x + 3y = -112/9\n\nUsing elimination\n10*(6x + 9y = -8/3)\n6*(10x + 3y = -112/9)\n60x + 90y = -80/3\n60x + 18y = -224/3\nSubtract equations\n72y = 48\ny = 48/72\ny = 2/3\n\nSubstitute y\n6x + 9(2/3) = -8/3\n6x = -26/3\nx = -26/3/6\nx = -13/9"} {"input": "Compute the solution of 4x + 80/3 = 0", "output": "4x + 80/3 = 0\n4x = -80/3\nx = -80/3 / 4\nx = -20/3"} {"input": "Solve 1x - 19 = 0", "output": "1x - 19 = 0\n1x = 19\nx = 19 / 1\nx = 19"} {"input": "Find x in 6x - 120 = 0", "output": "6x - 120 = 0\n6x = 120\nx = 120 / 6\nx = 20"} {"input": "Solve x^2 - 67/21x + 52/21 = 0", "output": "x^2 - 67/21x + 52/21 = 0\n(x - 4/3)(x - 13/7) = 0\nx - 4/3 = 0 or x - 13/7 = 0\nx = 4/3\nx = 13/7"} {"input": "Find x for x^3 + 61/8x^2 + 1099/72x + 245/36 = 0", "output": "x^3 + 61/8x^2 + 1099/72x + 245/36 = 0\n(x - -7/3)(x - -14/3)(x - -5/8) = 0\nx - -7/3 = 0\nx - -14/3 = 0\nx - -5/8 = 0\nx = -7/3\nx = -14/3\nx = -5/8"} {"input": "Determine x in 1x - 2 = 0", "output": "1x - 2 = 0\n1x = 2\nx = 2 / 1\nx = 2"} {"input": "Compute the solution of 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Solve the equations:\n9x + 1y = 50/7\n8x + 5y = -157/7", "output": "9x + 1y = 50/7\n8x + 5y = -157/7\n\nUsing elimination\n8*(9x + 1y = 50/7)\n9*(8x + 5y = -157/7)\n72x + 8y = 400/7\n72x + 45y = -1413/7\nSubtract equations\n-37y = 259\ny = 259/-37\ny = -7\n\nSubstitute y\n9x + 1(-7) = 50/7\n9x = 99/7\nx = 99/7/9\nx = 11/7"} {"input": "Determine x in x^3 - 23/12x^2 + 3/8x + 3/8 = 0", "output": "x^3 - 23/12x^2 + 3/8x + 3/8 = 0\n(x - 3/2)(x - -1/3)(x - 3/4) = 0\nx - 3/2 = 0\nx - -1/3 = 0\nx - 3/4 = 0\nx = 3/2\nx = -1/3\nx = 3/4"} {"input": "Solve quickly: x^3 + 117/56x^2 - 311/224x - 195/56 = 0", "output": "x^3 + 117/56x^2 - 311/224x - 195/56 = 0\n(x - -12/7)(x - 5/4)(x - -13/8) = 0\nx - -12/7 = 0\nx - 5/4 = 0\nx - -13/8 = 0\nx = -12/7\nx = 5/4\nx = -13/8"} {"input": "Find x in x^2 - 7x = 0", "output": "x^2 - 7x = 0\n(x - 7)(x - 0) = 0\nx - 7 = 0 or x - 0 = 0\nx = 7\nx = 0"} {"input": "Find x for 4x - 20/7 = 0", "output": "4x - 20/7 = 0\n4x = 20/7\nx = 20/7 / 4\nx = 5/7"} {"input": "Solve the system:\n10x + 6y = 76\n4x + 6y = 16", "output": "10x + 6y = 76\n4x + 6y = 16\n\nUsing elimination\n4*(10x + 6y = 76)\n10*(4x + 6y = 16)\n40x + 24y = 304\n40x + 60y = 160\nSubtract equations\n-36y = 144\ny = 144/-36\ny = -4\n\nSubstitute y\n10x + 6(-4) = 76\n10x = 100\nx = 100/10\nx = 10"} {"input": "Find the solution to 1x + 3 = 0", "output": "1x + 3 = 0\n1x = -3\nx = -3 / 1\nx = -3"} {"input": "Solve quickly: 4x - 36/7 = 0", "output": "4x - 36/7 = 0\n4x = 36/7\nx = 36/7 / 4\nx = 9/7"} {"input": "Solve the equation x^3 - 189/10x^2 + 323/10x = 0", "output": "x^3 - 189/10x^2 + 323/10x = 0\n(x - 17)(x - 19/10)(x - 0) = 0\nx - 17 = 0\nx - 19/10 = 0\nx - 0 = 0\nx = 17\nx = 19/10\nx = 0"} {"input": "Find x for 9x + 117/10 = 0", "output": "9x + 117/10 = 0\n9x = -117/10\nx = -117/10 / 9\nx = -13/10"} {"input": "Find x for x^3 - 1x^2 - 23/4x + 15/2 = 0", "output": "x^3 - 1x^2 - 23/4x + 15/2 = 0\n(x - -5/2)(x - 3/2)(x - 2) = 0\nx - -5/2 = 0\nx - 3/2 = 0\nx - 2 = 0\nx = -5/2\nx = 3/2\nx = 2"} {"input": "Determine x in x^3 - 24/5x^2 - 1x = 0", "output": "x^3 - 24/5x^2 - 1x = 0\n(x - -1/5)(x - 0)(x - 5) = 0\nx - -1/5 = 0\nx - 0 = 0\nx - 5 = 0\nx = -1/5\nx = 0\nx = 5"} {"input": "Determine x in x^3 + 49/6x^2 - 112x + 640/3 = 0", "output": "x^3 + 49/6x^2 - 112x + 640/3 = 0\n(x - 16/3)(x - -16)(x - 5/2) = 0\nx - 16/3 = 0\nx - -16 = 0\nx - 5/2 = 0\nx = 16/3\nx = -16\nx = 5/2"} {"input": "Compute the solution of x^3 + 587/140x^2 - 577/70x - 34 = 0", "output": "x^3 + 587/140x^2 - 577/70x - 34 = 0\n(x - 20/7)(x - -17/4)(x - -14/5) = 0\nx - 20/7 = 0\nx - -17/4 = 0\nx - -14/5 = 0\nx = 20/7\nx = -17/4\nx = -14/5"} {"input": "Find x and y such that\n3x + 7y = 95/3\n4x + 2y = 50/9", "output": "3x + 7y = 95/3\n4x + 2y = 50/9\n\nUsing elimination\n4*(3x + 7y = 95/3)\n3*(4x + 2y = 50/9)\n12x + 28y = 380/3\n12x + 6y = 50/3\nSubtract equations\n22y = 110\ny = 110/22\ny = 5\n\nSubstitute y\n3x + 7(5) = 95/3\n3x = -10/3\nx = -10/3/3\nx = -10/9"} {"input": "Solve the equation x^3 + 131/56x^2 - 239/56x - 247/28 = 0", "output": "x^3 + 131/56x^2 - 239/56x - 247/28 = 0\n(x - -19/7)(x - -13/8)(x - 2) = 0\nx - -19/7 = 0\nx - -13/8 = 0\nx - 2 = 0\nx = -19/7\nx = -13/8\nx = 2"} {"input": "Solve the system:\n10x + 9y = 100\n9x + 4y = 8", "output": "10x + 9y = 100\n9x + 4y = 8\n\nUsing elimination\n9*(10x + 9y = 100)\n10*(9x + 4y = 8)\n90x + 81y = 900\n90x + 40y = 80\nSubtract equations\n41y = 820\ny = 820/41\ny = 20\n\nSubstitute y\n10x + 9(20) = 100\n10x = -80\nx = -80/10\nx = -8"} {"input": "Solve the equation x^3 + 1/2x^2 - 69/50x - 99/125 = 0", "output": "x^3 + 1/2x^2 - 69/50x - 99/125 = 0\n(x - -3/5)(x - 6/5)(x - -11/10) = 0\nx - -3/5 = 0\nx - 6/5 = 0\nx - -11/10 = 0\nx = -3/5\nx = 6/5\nx = -11/10"} {"input": "Solve the equation 1x + 4/7 = 0", "output": "1x + 4/7 = 0\n1x = -4/7\nx = -4/7 / 1\nx = -4/7"} {"input": "Solve x^3 + 53/40x^2 - 101/80x - 17/16 = 0", "output": "x^3 + 53/40x^2 - 101/80x - 17/16 = 0\n(x - 1)(x - -17/10)(x - -5/8) = 0\nx - 1 = 0\nx - -17/10 = 0\nx - -5/8 = 0\nx = 1\nx = -17/10\nx = -5/8"} {"input": "Find x and y such that\n3x + 1y = -295/63\n7x + 2y = -101/9", "output": "3x + 1y = -295/63\n7x + 2y = -101/9\n\nUsing elimination\n7*(3x + 1y = -295/63)\n3*(7x + 2y = -101/9)\n21x + 7y = -295/9\n21x + 6y = -101/3\nSubtract equations\n1y = 8/9\ny = 8/9/1\ny = 8/9\n\nSubstitute y\n3x + 1(8/9) = -295/63\n3x = -39/7\nx = -39/7/3\nx = -13/7"} {"input": "Find x and y such that\n6x + 6y = -71/7\n7x + 6y = -10", "output": "6x + 6y = -71/7\n7x + 6y = -10\n\nUsing elimination\n7*(6x + 6y = -71/7)\n6*(7x + 6y = -10)\n42x + 42y = -71\n42x + 36y = -60\nSubtract equations\n6y = -11\ny = -11/6\ny = -11/6\n\nSubstitute y\n6x + 6(-11/6) = -71/7\n6x = 6/7\nx = 6/7/6\nx = 1/7"} {"input": "Solve the system:\n1x + 2y = 13/15\n4x + 1y = 122/15", "output": "1x + 2y = 13/15\n4x + 1y = 122/15\n\nUsing elimination\n4*(1x + 2y = 13/15)\n1*(4x + 1y = 122/15)\n4x + 8y = 52/15\n4x + 1y = 122/15\nSubtract equations\n7y = -14/3\ny = -14/3/7\ny = -2/3\n\nSubstitute y\n1x + 2(-2/3) = 13/15\n1x = 11/5\nx = 11/5/1\nx = 11/5"} {"input": "Solve the system:\n9x + 8y = -149/2\n7x + 5y = -50", "output": "9x + 8y = -149/2\n7x + 5y = -50\n\nUsing elimination\n7*(9x + 8y = -149/2)\n9*(7x + 5y = -50)\n63x + 56y = -1043/2\n63x + 45y = -450\nSubtract equations\n11y = -143/2\ny = -143/2/11\ny = -13/2\n\nSubstitute y\n9x + 8(-13/2) = -149/2\n9x = -45/2\nx = -45/2/9\nx = -5/2"} {"input": "Find the solution to 2x - 7/2 = 0", "output": "2x - 7/2 = 0\n2x = 7/2\nx = 7/2 / 2\nx = 7/4"} {"input": "Compute the solution of x^2 + 37/72x - 65/36 = 0", "output": "x^2 + 37/72x - 65/36 = 0\n(x - -13/8)(x - 10/9) = 0\nx - -13/8 = 0 or x - 10/9 = 0\nx = -13/8\nx = 10/9"} {"input": "Solve the system:\n6x + 7y = -48\n2x + 6y = -71", "output": "6x + 7y = -48\n2x + 6y = -71\n\nUsing elimination\n2*(6x + 7y = -48)\n6*(2x + 6y = -71)\n12x + 14y = -96\n12x + 36y = -426\nSubtract equations\n-22y = 330\ny = 330/-22\ny = -15\n\nSubstitute y\n6x + 7(-15) = -48\n6x = 57\nx = 57/6\nx = 19/2"} {"input": "Find x for x^3 + 31/90x^2 - 93/50x + 34/45 = 0", "output": "x^3 + 31/90x^2 - 93/50x + 34/45 = 0\n(x - 4/5)(x - 5/9)(x - -17/10) = 0\nx - 4/5 = 0\nx - 5/9 = 0\nx - -17/10 = 0\nx = 4/5\nx = 5/9\nx = -17/10"} {"input": "Solve the system:\n7x + 3y = 55/2\n3x + 4y = 49/6", "output": "7x + 3y = 55/2\n3x + 4y = 49/6\n\nUsing elimination\n3*(7x + 3y = 55/2)\n7*(3x + 4y = 49/6)\n21x + 9y = 165/2\n21x + 28y = 343/6\nSubtract equations\n-19y = 76/3\ny = 76/3/-19\ny = -4/3\n\nSubstitute y\n7x + 3(-4/3) = 55/2\n7x = 63/2\nx = 63/2/7\nx = 9/2"} {"input": "Solve the equations:\n9x + 9y = 594/5\n1x + 10y = 15", "output": "9x + 9y = 594/5\n1x + 10y = 15\n\nUsing elimination\n1*(9x + 9y = 594/5)\n9*(1x + 10y = 15)\n9x + 9y = 594/5\n9x + 90y = 135\nSubtract equations\n-81y = -81/5\ny = -81/5/-81\ny = 1/5\n\nSubstitute y\n9x + 9(1/5) = 594/5\n9x = 117\nx = 117/9\nx = 13"} {"input": "Find x for x^2 + 29/9x + 2/3 = 0", "output": "x^2 + 29/9x + 2/3 = 0\n(x - -3)(x - -2/9) = 0\nx - -3 = 0 or x - -2/9 = 0\nx = -3\nx = -2/9"} {"input": "Solve simultaneously:\n3x + 5y = 20\n10x + 10y = 60", "output": "3x + 5y = 20\n10x + 10y = 60\n\nUsing elimination\n10*(3x + 5y = 20)\n3*(10x + 10y = 60)\n30x + 50y = 200\n30x + 30y = 180\nSubtract equations\n20y = 20\ny = 20/20\ny = 1\n\nSubstitute y\n3x + 5(1) = 20\n3x = 15\nx = 15/3\nx = 5"} {"input": "Solve the equation x^3 + 6x^2 - 9/4x - 27/2 = 0", "output": "x^3 + 6x^2 - 9/4x - 27/2 = 0\n(x - -3/2)(x - 3/2)(x - -6) = 0\nx - -3/2 = 0\nx - 3/2 = 0\nx - -6 = 0\nx = -3/2\nx = 3/2\nx = -6"} {"input": "Solve simultaneously:\n8x + 7y = 46\n5x + 1y = -5", "output": "8x + 7y = 46\n5x + 1y = -5\n\nUsing elimination\n5*(8x + 7y = 46)\n8*(5x + 1y = -5)\n40x + 35y = 230\n40x + 8y = -40\nSubtract equations\n27y = 270\ny = 270/27\ny = 10\n\nSubstitute y\n8x + 7(10) = 46\n8x = -24\nx = -24/8\nx = -3"} {"input": "Compute the solution of 10x + 75/2 = 0", "output": "10x + 75/2 = 0\n10x = -75/2\nx = -75/2 / 10\nx = -15/4"} {"input": "What value of x satisfies 9x + 99/10 = 0", "output": "9x + 99/10 = 0\n9x = -99/10\nx = -99/10 / 9\nx = -11/10"} {"input": "Find x for 9x + 15 = 0", "output": "9x + 15 = 0\n9x = -15\nx = -15 / 9\nx = -5/3"} {"input": "Solve simultaneously:\n6x + 5y = 425/36\n8x + 8y = 143/9", "output": "6x + 5y = 425/36\n8x + 8y = 143/9\n\nUsing elimination\n8*(6x + 5y = 425/36)\n6*(8x + 8y = 143/9)\n48x + 40y = 850/9\n48x + 48y = 286/3\nSubtract equations\n-8y = -8/9\ny = -8/9/-8\ny = 1/9\n\nSubstitute y\n6x + 5(1/9) = 425/36\n6x = 45/4\nx = 45/4/6\nx = 15/8"} {"input": "Solve quickly: x^2 - 17/5x + 16/25 = 0", "output": "x^2 - 17/5x + 16/25 = 0\n(x - 1/5)(x - 16/5) = 0\nx - 1/5 = 0 or x - 16/5 = 0\nx = 1/5\nx = 16/5"} {"input": "Find the solution to x^2 + 18/5x + 81/25 = 0", "output": "x^2 + 18/5x + 81/25 = 0\n(x - -9/5)(x - -9/5) = 0\nx - -9/5 = 0 or x - -9/5 = 0\nx = -9/5\nx = -9/5"} {"input": "Solve quickly: 2x + 2/9 = 0", "output": "2x + 2/9 = 0\n2x = -2/9\nx = -2/9 / 2\nx = -1/9"} {"input": "Solve x^2 - 11/3x + 8/3 = 0", "output": "x^2 - 11/3x + 8/3 = 0\n(x - 1)(x - 8/3) = 0\nx - 1 = 0 or x - 8/3 = 0\nx = 1\nx = 8/3"} {"input": "Solve the equation x^3 - 136/21x^2 + 739/63x - 110/21 = 0", "output": "x^3 - 136/21x^2 + 739/63x - 110/21 = 0\n(x - 2/3)(x - 15/7)(x - 11/3) = 0\nx - 2/3 = 0\nx - 15/7 = 0\nx - 11/3 = 0\nx = 2/3\nx = 15/7\nx = 11/3"} {"input": "Solve the equations:\n3x + 2y = 19/7\n3x + 10y = 67/7", "output": "3x + 2y = 19/7\n3x + 10y = 67/7\n\nUsing elimination\n3*(3x + 2y = 19/7)\n3*(3x + 10y = 67/7)\n9x + 6y = 57/7\n9x + 30y = 201/7\nSubtract equations\n-24y = -144/7\ny = -144/7/-24\ny = 6/7\n\nSubstitute y\n3x + 2(6/7) = 19/7\n3x = 1\nx = 1/3\nx = 1/3"} {"input": "Solve x^3 - 823/360x^2 + 289/180x - 1/3 = 0", "output": "x^3 - 823/360x^2 + 289/180x - 1/3 = 0\n(x - 4/5)(x - 3/8)(x - 10/9) = 0\nx - 4/5 = 0\nx - 3/8 = 0\nx - 10/9 = 0\nx = 4/5\nx = 3/8\nx = 10/9"} {"input": "Find x for x^3 + 289/30x^2 + 18/5x - 189/10 = 0", "output": "x^3 + 289/30x^2 + 18/5x - 189/10 = 0\n(x - 7/6)(x - -9/5)(x - -9) = 0\nx - 7/6 = 0\nx - -9/5 = 0\nx - -9 = 0\nx = 7/6\nx = -9/5\nx = -9"} {"input": "Determine x in x^3 + 479/35x^2 + 1066/35x + 352/35 = 0", "output": "x^3 + 479/35x^2 + 1066/35x + 352/35 = 0\n(x - -11)(x - -2/5)(x - -16/7) = 0\nx - -11 = 0\nx - -2/5 = 0\nx - -16/7 = 0\nx = -11\nx = -2/5\nx = -16/7"} {"input": "Find x in x^2 - 2/5x - 51/5 = 0", "output": "x^2 - 2/5x - 51/5 = 0\n(x - -3)(x - 17/5) = 0\nx - -3 = 0 or x - 17/5 = 0\nx = -3\nx = 17/5"} {"input": "Determine x in 3x + 48 = 0", "output": "3x + 48 = 0\n3x = -48\nx = -48 / 3\nx = -16"} {"input": "Determine x in x^2 + 7/5x - 18 = 0", "output": "x^2 + 7/5x - 18 = 0\n(x - -5)(x - 18/5) = 0\nx - -5 = 0 or x - 18/5 = 0\nx = -5\nx = 18/5"} {"input": "Solve the equations:\n1x + 8y = -21/2\n3x + 6y = -45/2", "output": "1x + 8y = -21/2\n3x + 6y = -45/2\n\nUsing elimination\n3*(1x + 8y = -21/2)\n1*(3x + 6y = -45/2)\n3x + 24y = -63/2\n3x + 6y = -45/2\nSubtract equations\n18y = -9\ny = -9/18\ny = -1/2\n\nSubstitute y\n1x + 8(-1/2) = -21/2\n1x = -13/2\nx = -13/2/1\nx = -13/2"} {"input": "Solve simultaneously:\n10x + 6y = -47\n7x + 9y = -117/2", "output": "10x + 6y = -47\n7x + 9y = -117/2\n\nUsing elimination\n7*(10x + 6y = -47)\n10*(7x + 9y = -117/2)\n70x + 42y = -329\n70x + 90y = -585\nSubtract equations\n-48y = 256\ny = 256/-48\ny = -16/3\n\nSubstitute y\n10x + 6(-16/3) = -47\n10x = -15\nx = -15/10\nx = -3/2"} {"input": "Determine x in x^3 + 13/2x^2 + 2053/162x + 616/81 = 0", "output": "x^3 + 13/2x^2 + 2053/162x + 616/81 = 0\n(x - -7/2)(x - -11/9)(x - -16/9) = 0\nx - -7/2 = 0\nx - -11/9 = 0\nx - -16/9 = 0\nx = -7/2\nx = -11/9\nx = -16/9"} {"input": "What value of x satisfies 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Find x for x^3 - 92/15x^2 - 143/3x - 968/15 = 0", "output": "x^3 - 92/15x^2 - 143/3x - 968/15 = 0\n(x - -8/3)(x - -11/5)(x - 11) = 0\nx - -8/3 = 0\nx - -11/5 = 0\nx - 11 = 0\nx = -8/3\nx = -11/5\nx = 11"} {"input": "Determine x in 9x - 135 = 0", "output": "9x - 135 = 0\n9x = 135\nx = 135 / 9\nx = 15"} {"input": "Solve the system:\n6x + 9y = -75/7\n3x + 5y = -48/7", "output": "6x + 9y = -75/7\n3x + 5y = -48/7\n\nUsing elimination\n3*(6x + 9y = -75/7)\n6*(3x + 5y = -48/7)\n18x + 27y = -225/7\n18x + 30y = -288/7\nSubtract equations\n-3y = 9\ny = 9/-3\ny = -3\n\nSubstitute y\n6x + 9(-3) = -75/7\n6x = 114/7\nx = 114/7/6\nx = 19/7"} {"input": "Find x in 1x - 12/7 = 0", "output": "1x - 12/7 = 0\n1x = 12/7\nx = 12/7 / 1\nx = 12/7"} {"input": "Solve x^2 - 23/2x - 105/2 = 0", "output": "x^2 - 23/2x - 105/2 = 0\n(x - -7/2)(x - 15) = 0\nx - -7/2 = 0 or x - 15 = 0\nx = -7/2\nx = 15"} {"input": "Solve the system:\n4x + 8y = 76/5\n3x + 5y = 52/5", "output": "4x + 8y = 76/5\n3x + 5y = 52/5\n\nUsing elimination\n3*(4x + 8y = 76/5)\n4*(3x + 5y = 52/5)\n12x + 24y = 228/5\n12x + 20y = 208/5\nSubtract equations\n4y = 4\ny = 4/4\ny = 1\n\nSubstitute y\n4x + 8(1) = 76/5\n4x = 36/5\nx = 36/5/4\nx = 9/5"} {"input": "Find x in 10x - 80/3 = 0", "output": "10x - 80/3 = 0\n10x = 80/3\nx = 80/3 / 10\nx = 8/3"} {"input": "Find x and y such that\n6x + 6y = -42\n9x + 7y = -51", "output": "6x + 6y = -42\n9x + 7y = -51\n\nUsing elimination\n9*(6x + 6y = -42)\n6*(9x + 7y = -51)\n54x + 54y = -378\n54x + 42y = -306\nSubtract equations\n12y = -72\ny = -72/12\ny = -6\n\nSubstitute y\n6x + 6(-6) = -42\n6x = -6\nx = -6/6\nx = -1"} {"input": "Solve 9x + 9/2 = 0", "output": "9x + 9/2 = 0\n9x = -9/2\nx = -9/2 / 9\nx = -1/2"} {"input": "Compute the solution of x^2 - 23/12x + 5/12 = 0", "output": "x^2 - 23/12x + 5/12 = 0\n(x - 5/3)(x - 1/4) = 0\nx - 5/3 = 0 or x - 1/4 = 0\nx = 5/3\nx = 1/4"} {"input": "Determine x in x^3 - 83/15x^2 + 2201/300x - 57/20 = 0", "output": "x^3 - 83/15x^2 + 2201/300x - 57/20 = 0\n(x - 19/5)(x - 5/6)(x - 9/10) = 0\nx - 19/5 = 0\nx - 5/6 = 0\nx - 9/10 = 0\nx = 19/5\nx = 5/6\nx = 9/10"} {"input": "Find x for 5x - 10 = 0", "output": "5x - 10 = 0\n5x = 10\nx = 10 / 5\nx = 2"} {"input": "Solve the equation x^2 + 11/6x - 7/6 = 0", "output": "x^2 + 11/6x - 7/6 = 0\n(x - 1/2)(x - -7/3) = 0\nx - 1/2 = 0 or x - -7/3 = 0\nx = 1/2\nx = -7/3"} {"input": "Find the solution to x^2 - 13/3x = 0", "output": "x^2 - 13/3x = 0\n(x - 13/3)(x - 0) = 0\nx - 13/3 = 0 or x - 0 = 0\nx = 13/3\nx = 0"} {"input": "Solve the equations:\n10x + 7y = -10\n4x + 1y = -104/35", "output": "10x + 7y = -10\n4x + 1y = -104/35\n\nUsing elimination\n4*(10x + 7y = -10)\n10*(4x + 1y = -104/35)\n40x + 28y = -40\n40x + 10y = -208/7\nSubtract equations\n18y = -72/7\ny = -72/7/18\ny = -4/7\n\nSubstitute y\n10x + 7(-4/7) = -10\n10x = -6\nx = -6/10\nx = -3/5"} {"input": "Solve simultaneously:\n9x + 4y = 9\n1x + 4y = 1", "output": "9x + 4y = 9\n1x + 4y = 1\n\nUsing elimination\n1*(9x + 4y = 9)\n9*(1x + 4y = 1)\n9x + 4y = 9\n9x + 36y = 9\nSubtract equations\n-32y = 0\ny = 0/-32\ny = 0\n\nSubstitute y\n9x + 4(0) = 9\n9x = 9\nx = 9/9\nx = 1"} {"input": "Solve quickly: 2x + 11 = 0", "output": "2x + 11 = 0\n2x = -11\nx = -11 / 2\nx = -11/2"} {"input": "What value of x satisfies x^3 + 11/15x^2 - 7/15x - 1/5 = 0", "output": "x^3 + 11/15x^2 - 7/15x - 1/5 = 0\n(x - 3/5)(x - -1/3)(x - -1) = 0\nx - 3/5 = 0\nx - -1/3 = 0\nx - -1 = 0\nx = 3/5\nx = -1/3\nx = -1"} {"input": "Solve quickly: x^2 - 26/9x - 40/9 = 0", "output": "x^2 - 26/9x - 40/9 = 0\n(x - -10/9)(x - 4) = 0\nx - -10/9 = 0 or x - 4 = 0\nx = -10/9\nx = 4"} {"input": "Find x for 5x + 1 = 0", "output": "5x + 1 = 0\n5x = -1\nx = -1 / 5\nx = -1/5"} {"input": "Solve quickly: x^3 - 10/3x^2 - 37/3x + 20 = 0", "output": "x^3 - 10/3x^2 - 37/3x + 20 = 0\n(x - -3)(x - 4/3)(x - 5) = 0\nx - -3 = 0\nx - 4/3 = 0\nx - 5 = 0\nx = -3\nx = 4/3\nx = 5"} {"input": "Find the solution to x^3 - 39/7x^2 - 481/49x - 9/7 = 0", "output": "x^3 - 39/7x^2 - 481/49x - 9/7 = 0\n(x - -1/7)(x - -9/7)(x - 7) = 0\nx - -1/7 = 0\nx - -9/7 = 0\nx - 7 = 0\nx = -1/7\nx = -9/7\nx = 7"} {"input": "Find the solution to x^3 - 37/8x^2 - 13/4x + 55/8 = 0", "output": "x^3 - 37/8x^2 - 13/4x + 55/8 = 0\n(x - 1)(x - -11/8)(x - 5) = 0\nx - 1 = 0\nx - -11/8 = 0\nx - 5 = 0\nx = 1\nx = -11/8\nx = 5"} {"input": "Find x in x^2 - 130/9x + 56/9 = 0", "output": "x^2 - 130/9x + 56/9 = 0\n(x - 14)(x - 4/9) = 0\nx - 14 = 0 or x - 4/9 = 0\nx = 14\nx = 4/9"} {"input": "Solve x^2 - 59/35x + 2/5 = 0", "output": "x^2 - 59/35x + 2/5 = 0\n(x - 7/5)(x - 2/7) = 0\nx - 7/5 = 0 or x - 2/7 = 0\nx = 7/5\nx = 2/7"} {"input": "Find x in 2x + 16/3 = 0", "output": "2x + 16/3 = 0\n2x = -16/3\nx = -16/3 / 2\nx = -8/3"} {"input": "Find x in 7x - 16 = 0", "output": "7x - 16 = 0\n7x = 16\nx = 16 / 7\nx = 16/7"} {"input": "Find x in 9x + 12 = 0", "output": "9x + 12 = 0\n9x = -12\nx = -12 / 9\nx = -4/3"} {"input": "Solve the equations:\n2x + 7y = 71/8\n7x + 2y = 113/4", "output": "2x + 7y = 71/8\n7x + 2y = 113/4\n\nUsing elimination\n7*(2x + 7y = 71/8)\n2*(7x + 2y = 113/4)\n14x + 49y = 497/8\n14x + 4y = 113/2\nSubtract equations\n45y = 45/8\ny = 45/8/45\ny = 1/8\n\nSubstitute y\n2x + 7(1/8) = 71/8\n2x = 8\nx = 8/2\nx = 4"} {"input": "Find x and y such that\n1x + 9y = -53/2\n6x + 10y = -71", "output": "1x + 9y = -53/2\n6x + 10y = -71\n\nUsing elimination\n6*(1x + 9y = -53/2)\n1*(6x + 10y = -71)\n6x + 54y = -159\n6x + 10y = -71\nSubtract equations\n44y = -88\ny = -88/44\ny = -2\n\nSubstitute y\n1x + 9(-2) = -53/2\n1x = -17/2\nx = -17/2/1\nx = -17/2"} {"input": "Solve the equation x^3 - 49/12x^2 - 33/2x + 57/4 = 0", "output": "x^3 - 49/12x^2 - 33/2x + 57/4 = 0\n(x - 19/3)(x - 3/4)(x - -3) = 0\nx - 19/3 = 0\nx - 3/4 = 0\nx - -3 = 0\nx = 19/3\nx = 3/4\nx = -3"} {"input": "Determine x in 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Solve the system:\n10x + 1y = 46/3\n3x + 2y = -9", "output": "10x + 1y = 46/3\n3x + 2y = -9\n\nUsing elimination\n3*(10x + 1y = 46/3)\n10*(3x + 2y = -9)\n30x + 3y = 46\n30x + 20y = -90\nSubtract equations\n-17y = 136\ny = 136/-17\ny = -8\n\nSubstitute y\n10x + 1(-8) = 46/3\n10x = 70/3\nx = 70/3/10\nx = 7/3"} {"input": "Solve x^2 - 3x - 4 = 0", "output": "x^2 - 3x - 4 = 0\n(x - 4)(x - -1) = 0\nx - 4 = 0 or x - -1 = 0\nx = 4\nx = -1"} {"input": "Solve quickly: x^2 + 2x - 3 = 0", "output": "x^2 + 2x - 3 = 0\n(x - -3)(x - 1) = 0\nx - -3 = 0 or x - 1 = 0\nx = -3\nx = 1"} {"input": "Find x and y such that\n2x + 9y = -23/3\n1x + 4y = -11/3", "output": "2x + 9y = -23/3\n1x + 4y = -11/3\n\nUsing elimination\n1*(2x + 9y = -23/3)\n2*(1x + 4y = -11/3)\n2x + 9y = -23/3\n2x + 8y = -22/3\nSubtract equations\n1y = -1/3\ny = -1/3/1\ny = -1/3\n\nSubstitute y\n2x + 9(-1/3) = -23/3\n2x = -14/3\nx = -14/3/2\nx = -7/3"} {"input": "Find the solution to x^2 + 51/35x - 26/35 = 0", "output": "x^2 + 51/35x - 26/35 = 0\n(x - 2/5)(x - -13/7) = 0\nx - 2/5 = 0 or x - -13/7 = 0\nx = 2/5\nx = -13/7"} {"input": "What value of x satisfies 9x + 60 = 0", "output": "9x + 60 = 0\n9x = -60\nx = -60 / 9\nx = -20/3"} {"input": "Find x and y such that\n3x + 1y = 61/9\n6x + 7y = 157/9", "output": "3x + 1y = 61/9\n6x + 7y = 157/9\n\nUsing elimination\n6*(3x + 1y = 61/9)\n3*(6x + 7y = 157/9)\n18x + 6y = 122/3\n18x + 21y = 157/3\nSubtract equations\n-15y = -35/3\ny = -35/3/-15\ny = 7/9\n\nSubstitute y\n3x + 1(7/9) = 61/9\n3x = 6\nx = 6/3\nx = 2"} {"input": "Solve the equations:\n3x + 10y = -81\n1x + 6y = -39", "output": "3x + 10y = -81\n1x + 6y = -39\n\nUsing elimination\n1*(3x + 10y = -81)\n3*(1x + 6y = -39)\n3x + 10y = -81\n3x + 18y = -117\nSubtract equations\n-8y = 36\ny = 36/-8\ny = -9/2\n\nSubstitute y\n3x + 10(-9/2) = -81\n3x = -36\nx = -36/3\nx = -12"} {"input": "Compute the solution of x^2 - 64/9x + 20/3 = 0", "output": "x^2 - 64/9x + 20/3 = 0\n(x - 6)(x - 10/9) = 0\nx - 6 = 0 or x - 10/9 = 0\nx = 6\nx = 10/9"} {"input": "Find x for 3x - 33/7 = 0", "output": "3x - 33/7 = 0\n3x = 33/7\nx = 33/7 / 3\nx = 11/7"} {"input": "Find x in 1x - 8/7 = 0", "output": "1x - 8/7 = 0\n1x = 8/7\nx = 8/7 / 1\nx = 8/7"} {"input": "Find the solution to x^2 - 23/6x + 11/3 = 0", "output": "x^2 - 23/6x + 11/3 = 0\n(x - 11/6)(x - 2) = 0\nx - 11/6 = 0 or x - 2 = 0\nx = 11/6\nx = 2"} {"input": "Solve the equations:\n10x + 6y = 6\n7x + 5y = 5", "output": "10x + 6y = 6\n7x + 5y = 5\n\nUsing elimination\n7*(10x + 6y = 6)\n10*(7x + 5y = 5)\n70x + 42y = 42\n70x + 50y = 50\nSubtract equations\n-8y = -8\ny = -8/-8\ny = 1\n\nSubstitute y\n10x + 6(1) = 6\n10x = 0\nx = 0/10\nx = 0"} {"input": "What value of x satisfies x^3 - 229/12x^2 - 109/6x - 10/3 = 0", "output": "x^3 - 229/12x^2 - 109/6x - 10/3 = 0\n(x - 20)(x - -1/4)(x - -2/3) = 0\nx - 20 = 0\nx - -1/4 = 0\nx - -2/3 = 0\nx = 20\nx = -1/4\nx = -2/3"} {"input": "Solve simultaneously:\n10x + 6y = 37/2\n9x + 8y = 179/12", "output": "10x + 6y = 37/2\n9x + 8y = 179/12\n\nUsing elimination\n9*(10x + 6y = 37/2)\n10*(9x + 8y = 179/12)\n90x + 54y = 333/2\n90x + 80y = 895/6\nSubtract equations\n-26y = 52/3\ny = 52/3/-26\ny = -2/3\n\nSubstitute y\n10x + 6(-2/3) = 37/2\n10x = 45/2\nx = 45/2/10\nx = 9/4"} {"input": "Find x and y such that\n1x + 4y = 3/10\n4x + 2y = -29/5", "output": "1x + 4y = 3/10\n4x + 2y = -29/5\n\nUsing elimination\n4*(1x + 4y = 3/10)\n1*(4x + 2y = -29/5)\n4x + 16y = 6/5\n4x + 2y = -29/5\nSubtract equations\n14y = 7\ny = 7/14\ny = 1/2\n\nSubstitute y\n1x + 4(1/2) = 3/10\n1x = -17/10\nx = -17/10/1\nx = -17/10"} {"input": "Solve the system:\n7x + 10y = -153\n10x + 5y = -70", "output": "7x + 10y = -153\n10x + 5y = -70\n\nUsing elimination\n10*(7x + 10y = -153)\n7*(10x + 5y = -70)\n70x + 100y = -1530\n70x + 35y = -490\nSubtract equations\n65y = -1040\ny = -1040/65\ny = -16\n\nSubstitute y\n7x + 10(-16) = -153\n7x = 7\nx = 7/7\nx = 1"} {"input": "Find the solution to 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Determine x in 6x - 3/4 = 0", "output": "6x - 3/4 = 0\n6x = 3/4\nx = 3/4 / 6\nx = 1/8"} {"input": "Solve quickly: 5x - 5 = 0", "output": "5x - 5 = 0\n5x = 5\nx = 5 / 5\nx = 1"} {"input": "Determine x in x^2 - 26/7x + 15/7 = 0", "output": "x^2 - 26/7x + 15/7 = 0\n(x - 3)(x - 5/7) = 0\nx - 3 = 0 or x - 5/7 = 0\nx = 3\nx = 5/7"} {"input": "Solve the system:\n3x + 8y = -86/5\n3x + 7y = -76/5", "output": "3x + 8y = -86/5\n3x + 7y = -76/5\n\nUsing elimination\n3*(3x + 8y = -86/5)\n3*(3x + 7y = -76/5)\n9x + 24y = -258/5\n9x + 21y = -228/5\nSubtract equations\n3y = -6\ny = -6/3\ny = -2\n\nSubstitute y\n3x + 8(-2) = -86/5\n3x = -6/5\nx = -6/5/3\nx = -2/5"} {"input": "Solve 5x - 25/6 = 0", "output": "5x - 25/6 = 0\n5x = 25/6\nx = 25/6 / 5\nx = 5/6"} {"input": "Find x and y such that\n6x + 5y = 1/10\n2x + 2y = 0", "output": "6x + 5y = 1/10\n2x + 2y = 0\n\nUsing elimination\n2*(6x + 5y = 1/10)\n6*(2x + 2y = 0)\n12x + 10y = 1/5\n12x + 12y = 0\nSubtract equations\n-2y = 1/5\ny = 1/5/-2\ny = -1/10\n\nSubstitute y\n6x + 5(-1/10) = 1/10\n6x = 3/5\nx = 3/5/6\nx = 1/10"} {"input": "Determine x in x^3 - 451/60x^2 + 331/20x - 34/3 = 0", "output": "x^3 - 451/60x^2 + 331/20x - 34/3 = 0\n(x - 5/3)(x - 8/5)(x - 17/4) = 0\nx - 5/3 = 0\nx - 8/5 = 0\nx - 17/4 = 0\nx = 5/3\nx = 8/5\nx = 17/4"} {"input": "Compute the solution of 5x + 20/3 = 0", "output": "5x + 20/3 = 0\n5x = -20/3\nx = -20/3 / 5\nx = -4/3"} {"input": "What value of x satisfies x^3 - 281/12x^2 + 1037/12x - 95/2 = 0", "output": "x^3 - 281/12x^2 + 1037/12x - 95/2 = 0\n(x - 15/4)(x - 2/3)(x - 19) = 0\nx - 15/4 = 0\nx - 2/3 = 0\nx - 19 = 0\nx = 15/4\nx = 2/3\nx = 19"} {"input": "Determine x in x^3 - 22/7x^2 + 1/7x + 30/7 = 0", "output": "x^3 - 22/7x^2 + 1/7x + 30/7 = 0\n(x - 2)(x - -1)(x - 15/7) = 0\nx - 2 = 0\nx - -1 = 0\nx - 15/7 = 0\nx = 2\nx = -1\nx = 15/7"} {"input": "Solve simultaneously:\n3x + 6y = -129/14\n6x + 10y = -181/14", "output": "3x + 6y = -129/14\n6x + 10y = -181/14\n\nUsing elimination\n6*(3x + 6y = -129/14)\n3*(6x + 10y = -181/14)\n18x + 36y = -387/7\n18x + 30y = -543/14\nSubtract equations\n6y = -33/2\ny = -33/2/6\ny = -11/4\n\nSubstitute y\n3x + 6(-11/4) = -129/14\n3x = 51/7\nx = 51/7/3\nx = 17/7"} {"input": "Solve the system:\n9x + 10y = -29\n3x + 1y = -17/2", "output": "9x + 10y = -29\n3x + 1y = -17/2\n\nUsing elimination\n3*(9x + 10y = -29)\n9*(3x + 1y = -17/2)\n27x + 30y = -87\n27x + 9y = -153/2\nSubtract equations\n21y = -21/2\ny = -21/2/21\ny = -1/2\n\nSubstitute y\n9x + 10(-1/2) = -29\n9x = -24\nx = -24/9\nx = -8/3"} {"input": "Find x for 7x + 70/9 = 0", "output": "7x + 70/9 = 0\n7x = -70/9\nx = -70/9 / 7\nx = -10/9"} {"input": "Determine x in x^3 - 203/90x^2 - 11/18x + 119/45 = 0", "output": "x^3 - 203/90x^2 - 11/18x + 119/45 = 0\n(x - 17/10)(x - 14/9)(x - -1) = 0\nx - 17/10 = 0\nx - 14/9 = 0\nx - -1 = 0\nx = 17/10\nx = 14/9\nx = -1"} {"input": "Solve simultaneously:\n5x + 10y = -40/3\n5x + 2y = -88/3", "output": "5x + 10y = -40/3\n5x + 2y = -88/3\n\nUsing elimination\n5*(5x + 10y = -40/3)\n5*(5x + 2y = -88/3)\n25x + 50y = -200/3\n25x + 10y = -440/3\nSubtract equations\n40y = 80\ny = 80/40\ny = 2\n\nSubstitute y\n5x + 10(2) = -40/3\n5x = -100/3\nx = -100/3/5\nx = -20/3"} {"input": "Solve x^2 + 8/9x = 0", "output": "x^2 + 8/9x = 0\n(x - 0)(x - -8/9) = 0\nx - 0 = 0 or x - -8/9 = 0\nx = 0\nx = -8/9"} {"input": "Find x for x^2 + 2/3x - 8/3 = 0", "output": "x^2 + 2/3x - 8/3 = 0\n(x - -2)(x - 4/3) = 0\nx - -2 = 0 or x - 4/3 = 0\nx = -2\nx = 4/3"} {"input": "Solve the system:\n8x + 3y = -121/3\n5x + 5y = -230/9", "output": "8x + 3y = -121/3\n5x + 5y = -230/9\n\nUsing elimination\n5*(8x + 3y = -121/3)\n8*(5x + 5y = -230/9)\n40x + 15y = -605/3\n40x + 40y = -1840/9\nSubtract equations\n-25y = 25/9\ny = 25/9/-25\ny = -1/9\n\nSubstitute y\n8x + 3(-1/9) = -121/3\n8x = -40\nx = -40/8\nx = -5"} {"input": "Solve x^2 + 2x - 15 = 0", "output": "x^2 + 2x - 15 = 0\n(x - 3)(x - -5) = 0\nx - 3 = 0 or x - -5 = 0\nx = 3\nx = -5"} {"input": "Compute the solution of x^3 + 7/10x^2 - 9/50x = 0", "output": "x^3 + 7/10x^2 - 9/50x = 0\n(x - 0)(x - -9/10)(x - 1/5) = 0\nx - 0 = 0\nx - -9/10 = 0\nx - 1/5 = 0\nx = 0\nx = -9/10\nx = 1/5"} {"input": "Find x for x^3 + 116/105x^2 - 44/7x + 80/21 = 0", "output": "x^3 + 116/105x^2 - 44/7x + 80/21 = 0\n(x - 4/5)(x - -10/3)(x - 10/7) = 0\nx - 4/5 = 0\nx - -10/3 = 0\nx - 10/7 = 0\nx = 4/5\nx = -10/3\nx = 10/7"} {"input": "What value of x satisfies x^2 - 19/9x + 26/27 = 0", "output": "x^2 - 19/9x + 26/27 = 0\n(x - 13/9)(x - 2/3) = 0\nx - 13/9 = 0 or x - 2/3 = 0\nx = 13/9\nx = 2/3"} {"input": "Compute the solution of x^3 - 73/60x^2 - 113/60x + 3/2 = 0", "output": "x^3 - 73/60x^2 - 113/60x + 3/2 = 0\n(x - 9/5)(x - -5/4)(x - 2/3) = 0\nx - 9/5 = 0\nx - -5/4 = 0\nx - 2/3 = 0\nx = 9/5\nx = -5/4\nx = 2/3"} {"input": "Solve the system:\n3x + 7y = -17/3\n1x + 10y = -809/63", "output": "3x + 7y = -17/3\n1x + 10y = -809/63\n\nUsing elimination\n1*(3x + 7y = -17/3)\n3*(1x + 10y = -809/63)\n3x + 7y = -17/3\n3x + 30y = -809/21\nSubtract equations\n-23y = 230/7\ny = 230/7/-23\ny = -10/7\n\nSubstitute y\n3x + 7(-10/7) = -17/3\n3x = 13/3\nx = 13/3/3\nx = 13/9"} {"input": "Solve quickly: x^3 + 23/18x^2 - 491/18x + 130/3 = 0", "output": "x^3 + 23/18x^2 - 491/18x + 130/3 = 0\n(x - 20/9)(x - -13/2)(x - 3) = 0\nx - 20/9 = 0\nx - -13/2 = 0\nx - 3 = 0\nx = 20/9\nx = -13/2\nx = 3"} {"input": "Solve simultaneously:\n4x + 5y = 22\n4x + 9y = 182/5", "output": "4x + 5y = 22\n4x + 9y = 182/5\n\nUsing elimination\n4*(4x + 5y = 22)\n4*(4x + 9y = 182/5)\n16x + 20y = 88\n16x + 36y = 728/5\nSubtract equations\n-16y = -288/5\ny = -288/5/-16\ny = 18/5\n\nSubstitute y\n4x + 5(18/5) = 22\n4x = 4\nx = 4/4\nx = 1"} {"input": "Determine x in x^3 - 113/4x^2 + 343/2x + 392 = 0", "output": "x^3 - 113/4x^2 + 343/2x + 392 = 0\n(x - -7/4)(x - 16)(x - 14) = 0\nx - -7/4 = 0\nx - 16 = 0\nx - 14 = 0\nx = -7/4\nx = 16\nx = 14"} {"input": "Compute the solution of x^3 + 2/5x^2 - 311/100x - 153/100 = 0", "output": "x^3 + 2/5x^2 - 311/100x - 153/100 = 0\n(x - -1/2)(x - -17/10)(x - 9/5) = 0\nx - -1/2 = 0\nx - -17/10 = 0\nx - 9/5 = 0\nx = -1/2\nx = -17/10\nx = 9/5"} {"input": "Find x for x^3 - 408/35x^2 - 2304/35x - 2048/35 = 0", "output": "x^3 - 408/35x^2 - 2304/35x - 2048/35 = 0\n(x - 16)(x - -8/7)(x - -16/5) = 0\nx - 16 = 0\nx - -8/7 = 0\nx - -16/5 = 0\nx = 16\nx = -8/7\nx = -16/5"} {"input": "Determine x in x^2 + 62/7x - 80/7 = 0", "output": "x^2 + 62/7x - 80/7 = 0\n(x - 8/7)(x - -10) = 0\nx - 8/7 = 0 or x - -10 = 0\nx = 8/7\nx = -10"} {"input": "Solve the system:\n8x + 2y = -295/4\n6x + 9y = -495/8", "output": "8x + 2y = -295/4\n6x + 9y = -495/8\n\nUsing elimination\n6*(8x + 2y = -295/4)\n8*(6x + 9y = -495/8)\n48x + 12y = -885/2\n48x + 72y = -495\nSubtract equations\n-60y = 105/2\ny = 105/2/-60\ny = -7/8\n\nSubstitute y\n8x + 2(-7/8) = -295/4\n8x = -72\nx = -72/8\nx = -9"} {"input": "Compute the solution of x^3 + 167/90x^2 + 5/18x - 26/45 = 0", "output": "x^3 + 167/90x^2 + 5/18x - 26/45 = 0\n(x - 4/9)(x - -13/10)(x - -1) = 0\nx - 4/9 = 0\nx - -13/10 = 0\nx - -1 = 0\nx = 4/9\nx = -13/10\nx = -1"} {"input": "Find x and y such that\n7x + 7y = 16/3\n5x + 8y = 101/21", "output": "7x + 7y = 16/3\n5x + 8y = 101/21\n\nUsing elimination\n5*(7x + 7y = 16/3)\n7*(5x + 8y = 101/21)\n35x + 35y = 80/3\n35x + 56y = 101/3\nSubtract equations\n-21y = -7\ny = -7/-21\ny = 1/3\n\nSubstitute y\n7x + 7(1/3) = 16/3\n7x = 3\nx = 3/7\nx = 3/7"} {"input": "Solve simultaneously:\n10x + 5y = 2\n7x + 2y = -2/5", "output": "10x + 5y = 2\n7x + 2y = -2/5\n\nUsing elimination\n7*(10x + 5y = 2)\n10*(7x + 2y = -2/5)\n70x + 35y = 14\n70x + 20y = -4\nSubtract equations\n15y = 18\ny = 18/15\ny = 6/5\n\nSubstitute y\n10x + 5(6/5) = 2\n10x = -4\nx = -4/10\nx = -2/5"} {"input": "Solve x^2 - 103/24x - 95/6 = 0", "output": "x^2 - 103/24x - 95/6 = 0\n(x - -19/8)(x - 20/3) = 0\nx - -19/8 = 0 or x - 20/3 = 0\nx = -19/8\nx = 20/3"} {"input": "Find x in x^2 + 22x + 85 = 0", "output": "x^2 + 22x + 85 = 0\n(x - -17)(x - -5) = 0\nx - -17 = 0 or x - -5 = 0\nx = -17\nx = -5"} {"input": "Solve quickly: x^2 - 34/15x - 13/15 = 0", "output": "x^2 - 34/15x - 13/15 = 0\n(x - 13/5)(x - -1/3) = 0\nx - 13/5 = 0 or x - -1/3 = 0\nx = 13/5\nx = -1/3"} {"input": "Find x for x^2 + 31/3x + 95/12 = 0", "output": "x^2 + 31/3x + 95/12 = 0\n(x - -5/6)(x - -19/2) = 0\nx - -5/6 = 0 or x - -19/2 = 0\nx = -5/6\nx = -19/2"} {"input": "Find x and y such that\n1x + 5y = 68/3\n4x + 3y = 544/15", "output": "1x + 5y = 68/3\n4x + 3y = 544/15\n\nUsing elimination\n4*(1x + 5y = 68/3)\n1*(4x + 3y = 544/15)\n4x + 20y = 272/3\n4x + 3y = 544/15\nSubtract equations\n17y = 272/5\ny = 272/5/17\ny = 16/5\n\nSubstitute y\n1x + 5(16/5) = 68/3\n1x = 20/3\nx = 20/3/1\nx = 20/3"} {"input": "Solve quickly: x^3 - 159/20x^2 + 63/5x - 27/5 = 0", "output": "x^3 - 159/20x^2 + 63/5x - 27/5 = 0\n(x - 6/5)(x - 6)(x - 3/4) = 0\nx - 6/5 = 0\nx - 6 = 0\nx - 3/4 = 0\nx = 6/5\nx = 6\nx = 3/4"} {"input": "Solve the equations:\n4x + 3y = -113/10\n5x + 1y = -89/10", "output": "4x + 3y = -113/10\n5x + 1y = -89/10\n\nUsing elimination\n5*(4x + 3y = -113/10)\n4*(5x + 1y = -89/10)\n20x + 15y = -113/2\n20x + 4y = -178/5\nSubtract equations\n11y = -209/10\ny = -209/10/11\ny = -19/10\n\nSubstitute y\n4x + 3(-19/10) = -113/10\n4x = -28/5\nx = -28/5/4\nx = -7/5"} {"input": "Find x in x^3 + 605/72x^2 - 221/36x - 55/8 = 0", "output": "x^3 + 605/72x^2 - 221/36x - 55/8 = 0\n(x - 11/9)(x - -5/8)(x - -9) = 0\nx - 11/9 = 0\nx - -5/8 = 0\nx - -9 = 0\nx = 11/9\nx = -5/8\nx = -9"} {"input": "Find x in x^3 - 134/45x^2 + 77/45x = 0", "output": "x^3 - 134/45x^2 + 77/45x = 0\n(x - 11/5)(x - 7/9)(x - 0) = 0\nx - 11/5 = 0\nx - 7/9 = 0\nx - 0 = 0\nx = 11/5\nx = 7/9\nx = 0"} {"input": "Find x in 5x = 0", "output": "5x = 0\n5x = 0\nx = 0 / 5\nx = 0"} {"input": "Solve the equation 1x - 9/7 = 0", "output": "1x - 9/7 = 0\n1x = 9/7\nx = 9/7 / 1\nx = 9/7"} {"input": "Solve the equation x^3 - 91/10x^2 + 23x - 88/5 = 0", "output": "x^3 - 91/10x^2 + 23x - 88/5 = 0\n(x - 11/2)(x - 2)(x - 8/5) = 0\nx - 11/2 = 0\nx - 2 = 0\nx - 8/5 = 0\nx = 11/2\nx = 2\nx = 8/5"} {"input": "What value of x satisfies 3x + 3 = 0", "output": "3x + 3 = 0\n3x = -3\nx = -3 / 3\nx = -1"} {"input": "Solve 4x - 5 = 0", "output": "4x - 5 = 0\n4x = 5\nx = 5 / 4\nx = 5/4"} {"input": "Solve 10x - 35 = 0", "output": "10x - 35 = 0\n10x = 35\nx = 35 / 10\nx = 7/2"} {"input": "Solve simultaneously:\n9x + 7y = 311/4\n7x + 7y = 273/4", "output": "9x + 7y = 311/4\n7x + 7y = 273/4\n\nUsing elimination\n7*(9x + 7y = 311/4)\n9*(7x + 7y = 273/4)\n63x + 49y = 2177/4\n63x + 63y = 2457/4\nSubtract equations\n-14y = -70\ny = -70/-14\ny = 5\n\nSubstitute y\n9x + 7(5) = 311/4\n9x = 171/4\nx = 171/4/9\nx = 19/4"} {"input": "Determine x in 4x - 6 = 0", "output": "4x - 6 = 0\n4x = 6\nx = 6 / 4\nx = 3/2"} {"input": "Determine x in x^2 + 13/21x - 20/21 = 0", "output": "x^2 + 13/21x - 20/21 = 0\n(x - -4/3)(x - 5/7) = 0\nx - -4/3 = 0 or x - 5/7 = 0\nx = -4/3\nx = 5/7"} {"input": "Solve quickly: x^2 + 23/10x - 21/10 = 0", "output": "x^2 + 23/10x - 21/10 = 0\n(x - 7/10)(x - -3) = 0\nx - 7/10 = 0 or x - -3 = 0\nx = 7/10\nx = -3"} {"input": "Find x for 3x - 21/5 = 0", "output": "3x - 21/5 = 0\n3x = 21/5\nx = 21/5 / 3\nx = 7/5"} {"input": "What value of x satisfies x^3 - 17/5x^2 + 43/20x + 1/4 = 0", "output": "x^3 - 17/5x^2 + 43/20x + 1/4 = 0\n(x - 1)(x - 5/2)(x - -1/10) = 0\nx - 1 = 0\nx - 5/2 = 0\nx - -1/10 = 0\nx = 1\nx = 5/2\nx = -1/10"} {"input": "Find x in x^2 - 1/2x - 15/2 = 0", "output": "x^2 - 1/2x - 15/2 = 0\n(x - 3)(x - -5/2) = 0\nx - 3 = 0 or x - -5/2 = 0\nx = 3\nx = -5/2"} {"input": "Find x for x^2 - 9/5x + 9/20 = 0", "output": "x^2 - 9/5x + 9/20 = 0\n(x - 3/10)(x - 3/2) = 0\nx - 3/10 = 0 or x - 3/2 = 0\nx = 3/10\nx = 3/2"} {"input": "Solve the equations:\n2x + 3y = -291/35\n3x + 8y = -1503/70", "output": "2x + 3y = -291/35\n3x + 8y = -1503/70\n\nUsing elimination\n3*(2x + 3y = -291/35)\n2*(3x + 8y = -1503/70)\n6x + 9y = -873/35\n6x + 16y = -1503/35\nSubtract equations\n-7y = 18\ny = 18/-7\ny = -18/7\n\nSubstitute y\n2x + 3(-18/7) = -291/35\n2x = -3/5\nx = -3/5/2\nx = -3/10"} {"input": "Solve simultaneously:\n5x + 6y = -43\n5x + 3y = -39", "output": "5x + 6y = -43\n5x + 3y = -39\n\nUsing elimination\n5*(5x + 6y = -43)\n5*(5x + 3y = -39)\n25x + 30y = -215\n25x + 15y = -195\nSubtract equations\n15y = -20\ny = -20/15\ny = -4/3\n\nSubstitute y\n5x + 6(-4/3) = -43\n5x = -35\nx = -35/5\nx = -7"} {"input": "Find x for x^2 - 41/3x - 380/3 = 0", "output": "x^2 - 41/3x - 380/3 = 0\n(x - 20)(x - -19/3) = 0\nx - 20 = 0 or x - -19/3 = 0\nx = 20\nx = -19/3"} {"input": "Compute the solution of 4x - 8 = 0", "output": "4x - 8 = 0\n4x = 8\nx = 8 / 4\nx = 2"} {"input": "Compute the solution of x^2 - 166/63x + 13/9 = 0", "output": "x^2 - 166/63x + 13/9 = 0\n(x - 7/9)(x - 13/7) = 0\nx - 7/9 = 0 or x - 13/7 = 0\nx = 7/9\nx = 13/7"} {"input": "Find x for x^3 - 49/18x^2 - 1187/18x + 133/9 = 0", "output": "x^3 - 49/18x^2 - 1187/18x + 133/9 = 0\n(x - 19/2)(x - 2/9)(x - -7) = 0\nx - 19/2 = 0\nx - 2/9 = 0\nx - -7 = 0\nx = 19/2\nx = 2/9\nx = -7"} {"input": "Find x in 9x + 153/7 = 0", "output": "9x + 153/7 = 0\n9x = -153/7\nx = -153/7 / 9\nx = -17/7"} {"input": "Find the solution to 4x - 19 = 0", "output": "4x - 19 = 0\n4x = 19\nx = 19 / 4\nx = 19/4"} {"input": "Find x in x^3 - 8/9x^2 - 1/9x = 0", "output": "x^3 - 8/9x^2 - 1/9x = 0\n(x - -1/9)(x - 0)(x - 1) = 0\nx - -1/9 = 0\nx - 0 = 0\nx - 1 = 0\nx = -1/9\nx = 0\nx = 1"} {"input": "Solve the equations:\n7x + 8y = 44/5\n7x + 7y = 42/5", "output": "7x + 8y = 44/5\n7x + 7y = 42/5\n\nUsing elimination\n7*(7x + 8y = 44/5)\n7*(7x + 7y = 42/5)\n49x + 56y = 308/5\n49x + 49y = 294/5\nSubtract equations\n7y = 14/5\ny = 14/5/7\ny = 2/5\n\nSubstitute y\n7x + 8(2/5) = 44/5\n7x = 28/5\nx = 28/5/7\nx = 4/5"} {"input": "Compute the solution of x^2 - 65/12x + 77/12 = 0", "output": "x^2 - 65/12x + 77/12 = 0\n(x - 7/4)(x - 11/3) = 0\nx - 7/4 = 0 or x - 11/3 = 0\nx = 7/4\nx = 11/3"} {"input": "Solve the equation x^3 - 109/10x^2 - 1043/25x - 588/25 = 0", "output": "x^3 - 109/10x^2 - 1043/25x - 588/25 = 0\n(x - -12/5)(x - -7/10)(x - 14) = 0\nx - -12/5 = 0\nx - -7/10 = 0\nx - 14 = 0\nx = -12/5\nx = -7/10\nx = 14"} {"input": "Find x for x^2 - 15/7x + 8/7 = 0", "output": "x^2 - 15/7x + 8/7 = 0\n(x - 8/7)(x - 1) = 0\nx - 8/7 = 0 or x - 1 = 0\nx = 8/7\nx = 1"} {"input": "Solve the equations:\n3x + 1y = 5/3\n2x + 2y = 10/3", "output": "3x + 1y = 5/3\n2x + 2y = 10/3\n\nUsing elimination\n2*(3x + 1y = 5/3)\n3*(2x + 2y = 10/3)\n6x + 2y = 10/3\n6x + 6y = 10\nSubtract equations\n-4y = -20/3\ny = -20/3/-4\ny = 5/3\n\nSubstitute y\n3x + 1(5/3) = 5/3\n3x = 0\nx = 0/3\nx = 0"} {"input": "Find x in x^2 - 127/40x - 19/8 = 0", "output": "x^2 - 127/40x - 19/8 = 0\n(x - 19/5)(x - -5/8) = 0\nx - 19/5 = 0 or x - -5/8 = 0\nx = 19/5\nx = -5/8"} {"input": "Solve the system:\n4x + 8y = -14\n1x + 7y = 13/2", "output": "4x + 8y = -14\n1x + 7y = 13/2\n\nUsing elimination\n1*(4x + 8y = -14)\n4*(1x + 7y = 13/2)\n4x + 8y = -14\n4x + 28y = 26\nSubtract equations\n-20y = -40\ny = -40/-20\ny = 2\n\nSubstitute y\n4x + 8(2) = -14\n4x = -30\nx = -30/4\nx = -15/2"} {"input": "Find x for 7x - 91/10 = 0", "output": "7x - 91/10 = 0\n7x = 91/10\nx = 91/10 / 7\nx = 13/10"} {"input": "Find x and y such that\n8x + 6y = 5\n10x + 1y = -33/2", "output": "8x + 6y = 5\n10x + 1y = -33/2\n\nUsing elimination\n10*(8x + 6y = 5)\n8*(10x + 1y = -33/2)\n80x + 60y = 50\n80x + 8y = -132\nSubtract equations\n52y = 182\ny = 182/52\ny = 7/2\n\nSubstitute y\n8x + 6(7/2) = 5\n8x = -16\nx = -16/8\nx = -2"} {"input": "What value of x satisfies 4x - 16/3 = 0", "output": "4x - 16/3 = 0\n4x = 16/3\nx = 16/3 / 4\nx = 4/3"} {"input": "Find x in x^2 + 31/6x + 11/2 = 0", "output": "x^2 + 31/6x + 11/2 = 0\n(x - -3/2)(x - -11/3) = 0\nx - -3/2 = 0 or x - -11/3 = 0\nx = -3/2\nx = -11/3"} {"input": "Solve the equation 8x + 136/9 = 0", "output": "8x + 136/9 = 0\n8x = -136/9\nx = -136/9 / 8\nx = -17/9"} {"input": "Compute the solution of x^3 - 38/3x^2 + 85/3x - 50/3 = 0", "output": "x^3 - 38/3x^2 + 85/3x - 50/3 = 0\n(x - 10)(x - 1)(x - 5/3) = 0\nx - 10 = 0\nx - 1 = 0\nx - 5/3 = 0\nx = 10\nx = 1\nx = 5/3"} {"input": "Solve quickly: x^2 + 17x + 16 = 0", "output": "x^2 + 17x + 16 = 0\n(x - -16)(x - -1) = 0\nx - -16 = 0 or x - -1 = 0\nx = -16\nx = -1"} {"input": "Find x in x^2 - 13/3x + 14/3 = 0", "output": "x^2 - 13/3x + 14/3 = 0\n(x - 2)(x - 7/3) = 0\nx - 2 = 0 or x - 7/3 = 0\nx = 2\nx = 7/3"} {"input": "Solve x^2 - 79/9x + 56/9 = 0", "output": "x^2 - 79/9x + 56/9 = 0\n(x - 7/9)(x - 8) = 0\nx - 7/9 = 0 or x - 8 = 0\nx = 7/9\nx = 8"} {"input": "Find x in x^2 + 27/14x - 11/2 = 0", "output": "x^2 + 27/14x - 11/2 = 0\n(x - -7/2)(x - 11/7) = 0\nx - -7/2 = 0 or x - 11/7 = 0\nx = -7/2\nx = 11/7"} {"input": "Solve the equations:\n5x + 4y = -11/2\n4x + 6y = -38", "output": "5x + 4y = -11/2\n4x + 6y = -38\n\nUsing elimination\n4*(5x + 4y = -11/2)\n5*(4x + 6y = -38)\n20x + 16y = -22\n20x + 30y = -190\nSubtract equations\n-14y = 168\ny = 168/-14\ny = -12\n\nSubstitute y\n5x + 4(-12) = -11/2\n5x = 85/2\nx = 85/2/5\nx = 17/2"} {"input": "Find x in x^2 - 16/45x - 1/9 = 0", "output": "x^2 - 16/45x - 1/9 = 0\n(x - -1/5)(x - 5/9) = 0\nx - -1/5 = 0 or x - 5/9 = 0\nx = -1/5\nx = 5/9"} {"input": "Solve the system:\n4x + 1y = -91/15\n6x + 9y = -173/5", "output": "4x + 1y = -91/15\n6x + 9y = -173/5\n\nUsing elimination\n6*(4x + 1y = -91/15)\n4*(6x + 9y = -173/5)\n24x + 6y = -182/5\n24x + 36y = -692/5\nSubtract equations\n-30y = 102\ny = 102/-30\ny = -17/5\n\nSubstitute y\n4x + 1(-17/5) = -91/15\n4x = -8/3\nx = -8/3/4\nx = -2/3"} {"input": "Solve x^3 + 137/42x^2 + 61/42x - 5/3 = 0", "output": "x^3 + 137/42x^2 + 61/42x - 5/3 = 0\n(x - -7/3)(x - 1/2)(x - -10/7) = 0\nx - -7/3 = 0\nx - 1/2 = 0\nx - -10/7 = 0\nx = -7/3\nx = 1/2\nx = -10/7"} {"input": "Solve simultaneously:\n5x + 6y = -77/3\n8x + 7y = -92/3", "output": "5x + 6y = -77/3\n8x + 7y = -92/3\n\nUsing elimination\n8*(5x + 6y = -77/3)\n5*(8x + 7y = -92/3)\n40x + 48y = -616/3\n40x + 35y = -460/3\nSubtract equations\n13y = -52\ny = -52/13\ny = -4\n\nSubstitute y\n5x + 6(-4) = -77/3\n5x = -5/3\nx = -5/3/5\nx = -1/3"} {"input": "What value of x satisfies x^3 - 425/84x^2 + 691/84x - 30/7 = 0", "output": "x^3 - 425/84x^2 + 691/84x - 30/7 = 0\n(x - 9/4)(x - 8/7)(x - 5/3) = 0\nx - 9/4 = 0\nx - 8/7 = 0\nx - 5/3 = 0\nx = 9/4\nx = 8/7\nx = 5/3"} {"input": "Compute the solution of x^2 + 12/7x - 27/7 = 0", "output": "x^2 + 12/7x - 27/7 = 0\n(x - 9/7)(x - -3) = 0\nx - 9/7 = 0 or x - -3 = 0\nx = 9/7\nx = -3"} {"input": "Solve the equation x^3 + 28/45x^2 - 28/135x - 16/135 = 0", "output": "x^3 + 28/45x^2 - 28/135x - 16/135 = 0\n(x - -2/3)(x - -2/5)(x - 4/9) = 0\nx - -2/3 = 0\nx - -2/5 = 0\nx - 4/9 = 0\nx = -2/3\nx = -2/5\nx = 4/9"} {"input": "Solve x^2 + 15/28x - 27/28 = 0", "output": "x^2 + 15/28x - 27/28 = 0\n(x - 3/4)(x - -9/7) = 0\nx - 3/4 = 0 or x - -9/7 = 0\nx = 3/4\nx = -9/7"} {"input": "Find x for x^2 + 112/45x - 4 = 0", "output": "x^2 + 112/45x - 4 = 0\n(x - -18/5)(x - 10/9) = 0\nx - -18/5 = 0 or x - 10/9 = 0\nx = -18/5\nx = 10/9"} {"input": "Find x for x^2 + 5/14x - 3/7 = 0", "output": "x^2 + 5/14x - 3/7 = 0\n(x - 1/2)(x - -6/7) = 0\nx - 1/2 = 0 or x - -6/7 = 0\nx = 1/2\nx = -6/7"} {"input": "Solve the equations:\n8x + 9y = -439/7\n5x + 4y = -607/21", "output": "8x + 9y = -439/7\n5x + 4y = -607/21\n\nUsing elimination\n5*(8x + 9y = -439/7)\n8*(5x + 4y = -607/21)\n40x + 45y = -2195/7\n40x + 32y = -4856/21\nSubtract equations\n13y = -247/3\ny = -247/3/13\ny = -19/3\n\nSubstitute y\n8x + 9(-19/3) = -439/7\n8x = -40/7\nx = -40/7/8\nx = -5/7"} {"input": "Find x and y such that\n6x + 2y = -69/4\n2x + 10y = -65/4", "output": "6x + 2y = -69/4\n2x + 10y = -65/4\n\nUsing elimination\n2*(6x + 2y = -69/4)\n6*(2x + 10y = -65/4)\n12x + 4y = -69/2\n12x + 60y = -195/2\nSubtract equations\n-56y = 63\ny = 63/-56\ny = -9/8\n\nSubstitute y\n6x + 2(-9/8) = -69/4\n6x = -15\nx = -15/6\nx = -5/2"} {"input": "Solve the system:\n7x + 1y = -96/5\n2x + 9y = -193/5", "output": "7x + 1y = -96/5\n2x + 9y = -193/5\n\nUsing elimination\n2*(7x + 1y = -96/5)\n7*(2x + 9y = -193/5)\n14x + 2y = -192/5\n14x + 63y = -1351/5\nSubtract equations\n-61y = 1159/5\ny = 1159/5/-61\ny = -19/5\n\nSubstitute y\n7x + 1(-19/5) = -96/5\n7x = -77/5\nx = -77/5/7\nx = -11/5"} {"input": "Compute the solution of x^2 + 59/8x + 33/4 = 0", "output": "x^2 + 59/8x + 33/4 = 0\n(x - -6)(x - -11/8) = 0\nx - -6 = 0 or x - -11/8 = 0\nx = -6\nx = -11/8"} {"input": "Find x in 5x + 5/7 = 0", "output": "5x + 5/7 = 0\n5x = -5/7\nx = -5/7 / 5\nx = -1/7"} {"input": "Compute the solution of x^3 + 13/10x^2 - 39/2x + 99/5 = 0", "output": "x^3 + 13/10x^2 - 39/2x + 99/5 = 0\n(x - -11/2)(x - 3)(x - 6/5) = 0\nx - -11/2 = 0\nx - 3 = 0\nx - 6/5 = 0\nx = -11/2\nx = 3\nx = 6/5"} {"input": "Solve the equation 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Find the solution to x^3 + 81/10x^2 + 512/25x + 408/25 = 0", "output": "x^3 + 81/10x^2 + 512/25x + 408/25 = 0\n(x - -12/5)(x - -4)(x - -17/10) = 0\nx - -12/5 = 0\nx - -4 = 0\nx - -17/10 = 0\nx = -12/5\nx = -4\nx = -17/10"} {"input": "Solve x^2 - 29/10x - 117/5 = 0", "output": "x^2 - 29/10x - 117/5 = 0\n(x - 13/2)(x - -18/5) = 0\nx - 13/2 = 0 or x - -18/5 = 0\nx = 13/2\nx = -18/5"} {"input": "Find x for x^3 + 1/5x^2 - 669/100x + 513/100 = 0", "output": "x^3 + 1/5x^2 - 669/100x + 513/100 = 0\n(x - 9/10)(x - -3)(x - 19/10) = 0\nx - 9/10 = 0\nx - -3 = 0\nx - 19/10 = 0\nx = 9/10\nx = -3\nx = 19/10"} {"input": "Solve quickly: x^3 + 151/168x^2 - 1535/336x - 221/56 = 0", "output": "x^3 + 151/168x^2 - 1535/336x - 221/56 = 0\n(x - -6/7)(x - -13/6)(x - 17/8) = 0\nx - -6/7 = 0\nx - -13/6 = 0\nx - 17/8 = 0\nx = -6/7\nx = -13/6\nx = 17/8"} {"input": "Find x and y such that\n8x + 2y = -139/9\n5x + 2y = -88/9", "output": "8x + 2y = -139/9\n5x + 2y = -88/9\n\nUsing elimination\n5*(8x + 2y = -139/9)\n8*(5x + 2y = -88/9)\n40x + 10y = -695/9\n40x + 16y = -704/9\nSubtract equations\n-6y = 1\ny = 1/-6\ny = -1/6\n\nSubstitute y\n8x + 2(-1/6) = -139/9\n8x = -136/9\nx = -136/9/8\nx = -17/9"} {"input": "Compute the solution of x^3 + 8/15x^2 + 37/405x + 2/405 = 0", "output": "x^3 + 8/15x^2 + 37/405x + 2/405 = 0\n(x - -2/9)(x - -1/9)(x - -1/5) = 0\nx - -2/9 = 0\nx - -1/9 = 0\nx - -1/5 = 0\nx = -2/9\nx = -1/9\nx = -1/5"} {"input": "Solve x^3 - 17/2x^2 + 247/18x = 0", "output": "x^3 - 17/2x^2 + 247/18x = 0\n(x - 0)(x - 13/6)(x - 19/3) = 0\nx - 0 = 0\nx - 13/6 = 0\nx - 19/3 = 0\nx = 0\nx = 13/6\nx = 19/3"} {"input": "Determine x in x^3 + 1/10x^2 - 15/2x + 18/5 = 0", "output": "x^3 + 1/10x^2 - 15/2x + 18/5 = 0\n(x - -3)(x - 12/5)(x - 1/2) = 0\nx - -3 = 0\nx - 12/5 = 0\nx - 1/2 = 0\nx = -3\nx = 12/5\nx = 1/2"} {"input": "Find x and y such that\n1x + 10y = 31/4\n5x + 9y = -9/4", "output": "1x + 10y = 31/4\n5x + 9y = -9/4\n\nUsing elimination\n5*(1x + 10y = 31/4)\n1*(5x + 9y = -9/4)\n5x + 50y = 155/4\n5x + 9y = -9/4\nSubtract equations\n41y = 41\ny = 41/41\ny = 1\n\nSubstitute y\n1x + 10(1) = 31/4\n1x = -9/4\nx = -9/4/1\nx = -9/4"} {"input": "Find x for x^2 + 32/15x + 16/15 = 0", "output": "x^2 + 32/15x + 16/15 = 0\n(x - -4/3)(x - -4/5) = 0\nx - -4/3 = 0 or x - -4/5 = 0\nx = -4/3\nx = -4/5"} {"input": "Solve simultaneously:\n3x + 1y = -2\n6x + 1y = 1", "output": "3x + 1y = -2\n6x + 1y = 1\n\nUsing elimination\n6*(3x + 1y = -2)\n3*(6x + 1y = 1)\n18x + 6y = -12\n18x + 3y = 3\nSubtract equations\n3y = -15\ny = -15/3\ny = -5\n\nSubstitute y\n3x + 1(-5) = -2\n3x = 3\nx = 3/3\nx = 1"} {"input": "Solve simultaneously:\n5x + 2y = -119/4\n5x + 10y = -115/4", "output": "5x + 2y = -119/4\n5x + 10y = -115/4\n\nUsing elimination\n5*(5x + 2y = -119/4)\n5*(5x + 10y = -115/4)\n25x + 10y = -595/4\n25x + 50y = -575/4\nSubtract equations\n-40y = -5\ny = -5/-40\ny = 1/8\n\nSubstitute y\n5x + 2(1/8) = -119/4\n5x = -30\nx = -30/5\nx = -6"} {"input": "Solve simultaneously:\n2x + 2y = -7/9\n10x + 7y = -83/9", "output": "2x + 2y = -7/9\n10x + 7y = -83/9\n\nUsing elimination\n10*(2x + 2y = -7/9)\n2*(10x + 7y = -83/9)\n20x + 20y = -70/9\n20x + 14y = -166/9\nSubtract equations\n6y = 32/3\ny = 32/3/6\ny = 16/9\n\nSubstitute y\n2x + 2(16/9) = -7/9\n2x = -13/3\nx = -13/3/2\nx = -13/6"} {"input": "Determine x in x^2 - 7/9x - 22/9 = 0", "output": "x^2 - 7/9x - 22/9 = 0\n(x - 2)(x - -11/9) = 0\nx - 2 = 0 or x - -11/9 = 0\nx = 2\nx = -11/9"} {"input": "What value of x satisfies x^2 + 13/2x + 15/2 = 0", "output": "x^2 + 13/2x + 15/2 = 0\n(x - -5)(x - -3/2) = 0\nx - -5 = 0 or x - -3/2 = 0\nx = -5\nx = -3/2"} {"input": "Solve the system:\n10x + 10y = -45\n3x + 5y = -39/2", "output": "10x + 10y = -45\n3x + 5y = -39/2\n\nUsing elimination\n3*(10x + 10y = -45)\n10*(3x + 5y = -39/2)\n30x + 30y = -135\n30x + 50y = -195\nSubtract equations\n-20y = 60\ny = 60/-20\ny = -3\n\nSubstitute y\n10x + 10(-3) = -45\n10x = -15\nx = -15/10\nx = -3/2"} {"input": "Determine x in x^3 + 44/9x^2 + 68/9x + 32/9 = 0", "output": "x^3 + 44/9x^2 + 68/9x + 32/9 = 0\n(x - -2)(x - -8/9)(x - -2) = 0\nx - -2 = 0\nx - -8/9 = 0\nx - -2 = 0\nx = -2\nx = -8/9\nx = -2"} {"input": "Solve the system:\n10x + 7y = 116/3\n3x + 1y = 26/3", "output": "10x + 7y = 116/3\n3x + 1y = 26/3\n\nUsing elimination\n3*(10x + 7y = 116/3)\n10*(3x + 1y = 26/3)\n30x + 21y = 116\n30x + 10y = 260/3\nSubtract equations\n11y = 88/3\ny = 88/3/11\ny = 8/3\n\nSubstitute y\n10x + 7(8/3) = 116/3\n10x = 20\nx = 20/10\nx = 2"} {"input": "Solve the system:\n2x + 3y = -7/3\n3x + 6y = -6", "output": "2x + 3y = -7/3\n3x + 6y = -6\n\nUsing elimination\n3*(2x + 3y = -7/3)\n2*(3x + 6y = -6)\n6x + 9y = -7\n6x + 12y = -12\nSubtract equations\n-3y = 5\ny = 5/-3\ny = -5/3\n\nSubstitute y\n2x + 3(-5/3) = -7/3\n2x = 8/3\nx = 8/3/2\nx = 4/3"} {"input": "Solve x^3 - 19/2x^2 + 12x = 0", "output": "x^3 - 19/2x^2 + 12x = 0\n(x - 8)(x - 0)(x - 3/2) = 0\nx - 8 = 0\nx - 0 = 0\nx - 3/2 = 0\nx = 8\nx = 0\nx = 3/2"} {"input": "Find the solution to 6x + 6 = 0", "output": "6x + 6 = 0\n6x = -6\nx = -6 / 6\nx = -1"} {"input": "Solve the equations:\n3x + 10y = -25\n7x + 9y = -45/2", "output": "3x + 10y = -25\n7x + 9y = -45/2\n\nUsing elimination\n7*(3x + 10y = -25)\n3*(7x + 9y = -45/2)\n21x + 70y = -175\n21x + 27y = -135/2\nSubtract equations\n43y = -215/2\ny = -215/2/43\ny = -5/2\n\nSubstitute y\n3x + 10(-5/2) = -25\n3x = 0\nx = 0/3\nx = 0"} {"input": "Solve simultaneously:\n3x + 6y = -8\n3x + 9y = -11", "output": "3x + 6y = -8\n3x + 9y = -11\n\nUsing elimination\n3*(3x + 6y = -8)\n3*(3x + 9y = -11)\n9x + 18y = -24\n9x + 27y = -33\nSubtract equations\n-9y = 9\ny = 9/-9\ny = -1\n\nSubstitute y\n3x + 6(-1) = -8\n3x = -2\nx = -2/3\nx = -2/3"} {"input": "Solve simultaneously:\n9x + 1y = 83/10\n10x + 7y = 95/2", "output": "9x + 1y = 83/10\n10x + 7y = 95/2\n\nUsing elimination\n10*(9x + 1y = 83/10)\n9*(10x + 7y = 95/2)\n90x + 10y = 83\n90x + 63y = 855/2\nSubtract equations\n-53y = -689/2\ny = -689/2/-53\ny = 13/2\n\nSubstitute y\n9x + 1(13/2) = 83/10\n9x = 9/5\nx = 9/5/9\nx = 1/5"} {"input": "Solve simultaneously:\n10x + 4y = -189/10\n10x + 5y = -18", "output": "10x + 4y = -189/10\n10x + 5y = -18\n\nUsing elimination\n10*(10x + 4y = -189/10)\n10*(10x + 5y = -18)\n100x + 40y = -189\n100x + 50y = -180\nSubtract equations\n-10y = -9\ny = -9/-10\ny = 9/10\n\nSubstitute y\n10x + 4(9/10) = -189/10\n10x = -45/2\nx = -45/2/10\nx = -9/4"} {"input": "Solve the system:\n3x + 5y = 41/10\n9x + 1y = -17/10", "output": "3x + 5y = 41/10\n9x + 1y = -17/10\n\nUsing elimination\n9*(3x + 5y = 41/10)\n3*(9x + 1y = -17/10)\n27x + 45y = 369/10\n27x + 3y = -51/10\nSubtract equations\n42y = 42\ny = 42/42\ny = 1\n\nSubstitute y\n3x + 5(1) = 41/10\n3x = -9/10\nx = -9/10/3\nx = -3/10"} {"input": "Find x for 10x + 170 = 0", "output": "10x + 170 = 0\n10x = -170\nx = -170 / 10\nx = -17"} {"input": "Compute the solution of x^3 + 57/10x^2 - 152/5x - 63/10 = 0", "output": "x^3 + 57/10x^2 - 152/5x - 63/10 = 0\n(x - -1/5)(x - -9)(x - 7/2) = 0\nx - -1/5 = 0\nx - -9 = 0\nx - 7/2 = 0\nx = -1/5\nx = -9\nx = 7/2"} {"input": "Solve quickly: x^3 - 27/10x^2 - 89/45x + 68/15 = 0", "output": "x^3 - 27/10x^2 - 89/45x + 68/15 = 0\n(x - 17/6)(x - 6/5)(x - -4/3) = 0\nx - 17/6 = 0\nx - 6/5 = 0\nx - -4/3 = 0\nx = 17/6\nx = 6/5\nx = -4/3"} {"input": "Solve x^2 + 23/3x - 12 = 0", "output": "x^2 + 23/3x - 12 = 0\n(x - -9)(x - 4/3) = 0\nx - -9 = 0 or x - 4/3 = 0\nx = -9\nx = 4/3"} {"input": "Find x for x^3 - 3/2x^2 - 31/25x + 12/25 = 0", "output": "x^3 - 3/2x^2 - 31/25x + 12/25 = 0\n(x - 3/10)(x - 2)(x - -4/5) = 0\nx - 3/10 = 0\nx - 2 = 0\nx - -4/5 = 0\nx = 3/10\nx = 2\nx = -4/5"} {"input": "Solve the equation x^2 - 10/3x + 1 = 0", "output": "x^2 - 10/3x + 1 = 0\n(x - 1/3)(x - 3) = 0\nx - 1/3 = 0 or x - 3 = 0\nx = 1/3\nx = 3"} {"input": "Determine x in x^3 + 23/20x^2 - 19/8x + 9/40 = 0", "output": "x^3 + 23/20x^2 - 19/8x + 9/40 = 0\n(x - 1/10)(x - 1)(x - -9/4) = 0\nx - 1/10 = 0\nx - 1 = 0\nx - -9/4 = 0\nx = 1/10\nx = 1\nx = -9/4"} {"input": "Find the solution to x^3 - 27x^2 + 1610/9x - 304 = 0", "output": "x^3 - 27x^2 + 1610/9x - 304 = 0\n(x - 8/3)(x - 19/3)(x - 18) = 0\nx - 8/3 = 0\nx - 19/3 = 0\nx - 18 = 0\nx = 8/3\nx = 19/3\nx = 18"} {"input": "Solve simultaneously:\n4x + 1y = -23/2\n4x + 10y = -97", "output": "4x + 1y = -23/2\n4x + 10y = -97\n\nUsing elimination\n4*(4x + 1y = -23/2)\n4*(4x + 10y = -97)\n16x + 4y = -46\n16x + 40y = -388\nSubtract equations\n-36y = 342\ny = 342/-36\ny = -19/2\n\nSubstitute y\n4x + 1(-19/2) = -23/2\n4x = -2\nx = -2/4\nx = -1/2"} {"input": "Solve the equations:\n7x + 7y = 19\n8x + 7y = 150/7", "output": "7x + 7y = 19\n8x + 7y = 150/7\n\nUsing elimination\n8*(7x + 7y = 19)\n7*(8x + 7y = 150/7)\n56x + 56y = 152\n56x + 49y = 150\nSubtract equations\n7y = 2\ny = 2/7\ny = 2/7\n\nSubstitute y\n7x + 7(2/7) = 19\n7x = 17\nx = 17/7\nx = 17/7"} {"input": "Solve quickly: x^3 - 17/7x^2 - 44/7x = 0", "output": "x^3 - 17/7x^2 - 44/7x = 0\n(x - -11/7)(x - 4)(x - 0) = 0\nx - -11/7 = 0\nx - 4 = 0\nx - 0 = 0\nx = -11/7\nx = 4\nx = 0"} {"input": "Solve the equation x^3 + 2/3x^2 - 103/3x - 190/3 = 0", "output": "x^3 + 2/3x^2 - 103/3x - 190/3 = 0\n(x - 19/3)(x - -5)(x - -2) = 0\nx - 19/3 = 0\nx - -5 = 0\nx - -2 = 0\nx = 19/3\nx = -5\nx = -2"} {"input": "Solve the system:\n1x + 4y = -2\n4x + 10y = -2", "output": "1x + 4y = -2\n4x + 10y = -2\n\nUsing elimination\n4*(1x + 4y = -2)\n1*(4x + 10y = -2)\n4x + 16y = -8\n4x + 10y = -2\nSubtract equations\n6y = -6\ny = -6/6\ny = -1\n\nSubstitute y\n1x + 4(-1) = -2\n1x = 2\nx = 2/1\nx = 2"} {"input": "Solve the equation x^2 - 39/8x + 7/2 = 0", "output": "x^2 - 39/8x + 7/2 = 0\n(x - 7/8)(x - 4) = 0\nx - 7/8 = 0 or x - 4 = 0\nx = 7/8\nx = 4"} {"input": "Solve the equations:\n7x + 2y = -29/10\n4x + 5y = -14", "output": "7x + 2y = -29/10\n4x + 5y = -14\n\nUsing elimination\n4*(7x + 2y = -29/10)\n7*(4x + 5y = -14)\n28x + 8y = -58/5\n28x + 35y = -98\nSubtract equations\n-27y = 432/5\ny = 432/5/-27\ny = -16/5\n\nSubstitute y\n7x + 2(-16/5) = -29/10\n7x = 7/2\nx = 7/2/7\nx = 1/2"} {"input": "Find x for 7x + 77 = 0", "output": "7x + 77 = 0\n7x = -77\nx = -77 / 7\nx = -11"} {"input": "Find the solution to 3x + 6/5 = 0", "output": "3x + 6/5 = 0\n3x = -6/5\nx = -6/5 / 3\nx = -2/5"} {"input": "Solve quickly: x^3 - 47/10x^2 + 179/25x - 88/25 = 0", "output": "x^3 - 47/10x^2 + 179/25x - 88/25 = 0\n(x - 2)(x - 8/5)(x - 11/10) = 0\nx - 2 = 0\nx - 8/5 = 0\nx - 11/10 = 0\nx = 2\nx = 8/5\nx = 11/10"} {"input": "Find the solution to x^3 - 5x^2 - 22x + 56 = 0", "output": "x^3 - 5x^2 - 22x + 56 = 0\n(x - -4)(x - 7)(x - 2) = 0\nx - -4 = 0\nx - 7 = 0\nx - 2 = 0\nx = -4\nx = 7\nx = 2"} {"input": "Solve the equations:\n10x + 3y = -959/72\n10x + 8y = -103/9", "output": "10x + 3y = -959/72\n10x + 8y = -103/9\n\nUsing elimination\n10*(10x + 3y = -959/72)\n10*(10x + 8y = -103/9)\n100x + 30y = -4795/36\n100x + 80y = -1030/9\nSubtract equations\n-50y = -75/4\ny = -75/4/-50\ny = 3/8\n\nSubstitute y\n10x + 3(3/8) = -959/72\n10x = -130/9\nx = -130/9/10\nx = -13/9"} {"input": "Compute the solution of 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve the equation x^3 - 443/24x^2 + 113/24x + 255/4 = 0", "output": "x^3 - 443/24x^2 + 113/24x + 255/4 = 0\n(x - -5/3)(x - 18)(x - 17/8) = 0\nx - -5/3 = 0\nx - 18 = 0\nx - 17/8 = 0\nx = -5/3\nx = 18\nx = 17/8"} {"input": "Find x for x^3 + 43/14x^2 - 10/7x - 50/7 = 0", "output": "x^3 + 43/14x^2 - 10/7x - 50/7 = 0\n(x - 10/7)(x - -2)(x - -5/2) = 0\nx - 10/7 = 0\nx - -2 = 0\nx - -5/2 = 0\nx = 10/7\nx = -2\nx = -5/2"} {"input": "Determine x in 1x - 2 = 0", "output": "1x - 2 = 0\n1x = 2\nx = 2 / 1\nx = 2"} {"input": "Find x in x^3 - 279/14x^2 + 51x - 289/14 = 0", "output": "x^3 - 279/14x^2 + 51x - 289/14 = 0\n(x - 17)(x - 1/2)(x - 17/7) = 0\nx - 17 = 0\nx - 1/2 = 0\nx - 17/7 = 0\nx = 17\nx = 1/2\nx = 17/7"} {"input": "Determine x in 10x - 5/2 = 0", "output": "10x - 5/2 = 0\n10x = 5/2\nx = 5/2 / 10\nx = 1/4"} {"input": "Determine x in 6x - 72 = 0", "output": "6x - 72 = 0\n6x = 72\nx = 72 / 6\nx = 12"} {"input": "Find x and y such that\n10x + 3y = -37/2\n1x + 6y = -53/4", "output": "10x + 3y = -37/2\n1x + 6y = -53/4\n\nUsing elimination\n1*(10x + 3y = -37/2)\n10*(1x + 6y = -53/4)\n10x + 3y = -37/2\n10x + 60y = -265/2\nSubtract equations\n-57y = 114\ny = 114/-57\ny = -2\n\nSubstitute y\n10x + 3(-2) = -37/2\n10x = -25/2\nx = -25/2/10\nx = -5/4"} {"input": "Solve the system:\n8x + 1y = 16/3\n7x + 5y = 61/6", "output": "8x + 1y = 16/3\n7x + 5y = 61/6\n\nUsing elimination\n7*(8x + 1y = 16/3)\n8*(7x + 5y = 61/6)\n56x + 7y = 112/3\n56x + 40y = 244/3\nSubtract equations\n-33y = -44\ny = -44/-33\ny = 4/3\n\nSubstitute y\n8x + 1(4/3) = 16/3\n8x = 4\nx = 4/8\nx = 1/2"} {"input": "Solve 1x - 17/10 = 0", "output": "1x - 17/10 = 0\n1x = 17/10\nx = 17/10 / 1\nx = 17/10"} {"input": "Solve quickly: 1x - 8/7 = 0", "output": "1x - 8/7 = 0\n1x = 8/7\nx = 8/7 / 1\nx = 8/7"} {"input": "Determine x in x^2 + 21/5x - 152/5 = 0", "output": "x^2 + 21/5x - 152/5 = 0\n(x - 19/5)(x - -8) = 0\nx - 19/5 = 0 or x - -8 = 0\nx = 19/5\nx = -8"} {"input": "Find x for x^3 + 1/2x^2 - 149/18x + 35/9 = 0", "output": "x^3 + 1/2x^2 - 149/18x + 35/9 = 0\n(x - 7/3)(x - 1/2)(x - -10/3) = 0\nx - 7/3 = 0\nx - 1/2 = 0\nx - -10/3 = 0\nx = 7/3\nx = 1/2\nx = -10/3"} {"input": "Find x and y such that\n8x + 5y = -1\n5x + 6y = 8", "output": "8x + 5y = -1\n5x + 6y = 8\n\nUsing elimination\n5*(8x + 5y = -1)\n8*(5x + 6y = 8)\n40x + 25y = -5\n40x + 48y = 64\nSubtract equations\n-23y = -69\ny = -69/-23\ny = 3\n\nSubstitute y\n8x + 5(3) = -1\n8x = -16\nx = -16/8\nx = -2"} {"input": "Find x for 9x - 63/5 = 0", "output": "9x - 63/5 = 0\n9x = 63/5\nx = 63/5 / 9\nx = 7/5"} {"input": "Solve quickly: 10x + 13 = 0", "output": "10x + 13 = 0\n10x = -13\nx = -13 / 10\nx = -13/10"} {"input": "Find x for x^2 + 19/2x + 22 = 0", "output": "x^2 + 19/2x + 22 = 0\n(x - -11/2)(x - -4) = 0\nx - -11/2 = 0 or x - -4 = 0\nx = -11/2\nx = -4"} {"input": "Find x and y such that\n9x + 6y = -72\n3x + 7y = -84", "output": "9x + 6y = -72\n3x + 7y = -84\n\nUsing elimination\n3*(9x + 6y = -72)\n9*(3x + 7y = -84)\n27x + 18y = -216\n27x + 63y = -756\nSubtract equations\n-45y = 540\ny = 540/-45\ny = -12\n\nSubstitute y\n9x + 6(-12) = -72\n9x = 0\nx = 0/9\nx = 0"} {"input": "Solve the system:\n5x + 3y = -17/2\n10x + 4y = -18", "output": "5x + 3y = -17/2\n10x + 4y = -18\n\nUsing elimination\n10*(5x + 3y = -17/2)\n5*(10x + 4y = -18)\n50x + 30y = -85\n50x + 20y = -90\nSubtract equations\n10y = 5\ny = 5/10\ny = 1/2\n\nSubstitute y\n5x + 3(1/2) = -17/2\n5x = -10\nx = -10/5\nx = -2"} {"input": "What value of x satisfies 10x + 140/3 = 0", "output": "10x + 140/3 = 0\n10x = -140/3\nx = -140/3 / 10\nx = -14/3"} {"input": "Solve the equations:\n7x + 4y = 106/5\n2x + 4y = 76/5", "output": "7x + 4y = 106/5\n2x + 4y = 76/5\n\nUsing elimination\n2*(7x + 4y = 106/5)\n7*(2x + 4y = 76/5)\n14x + 8y = 212/5\n14x + 28y = 532/5\nSubtract equations\n-20y = -64\ny = -64/-20\ny = 16/5\n\nSubstitute y\n7x + 4(16/5) = 106/5\n7x = 42/5\nx = 42/5/7\nx = 6/5"} {"input": "Determine x in 8x + 76/5 = 0", "output": "8x + 76/5 = 0\n8x = -76/5\nx = -76/5 / 8\nx = -19/10"} {"input": "Find the solution to x^2 + 91/40x - 19/80 = 0", "output": "x^2 + 91/40x - 19/80 = 0\n(x - 1/10)(x - -19/8) = 0\nx - 1/10 = 0 or x - -19/8 = 0\nx = 1/10\nx = -19/8"} {"input": "Solve quickly: 5x + 2 = 0", "output": "5x + 2 = 0\n5x = -2\nx = -2 / 5\nx = -2/5"} {"input": "Compute the solution of 4x - 48/5 = 0", "output": "4x - 48/5 = 0\n4x = 48/5\nx = 48/5 / 4\nx = 12/5"} {"input": "Determine x in x^2 - 23/6x + 11/3 = 0", "output": "x^2 - 23/6x + 11/3 = 0\n(x - 2)(x - 11/6) = 0\nx - 2 = 0 or x - 11/6 = 0\nx = 2\nx = 11/6"} {"input": "Solve simultaneously:\n3x + 5y = -173/2\n7x + 1y = -59/6", "output": "3x + 5y = -173/2\n7x + 1y = -59/6\n\nUsing elimination\n7*(3x + 5y = -173/2)\n3*(7x + 1y = -59/6)\n21x + 35y = -1211/2\n21x + 3y = -59/2\nSubtract equations\n32y = -576\ny = -576/32\ny = -18\n\nSubstitute y\n3x + 5(-18) = -173/2\n3x = 7/2\nx = 7/2/3\nx = 7/6"} {"input": "Find x for 10x - 70/3 = 0", "output": "10x - 70/3 = 0\n10x = 70/3\nx = 70/3 / 10\nx = 7/3"} {"input": "Compute the solution of x^3 - 21/40x^2 - 79/10x - 51/8 = 0", "output": "x^3 - 21/40x^2 - 79/10x - 51/8 = 0\n(x - -1)(x - -15/8)(x - 17/5) = 0\nx - -1 = 0\nx - -15/8 = 0\nx - 17/5 = 0\nx = -1\nx = -15/8\nx = 17/5"} {"input": "Find the solution to 8x - 12/5 = 0", "output": "8x - 12/5 = 0\n8x = 12/5\nx = 12/5 / 8\nx = 3/10"} {"input": "Solve the equations:\n3x + 10y = 73/7\n2x + 6y = 44/7", "output": "3x + 10y = 73/7\n2x + 6y = 44/7\n\nUsing elimination\n2*(3x + 10y = 73/7)\n3*(2x + 6y = 44/7)\n6x + 20y = 146/7\n6x + 18y = 132/7\nSubtract equations\n2y = 2\ny = 2/2\ny = 1\n\nSubstitute y\n3x + 10(1) = 73/7\n3x = 3/7\nx = 3/7/3\nx = 1/7"} {"input": "Solve x^3 + 124/9x^2 + 77/3x - 484/9 = 0", "output": "x^3 + 124/9x^2 + 77/3x - 484/9 = 0\n(x - -11)(x - -4)(x - 11/9) = 0\nx - -11 = 0\nx - -4 = 0\nx - 11/9 = 0\nx = -11\nx = -4\nx = 11/9"} {"input": "Compute the solution of x^2 + 89/56x - 15/28 = 0", "output": "x^2 + 89/56x - 15/28 = 0\n(x - -15/8)(x - 2/7) = 0\nx - -15/8 = 0 or x - 2/7 = 0\nx = -15/8\nx = 2/7"} {"input": "Solve the equations:\n2x + 10y = -255/7\n10x + 3y = -247/14", "output": "2x + 10y = -255/7\n10x + 3y = -247/14\n\nUsing elimination\n10*(2x + 10y = -255/7)\n2*(10x + 3y = -247/14)\n20x + 100y = -2550/7\n20x + 6y = -247/7\nSubtract equations\n94y = -329\ny = -329/94\ny = -7/2\n\nSubstitute y\n2x + 10(-7/2) = -255/7\n2x = -10/7\nx = -10/7/2\nx = -5/7"} {"input": "Solve 2x - 3 = 0", "output": "2x - 3 = 0\n2x = 3\nx = 3 / 2\nx = 3/2"} {"input": "Solve x^3 - 301/30x^2 + 773/30x - 91/5 = 0", "output": "x^3 - 301/30x^2 + 773/30x - 91/5 = 0\n(x - 6/5)(x - 13/2)(x - 7/3) = 0\nx - 6/5 = 0\nx - 13/2 = 0\nx - 7/3 = 0\nx = 6/5\nx = 13/2\nx = 7/3"} {"input": "Solve the equation x^2 - 19/42x - 88/21 = 0", "output": "x^2 - 19/42x - 88/21 = 0\n(x - 16/7)(x - -11/6) = 0\nx - 16/7 = 0 or x - -11/6 = 0\nx = 16/7\nx = -11/6"} {"input": "Solve x^3 - 157/9x^2 + 1378/27x - 1064/27 = 0", "output": "x^3 - 157/9x^2 + 1378/27x - 1064/27 = 0\n(x - 4/3)(x - 14)(x - 19/9) = 0\nx - 4/3 = 0\nx - 14 = 0\nx - 19/9 = 0\nx = 4/3\nx = 14\nx = 19/9"} {"input": "Solve the system:\n1x + 9y = -145/8\n7x + 8y = -10", "output": "1x + 9y = -145/8\n7x + 8y = -10\n\nUsing elimination\n7*(1x + 9y = -145/8)\n1*(7x + 8y = -10)\n7x + 63y = -1015/8\n7x + 8y = -10\nSubtract equations\n55y = -935/8\ny = -935/8/55\ny = -17/8\n\nSubstitute y\n1x + 9(-17/8) = -145/8\n1x = 1\nx = 1/1\nx = 1"} {"input": "What value of x satisfies x^2 - 73/15x + 22/5 = 0", "output": "x^2 - 73/15x + 22/5 = 0\n(x - 11/3)(x - 6/5) = 0\nx - 11/3 = 0 or x - 6/5 = 0\nx = 11/3\nx = 6/5"} {"input": "Find x for x^2 + 22/9x + 8/9 = 0", "output": "x^2 + 22/9x + 8/9 = 0\n(x - -2)(x - -4/9) = 0\nx - -2 = 0 or x - -4/9 = 0\nx = -2\nx = -4/9"} {"input": "Find x in x^2 + 30/7x + 216/49 = 0", "output": "x^2 + 30/7x + 216/49 = 0\n(x - -18/7)(x - -12/7) = 0\nx - -18/7 = 0 or x - -12/7 = 0\nx = -18/7\nx = -12/7"} {"input": "Find x for x^2 + 81/5x - 76 = 0", "output": "x^2 + 81/5x - 76 = 0\n(x - 19/5)(x - -20) = 0\nx - 19/5 = 0 or x - -20 = 0\nx = 19/5\nx = -20"} {"input": "Solve the system:\n1x + 1y = -53/10\n5x + 8y = -40", "output": "1x + 1y = -53/10\n5x + 8y = -40\n\nUsing elimination\n5*(1x + 1y = -53/10)\n1*(5x + 8y = -40)\n5x + 5y = -53/2\n5x + 8y = -40\nSubtract equations\n-3y = 27/2\ny = 27/2/-3\ny = -9/2\n\nSubstitute y\n1x + 1(-9/2) = -53/10\n1x = -4/5\nx = -4/5/1\nx = -4/5"} {"input": "Find the solution to x^3 + 71/10x^2 + 51/10x - 27 = 0", "output": "x^3 + 71/10x^2 + 51/10x - 27 = 0\n(x - -5)(x - -18/5)(x - 3/2) = 0\nx - -5 = 0\nx - -18/5 = 0\nx - 3/2 = 0\nx = -5\nx = -18/5\nx = 3/2"} {"input": "Solve the equations:\n8x + 1y = 18/5\n1x + 1y = -33/20", "output": "8x + 1y = 18/5\n1x + 1y = -33/20\n\nUsing elimination\n1*(8x + 1y = 18/5)\n8*(1x + 1y = -33/20)\n8x + 1y = 18/5\n8x + 8y = -66/5\nSubtract equations\n-7y = 84/5\ny = 84/5/-7\ny = -12/5\n\nSubstitute y\n8x + 1(-12/5) = 18/5\n8x = 6\nx = 6/8\nx = 3/4"} {"input": "Solve quickly: 2x - 12/5 = 0", "output": "2x - 12/5 = 0\n2x = 12/5\nx = 12/5 / 2\nx = 6/5"} {"input": "Solve x^2 - 103/5x + 12 = 0", "output": "x^2 - 103/5x + 12 = 0\n(x - 20)(x - 3/5) = 0\nx - 20 = 0 or x - 3/5 = 0\nx = 20\nx = 3/5"} {"input": "Find the solution to x^3 - 1249/252x^2 + 15/2x - 119/36 = 0", "output": "x^3 - 1249/252x^2 + 15/2x - 119/36 = 0\n(x - 17/7)(x - 7/9)(x - 7/4) = 0\nx - 17/7 = 0\nx - 7/9 = 0\nx - 7/4 = 0\nx = 17/7\nx = 7/9\nx = 7/4"} {"input": "Compute the solution of x^2 + 9/5x = 0", "output": "x^2 + 9/5x = 0\n(x - -9/5)(x - 0) = 0\nx - -9/5 = 0 or x - 0 = 0\nx = -9/5\nx = 0"} {"input": "Find x and y such that\n1x + 8y = 101\n8x + 6y = 54", "output": "1x + 8y = 101\n8x + 6y = 54\n\nUsing elimination\n8*(1x + 8y = 101)\n1*(8x + 6y = 54)\n8x + 64y = 808\n8x + 6y = 54\nSubtract equations\n58y = 754\ny = 754/58\ny = 13\n\nSubstitute y\n1x + 8(13) = 101\n1x = -3\nx = -3/1\nx = -3"} {"input": "Find x and y such that\n9x + 2y = 811/14\n8x + 7y = 50", "output": "9x + 2y = 811/14\n8x + 7y = 50\n\nUsing elimination\n8*(9x + 2y = 811/14)\n9*(8x + 7y = 50)\n72x + 16y = 3244/7\n72x + 63y = 450\nSubtract equations\n-47y = 94/7\ny = 94/7/-47\ny = -2/7\n\nSubstitute y\n9x + 2(-2/7) = 811/14\n9x = 117/2\nx = 117/2/9\nx = 13/2"} {"input": "Find x and y such that\n2x + 7y = 47/8\n2x + 1y = 41/8", "output": "2x + 7y = 47/8\n2x + 1y = 41/8\n\nUsing elimination\n2*(2x + 7y = 47/8)\n2*(2x + 1y = 41/8)\n4x + 14y = 47/4\n4x + 2y = 41/4\nSubtract equations\n12y = 3/2\ny = 3/2/12\ny = 1/8\n\nSubstitute y\n2x + 7(1/8) = 47/8\n2x = 5\nx = 5/2\nx = 5/2"} {"input": "Solve 1x - 9 = 0", "output": "1x - 9 = 0\n1x = 9\nx = 9 / 1\nx = 9"} {"input": "Determine x in 2x - 40/3 = 0", "output": "2x - 40/3 = 0\n2x = 40/3\nx = 40/3 / 2\nx = 20/3"} {"input": "What value of x satisfies 10x - 65/2 = 0", "output": "10x - 65/2 = 0\n10x = 65/2\nx = 65/2 / 10\nx = 13/4"} {"input": "What value of x satisfies 3x + 33/2 = 0", "output": "3x + 33/2 = 0\n3x = -33/2\nx = -33/2 / 3\nx = -11/2"} {"input": "What value of x satisfies x^3 + 68/21x^2 + 145/63x + 4/9 = 0", "output": "x^3 + 68/21x^2 + 145/63x + 4/9 = 0\n(x - -1/3)(x - -4/7)(x - -7/3) = 0\nx - -1/3 = 0\nx - -4/7 = 0\nx - -7/3 = 0\nx = -1/3\nx = -4/7\nx = -7/3"} {"input": "Determine x in x^3 - 31/36x^2 - 185/216x + 25/54 = 0", "output": "x^3 - 31/36x^2 - 185/216x + 25/54 = 0\n(x - -5/6)(x - 4/9)(x - 5/4) = 0\nx - -5/6 = 0\nx - 4/9 = 0\nx - 5/4 = 0\nx = -5/6\nx = 4/9\nx = 5/4"} {"input": "Solve the system:\n6x + 3y = -35/2\n6x + 6y = -31/2", "output": "6x + 3y = -35/2\n6x + 6y = -31/2\n\nUsing elimination\n6*(6x + 3y = -35/2)\n6*(6x + 6y = -31/2)\n36x + 18y = -105\n36x + 36y = -93\nSubtract equations\n-18y = -12\ny = -12/-18\ny = 2/3\n\nSubstitute y\n6x + 3(2/3) = -35/2\n6x = -39/2\nx = -39/2/6\nx = -13/4"} {"input": "Solve x^2 - 16 = 0", "output": "x^2 - 16 = 0\n(x - 4)(x - -4) = 0\nx - 4 = 0 or x - -4 = 0\nx = 4\nx = -4"} {"input": "Find x in x^3 - 181/20x^2 + 57/10x + 108/5 = 0", "output": "x^3 - 181/20x^2 + 57/10x + 108/5 = 0\n(x - 9/4)(x - 8)(x - -6/5) = 0\nx - 9/4 = 0\nx - 8 = 0\nx - -6/5 = 0\nx = 9/4\nx = 8\nx = -6/5"} {"input": "Determine x in x^3 - 5/2x^2 + 17/16x + 7/16 = 0", "output": "x^3 - 5/2x^2 + 17/16x + 7/16 = 0\n(x - -1/4)(x - 1)(x - 7/4) = 0\nx - -1/4 = 0\nx - 1 = 0\nx - 7/4 = 0\nx = -1/4\nx = 1\nx = 7/4"} {"input": "Solve the equation x^2 - 3x - 55/4 = 0", "output": "x^2 - 3x - 55/4 = 0\n(x - 11/2)(x - -5/2) = 0\nx - 11/2 = 0 or x - -5/2 = 0\nx = 11/2\nx = -5/2"} {"input": "Find x in x^2 - 3/4x - 7/4 = 0", "output": "x^2 - 3/4x - 7/4 = 0\n(x - 7/4)(x - -1) = 0\nx - 7/4 = 0 or x - -1 = 0\nx = 7/4\nx = -1"} {"input": "Determine x in 3x - 13/3 = 0", "output": "3x - 13/3 = 0\n3x = 13/3\nx = 13/3 / 3\nx = 13/9"} {"input": "Solve simultaneously:\n6x + 2y = -11/35\n5x + 3y = 47/70", "output": "6x + 2y = -11/35\n5x + 3y = 47/70\n\nUsing elimination\n5*(6x + 2y = -11/35)\n6*(5x + 3y = 47/70)\n30x + 10y = -11/7\n30x + 18y = 141/35\nSubtract equations\n-8y = -28/5\ny = -28/5/-8\ny = 7/10\n\nSubstitute y\n6x + 2(7/10) = -11/35\n6x = -12/7\nx = -12/7/6\nx = -2/7"} {"input": "Determine x in x^2 - 15/2x + 13/2 = 0", "output": "x^2 - 15/2x + 13/2 = 0\n(x - 13/2)(x - 1) = 0\nx - 13/2 = 0 or x - 1 = 0\nx = 13/2\nx = 1"} {"input": "Solve quickly: x^3 + 17/3x^2 + 65/12x + 3/4 = 0", "output": "x^3 + 17/3x^2 + 65/12x + 3/4 = 0\n(x - -1/6)(x - -1)(x - -9/2) = 0\nx - -1/6 = 0\nx - -1 = 0\nx - -9/2 = 0\nx = -1/6\nx = -1\nx = -9/2"} {"input": "Solve the system:\n6x + 10y = -134/9\n3x + 2y = -25/9", "output": "6x + 10y = -134/9\n3x + 2y = -25/9\n\nUsing elimination\n3*(6x + 10y = -134/9)\n6*(3x + 2y = -25/9)\n18x + 30y = -134/3\n18x + 12y = -50/3\nSubtract equations\n18y = -28\ny = -28/18\ny = -14/9\n\nSubstitute y\n6x + 10(-14/9) = -134/9\n6x = 2/3\nx = 2/3/6\nx = 1/9"} {"input": "Solve the equation x^3 + 281/12x^2 + 177/2x + 1045/12 = 0", "output": "x^3 + 281/12x^2 + 177/2x + 1045/12 = 0\n(x - -5/3)(x - -11/4)(x - -19) = 0\nx - -5/3 = 0\nx - -11/4 = 0\nx - -19 = 0\nx = -5/3\nx = -11/4\nx = -19"} {"input": "Solve simultaneously:\n7x + 7y = -35/8\n8x + 7y = -45/8", "output": "7x + 7y = -35/8\n8x + 7y = -45/8\n\nUsing elimination\n8*(7x + 7y = -35/8)\n7*(8x + 7y = -45/8)\n56x + 56y = -35\n56x + 49y = -315/8\nSubtract equations\n7y = 35/8\ny = 35/8/7\ny = 5/8\n\nSubstitute y\n7x + 7(5/8) = -35/8\n7x = -35/4\nx = -35/4/7\nx = -5/4"} {"input": "Solve the equation 4x - 56/9 = 0", "output": "4x - 56/9 = 0\n4x = 56/9\nx = 56/9 / 4\nx = 14/9"} {"input": "Find the solution to x^3 - 277/30x^2 + 84/5x - 49/6 = 0", "output": "x^3 - 277/30x^2 + 84/5x - 49/6 = 0\n(x - 7)(x - 5/6)(x - 7/5) = 0\nx - 7 = 0\nx - 5/6 = 0\nx - 7/5 = 0\nx = 7\nx = 5/6\nx = 7/5"} {"input": "Solve 6x + 51/5 = 0", "output": "6x + 51/5 = 0\n6x = -51/5\nx = -51/5 / 6\nx = -17/10"} {"input": "Solve 6x + 2 = 0", "output": "6x + 2 = 0\n6x = -2\nx = -2 / 6\nx = -1/3"} {"input": "Solve the system:\n7x + 1y = 23/6\n1x + 4y = -83/21", "output": "7x + 1y = 23/6\n1x + 4y = -83/21\n\nUsing elimination\n1*(7x + 1y = 23/6)\n7*(1x + 4y = -83/21)\n7x + 1y = 23/6\n7x + 28y = -83/3\nSubtract equations\n-27y = 63/2\ny = 63/2/-27\ny = -7/6\n\nSubstitute y\n7x + 1(-7/6) = 23/6\n7x = 5\nx = 5/7\nx = 5/7"} {"input": "Compute the solution of 7x + 7 = 0", "output": "7x + 7 = 0\n7x = -7\nx = -7 / 7\nx = -1"} {"input": "Find x and y such that\n6x + 6y = 90/7\n9x + 4y = 160/7", "output": "6x + 6y = 90/7\n9x + 4y = 160/7\n\nUsing elimination\n9*(6x + 6y = 90/7)\n6*(9x + 4y = 160/7)\n54x + 54y = 810/7\n54x + 24y = 960/7\nSubtract equations\n30y = -150/7\ny = -150/7/30\ny = -5/7\n\nSubstitute y\n6x + 6(-5/7) = 90/7\n6x = 120/7\nx = 120/7/6\nx = 20/7"} {"input": "Find x and y such that\n3x + 10y = -82/5\n7x + 8y = -38/5", "output": "3x + 10y = -82/5\n7x + 8y = -38/5\n\nUsing elimination\n7*(3x + 10y = -82/5)\n3*(7x + 8y = -38/5)\n21x + 70y = -574/5\n21x + 24y = -114/5\nSubtract equations\n46y = -92\ny = -92/46\ny = -2\n\nSubstitute y\n3x + 10(-2) = -82/5\n3x = 18/5\nx = 18/5/3\nx = 6/5"} {"input": "Solve simultaneously:\n5x + 4y = 13/4\n5x + 9y = -1/2", "output": "5x + 4y = 13/4\n5x + 9y = -1/2\n\nUsing elimination\n5*(5x + 4y = 13/4)\n5*(5x + 9y = -1/2)\n25x + 20y = 65/4\n25x + 45y = -5/2\nSubtract equations\n-25y = 75/4\ny = 75/4/-25\ny = -3/4\n\nSubstitute y\n5x + 4(-3/4) = 13/4\n5x = 25/4\nx = 25/4/5\nx = 5/4"} {"input": "Determine x in 5x = 0", "output": "5x = 0\n5x = 0\nx = 0 / 5\nx = 0"} {"input": "Solve the equations:\n5x + 4y = 5\n3x + 10y = 201/10", "output": "5x + 4y = 5\n3x + 10y = 201/10\n\nUsing elimination\n3*(5x + 4y = 5)\n5*(3x + 10y = 201/10)\n15x + 12y = 15\n15x + 50y = 201/2\nSubtract equations\n-38y = -171/2\ny = -171/2/-38\ny = 9/4\n\nSubstitute y\n5x + 4(9/4) = 5\n5x = -4\nx = -4/5\nx = -4/5"} {"input": "Solve the system:\n2x + 8y = 445/21\n8x + 3y = 649/21", "output": "2x + 8y = 445/21\n8x + 3y = 649/21\n\nUsing elimination\n8*(2x + 8y = 445/21)\n2*(8x + 3y = 649/21)\n16x + 64y = 3560/21\n16x + 6y = 1298/21\nSubtract equations\n58y = 754/7\ny = 754/7/58\ny = 13/7\n\nSubstitute y\n2x + 8(13/7) = 445/21\n2x = 19/3\nx = 19/3/2\nx = 19/6"} {"input": "Find x and y such that\n7x + 10y = -75/2\n5x + 10y = -65/2", "output": "7x + 10y = -75/2\n5x + 10y = -65/2\n\nUsing elimination\n5*(7x + 10y = -75/2)\n7*(5x + 10y = -65/2)\n35x + 50y = -375/2\n35x + 70y = -455/2\nSubtract equations\n-20y = 40\ny = 40/-20\ny = -2\n\nSubstitute y\n7x + 10(-2) = -75/2\n7x = -35/2\nx = -35/2/7\nx = -5/2"} {"input": "Solve quickly: 1x + 11/3 = 0", "output": "1x + 11/3 = 0\n1x = -11/3\nx = -11/3 / 1\nx = -11/3"} {"input": "Compute the solution of 9x + 144 = 0", "output": "9x + 144 = 0\n9x = -144\nx = -144 / 9\nx = -16"} {"input": "Find x for x^3 + 7/12x^2 - 593/12x + 238/3 = 0", "output": "x^3 + 7/12x^2 - 593/12x + 238/3 = 0\n(x - 17/3)(x - -8)(x - 7/4) = 0\nx - 17/3 = 0\nx - -8 = 0\nx - 7/4 = 0\nx = 17/3\nx = -8\nx = 7/4"} {"input": "Find x for 7x + 119/6 = 0", "output": "7x + 119/6 = 0\n7x = -119/6\nx = -119/6 / 7\nx = -17/6"} {"input": "Solve 3x - 51/5 = 0", "output": "3x - 51/5 = 0\n3x = 51/5\nx = 51/5 / 3\nx = 17/5"} {"input": "Find x in x^2 - 4x - 5 = 0", "output": "x^2 - 4x - 5 = 0\n(x - -1)(x - 5) = 0\nx - -1 = 0 or x - 5 = 0\nx = -1\nx = 5"} {"input": "Determine x in x^3 - 1/3x^2 - 88/81x = 0", "output": "x^3 - 1/3x^2 - 88/81x = 0\n(x - 0)(x - 11/9)(x - -8/9) = 0\nx - 0 = 0\nx - 11/9 = 0\nx - -8/9 = 0\nx = 0\nx = 11/9\nx = -8/9"} {"input": "Compute the solution of 2x + 16/7 = 0", "output": "2x + 16/7 = 0\n2x = -16/7\nx = -16/7 / 2\nx = -8/7"} {"input": "Solve quickly: x^2 + 44/9x + 32/9 = 0", "output": "x^2 + 44/9x + 32/9 = 0\n(x - -4)(x - -8/9) = 0\nx - -4 = 0 or x - -8/9 = 0\nx = -4\nx = -8/9"} {"input": "Find x and y such that\n5x + 5y = -85/14\n5x + 6y = -39/7", "output": "5x + 5y = -85/14\n5x + 6y = -39/7\n\nUsing elimination\n5*(5x + 5y = -85/14)\n5*(5x + 6y = -39/7)\n25x + 25y = -425/14\n25x + 30y = -195/7\nSubtract equations\n-5y = -5/2\ny = -5/2/-5\ny = 1/2\n\nSubstitute y\n5x + 5(1/2) = -85/14\n5x = -60/7\nx = -60/7/5\nx = -12/7"} {"input": "Solve the equation 8x - 56/9 = 0", "output": "8x - 56/9 = 0\n8x = 56/9\nx = 56/9 / 8\nx = 7/9"} {"input": "Solve the equations:\n6x + 2y = 7\n3x + 3y = 29/2", "output": "6x + 2y = 7\n3x + 3y = 29/2\n\nUsing elimination\n3*(6x + 2y = 7)\n6*(3x + 3y = 29/2)\n18x + 6y = 21\n18x + 18y = 87\nSubtract equations\n-12y = -66\ny = -66/-12\ny = 11/2\n\nSubstitute y\n6x + 2(11/2) = 7\n6x = -4\nx = -4/6\nx = -2/3"} {"input": "Solve the equation 2x + 28/9 = 0", "output": "2x + 28/9 = 0\n2x = -28/9\nx = -28/9 / 2\nx = -14/9"} {"input": "Find x in x^2 + 7/2x - 36 = 0", "output": "x^2 + 7/2x - 36 = 0\n(x - 9/2)(x - -8) = 0\nx - 9/2 = 0 or x - -8 = 0\nx = 9/2\nx = -8"} {"input": "Find x in 5x - 25/3 = 0", "output": "5x - 25/3 = 0\n5x = 25/3\nx = 25/3 / 5\nx = 5/3"} {"input": "Find the solution to x^2 - 9/2x + 187/50 = 0", "output": "x^2 - 9/2x + 187/50 = 0\n(x - 17/5)(x - 11/10) = 0\nx - 17/5 = 0 or x - 11/10 = 0\nx = 17/5\nx = 11/10"} {"input": "Solve the equations:\n5x + 6y = 187/8\n7x + 7y = 217/8", "output": "5x + 6y = 187/8\n7x + 7y = 217/8\n\nUsing elimination\n7*(5x + 6y = 187/8)\n5*(7x + 7y = 217/8)\n35x + 42y = 1309/8\n35x + 35y = 1085/8\nSubtract equations\n7y = 28\ny = 28/7\ny = 4\n\nSubstitute y\n5x + 6(4) = 187/8\n5x = -5/8\nx = -5/8/5\nx = -1/8"} {"input": "Solve x^2 + 69/28x + 9/7 = 0", "output": "x^2 + 69/28x + 9/7 = 0\n(x - -3/4)(x - -12/7) = 0\nx - -3/4 = 0 or x - -12/7 = 0\nx = -3/4\nx = -12/7"} {"input": "Find the solution to x^2 + 139/40x + 209/80 = 0", "output": "x^2 + 139/40x + 209/80 = 0\n(x - -19/8)(x - -11/10) = 0\nx - -19/8 = 0 or x - -11/10 = 0\nx = -19/8\nx = -11/10"} {"input": "Solve the equations:\n5x + 6y = -7/2\n2x + 9y = -8", "output": "5x + 6y = -7/2\n2x + 9y = -8\n\nUsing elimination\n2*(5x + 6y = -7/2)\n5*(2x + 9y = -8)\n10x + 12y = -7\n10x + 45y = -40\nSubtract equations\n-33y = 33\ny = 33/-33\ny = -1\n\nSubstitute y\n5x + 6(-1) = -7/2\n5x = 5/2\nx = 5/2/5\nx = 1/2"} {"input": "Solve quickly: 5x + 35/6 = 0", "output": "5x + 35/6 = 0\n5x = -35/6\nx = -35/6 / 5\nx = -7/6"} {"input": "Solve simultaneously:\n8x + 1y = 207/7\n9x + 10y = 661/14", "output": "8x + 1y = 207/7\n9x + 10y = 661/14\n\nUsing elimination\n9*(8x + 1y = 207/7)\n8*(9x + 10y = 661/14)\n72x + 9y = 1863/7\n72x + 80y = 2644/7\nSubtract equations\n-71y = -781/7\ny = -781/7/-71\ny = 11/7\n\nSubstitute y\n8x + 1(11/7) = 207/7\n8x = 28\nx = 28/8\nx = 7/2"} {"input": "Solve simultaneously:\n5x + 1y = 2/3\n4x + 9y = -134/5", "output": "5x + 1y = 2/3\n4x + 9y = -134/5\n\nUsing elimination\n4*(5x + 1y = 2/3)\n5*(4x + 9y = -134/5)\n20x + 4y = 8/3\n20x + 45y = -134\nSubtract equations\n-41y = 410/3\ny = 410/3/-41\ny = -10/3\n\nSubstitute y\n5x + 1(-10/3) = 2/3\n5x = 4\nx = 4/5\nx = 4/5"} {"input": "Determine x in x^3 - 43/30x^2 - 703/150x + 51/25 = 0", "output": "x^3 - 43/30x^2 - 703/150x + 51/25 = 0\n(x - -9/5)(x - 17/6)(x - 2/5) = 0\nx - -9/5 = 0\nx - 17/6 = 0\nx - 2/5 = 0\nx = -9/5\nx = 17/6\nx = 2/5"} {"input": "Find the solution to x^2 - 41/4x + 5/2 = 0", "output": "x^2 - 41/4x + 5/2 = 0\n(x - 1/4)(x - 10) = 0\nx - 1/4 = 0 or x - 10 = 0\nx = 1/4\nx = 10"} {"input": "Solve x^3 + 59/36x^2 - 115/24x - 475/72 = 0", "output": "x^3 + 59/36x^2 - 115/24x - 475/72 = 0\n(x - -5/2)(x - 19/9)(x - -5/4) = 0\nx - -5/2 = 0\nx - 19/9 = 0\nx - -5/4 = 0\nx = -5/2\nx = 19/9\nx = -5/4"} {"input": "Compute the solution of 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "What value of x satisfies x^3 - 77/6x^2 + 107/3x - 21/2 = 0", "output": "x^3 - 77/6x^2 + 107/3x - 21/2 = 0\n(x - 9)(x - 7/2)(x - 1/3) = 0\nx - 9 = 0\nx - 7/2 = 0\nx - 1/3 = 0\nx = 9\nx = 7/2\nx = 1/3"} {"input": "What value of x satisfies 1x + 5 = 0", "output": "1x + 5 = 0\n1x = -5\nx = -5 / 1\nx = -5"} {"input": "Compute the solution of x^2 + 9/2x + 9/2 = 0", "output": "x^2 + 9/2x + 9/2 = 0\n(x - -3)(x - -3/2) = 0\nx - -3 = 0 or x - -3/2 = 0\nx = -3\nx = -3/2"} {"input": "Find x and y such that\n3x + 4y = 113/6\n3x + 10y = 161/6", "output": "3x + 4y = 113/6\n3x + 10y = 161/6\n\nUsing elimination\n3*(3x + 4y = 113/6)\n3*(3x + 10y = 161/6)\n9x + 12y = 113/2\n9x + 30y = 161/2\nSubtract equations\n-18y = -24\ny = -24/-18\ny = 4/3\n\nSubstitute y\n3x + 4(4/3) = 113/6\n3x = 27/2\nx = 27/2/3\nx = 9/2"} {"input": "What value of x satisfies x^2 - 57/35x - 176/35 = 0", "output": "x^2 - 57/35x - 176/35 = 0\n(x - 16/5)(x - -11/7) = 0\nx - 16/5 = 0 or x - -11/7 = 0\nx = 16/5\nx = -11/7"} {"input": "Solve the equations:\n10x + 8y = 329/10\n7x + 5y = 89/4", "output": "10x + 8y = 329/10\n7x + 5y = 89/4\n\nUsing elimination\n7*(10x + 8y = 329/10)\n10*(7x + 5y = 89/4)\n70x + 56y = 2303/10\n70x + 50y = 445/2\nSubtract equations\n6y = 39/5\ny = 39/5/6\ny = 13/10\n\nSubstitute y\n10x + 8(13/10) = 329/10\n10x = 45/2\nx = 45/2/10\nx = 9/4"} {"input": "Solve x^2 - 37/7x + 48/7 = 0", "output": "x^2 - 37/7x + 48/7 = 0\n(x - 16/7)(x - 3) = 0\nx - 16/7 = 0 or x - 3 = 0\nx = 16/7\nx = 3"} {"input": "Find x for x^3 - 229/15x^2 + 832/15x - 28 = 0", "output": "x^3 - 229/15x^2 + 832/15x - 28 = 0\n(x - 10)(x - 3/5)(x - 14/3) = 0\nx - 10 = 0\nx - 3/5 = 0\nx - 14/3 = 0\nx = 10\nx = 3/5\nx = 14/3"} {"input": "Solve the equations:\n1x + 9y = 83/5\n2x + 6y = 46/5", "output": "1x + 9y = 83/5\n2x + 6y = 46/5\n\nUsing elimination\n2*(1x + 9y = 83/5)\n1*(2x + 6y = 46/5)\n2x + 18y = 166/5\n2x + 6y = 46/5\nSubtract equations\n12y = 24\ny = 24/12\ny = 2\n\nSubstitute y\n1x + 9(2) = 83/5\n1x = -7/5\nx = -7/5/1\nx = -7/5"} {"input": "Solve simultaneously:\n7x + 1y = 729/14\n5x + 2y = 513/14", "output": "7x + 1y = 729/14\n5x + 2y = 513/14\n\nUsing elimination\n5*(7x + 1y = 729/14)\n7*(5x + 2y = 513/14)\n35x + 5y = 3645/14\n35x + 14y = 513/2\nSubtract equations\n-9y = 27/7\ny = 27/7/-9\ny = -3/7\n\nSubstitute y\n7x + 1(-3/7) = 729/14\n7x = 105/2\nx = 105/2/7\nx = 15/2"} {"input": "Find x and y such that\n5x + 9y = -53\n6x + 1y = 5", "output": "5x + 9y = -53\n6x + 1y = 5\n\nUsing elimination\n6*(5x + 9y = -53)\n5*(6x + 1y = 5)\n30x + 54y = -318\n30x + 5y = 25\nSubtract equations\n49y = -343\ny = -343/49\ny = -7\n\nSubstitute y\n5x + 9(-7) = -53\n5x = 10\nx = 10/5\nx = 2"} {"input": "Solve the equations:\n8x + 10y = -264/7\n1x + 4y = -110/7", "output": "8x + 10y = -264/7\n1x + 4y = -110/7\n\nUsing elimination\n1*(8x + 10y = -264/7)\n8*(1x + 4y = -110/7)\n8x + 10y = -264/7\n8x + 32y = -880/7\nSubtract equations\n-22y = 88\ny = 88/-22\ny = -4\n\nSubstitute y\n8x + 10(-4) = -264/7\n8x = 16/7\nx = 16/7/8\nx = 2/7"} {"input": "Solve the system:\n5x + 7y = -65/4\n4x + 9y = -35/4", "output": "5x + 7y = -65/4\n4x + 9y = -35/4\n\nUsing elimination\n4*(5x + 7y = -65/4)\n5*(4x + 9y = -35/4)\n20x + 28y = -65\n20x + 45y = -175/4\nSubtract equations\n-17y = -85/4\ny = -85/4/-17\ny = 5/4\n\nSubstitute y\n5x + 7(5/4) = -65/4\n5x = -25\nx = -25/5\nx = -5"} {"input": "Determine x in 3x + 21/4 = 0", "output": "3x + 21/4 = 0\n3x = -21/4\nx = -21/4 / 3\nx = -7/4"} {"input": "Solve the equation x^2 - 145/36x + 4 = 0", "output": "x^2 - 145/36x + 4 = 0\n(x - 9/4)(x - 16/9) = 0\nx - 9/4 = 0 or x - 16/9 = 0\nx = 9/4\nx = 16/9"} {"input": "Solve the equations:\n10x + 1y = -151/10\n7x + 7y = -56/5", "output": "10x + 1y = -151/10\n7x + 7y = -56/5\n\nUsing elimination\n7*(10x + 1y = -151/10)\n10*(7x + 7y = -56/5)\n70x + 7y = -1057/10\n70x + 70y = -112\nSubtract equations\n-63y = 63/10\ny = 63/10/-63\ny = -1/10\n\nSubstitute y\n10x + 1(-1/10) = -151/10\n10x = -15\nx = -15/10\nx = -3/2"} {"input": "Determine x in x^3 - 24/35x^2 - 55/7x + 48/5 = 0", "output": "x^3 - 24/35x^2 - 55/7x + 48/5 = 0\n(x - -3)(x - 7/5)(x - 16/7) = 0\nx - -3 = 0\nx - 7/5 = 0\nx - 16/7 = 0\nx = -3\nx = 7/5\nx = 16/7"} {"input": "Solve the equations:\n7x + 4y = -29/2\n5x + 5y = -25/2", "output": "7x + 4y = -29/2\n5x + 5y = -25/2\n\nUsing elimination\n5*(7x + 4y = -29/2)\n7*(5x + 5y = -25/2)\n35x + 20y = -145/2\n35x + 35y = -175/2\nSubtract equations\n-15y = 15\ny = 15/-15\ny = -1\n\nSubstitute y\n7x + 4(-1) = -29/2\n7x = -21/2\nx = -21/2/7\nx = -3/2"} {"input": "Determine x in x^2 - 129/7x + 272/7 = 0", "output": "x^2 - 129/7x + 272/7 = 0\n(x - 17/7)(x - 16) = 0\nx - 17/7 = 0 or x - 16 = 0\nx = 17/7\nx = 16"} {"input": "Determine x in x^2 - 78/7x + 80/7 = 0", "output": "x^2 - 78/7x + 80/7 = 0\n(x - 8/7)(x - 10) = 0\nx - 8/7 = 0 or x - 10 = 0\nx = 8/7\nx = 10"} {"input": "Find x for x^2 - 2x = 0", "output": "x^2 - 2x = 0\n(x - 0)(x - 2) = 0\nx - 0 = 0 or x - 2 = 0\nx = 0\nx = 2"} {"input": "Compute the solution of x^2 + 83/21x + 24/7 = 0", "output": "x^2 + 83/21x + 24/7 = 0\n(x - -9/7)(x - -8/3) = 0\nx - -9/7 = 0 or x - -8/3 = 0\nx = -9/7\nx = -8/3"} {"input": "Find x for x^3 + 47/12x^2 + 7/3x - 5/4 = 0", "output": "x^3 + 47/12x^2 + 7/3x - 5/4 = 0\n(x - -5/4)(x - 1/3)(x - -3) = 0\nx - -5/4 = 0\nx - 1/3 = 0\nx - -3 = 0\nx = -5/4\nx = 1/3\nx = -3"} {"input": "Solve the equation x^2 + 7x - 8 = 0", "output": "x^2 + 7x - 8 = 0\n(x - -8)(x - 1) = 0\nx - -8 = 0 or x - 1 = 0\nx = -8\nx = 1"} {"input": "Solve x^3 + 17/15x^2 - 71/12x - 187/60 = 0", "output": "x^3 + 17/15x^2 - 71/12x - 187/60 = 0\n(x - 11/5)(x - -17/6)(x - -1/2) = 0\nx - 11/5 = 0\nx - -17/6 = 0\nx - -1/2 = 0\nx = 11/5\nx = -17/6\nx = -1/2"} {"input": "Compute the solution of 10x + 20 = 0", "output": "10x + 20 = 0\n10x = -20\nx = -20 / 10\nx = -2"} {"input": "Find x for x^3 - 23/5x^2 - 266/45x + 392/15 = 0", "output": "x^3 - 23/5x^2 - 266/45x + 392/15 = 0\n(x - 14/3)(x - -12/5)(x - 7/3) = 0\nx - 14/3 = 0\nx - -12/5 = 0\nx - 7/3 = 0\nx = 14/3\nx = -12/5\nx = 7/3"} {"input": "Solve quickly: x^3 - 83/14x^2 - 1125/14x - 1053/7 = 0", "output": "x^3 - 83/14x^2 - 1125/14x - 1053/7 = 0\n(x - -9/2)(x - 13)(x - -18/7) = 0\nx - -9/2 = 0\nx - 13 = 0\nx - -18/7 = 0\nx = -9/2\nx = 13\nx = -18/7"} {"input": "Solve the equation 5x + 100/7 = 0", "output": "5x + 100/7 = 0\n5x = -100/7\nx = -100/7 / 5\nx = -20/7"} {"input": "Solve x^3 + 363/56x^2 - 243/56x - 5 = 0", "output": "x^3 + 363/56x^2 - 243/56x - 5 = 0\n(x - -5/8)(x - 8/7)(x - -7) = 0\nx - -5/8 = 0\nx - 8/7 = 0\nx - -7 = 0\nx = -5/8\nx = 8/7\nx = -7"} {"input": "Determine x in x^3 - 8x^2 - 51/4x + 135/4 = 0", "output": "x^3 - 8x^2 - 51/4x + 135/4 = 0\n(x - 3/2)(x - -5/2)(x - 9) = 0\nx - 3/2 = 0\nx - -5/2 = 0\nx - 9 = 0\nx = 3/2\nx = -5/2\nx = 9"} {"input": "Find the solution to x^2 - 3/2x - 27 = 0", "output": "x^2 - 3/2x - 27 = 0\n(x - -9/2)(x - 6) = 0\nx - -9/2 = 0 or x - 6 = 0\nx = -9/2\nx = 6"} {"input": "Compute the solution of x^2 - 96/5x + 187/5 = 0", "output": "x^2 - 96/5x + 187/5 = 0\n(x - 11/5)(x - 17) = 0\nx - 11/5 = 0 or x - 17 = 0\nx = 11/5\nx = 17"} {"input": "Solve the equations:\n5x + 10y = -495/14\n8x + 3y = -279/7", "output": "5x + 10y = -495/14\n8x + 3y = -279/7\n\nUsing elimination\n8*(5x + 10y = -495/14)\n5*(8x + 3y = -279/7)\n40x + 80y = -1980/7\n40x + 15y = -1395/7\nSubtract equations\n65y = -585/7\ny = -585/7/65\ny = -9/7\n\nSubstitute y\n5x + 10(-9/7) = -495/14\n5x = -45/2\nx = -45/2/5\nx = -9/2"} {"input": "Find x and y such that\n5x + 1y = -319/8\n7x + 4y = -62", "output": "5x + 1y = -319/8\n7x + 4y = -62\n\nUsing elimination\n7*(5x + 1y = -319/8)\n5*(7x + 4y = -62)\n35x + 7y = -2233/8\n35x + 20y = -310\nSubtract equations\n-13y = 247/8\ny = 247/8/-13\ny = -19/8\n\nSubstitute y\n5x + 1(-19/8) = -319/8\n5x = -75/2\nx = -75/2/5\nx = -15/2"} {"input": "Find the solution to x^3 + 92/5x^2 + 199/5x + 112/5 = 0", "output": "x^3 + 92/5x^2 + 199/5x + 112/5 = 0\n(x - -7/5)(x - -16)(x - -1) = 0\nx - -7/5 = 0\nx - -16 = 0\nx - -1 = 0\nx = -7/5\nx = -16\nx = -1"} {"input": "Solve 5x - 25/4 = 0", "output": "5x - 25/4 = 0\n5x = 25/4\nx = 25/4 / 5\nx = 5/4"} {"input": "Find x for x^2 + 1/5x - 3/20 = 0", "output": "x^2 + 1/5x - 3/20 = 0\n(x - -1/2)(x - 3/10) = 0\nx - -1/2 = 0 or x - 3/10 = 0\nx = -1/2\nx = 3/10"} {"input": "Find x and y such that\n2x + 3y = -41/6\n8x + 7y = -89/6", "output": "2x + 3y = -41/6\n8x + 7y = -89/6\n\nUsing elimination\n8*(2x + 3y = -41/6)\n2*(8x + 7y = -89/6)\n16x + 24y = -164/3\n16x + 14y = -89/3\nSubtract equations\n10y = -25\ny = -25/10\ny = -5/2\n\nSubstitute y\n2x + 3(-5/2) = -41/6\n2x = 2/3\nx = 2/3/2\nx = 1/3"} {"input": "Solve the equations:\n1x + 3y = 87/35\n10x + 7y = 548/35", "output": "1x + 3y = 87/35\n10x + 7y = 548/35\n\nUsing elimination\n10*(1x + 3y = 87/35)\n1*(10x + 7y = 548/35)\n10x + 30y = 174/7\n10x + 7y = 548/35\nSubtract equations\n23y = 46/5\ny = 46/5/23\ny = 2/5\n\nSubstitute y\n1x + 3(2/5) = 87/35\n1x = 9/7\nx = 9/7/1\nx = 9/7"} {"input": "Find the solution to x^3 + 19/140x^2 - 541/140x + 12/5 = 0", "output": "x^3 + 19/140x^2 - 541/140x + 12/5 = 0\n(x - 3/4)(x - 7/5)(x - -16/7) = 0\nx - 3/4 = 0\nx - 7/5 = 0\nx - -16/7 = 0\nx = 3/4\nx = 7/5\nx = -16/7"} {"input": "Solve the system:\n1x + 5y = -163/36\n5x + 10y = -205/18", "output": "1x + 5y = -163/36\n5x + 10y = -205/18\n\nUsing elimination\n5*(1x + 5y = -163/36)\n1*(5x + 10y = -205/18)\n5x + 25y = -815/36\n5x + 10y = -205/18\nSubtract equations\n15y = -45/4\ny = -45/4/15\ny = -3/4\n\nSubstitute y\n1x + 5(-3/4) = -163/36\n1x = -7/9\nx = -7/9/1\nx = -7/9"} {"input": "Compute the solution of x^2 + 31/12x - 17/24 = 0", "output": "x^2 + 31/12x - 17/24 = 0\n(x - 1/4)(x - -17/6) = 0\nx - 1/4 = 0 or x - -17/6 = 0\nx = 1/4\nx = -17/6"} {"input": "Find the solution to x^2 - 27/40x - 9/4 = 0", "output": "x^2 - 27/40x - 9/4 = 0\n(x - -6/5)(x - 15/8) = 0\nx - -6/5 = 0 or x - 15/8 = 0\nx = -6/5\nx = 15/8"} {"input": "Solve the system:\n9x + 8y = -365/14\n8x + 4y = -128/7", "output": "9x + 8y = -365/14\n8x + 4y = -128/7\n\nUsing elimination\n8*(9x + 8y = -365/14)\n9*(8x + 4y = -128/7)\n72x + 64y = -1460/7\n72x + 36y = -1152/7\nSubtract equations\n28y = -44\ny = -44/28\ny = -11/7\n\nSubstitute y\n9x + 8(-11/7) = -365/14\n9x = -27/2\nx = -27/2/9\nx = -3/2"} {"input": "Solve the system:\n10x + 9y = -215/2\n8x + 10y = -314/3", "output": "10x + 9y = -215/2\n8x + 10y = -314/3\n\nUsing elimination\n8*(10x + 9y = -215/2)\n10*(8x + 10y = -314/3)\n80x + 72y = -860\n80x + 100y = -3140/3\nSubtract equations\n-28y = 560/3\ny = 560/3/-28\ny = -20/3\n\nSubstitute y\n10x + 9(-20/3) = -215/2\n10x = -95/2\nx = -95/2/10\nx = -19/4"} {"input": "Solve the equations:\n8x + 4y = 36\n5x + 9y = 16", "output": "8x + 4y = 36\n5x + 9y = 16\n\nUsing elimination\n5*(8x + 4y = 36)\n8*(5x + 9y = 16)\n40x + 20y = 180\n40x + 72y = 128\nSubtract equations\n-52y = 52\ny = 52/-52\ny = -1\n\nSubstitute y\n8x + 4(-1) = 36\n8x = 40\nx = 40/8\nx = 5"} {"input": "Solve the equations:\n4x + 3y = -19/4\n10x + 4y = -11", "output": "4x + 3y = -19/4\n10x + 4y = -11\n\nUsing elimination\n10*(4x + 3y = -19/4)\n4*(10x + 4y = -11)\n40x + 30y = -95/2\n40x + 16y = -44\nSubtract equations\n14y = -7/2\ny = -7/2/14\ny = -1/4\n\nSubstitute y\n4x + 3(-1/4) = -19/4\n4x = -4\nx = -4/4\nx = -1"} {"input": "Find x in 4x - 8/3 = 0", "output": "4x - 8/3 = 0\n4x = 8/3\nx = 8/3 / 4\nx = 2/3"} {"input": "Solve quickly: x^2 - 95/9x + 50/9 = 0", "output": "x^2 - 95/9x + 50/9 = 0\n(x - 10)(x - 5/9) = 0\nx - 10 = 0 or x - 5/9 = 0\nx = 10\nx = 5/9"} {"input": "Solve the system:\n2x + 5y = -49/9\n8x + 8y = -656/45", "output": "2x + 5y = -49/9\n8x + 8y = -656/45\n\nUsing elimination\n8*(2x + 5y = -49/9)\n2*(8x + 8y = -656/45)\n16x + 40y = -392/9\n16x + 16y = -1312/45\nSubtract equations\n24y = -72/5\ny = -72/5/24\ny = -3/5\n\nSubstitute y\n2x + 5(-3/5) = -49/9\n2x = -22/9\nx = -22/9/2\nx = -11/9"} {"input": "Solve quickly: 8x - 12 = 0", "output": "8x - 12 = 0\n8x = 12\nx = 12 / 8\nx = 3/2"} {"input": "Solve the equations:\n10x + 8y = 308/3\n5x + 7y = 202/3", "output": "10x + 8y = 308/3\n5x + 7y = 202/3\n\nUsing elimination\n5*(10x + 8y = 308/3)\n10*(5x + 7y = 202/3)\n50x + 40y = 1540/3\n50x + 70y = 2020/3\nSubtract equations\n-30y = -160\ny = -160/-30\ny = 16/3\n\nSubstitute y\n10x + 8(16/3) = 308/3\n10x = 60\nx = 60/10\nx = 6"} {"input": "Find x for x^3 - 13/12x^2 - 1285/324x - 275/162 = 0", "output": "x^3 - 13/12x^2 - 1285/324x - 275/162 = 0\n(x - 11/4)(x - -10/9)(x - -5/9) = 0\nx - 11/4 = 0\nx - -10/9 = 0\nx - -5/9 = 0\nx = 11/4\nx = -10/9\nx = -5/9"} {"input": "Find x in x^3 - 53/6x^2 + 43/2x - 26/3 = 0", "output": "x^3 - 53/6x^2 + 43/2x - 26/3 = 0\n(x - 4)(x - 13/3)(x - 1/2) = 0\nx - 4 = 0\nx - 13/3 = 0\nx - 1/2 = 0\nx = 4\nx = 13/3\nx = 1/2"} {"input": "Determine x in 1x + 7/8 = 0", "output": "1x + 7/8 = 0\n1x = -7/8\nx = -7/8 / 1\nx = -7/8"} {"input": "Solve the equations:\n3x + 5y = -35/3\n7x + 8y = -89/3", "output": "3x + 5y = -35/3\n7x + 8y = -89/3\n\nUsing elimination\n7*(3x + 5y = -35/3)\n3*(7x + 8y = -89/3)\n21x + 35y = -245/3\n21x + 24y = -89\nSubtract equations\n11y = 22/3\ny = 22/3/11\ny = 2/3\n\nSubstitute y\n3x + 5(2/3) = -35/3\n3x = -15\nx = -15/3\nx = -5"} {"input": "Find the solution to 4x - 12 = 0", "output": "4x - 12 = 0\n4x = 12\nx = 12 / 4\nx = 3"} {"input": "Solve the equation x^3 + 53/8x^2 - 943/8x - 819/4 = 0", "output": "x^3 + 53/8x^2 - 943/8x - 819/4 = 0\n(x - 9)(x - -13/8)(x - -14) = 0\nx - 9 = 0\nx - -13/8 = 0\nx - -14 = 0\nx = 9\nx = -13/8\nx = -14"} {"input": "Solve the equation 5x + 35/6 = 0", "output": "5x + 35/6 = 0\n5x = -35/6\nx = -35/6 / 5\nx = -7/6"} {"input": "Find the solution to x^2 - 28/3x - 20/3 = 0", "output": "x^2 - 28/3x - 20/3 = 0\n(x - 10)(x - -2/3) = 0\nx - 10 = 0 or x - -2/3 = 0\nx = 10\nx = -2/3"} {"input": "Solve quickly: x^2 - 161/30x + 209/30 = 0", "output": "x^2 - 161/30x + 209/30 = 0\n(x - 19/6)(x - 11/5) = 0\nx - 19/6 = 0 or x - 11/5 = 0\nx = 19/6\nx = 11/5"} {"input": "Compute the solution of x^3 + 54/7x^2 - 160/7x = 0", "output": "x^3 + 54/7x^2 - 160/7x = 0\n(x - -10)(x - 16/7)(x - 0) = 0\nx - -10 = 0\nx - 16/7 = 0\nx - 0 = 0\nx = -10\nx = 16/7\nx = 0"} {"input": "Solve quickly: x^2 - 23/4x + 51/8 = 0", "output": "x^2 - 23/4x + 51/8 = 0\n(x - 17/4)(x - 3/2) = 0\nx - 17/4 = 0 or x - 3/2 = 0\nx = 17/4\nx = 3/2"} {"input": "Solve the equation 10x - 160/7 = 0", "output": "10x - 160/7 = 0\n10x = 160/7\nx = 160/7 / 10\nx = 16/7"} {"input": "Solve quickly: x^2 + 13/9x - 56/27 = 0", "output": "x^2 + 13/9x - 56/27 = 0\n(x - -7/3)(x - 8/9) = 0\nx - -7/3 = 0 or x - 8/9 = 0\nx = -7/3\nx = 8/9"} {"input": "Find x and y such that\n6x + 6y = 144/7\n4x + 5y = 110/7", "output": "6x + 6y = 144/7\n4x + 5y = 110/7\n\nUsing elimination\n4*(6x + 6y = 144/7)\n6*(4x + 5y = 110/7)\n24x + 24y = 576/7\n24x + 30y = 660/7\nSubtract equations\n-6y = -12\ny = -12/-6\ny = 2\n\nSubstitute y\n6x + 6(2) = 144/7\n6x = 60/7\nx = 60/7/6\nx = 10/7"} {"input": "Solve quickly: 9x + 81/5 = 0", "output": "9x + 81/5 = 0\n9x = -81/5\nx = -81/5 / 9\nx = -9/5"} {"input": "Determine x in 2x + 7/4 = 0", "output": "2x + 7/4 = 0\n2x = -7/4\nx = -7/4 / 2\nx = -7/8"} {"input": "What value of x satisfies x^3 + 83/7x^2 + 320/7x + 400/7 = 0", "output": "x^3 + 83/7x^2 + 320/7x + 400/7 = 0\n(x - -5)(x - -20/7)(x - -4) = 0\nx - -5 = 0\nx - -20/7 = 0\nx - -4 = 0\nx = -5\nx = -20/7\nx = -4"} {"input": "Determine x in x^2 + 7/30x - 1/2 = 0", "output": "x^2 + 7/30x - 1/2 = 0\n(x - 3/5)(x - -5/6) = 0\nx - 3/5 = 0 or x - -5/6 = 0\nx = 3/5\nx = -5/6"} {"input": "Solve quickly: x^3 - 163/72x^2 - 617/216x + 665/108 = 0", "output": "x^3 - 163/72x^2 - 617/216x + 665/108 = 0\n(x - 19/8)(x - -5/3)(x - 14/9) = 0\nx - 19/8 = 0\nx - -5/3 = 0\nx - 14/9 = 0\nx = 19/8\nx = -5/3\nx = 14/9"} {"input": "Solve the equation 6x + 30 = 0", "output": "6x + 30 = 0\n6x = -30\nx = -30 / 6\nx = -5"} {"input": "Determine x in 1x + 4 = 0", "output": "1x + 4 = 0\n1x = -4\nx = -4 / 1\nx = -4"} {"input": "Compute the solution of 7x - 7/8 = 0", "output": "7x - 7/8 = 0\n7x = 7/8\nx = 7/8 / 7\nx = 1/8"} {"input": "Solve the equations:\n4x + 3y = -169/18\n3x + 8y = -47/3", "output": "4x + 3y = -169/18\n3x + 8y = -47/3\n\nUsing elimination\n3*(4x + 3y = -169/18)\n4*(3x + 8y = -47/3)\n12x + 9y = -169/6\n12x + 32y = -188/3\nSubtract equations\n-23y = 69/2\ny = 69/2/-23\ny = -3/2\n\nSubstitute y\n4x + 3(-3/2) = -169/18\n4x = -44/9\nx = -44/9/4\nx = -11/9"} {"input": "Find the solution to x^3 - 23/6x^2 - 58/3x + 133/6 = 0", "output": "x^3 - 23/6x^2 - 58/3x + 133/6 = 0\n(x - -7/2)(x - 19/3)(x - 1) = 0\nx - -7/2 = 0\nx - 19/3 = 0\nx - 1 = 0\nx = -7/2\nx = 19/3\nx = 1"} {"input": "Solve the equations:\n4x + 10y = -1688/63\n5x + 1y = -500/63", "output": "4x + 10y = -1688/63\n5x + 1y = -500/63\n\nUsing elimination\n5*(4x + 10y = -1688/63)\n4*(5x + 1y = -500/63)\n20x + 50y = -8440/63\n20x + 4y = -2000/63\nSubtract equations\n46y = -920/9\ny = -920/9/46\ny = -20/9\n\nSubstitute y\n4x + 10(-20/9) = -1688/63\n4x = -32/7\nx = -32/7/4\nx = -8/7"} {"input": "What value of x satisfies 1x - 2/7 = 0", "output": "1x - 2/7 = 0\n1x = 2/7\nx = 2/7 / 1\nx = 2/7"} {"input": "Solve quickly: x^2 + 13x + 165/4 = 0", "output": "x^2 + 13x + 165/4 = 0\n(x - -11/2)(x - -15/2) = 0\nx - -11/2 = 0 or x - -15/2 = 0\nx = -11/2\nx = -15/2"} {"input": "Solve the equation x^3 + 39/40x^2 - 621/80x + 243/40 = 0", "output": "x^3 + 39/40x^2 - 621/80x + 243/40 = 0\n(x - 9/8)(x - -18/5)(x - 3/2) = 0\nx - 9/8 = 0\nx - -18/5 = 0\nx - 3/2 = 0\nx = 9/8\nx = -18/5\nx = 3/2"} {"input": "Solve quickly: x^2 - 31/40x - 171/80 = 0", "output": "x^2 - 31/40x - 171/80 = 0\n(x - -9/8)(x - 19/10) = 0\nx - -9/8 = 0 or x - 19/10 = 0\nx = -9/8\nx = 19/10"} {"input": "Solve the system:\n3x + 3y = 105/8\n4x + 1y = -1/2", "output": "3x + 3y = 105/8\n4x + 1y = -1/2\n\nUsing elimination\n4*(3x + 3y = 105/8)\n3*(4x + 1y = -1/2)\n12x + 12y = 105/2\n12x + 3y = -3/2\nSubtract equations\n9y = 54\ny = 54/9\ny = 6\n\nSubstitute y\n3x + 3(6) = 105/8\n3x = -39/8\nx = -39/8/3\nx = -13/8"} {"input": "Compute the solution of x^3 + 29/4x^2 + 89/8x - 15/2 = 0", "output": "x^3 + 29/4x^2 + 89/8x - 15/2 = 0\n(x - 1/2)(x - -15/4)(x - -4) = 0\nx - 1/2 = 0\nx - -15/4 = 0\nx - -4 = 0\nx = 1/2\nx = -15/4\nx = -4"} {"input": "Find x and y such that\n4x + 8y = 2/3\n1x + 9y = 71/6", "output": "4x + 8y = 2/3\n1x + 9y = 71/6\n\nUsing elimination\n1*(4x + 8y = 2/3)\n4*(1x + 9y = 71/6)\n4x + 8y = 2/3\n4x + 36y = 142/3\nSubtract equations\n-28y = -140/3\ny = -140/3/-28\ny = 5/3\n\nSubstitute y\n4x + 8(5/3) = 2/3\n4x = -38/3\nx = -38/3/4\nx = -19/6"} {"input": "Solve x^2 + 27/5x + 34/5 = 0", "output": "x^2 + 27/5x + 34/5 = 0\n(x - -17/5)(x - -2) = 0\nx - -17/5 = 0 or x - -2 = 0\nx = -17/5\nx = -2"} {"input": "What value of x satisfies x^2 + 35/3x + 88/3 = 0", "output": "x^2 + 35/3x + 88/3 = 0\n(x - -11/3)(x - -8) = 0\nx - -11/3 = 0 or x - -8 = 0\nx = -11/3\nx = -8"} {"input": "Solve the equation x^2 + 39/4x - 5/2 = 0", "output": "x^2 + 39/4x - 5/2 = 0\n(x - -10)(x - 1/4) = 0\nx - -10 = 0 or x - 1/4 = 0\nx = -10\nx = 1/4"} {"input": "Solve the equation x^2 + 26/3x + 17 = 0", "output": "x^2 + 26/3x + 17 = 0\n(x - -17/3)(x - -3) = 0\nx - -17/3 = 0 or x - -3 = 0\nx = -17/3\nx = -3"} {"input": "Find the solution to x^3 + 28/9x^2 - 89/9x - 76/3 = 0", "output": "x^3 + 28/9x^2 - 89/9x - 76/3 = 0\n(x - 3)(x - -19/9)(x - -4) = 0\nx - 3 = 0\nx - -19/9 = 0\nx - -4 = 0\nx = 3\nx = -19/9\nx = -4"} {"input": "What value of x satisfies 10x - 45/4 = 0", "output": "10x - 45/4 = 0\n10x = 45/4\nx = 45/4 / 10\nx = 9/8"} {"input": "Determine x in 1x + 7/4 = 0", "output": "1x + 7/4 = 0\n1x = -7/4\nx = -7/4 / 1\nx = -7/4"} {"input": "Find x and y such that\n6x + 8y = 40/3\n1x + 9y = 38", "output": "6x + 8y = 40/3\n1x + 9y = 38\n\nUsing elimination\n1*(6x + 8y = 40/3)\n6*(1x + 9y = 38)\n6x + 8y = 40/3\n6x + 54y = 228\nSubtract equations\n-46y = -644/3\ny = -644/3/-46\ny = 14/3\n\nSubstitute y\n6x + 8(14/3) = 40/3\n6x = -24\nx = -24/6\nx = -4"} {"input": "Solve the system:\n10x + 8y = 394/3\n10x + 2y = 106/3", "output": "10x + 8y = 394/3\n10x + 2y = 106/3\n\nUsing elimination\n10*(10x + 8y = 394/3)\n10*(10x + 2y = 106/3)\n100x + 80y = 3940/3\n100x + 20y = 1060/3\nSubtract equations\n60y = 960\ny = 960/60\ny = 16\n\nSubstitute y\n10x + 8(16) = 394/3\n10x = 10/3\nx = 10/3/10\nx = 1/3"} {"input": "Compute the solution of x^3 - 9x^2 + 35/4x + 75/4 = 0", "output": "x^3 - 9x^2 + 35/4x + 75/4 = 0\n(x - -1)(x - 5/2)(x - 15/2) = 0\nx - -1 = 0\nx - 5/2 = 0\nx - 15/2 = 0\nx = -1\nx = 5/2\nx = 15/2"} {"input": "Solve x^2 - 4/3x - 20/3 = 0", "output": "x^2 - 4/3x - 20/3 = 0\n(x - -2)(x - 10/3) = 0\nx - -2 = 0 or x - 10/3 = 0\nx = -2\nx = 10/3"} {"input": "Solve the equation 7x + 70/3 = 0", "output": "7x + 70/3 = 0\n7x = -70/3\nx = -70/3 / 7\nx = -10/3"} {"input": "Solve the equations:\n1x + 6y = -8\n7x + 5y = -1/2", "output": "1x + 6y = -8\n7x + 5y = -1/2\n\nUsing elimination\n7*(1x + 6y = -8)\n1*(7x + 5y = -1/2)\n7x + 42y = -56\n7x + 5y = -1/2\nSubtract equations\n37y = -111/2\ny = -111/2/37\ny = -3/2\n\nSubstitute y\n1x + 6(-3/2) = -8\n1x = 1\nx = 1/1\nx = 1"} {"input": "Solve simultaneously:\n9x + 9y = 81/4\n1x + 2y = 17/4", "output": "9x + 9y = 81/4\n1x + 2y = 17/4\n\nUsing elimination\n1*(9x + 9y = 81/4)\n9*(1x + 2y = 17/4)\n9x + 9y = 81/4\n9x + 18y = 153/4\nSubtract equations\n-9y = -18\ny = -18/-9\ny = 2\n\nSubstitute y\n9x + 9(2) = 81/4\n9x = 9/4\nx = 9/4/9\nx = 1/4"} {"input": "Find x in 2x - 16 = 0", "output": "2x - 16 = 0\n2x = 16\nx = 16 / 2\nx = 8"} {"input": "What value of x satisfies x^3 - 107/5x^2 + 692/25x + 32/5 = 0", "output": "x^3 - 107/5x^2 + 692/25x + 32/5 = 0\n(x - 20)(x - -1/5)(x - 8/5) = 0\nx - 20 = 0\nx - -1/5 = 0\nx - 8/5 = 0\nx = 20\nx = -1/5\nx = 8/5"} {"input": "Compute the solution of 8x - 24 = 0", "output": "8x - 24 = 0\n8x = 24\nx = 24 / 8\nx = 3"} {"input": "Find the solution to x^2 + 1/2x - 3 = 0", "output": "x^2 + 1/2x - 3 = 0\n(x - -2)(x - 3/2) = 0\nx - -2 = 0 or x - 3/2 = 0\nx = -2\nx = 3/2"} {"input": "Solve 1x + 19/10 = 0", "output": "1x + 19/10 = 0\n1x = -19/10\nx = -19/10 / 1\nx = -19/10"} {"input": "Solve x^2 - 29/45x - 52/45 = 0", "output": "x^2 - 29/45x - 52/45 = 0\n(x - 13/9)(x - -4/5) = 0\nx - 13/9 = 0 or x - -4/5 = 0\nx = 13/9\nx = -4/5"} {"input": "Find x for 9x + 24 = 0", "output": "9x + 24 = 0\n9x = -24\nx = -24 / 9\nx = -8/3"} {"input": "Find x for x^2 + 47/28x + 5/14 = 0", "output": "x^2 + 47/28x + 5/14 = 0\n(x - -1/4)(x - -10/7) = 0\nx - -1/4 = 0 or x - -10/7 = 0\nx = -1/4\nx = -10/7"} {"input": "Find x in 4x - 8 = 0", "output": "4x - 8 = 0\n4x = 8\nx = 8 / 4\nx = 2"} {"input": "Determine x in x^3 - 208/45x^2 + 389/135x + 308/135 = 0", "output": "x^3 - 208/45x^2 + 389/135x + 308/135 = 0\n(x - -4/9)(x - 7/5)(x - 11/3) = 0\nx - -4/9 = 0\nx - 7/5 = 0\nx - 11/3 = 0\nx = -4/9\nx = 7/5\nx = 11/3"} {"input": "Find x in x^3 + 13/10x^2 - 38/45x + 1/10 = 0", "output": "x^3 + 13/10x^2 - 38/45x + 1/10 = 0\n(x - -9/5)(x - 1/6)(x - 1/3) = 0\nx - -9/5 = 0\nx - 1/6 = 0\nx - 1/3 = 0\nx = -9/5\nx = 1/6\nx = 1/3"} {"input": "Solve simultaneously:\n2x + 5y = -25/2\n4x + 5y = -35/2", "output": "2x + 5y = -25/2\n4x + 5y = -35/2\n\nUsing elimination\n4*(2x + 5y = -25/2)\n2*(4x + 5y = -35/2)\n8x + 20y = -50\n8x + 10y = -35\nSubtract equations\n10y = -15\ny = -15/10\ny = -3/2\n\nSubstitute y\n2x + 5(-3/2) = -25/2\n2x = -5\nx = -5/2\nx = -5/2"} {"input": "Solve 5x - 9/2 = 0", "output": "5x - 9/2 = 0\n5x = 9/2\nx = 9/2 / 5\nx = 9/10"} {"input": "What value of x satisfies x^3 - 19/9x^2 - 152/27x + 140/27 = 0", "output": "x^3 - 19/9x^2 - 152/27x + 140/27 = 0\n(x - 10/3)(x - -2)(x - 7/9) = 0\nx - 10/3 = 0\nx - -2 = 0\nx - 7/9 = 0\nx = 10/3\nx = -2\nx = 7/9"} {"input": "Determine x in 3x - 11/3 = 0", "output": "3x - 11/3 = 0\n3x = 11/3\nx = 11/3 / 3\nx = 11/9"} {"input": "Determine x in 3x + 21/4 = 0", "output": "3x + 21/4 = 0\n3x = -21/4\nx = -21/4 / 3\nx = -7/4"} {"input": "Solve simultaneously:\n1x + 4y = -71/15\n2x + 9y = -49/5", "output": "1x + 4y = -71/15\n2x + 9y = -49/5\n\nUsing elimination\n2*(1x + 4y = -71/15)\n1*(2x + 9y = -49/5)\n2x + 8y = -142/15\n2x + 9y = -49/5\nSubtract equations\n-1y = 1/3\ny = 1/3/-1\ny = -1/3\n\nSubstitute y\n1x + 4(-1/3) = -71/15\n1x = -17/5\nx = -17/5/1\nx = -17/5"} {"input": "Solve quickly: 4x + 15/2 = 0", "output": "4x + 15/2 = 0\n4x = -15/2\nx = -15/2 / 4\nx = -15/8"} {"input": "Solve 1x + 2 = 0", "output": "1x + 2 = 0\n1x = -2\nx = -2 / 1\nx = -2"} {"input": "Find x in 2x - 9/2 = 0", "output": "2x - 9/2 = 0\n2x = 9/2\nx = 9/2 / 2\nx = 9/4"} {"input": "Determine x in 5x - 55/7 = 0", "output": "5x - 55/7 = 0\n5x = 55/7\nx = 55/7 / 5\nx = 11/7"} {"input": "Solve simultaneously:\n5x + 9y = -182/45\n10x + 9y = -607/45", "output": "5x + 9y = -182/45\n10x + 9y = -607/45\n\nUsing elimination\n10*(5x + 9y = -182/45)\n5*(10x + 9y = -607/45)\n50x + 90y = -364/9\n50x + 45y = -607/9\nSubtract equations\n45y = 27\ny = 27/45\ny = 3/5\n\nSubstitute y\n5x + 9(3/5) = -182/45\n5x = -85/9\nx = -85/9/5\nx = -17/9"} {"input": "Solve quickly: x^3 - 143/70x^2 - 242/245x + 1331/490 = 0", "output": "x^3 - 143/70x^2 - 242/245x + 1331/490 = 0\n(x - 11/7)(x - 11/7)(x - -11/10) = 0\nx - 11/7 = 0\nx - 11/7 = 0\nx - -11/10 = 0\nx = 11/7\nx = 11/7\nx = -11/10"} {"input": "Solve the equation 4x + 18 = 0", "output": "4x + 18 = 0\n4x = -18\nx = -18 / 4\nx = -9/2"} {"input": "Solve x^2 - 163/90x + 17/90 = 0", "output": "x^2 - 163/90x + 17/90 = 0\n(x - 17/10)(x - 1/9) = 0\nx - 17/10 = 0 or x - 1/9 = 0\nx = 17/10\nx = 1/9"} {"input": "What value of x satisfies x^3 - 11/30x^2 - 56/5x - 33/10 = 0", "output": "x^3 - 11/30x^2 - 56/5x - 33/10 = 0\n(x - -3/10)(x - -3)(x - 11/3) = 0\nx - -3/10 = 0\nx - -3 = 0\nx - 11/3 = 0\nx = -3/10\nx = -3\nx = 11/3"} {"input": "Find x and y such that\n3x + 10y = 733/10\n6x + 7y = 278/5", "output": "3x + 10y = 733/10\n6x + 7y = 278/5\n\nUsing elimination\n6*(3x + 10y = 733/10)\n3*(6x + 7y = 278/5)\n18x + 60y = 2199/5\n18x + 21y = 834/5\nSubtract equations\n39y = 273\ny = 273/39\ny = 7\n\nSubstitute y\n3x + 10(7) = 733/10\n3x = 33/10\nx = 33/10/3\nx = 11/10"} {"input": "Solve the equation 4x + 44/7 = 0", "output": "4x + 44/7 = 0\n4x = -44/7\nx = -44/7 / 4\nx = -11/7"} {"input": "Solve simultaneously:\n1x + 10y = 152/9\n4x + 10y = 98/9", "output": "1x + 10y = 152/9\n4x + 10y = 98/9\n\nUsing elimination\n4*(1x + 10y = 152/9)\n1*(4x + 10y = 98/9)\n4x + 40y = 608/9\n4x + 10y = 98/9\nSubtract equations\n30y = 170/3\ny = 170/3/30\ny = 17/9\n\nSubstitute y\n1x + 10(17/9) = 152/9\n1x = -2\nx = -2/1\nx = -2"} {"input": "Compute the solution of x^2 - 17/12x - 133/24 = 0", "output": "x^2 - 17/12x - 133/24 = 0\n(x - 19/6)(x - -7/4) = 0\nx - 19/6 = 0 or x - -7/4 = 0\nx = 19/6\nx = -7/4"} {"input": "Solve simultaneously:\n2x + 5y = 86\n2x + 4y = 68", "output": "2x + 5y = 86\n2x + 4y = 68\n\nUsing elimination\n2*(2x + 5y = 86)\n2*(2x + 4y = 68)\n4x + 10y = 172\n4x + 8y = 136\nSubtract equations\n2y = 36\ny = 36/2\ny = 18\n\nSubstitute y\n2x + 5(18) = 86\n2x = -4\nx = -4/2\nx = -2"} {"input": "Find x and y such that\n7x + 10y = 459/20\n2x + 2y = 99/20", "output": "7x + 10y = 459/20\n2x + 2y = 99/20\n\nUsing elimination\n2*(7x + 10y = 459/20)\n7*(2x + 2y = 99/20)\n14x + 20y = 459/10\n14x + 14y = 693/20\nSubtract equations\n6y = 45/4\ny = 45/4/6\ny = 15/8\n\nSubstitute y\n7x + 10(15/8) = 459/20\n7x = 21/5\nx = 21/5/7\nx = 3/5"} {"input": "Compute the solution of x^2 - 20/7x - 75/7 = 0", "output": "x^2 - 20/7x - 75/7 = 0\n(x - -15/7)(x - 5) = 0\nx - -15/7 = 0 or x - 5 = 0\nx = -15/7\nx = 5"} {"input": "Find x for x^3 - 25/6x^2 - 83/6x + 17 = 0", "output": "x^3 - 25/6x^2 - 83/6x + 17 = 0\n(x - -17/6)(x - 1)(x - 6) = 0\nx - -17/6 = 0\nx - 1 = 0\nx - 6 = 0\nx = -17/6\nx = 1\nx = 6"} {"input": "Find x in x^3 + 261/20x^2 + 247/20x - 3 = 0", "output": "x^3 + 261/20x^2 + 247/20x - 3 = 0\n(x - 1/5)(x - -12)(x - -5/4) = 0\nx - 1/5 = 0\nx - -12 = 0\nx - -5/4 = 0\nx = 1/5\nx = -12\nx = -5/4"} {"input": "Solve quickly: x^3 - 11/2x^2 + 5x + 4 = 0", "output": "x^3 - 11/2x^2 + 5x + 4 = 0\n(x - 2)(x - 4)(x - -1/2) = 0\nx - 2 = 0\nx - 4 = 0\nx - -1/2 = 0\nx = 2\nx = 4\nx = -1/2"} {"input": "Solve the system:\n3x + 7y = -181/7\n8x + 8y = -184/7", "output": "3x + 7y = -181/7\n8x + 8y = -184/7\n\nUsing elimination\n8*(3x + 7y = -181/7)\n3*(8x + 8y = -184/7)\n24x + 56y = -1448/7\n24x + 24y = -552/7\nSubtract equations\n32y = -128\ny = -128/32\ny = -4\n\nSubstitute y\n3x + 7(-4) = -181/7\n3x = 15/7\nx = 15/7/3\nx = 5/7"} {"input": "Solve simultaneously:\n4x + 10y = 39\n4x + 1y = 51/2", "output": "4x + 10y = 39\n4x + 1y = 51/2\n\nUsing elimination\n4*(4x + 10y = 39)\n4*(4x + 1y = 51/2)\n16x + 40y = 156\n16x + 4y = 102\nSubtract equations\n36y = 54\ny = 54/36\ny = 3/2\n\nSubstitute y\n4x + 10(3/2) = 39\n4x = 24\nx = 24/4\nx = 6"} {"input": "What value of x satisfies x^3 + 25/3x^2 - 334/3x + 544/3 = 0", "output": "x^3 + 25/3x^2 - 334/3x + 544/3 = 0\n(x - -16)(x - 2)(x - 17/3) = 0\nx - -16 = 0\nx - 2 = 0\nx - 17/3 = 0\nx = -16\nx = 2\nx = 17/3"} {"input": "Find the solution to x^2 + 14x + 33 = 0", "output": "x^2 + 14x + 33 = 0\n(x - -11)(x - -3) = 0\nx - -11 = 0 or x - -3 = 0\nx = -11\nx = -3"} {"input": "Solve x^3 + 61/12x^2 + 47/8x - 9/8 = 0", "output": "x^3 + 61/12x^2 + 47/8x - 9/8 = 0\n(x - -9/4)(x - 1/6)(x - -3) = 0\nx - -9/4 = 0\nx - 1/6 = 0\nx - -3 = 0\nx = -9/4\nx = 1/6\nx = -3"} {"input": "Solve the equation x^3 + 71/18x^2 + 109/27x + 65/162 = 0", "output": "x^3 + 71/18x^2 + 109/27x + 65/162 = 0\n(x - -1/9)(x - -5/3)(x - -13/6) = 0\nx - -1/9 = 0\nx - -5/3 = 0\nx - -13/6 = 0\nx = -1/9\nx = -5/3\nx = -13/6"} {"input": "Determine x in x^3 - 1x^2 - 16x - 20 = 0", "output": "x^3 - 1x^2 - 16x - 20 = 0\n(x - -2)(x - 5)(x - -2) = 0\nx - -2 = 0\nx - 5 = 0\nx - -2 = 0\nx = -2\nx = 5\nx = -2"} {"input": "Solve x^2 - 25/2x + 36 = 0", "output": "x^2 - 25/2x + 36 = 0\n(x - 9/2)(x - 8) = 0\nx - 9/2 = 0 or x - 8 = 0\nx = 9/2\nx = 8"} {"input": "Find x in 3x - 9/2 = 0", "output": "3x - 9/2 = 0\n3x = 9/2\nx = 9/2 / 3\nx = 3/2"} {"input": "Determine x in x^3 + 1/2x^2 - 49x - 49/2 = 0", "output": "x^3 + 1/2x^2 - 49x - 49/2 = 0\n(x - -7)(x - 7)(x - -1/2) = 0\nx - -7 = 0\nx - 7 = 0\nx - -1/2 = 0\nx = -7\nx = 7\nx = -1/2"} {"input": "Solve the equation x^2 - 43/15x - 76/3 = 0", "output": "x^2 - 43/15x - 76/3 = 0\n(x - 20/3)(x - -19/5) = 0\nx - 20/3 = 0 or x - -19/5 = 0\nx = 20/3\nx = -19/5"} {"input": "Find x in x^3 + 1/2x^2 - 20x - 75/2 = 0", "output": "x^3 + 1/2x^2 - 20x - 75/2 = 0\n(x - -3)(x - -5/2)(x - 5) = 0\nx - -3 = 0\nx - -5/2 = 0\nx - 5 = 0\nx = -3\nx = -5/2\nx = 5"} {"input": "Compute the solution of x^2 - 22x + 40 = 0", "output": "x^2 - 22x + 40 = 0\n(x - 2)(x - 20) = 0\nx - 2 = 0 or x - 20 = 0\nx = 2\nx = 20"} {"input": "Find x in x^3 - 15/28x^2 - 29/8x - 6/7 = 0", "output": "x^3 - 15/28x^2 - 29/8x - 6/7 = 0\n(x - 16/7)(x - -3/2)(x - -1/4) = 0\nx - 16/7 = 0\nx - -3/2 = 0\nx - -1/4 = 0\nx = 16/7\nx = -3/2\nx = -1/4"} {"input": "Solve the equation x^3 - 989/360x^2 + 53/90x + 187/120 = 0", "output": "x^3 - 989/360x^2 + 53/90x + 187/120 = 0\n(x - 11/9)(x - -3/5)(x - 17/8) = 0\nx - 11/9 = 0\nx - -3/5 = 0\nx - 17/8 = 0\nx = 11/9\nx = -3/5\nx = 17/8"} {"input": "Find the solution to x^2 + 9/8x = 0", "output": "x^2 + 9/8x = 0\n(x - -9/8)(x - 0) = 0\nx - -9/8 = 0 or x - 0 = 0\nx = -9/8\nx = 0"} {"input": "Solve the equation 6x - 36 = 0", "output": "6x - 36 = 0\n6x = 36\nx = 36 / 6\nx = 6"} {"input": "Compute the solution of 4x + 56/5 = 0", "output": "4x + 56/5 = 0\n4x = -56/5\nx = -56/5 / 4\nx = -14/5"} {"input": "Solve simultaneously:\n10x + 6y = 1072/9\n4x + 2y = 364/9", "output": "10x + 6y = 1072/9\n4x + 2y = 364/9\n\nUsing elimination\n4*(10x + 6y = 1072/9)\n10*(4x + 2y = 364/9)\n40x + 24y = 4288/9\n40x + 20y = 3640/9\nSubtract equations\n4y = 72\ny = 72/4\ny = 18\n\nSubstitute y\n10x + 6(18) = 1072/9\n10x = 100/9\nx = 100/9/10\nx = 10/9"} {"input": "Determine x in x^2 + 5/4x - 117/8 = 0", "output": "x^2 + 5/4x - 117/8 = 0\n(x - 13/4)(x - -9/2) = 0\nx - 13/4 = 0 or x - -9/2 = 0\nx = 13/4\nx = -9/2"} {"input": "Find x for x^2 + 2/3x - 8/3 = 0", "output": "x^2 + 2/3x - 8/3 = 0\n(x - -2)(x - 4/3) = 0\nx - -2 = 0 or x - 4/3 = 0\nx = -2\nx = 4/3"} {"input": "Find the solution to x^3 - 9/40x^2 - 303/80x + 19/40 = 0", "output": "x^3 - 9/40x^2 - 303/80x + 19/40 = 0\n(x - -19/10)(x - 1/8)(x - 2) = 0\nx - -19/10 = 0\nx - 1/8 = 0\nx - 2 = 0\nx = -19/10\nx = 1/8\nx = 2"} {"input": "Determine x in x^3 + 896/45x^2 + 1588/45x + 16 = 0", "output": "x^3 + 896/45x^2 + 1588/45x + 16 = 0\n(x - -18)(x - -10/9)(x - -4/5) = 0\nx - -18 = 0\nx - -10/9 = 0\nx - -4/5 = 0\nx = -18\nx = -10/9\nx = -4/5"} {"input": "Find x for 2x - 10 = 0", "output": "2x - 10 = 0\n2x = 10\nx = 10 / 2\nx = 5"} {"input": "Solve simultaneously:\n5x + 3y = -59/8\n9x + 2y = -373/24", "output": "5x + 3y = -59/8\n9x + 2y = -373/24\n\nUsing elimination\n9*(5x + 3y = -59/8)\n5*(9x + 2y = -373/24)\n45x + 27y = -531/8\n45x + 10y = -1865/24\nSubtract equations\n17y = 34/3\ny = 34/3/17\ny = 2/3\n\nSubstitute y\n5x + 3(2/3) = -59/8\n5x = -75/8\nx = -75/8/5\nx = -15/8"} {"input": "Solve the equation x^2 + 10/3x - 25/3 = 0", "output": "x^2 + 10/3x - 25/3 = 0\n(x - -5)(x - 5/3) = 0\nx - -5 = 0 or x - 5/3 = 0\nx = -5\nx = 5/3"} {"input": "Find x for x^2 + 9/14x - 9/7 = 0", "output": "x^2 + 9/14x - 9/7 = 0\n(x - -3/2)(x - 6/7) = 0\nx - -3/2 = 0 or x - 6/7 = 0\nx = -3/2\nx = 6/7"} {"input": "What value of x satisfies x^3 + 77/5x^2 + 27/5x - 9 = 0", "output": "x^3 + 77/5x^2 + 27/5x - 9 = 0\n(x - -1)(x - 3/5)(x - -15) = 0\nx - -1 = 0\nx - 3/5 = 0\nx - -15 = 0\nx = -1\nx = 3/5\nx = -15"} {"input": "Find the solution to x^2 - 19/10x - 3/2 = 0", "output": "x^2 - 19/10x - 3/2 = 0\n(x - 5/2)(x - -3/5) = 0\nx - 5/2 = 0 or x - -3/5 = 0\nx = 5/2\nx = -3/5"} {"input": "Compute the solution of 6x - 120 = 0", "output": "6x - 120 = 0\n6x = 120\nx = 120 / 6\nx = 20"} {"input": "What value of x satisfies 6x + 36/7 = 0", "output": "6x + 36/7 = 0\n6x = -36/7\nx = -36/7 / 6\nx = -6/7"} {"input": "Solve x^2 - 17/21x - 8/21 = 0", "output": "x^2 - 17/21x - 8/21 = 0\n(x - -1/3)(x - 8/7) = 0\nx - -1/3 = 0 or x - 8/7 = 0\nx = -1/3\nx = 8/7"} {"input": "Solve the equations:\n1x + 9y = 437/90\n2x + 3y = -71/90", "output": "1x + 9y = 437/90\n2x + 3y = -71/90\n\nUsing elimination\n2*(1x + 9y = 437/90)\n1*(2x + 3y = -71/90)\n2x + 18y = 437/45\n2x + 3y = -71/90\nSubtract equations\n15y = 21/2\ny = 21/2/15\ny = 7/10\n\nSubstitute y\n1x + 9(7/10) = 437/90\n1x = -13/9\nx = -13/9/1\nx = -13/9"} {"input": "Solve quickly: 6x + 24 = 0", "output": "6x + 24 = 0\n6x = -24\nx = -24 / 6\nx = -4"} {"input": "Determine x in 5x + 40 = 0", "output": "5x + 40 = 0\n5x = -40\nx = -40 / 5\nx = -8"} {"input": "Solve the equation x^2 + 3x + 2 = 0", "output": "x^2 + 3x + 2 = 0\n(x - -1)(x - -2) = 0\nx - -1 = 0 or x - -2 = 0\nx = -1\nx = -2"} {"input": "Solve the system:\n8x + 9y = 93/2\n8x + 7y = 99/2", "output": "8x + 9y = 93/2\n8x + 7y = 99/2\n\nUsing elimination\n8*(8x + 9y = 93/2)\n8*(8x + 7y = 99/2)\n64x + 72y = 372\n64x + 56y = 396\nSubtract equations\n16y = -24\ny = -24/16\ny = -3/2\n\nSubstitute y\n8x + 9(-3/2) = 93/2\n8x = 60\nx = 60/8\nx = 15/2"} {"input": "Solve the equations:\n5x + 5y = -15/4\n1x + 4y = 9/2", "output": "5x + 5y = -15/4\n1x + 4y = 9/2\n\nUsing elimination\n1*(5x + 5y = -15/4)\n5*(1x + 4y = 9/2)\n5x + 5y = -15/4\n5x + 20y = 45/2\nSubtract equations\n-15y = -105/4\ny = -105/4/-15\ny = 7/4\n\nSubstitute y\n5x + 5(7/4) = -15/4\n5x = -25/2\nx = -25/2/5\nx = -5/2"} {"input": "Solve the equation 10x + 15/2 = 0", "output": "10x + 15/2 = 0\n10x = -15/2\nx = -15/2 / 10\nx = -3/4"} {"input": "What value of x satisfies x^3 - 69/7x^2 + 153/7x - 13 = 0", "output": "x^3 - 69/7x^2 + 153/7x - 13 = 0\n(x - 1)(x - 7)(x - 13/7) = 0\nx - 1 = 0\nx - 7 = 0\nx - 13/7 = 0\nx = 1\nx = 7\nx = 13/7"} {"input": "Find the solution to x^3 - 13/10x^2 - 16x + 104/5 = 0", "output": "x^3 - 13/10x^2 - 16x + 104/5 = 0\n(x - 4)(x - 13/10)(x - -4) = 0\nx - 4 = 0\nx - 13/10 = 0\nx - -4 = 0\nx = 4\nx = 13/10\nx = -4"} {"input": "Solve the equations:\n7x + 9y = -27/5\n5x + 7y = -5", "output": "7x + 9y = -27/5\n5x + 7y = -5\n\nUsing elimination\n5*(7x + 9y = -27/5)\n7*(5x + 7y = -5)\n35x + 45y = -27\n35x + 49y = -35\nSubtract equations\n-4y = 8\ny = 8/-4\ny = -2\n\nSubstitute y\n7x + 9(-2) = -27/5\n7x = 63/5\nx = 63/5/7\nx = 9/5"} {"input": "Find x for 8x + 64/5 = 0", "output": "8x + 64/5 = 0\n8x = -64/5\nx = -64/5 / 8\nx = -8/5"} {"input": "Compute the solution of 8x + 16/7 = 0", "output": "8x + 16/7 = 0\n8x = -16/7\nx = -16/7 / 8\nx = -2/7"} {"input": "Solve x^3 - 83/56x^2 - 461/112x + 15/28 = 0", "output": "x^3 - 83/56x^2 - 461/112x + 15/28 = 0\n(x - -3/2)(x - 20/7)(x - 1/8) = 0\nx - -3/2 = 0\nx - 20/7 = 0\nx - 1/8 = 0\nx = -3/2\nx = 20/7\nx = 1/8"} {"input": "What value of x satisfies x^3 - 15/4x^2 - 9/25x + 27/20 = 0", "output": "x^3 - 15/4x^2 - 9/25x + 27/20 = 0\n(x - 15/4)(x - -3/5)(x - 3/5) = 0\nx - 15/4 = 0\nx - -3/5 = 0\nx - 3/5 = 0\nx = 15/4\nx = -3/5\nx = 3/5"} {"input": "Find the solution to x^2 + 53/4x - 105/4 = 0", "output": "x^2 + 53/4x - 105/4 = 0\n(x - 7/4)(x - -15) = 0\nx - 7/4 = 0 or x - -15 = 0\nx = 7/4\nx = -15"} {"input": "Solve the system:\n10x + 7y = -397/12\n4x + 10y = -263/6", "output": "10x + 7y = -397/12\n4x + 10y = -263/6\n\nUsing elimination\n4*(10x + 7y = -397/12)\n10*(4x + 10y = -263/6)\n40x + 28y = -397/3\n40x + 100y = -1315/3\nSubtract equations\n-72y = 306\ny = 306/-72\ny = -17/4\n\nSubstitute y\n10x + 7(-17/4) = -397/12\n10x = -10/3\nx = -10/3/10\nx = -1/3"} {"input": "Solve quickly: x^3 - 27/5x^2 + 207/25x - 81/25 = 0", "output": "x^3 - 27/5x^2 + 207/25x - 81/25 = 0\n(x - 3/5)(x - 9/5)(x - 3) = 0\nx - 3/5 = 0\nx - 9/5 = 0\nx - 3 = 0\nx = 3/5\nx = 9/5\nx = 3"} {"input": "Solve the equation 3x + 33/10 = 0", "output": "3x + 33/10 = 0\n3x = -33/10\nx = -33/10 / 3\nx = -11/10"} {"input": "What value of x satisfies 9x - 99 = 0", "output": "9x - 99 = 0\n9x = 99\nx = 99 / 9\nx = 11"} {"input": "Find x in 4x + 8/3 = 0", "output": "4x + 8/3 = 0\n4x = -8/3\nx = -8/3 / 4\nx = -2/3"} {"input": "Solve x^3 + 21/8x^2 - 463/144x - 1309/144 = 0", "output": "x^3 + 21/8x^2 - 463/144x - 1309/144 = 0\n(x - -17/8)(x - -7/3)(x - 11/6) = 0\nx - -17/8 = 0\nx - -7/3 = 0\nx - 11/6 = 0\nx = -17/8\nx = -7/3\nx = 11/6"} {"input": "Solve quickly: 5x + 15/2 = 0", "output": "5x + 15/2 = 0\n5x = -15/2\nx = -15/2 / 5\nx = -3/2"} {"input": "Solve the system:\n2x + 9y = 41\n7x + 5y = 404/3", "output": "2x + 9y = 41\n7x + 5y = 404/3\n\nUsing elimination\n7*(2x + 9y = 41)\n2*(7x + 5y = 404/3)\n14x + 63y = 287\n14x + 10y = 808/3\nSubtract equations\n53y = 53/3\ny = 53/3/53\ny = 1/3\n\nSubstitute y\n2x + 9(1/3) = 41\n2x = 38\nx = 38/2\nx = 19"} {"input": "Compute the solution of 6x - 39/2 = 0", "output": "6x - 39/2 = 0\n6x = 39/2\nx = 39/2 / 6\nx = 13/4"} {"input": "Determine x in x^2 + 11/10x - 4/5 = 0", "output": "x^2 + 11/10x - 4/5 = 0\n(x - -8/5)(x - 1/2) = 0\nx - -8/5 = 0 or x - 1/2 = 0\nx = -8/5\nx = 1/2"} {"input": "Solve 1x + 1 = 0", "output": "1x + 1 = 0\n1x = -1\nx = -1 / 1\nx = -1"} {"input": "Compute the solution of x^3 - 253/315x^2 - 2336/315x - 256/315 = 0", "output": "x^3 - 253/315x^2 - 2336/315x - 256/315 = 0\n(x - 16/5)(x - -1/9)(x - -16/7) = 0\nx - 16/5 = 0\nx - -1/9 = 0\nx - -16/7 = 0\nx = 16/5\nx = -1/9\nx = -16/7"} {"input": "Solve the equation x^3 - 58/15x^2 + 77/45x + 196/45 = 0", "output": "x^3 - 58/15x^2 + 77/45x + 196/45 = 0\n(x - -4/5)(x - 7/3)(x - 7/3) = 0\nx - -4/5 = 0\nx - 7/3 = 0\nx - 7/3 = 0\nx = -4/5\nx = 7/3\nx = 7/3"} {"input": "Solve quickly: x^3 - 38/35x^2 - 311/35x - 38/7 = 0", "output": "x^3 - 38/35x^2 - 311/35x - 38/7 = 0\n(x - -5/7)(x - 19/5)(x - -2) = 0\nx - -5/7 = 0\nx - 19/5 = 0\nx - -2 = 0\nx = -5/7\nx = 19/5\nx = -2"} {"input": "What value of x satisfies x^3 + 14x^2 - 49x + 34 = 0", "output": "x^3 + 14x^2 - 49x + 34 = 0\n(x - -17)(x - 1)(x - 2) = 0\nx - -17 = 0\nx - 1 = 0\nx - 2 = 0\nx = -17\nx = 1\nx = 2"} {"input": "Find x and y such that\n6x + 8y = -98/5\n10x + 9y = -61/2", "output": "6x + 8y = -98/5\n10x + 9y = -61/2\n\nUsing elimination\n10*(6x + 8y = -98/5)\n6*(10x + 9y = -61/2)\n60x + 80y = -196\n60x + 54y = -183\nSubtract equations\n26y = -13\ny = -13/26\ny = -1/2\n\nSubstitute y\n6x + 8(-1/2) = -98/5\n6x = -78/5\nx = -78/5/6\nx = -13/5"} {"input": "Find x for 3x - 11 = 0", "output": "3x - 11 = 0\n3x = 11\nx = 11 / 3\nx = 11/3"} {"input": "Find x for x^2 + 37/21x + 10/21 = 0", "output": "x^2 + 37/21x + 10/21 = 0\n(x - -10/7)(x - -1/3) = 0\nx - -10/7 = 0 or x - -1/3 = 0\nx = -10/7\nx = -1/3"} {"input": "Solve the system:\n9x + 6y = 214/5\n6x + 3y = 371/15", "output": "9x + 6y = 214/5\n6x + 3y = 371/15\n\nUsing elimination\n6*(9x + 6y = 214/5)\n9*(6x + 3y = 371/15)\n54x + 36y = 1284/5\n54x + 27y = 1113/5\nSubtract equations\n9y = 171/5\ny = 171/5/9\ny = 19/5\n\nSubstitute y\n9x + 6(19/5) = 214/5\n9x = 20\nx = 20/9\nx = 20/9"} {"input": "Solve simultaneously:\n9x + 10y = -46/3\n7x + 1y = -119/6", "output": "9x + 10y = -46/3\n7x + 1y = -119/6\n\nUsing elimination\n7*(9x + 10y = -46/3)\n9*(7x + 1y = -119/6)\n63x + 70y = -322/3\n63x + 9y = -357/2\nSubtract equations\n61y = 427/6\ny = 427/6/61\ny = 7/6\n\nSubstitute y\n9x + 10(7/6) = -46/3\n9x = -27\nx = -27/9\nx = -3"} {"input": "Find the solution to 7x - 49/2 = 0", "output": "7x - 49/2 = 0\n7x = 49/2\nx = 49/2 / 7\nx = 7/2"} {"input": "Find x in x^3 + 83/6x^2 - 203/6x + 40/3 = 0", "output": "x^3 + 83/6x^2 - 203/6x + 40/3 = 0\n(x - 1/2)(x - 5/3)(x - -16) = 0\nx - 1/2 = 0\nx - 5/3 = 0\nx - -16 = 0\nx = 1/2\nx = 5/3\nx = -16"} {"input": "Solve x^3 + 11/9x^2 - 74/9x - 40/3 = 0", "output": "x^3 + 11/9x^2 - 74/9x - 40/3 = 0\n(x - 3)(x - -20/9)(x - -2) = 0\nx - 3 = 0\nx - -20/9 = 0\nx - -2 = 0\nx = 3\nx = -20/9\nx = -2"} {"input": "Solve quickly: x^3 - 4x^2 - 235/4x + 247/4 = 0", "output": "x^3 - 4x^2 - 235/4x + 247/4 = 0\n(x - 1)(x - -13/2)(x - 19/2) = 0\nx - 1 = 0\nx - -13/2 = 0\nx - 19/2 = 0\nx = 1\nx = -13/2\nx = 19/2"} {"input": "Find x in x^2 + 35/6x - 49/6 = 0", "output": "x^2 + 35/6x - 49/6 = 0\n(x - 7/6)(x - -7) = 0\nx - 7/6 = 0 or x - -7 = 0\nx = 7/6\nx = -7"} {"input": "Find the solution to 2x + 6 = 0", "output": "2x + 6 = 0\n2x = -6\nx = -6 / 2\nx = -3"} {"input": "Find x in 6x - 4/3 = 0", "output": "6x - 4/3 = 0\n6x = 4/3\nx = 4/3 / 6\nx = 2/9"} {"input": "Solve simultaneously:\n4x + 10y = 14/3\n7x + 5y = 37/3", "output": "4x + 10y = 14/3\n7x + 5y = 37/3\n\nUsing elimination\n7*(4x + 10y = 14/3)\n4*(7x + 5y = 37/3)\n28x + 70y = 98/3\n28x + 20y = 148/3\nSubtract equations\n50y = -50/3\ny = -50/3/50\ny = -1/3\n\nSubstitute y\n4x + 10(-1/3) = 14/3\n4x = 8\nx = 8/4\nx = 2"} {"input": "Solve quickly: x^2 - 26/7x + 19/7 = 0", "output": "x^2 - 26/7x + 19/7 = 0\n(x - 19/7)(x - 1) = 0\nx - 19/7 = 0 or x - 1 = 0\nx = 19/7\nx = 1"} {"input": "Find x in 10x - 40 = 0", "output": "10x - 40 = 0\n10x = 40\nx = 40 / 10\nx = 4"} {"input": "Find x for 7x + 70/3 = 0", "output": "7x + 70/3 = 0\n7x = -70/3\nx = -70/3 / 7\nx = -10/3"} {"input": "Find x in x^3 - 7/120x^2 - 77/8x - 45/4 = 0", "output": "x^3 - 7/120x^2 - 77/8x - 45/4 = 0\n(x - 18/5)(x - -15/8)(x - -5/3) = 0\nx - 18/5 = 0\nx - -15/8 = 0\nx - -5/3 = 0\nx = 18/5\nx = -15/8\nx = -5/3"} {"input": "What value of x satisfies x^2 + 2/21x - 55/21 = 0", "output": "x^2 + 2/21x - 55/21 = 0\n(x - 11/7)(x - -5/3) = 0\nx - 11/7 = 0 or x - -5/3 = 0\nx = 11/7\nx = -5/3"} {"input": "Solve the equations:\n4x + 5y = -46/3\n5x + 5y = -50/3", "output": "4x + 5y = -46/3\n5x + 5y = -50/3\n\nUsing elimination\n5*(4x + 5y = -46/3)\n4*(5x + 5y = -50/3)\n20x + 25y = -230/3\n20x + 20y = -200/3\nSubtract equations\n5y = -10\ny = -10/5\ny = -2\n\nSubstitute y\n4x + 5(-2) = -46/3\n4x = -16/3\nx = -16/3/4\nx = -4/3"} {"input": "Find x for x^3 - 53/40x^2 - 41/10x + 51/10 = 0", "output": "x^3 - 53/40x^2 - 41/10x + 51/10 = 0\n(x - -2)(x - 6/5)(x - 17/8) = 0\nx - -2 = 0\nx - 6/5 = 0\nx - 17/8 = 0\nx = -2\nx = 6/5\nx = 17/8"} {"input": "Find x in x^3 - 17/12x^2 - 479/24x + 133/3 = 0", "output": "x^3 - 17/12x^2 - 479/24x + 133/3 = 0\n(x - 8/3)(x - 7/2)(x - -19/4) = 0\nx - 8/3 = 0\nx - 7/2 = 0\nx - -19/4 = 0\nx = 8/3\nx = 7/2\nx = -19/4"} {"input": "Solve the equation x^2 + 7/5x + 2/5 = 0", "output": "x^2 + 7/5x + 2/5 = 0\n(x - -2/5)(x - -1) = 0\nx - -2/5 = 0 or x - -1 = 0\nx = -2/5\nx = -1"} {"input": "What value of x satisfies x^2 - 73/24x + 19/12 = 0", "output": "x^2 - 73/24x + 19/12 = 0\n(x - 2/3)(x - 19/8) = 0\nx - 2/3 = 0 or x - 19/8 = 0\nx = 2/3\nx = 19/8"} {"input": "Find x in x^2 + 25/8x - 75/8 = 0", "output": "x^2 + 25/8x - 75/8 = 0\n(x - 15/8)(x - -5) = 0\nx - 15/8 = 0 or x - -5 = 0\nx = 15/8\nx = -5"} {"input": "Solve the equations:\n7x + 9y = 891/5\n9x + 7y = 757/5", "output": "7x + 9y = 891/5\n9x + 7y = 757/5\n\nUsing elimination\n9*(7x + 9y = 891/5)\n7*(9x + 7y = 757/5)\n63x + 81y = 8019/5\n63x + 49y = 5299/5\nSubtract equations\n32y = 544\ny = 544/32\ny = 17\n\nSubstitute y\n7x + 9(17) = 891/5\n7x = 126/5\nx = 126/5/7\nx = 18/5"} {"input": "Find the solution to x^3 + 793/40x^2 + 168/5x + 27/2 = 0", "output": "x^3 + 793/40x^2 + 168/5x + 27/2 = 0\n(x - -6/5)(x - -18)(x - -5/8) = 0\nx - -6/5 = 0\nx - -18 = 0\nx - -5/8 = 0\nx = -6/5\nx = -18\nx = -5/8"} {"input": "Find x and y such that\n4x + 10y = -310/9\n7x + 6y = -232/9", "output": "4x + 10y = -310/9\n7x + 6y = -232/9\n\nUsing elimination\n7*(4x + 10y = -310/9)\n4*(7x + 6y = -232/9)\n28x + 70y = -2170/9\n28x + 24y = -928/9\nSubtract equations\n46y = -138\ny = -138/46\ny = -3\n\nSubstitute y\n4x + 10(-3) = -310/9\n4x = -40/9\nx = -40/9/4\nx = -10/9"} {"input": "What value of x satisfies 8x + 32/5 = 0", "output": "8x + 32/5 = 0\n8x = -32/5\nx = -32/5 / 8\nx = -4/5"} {"input": "Find x for 1x - 17/3 = 0", "output": "1x - 17/3 = 0\n1x = 17/3\nx = 17/3 / 1\nx = 17/3"} {"input": "Determine x in x^2 - 4x + 3 = 0", "output": "x^2 - 4x + 3 = 0\n(x - 1)(x - 3) = 0\nx - 1 = 0 or x - 3 = 0\nx = 1\nx = 3"} {"input": "Find x for 4x - 15 = 0", "output": "4x - 15 = 0\n4x = 15\nx = 15 / 4\nx = 15/4"} {"input": "Solve the system:\n6x + 1y = -47/10\n4x + 6y = 19/5", "output": "6x + 1y = -47/10\n4x + 6y = 19/5\n\nUsing elimination\n4*(6x + 1y = -47/10)\n6*(4x + 6y = 19/5)\n24x + 4y = -94/5\n24x + 36y = 114/5\nSubtract equations\n-32y = -208/5\ny = -208/5/-32\ny = 13/10\n\nSubstitute y\n6x + 1(13/10) = -47/10\n6x = -6\nx = -6/6\nx = -1"} {"input": "Find the solution to 6x + 48 = 0", "output": "6x + 48 = 0\n6x = -48\nx = -48 / 6\nx = -8"} {"input": "What value of x satisfies 9x + 99 = 0", "output": "9x + 99 = 0\n9x = -99\nx = -99 / 9\nx = -11"} {"input": "Find x for 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Solve the equations:\n6x + 4y = -20\n10x + 8y = -92/3", "output": "6x + 4y = -20\n10x + 8y = -92/3\n\nUsing elimination\n10*(6x + 4y = -20)\n6*(10x + 8y = -92/3)\n60x + 40y = -200\n60x + 48y = -184\nSubtract equations\n-8y = -16\ny = -16/-8\ny = 2\n\nSubstitute y\n6x + 4(2) = -20\n6x = -28\nx = -28/6\nx = -14/3"} {"input": "Find x for x^3 + 154/15x^2 + 161/15x - 6 = 0", "output": "x^3 + 154/15x^2 + 161/15x - 6 = 0\n(x - -5/3)(x - -9)(x - 2/5) = 0\nx - -5/3 = 0\nx - -9 = 0\nx - 2/5 = 0\nx = -5/3\nx = -9\nx = 2/5"} {"input": "Find the solution to 8x + 72/5 = 0", "output": "8x + 72/5 = 0\n8x = -72/5\nx = -72/5 / 8\nx = -9/5"} {"input": "Find x for x^3 - 59/24x^2 - 533/48x - 385/48 = 0", "output": "x^3 - 59/24x^2 - 533/48x - 385/48 = 0\n(x - -7/6)(x - -11/8)(x - 5) = 0\nx - -7/6 = 0\nx - -11/8 = 0\nx - 5 = 0\nx = -7/6\nx = -11/8\nx = 5"} {"input": "Solve quickly: 10x - 150/7 = 0", "output": "10x - 150/7 = 0\n10x = 150/7\nx = 150/7 / 10\nx = 15/7"} {"input": "Solve the system:\n3x + 7y = 159/10\n1x + 1y = 29/10", "output": "3x + 7y = 159/10\n1x + 1y = 29/10\n\nUsing elimination\n1*(3x + 7y = 159/10)\n3*(1x + 1y = 29/10)\n3x + 7y = 159/10\n3x + 3y = 87/10\nSubtract equations\n4y = 36/5\ny = 36/5/4\ny = 9/5\n\nSubstitute y\n3x + 7(9/5) = 159/10\n3x = 33/10\nx = 33/10/3\nx = 11/10"} {"input": "What value of x satisfies x^2 + 36/35x - 32/35 = 0", "output": "x^2 + 36/35x - 32/35 = 0\n(x - 4/7)(x - -8/5) = 0\nx - 4/7 = 0 or x - -8/5 = 0\nx = 4/7\nx = -8/5"} {"input": "Find the solution to x^3 - 151/14x^2 + 2288/63x - 2432/63 = 0", "output": "x^3 - 151/14x^2 + 2288/63x - 2432/63 = 0\n(x - 16/7)(x - 19/6)(x - 16/3) = 0\nx - 16/7 = 0\nx - 19/6 = 0\nx - 16/3 = 0\nx = 16/7\nx = 19/6\nx = 16/3"} {"input": "Solve the equation x^3 - 53/5x^2 - 179/4x - 399/10 = 0", "output": "x^3 - 53/5x^2 - 179/4x - 399/10 = 0\n(x - -19/10)(x - -3/2)(x - 14) = 0\nx - -19/10 = 0\nx - -3/2 = 0\nx - 14 = 0\nx = -19/10\nx = -3/2\nx = 14"} {"input": "What value of x satisfies x^3 - 11/9x^2 - 580/27x - 64/27 = 0", "output": "x^3 - 11/9x^2 - 580/27x - 64/27 = 0\n(x - -4)(x - -1/9)(x - 16/3) = 0\nx - -4 = 0\nx - -1/9 = 0\nx - 16/3 = 0\nx = -4\nx = -1/9\nx = 16/3"} {"input": "Find x in 7x + 112/5 = 0", "output": "7x + 112/5 = 0\n7x = -112/5\nx = -112/5 / 7\nx = -16/5"} {"input": "Solve 9x - 36/5 = 0", "output": "9x - 36/5 = 0\n9x = 36/5\nx = 36/5 / 9\nx = 4/5"} {"input": "Find x for x^2 - 8/5x - 4/5 = 0", "output": "x^2 - 8/5x - 4/5 = 0\n(x - 2)(x - -2/5) = 0\nx - 2 = 0 or x - -2/5 = 0\nx = 2\nx = -2/5"} {"input": "What value of x satisfies x^3 + 317/84x^2 + 181/56x - 13/24 = 0", "output": "x^3 + 317/84x^2 + 181/56x - 13/24 = 0\n(x - 1/7)(x - -7/4)(x - -13/6) = 0\nx - 1/7 = 0\nx - -7/4 = 0\nx - -13/6 = 0\nx = 1/7\nx = -7/4\nx = -13/6"} {"input": "Compute the solution of 10x - 55/3 = 0", "output": "10x - 55/3 = 0\n10x = 55/3\nx = 55/3 / 10\nx = 11/6"} {"input": "Solve the equation x^3 + 65/28x^2 + 1x = 0", "output": "x^3 + 65/28x^2 + 1x = 0\n(x - -4/7)(x - 0)(x - -7/4) = 0\nx - -4/7 = 0\nx - 0 = 0\nx - -7/4 = 0\nx = -4/7\nx = 0\nx = -7/4"} {"input": "Find x in x^3 - 64/9x^2 - 121/9x + 152/3 = 0", "output": "x^3 - 64/9x^2 - 121/9x + 152/3 = 0\n(x - 8)(x - 19/9)(x - -3) = 0\nx - 8 = 0\nx - 19/9 = 0\nx - -3 = 0\nx = 8\nx = 19/9\nx = -3"} {"input": "Find x and y such that\n1x + 1y = 3\n10x + 6y = 32", "output": "1x + 1y = 3\n10x + 6y = 32\n\nUsing elimination\n10*(1x + 1y = 3)\n1*(10x + 6y = 32)\n10x + 10y = 30\n10x + 6y = 32\nSubtract equations\n4y = -2\ny = -2/4\ny = -1/2\n\nSubstitute y\n1x + 1(-1/2) = 3\n1x = 7/2\nx = 7/2/1\nx = 7/2"} {"input": "Find the solution to x^3 - 311/70x^2 + 239/70x - 2/5 = 0", "output": "x^3 - 311/70x^2 + 239/70x - 2/5 = 0\n(x - 1/7)(x - 4/5)(x - 7/2) = 0\nx - 1/7 = 0\nx - 4/5 = 0\nx - 7/2 = 0\nx = 1/7\nx = 4/5\nx = 7/2"} {"input": "Find x for x^3 - 61/14x^2 + 5/7x + 8 = 0", "output": "x^3 - 61/14x^2 + 5/7x + 8 = 0\n(x - 7/2)(x - -8/7)(x - 2) = 0\nx - 7/2 = 0\nx - -8/7 = 0\nx - 2 = 0\nx = 7/2\nx = -8/7\nx = 2"} {"input": "Determine x in x^3 - 2/5x^2 - 191/5x - 56 = 0", "output": "x^3 - 2/5x^2 - 191/5x - 56 = 0\n(x - -5)(x - 7)(x - -8/5) = 0\nx - -5 = 0\nx - 7 = 0\nx - -8/5 = 0\nx = -5\nx = 7\nx = -8/5"} {"input": "What value of x satisfies x^3 - 29/2x^2 + 37/2x + 13 = 0", "output": "x^3 - 29/2x^2 + 37/2x + 13 = 0\n(x - -1/2)(x - 13)(x - 2) = 0\nx - -1/2 = 0\nx - 13 = 0\nx - 2 = 0\nx = -1/2\nx = 13\nx = 2"} {"input": "Solve the equation 10x - 140 = 0", "output": "10x - 140 = 0\n10x = 140\nx = 140 / 10\nx = 14"} {"input": "Solve the equation x^2 - 221/30x + 289/30 = 0", "output": "x^2 - 221/30x + 289/30 = 0\n(x - 17/10)(x - 17/3) = 0\nx - 17/10 = 0 or x - 17/3 = 0\nx = 17/10\nx = 17/3"} {"input": "Compute the solution of x^2 - 8/15x - 11/3 = 0", "output": "x^2 - 8/15x - 11/3 = 0\n(x - 11/5)(x - -5/3) = 0\nx - 11/5 = 0 or x - -5/3 = 0\nx = 11/5\nx = -5/3"} {"input": "Compute the solution of x^3 + 221/60x^2 + 229/120x - 17/12 = 0", "output": "x^3 + 221/60x^2 + 229/120x - 17/12 = 0\n(x - 2/5)(x - -5/4)(x - -17/6) = 0\nx - 2/5 = 0\nx - -5/4 = 0\nx - -17/6 = 0\nx = 2/5\nx = -5/4\nx = -17/6"} {"input": "Solve quickly: x^3 - 11/8x^2 - 17/16x + 21/16 = 0", "output": "x^3 - 11/8x^2 - 17/16x + 21/16 = 0\n(x - 7/8)(x - -1)(x - 3/2) = 0\nx - 7/8 = 0\nx - -1 = 0\nx - 3/2 = 0\nx = 7/8\nx = -1\nx = 3/2"} {"input": "What value of x satisfies x^3 - 101/5x^2 + 2083/25x - 399/5 = 0", "output": "x^3 - 101/5x^2 + 2083/25x - 399/5 = 0\n(x - 7/5)(x - 19/5)(x - 15) = 0\nx - 7/5 = 0\nx - 19/5 = 0\nx - 15 = 0\nx = 7/5\nx = 19/5\nx = 15"} {"input": "Solve the equation x^2 + 2/3x - 8/3 = 0", "output": "x^2 + 2/3x - 8/3 = 0\n(x - 4/3)(x - -2) = 0\nx - 4/3 = 0 or x - -2 = 0\nx = 4/3\nx = -2"} {"input": "Compute the solution of 4x + 12/5 = 0", "output": "4x + 12/5 = 0\n4x = -12/5\nx = -12/5 / 4\nx = -3/5"} {"input": "Determine x in 2x + 16 = 0", "output": "2x + 16 = 0\n2x = -16\nx = -16 / 2\nx = -8"} {"input": "Find x for 2x + 40/7 = 0", "output": "2x + 40/7 = 0\n2x = -40/7\nx = -40/7 / 2\nx = -20/7"} {"input": "Find the solution to 3x + 4 = 0", "output": "3x + 4 = 0\n3x = -4\nx = -4 / 3\nx = -4/3"} {"input": "What value of x satisfies x^2 + 4x + 3 = 0", "output": "x^2 + 4x + 3 = 0\n(x - -1)(x - -3) = 0\nx - -1 = 0 or x - -3 = 0\nx = -1\nx = -3"} {"input": "Solve the system:\n6x + 5y = 14\n6x + 10y = 28", "output": "6x + 5y = 14\n6x + 10y = 28\n\nUsing elimination\n6*(6x + 5y = 14)\n6*(6x + 10y = 28)\n36x + 30y = 84\n36x + 60y = 168\nSubtract equations\n-30y = -84\ny = -84/-30\ny = 14/5\n\nSubstitute y\n6x + 5(14/5) = 14\n6x = 0\nx = 0/6\nx = 0"} {"input": "Solve the equations:\n10x + 1y = 193/35\n10x + 9y = 137/35", "output": "10x + 1y = 193/35\n10x + 9y = 137/35\n\nUsing elimination\n10*(10x + 1y = 193/35)\n10*(10x + 9y = 137/35)\n100x + 10y = 386/7\n100x + 90y = 274/7\nSubtract equations\n-80y = 16\ny = 16/-80\ny = -1/5\n\nSubstitute y\n10x + 1(-1/5) = 193/35\n10x = 40/7\nx = 40/7/10\nx = 4/7"} {"input": "Find the solution to x^3 - 125/28x^2 - 183/28x + 135/7 = 0", "output": "x^3 - 125/28x^2 - 183/28x + 135/7 = 0\n(x - 12/7)(x - 5)(x - -9/4) = 0\nx - 12/7 = 0\nx - 5 = 0\nx - -9/4 = 0\nx = 12/7\nx = 5\nx = -9/4"} {"input": "Find x and y such that\n7x + 3y = 1/8\n5x + 7y = -95/24", "output": "7x + 3y = 1/8\n5x + 7y = -95/24\n\nUsing elimination\n5*(7x + 3y = 1/8)\n7*(5x + 7y = -95/24)\n35x + 15y = 5/8\n35x + 49y = -665/24\nSubtract equations\n-34y = 85/3\ny = 85/3/-34\ny = -5/6\n\nSubstitute y\n7x + 3(-5/6) = 1/8\n7x = 21/8\nx = 21/8/7\nx = 3/8"} {"input": "Find x for x^3 + 83/24x^2 + 21/8x = 0", "output": "x^3 + 83/24x^2 + 21/8x = 0\n(x - -7/3)(x - 0)(x - -9/8) = 0\nx - -7/3 = 0\nx - 0 = 0\nx - -9/8 = 0\nx = -7/3\nx = 0\nx = -9/8"} {"input": "Find x in x^3 + 301/30x^2 + 301/10x + 117/5 = 0", "output": "x^3 + 301/30x^2 + 301/10x + 117/5 = 0\n(x - -13/3)(x - -9/2)(x - -6/5) = 0\nx - -13/3 = 0\nx - -9/2 = 0\nx - -6/5 = 0\nx = -13/3\nx = -9/2\nx = -6/5"} {"input": "Solve x^2 - 5/2x + 63/50 = 0", "output": "x^2 - 5/2x + 63/50 = 0\n(x - 9/5)(x - 7/10) = 0\nx - 9/5 = 0 or x - 7/10 = 0\nx = 9/5\nx = 7/10"} {"input": "Find x for x^3 + 200/63x^2 - 1/9x - 40/21 = 0", "output": "x^3 + 200/63x^2 - 1/9x - 40/21 = 0\n(x - 5/7)(x - -3)(x - -8/9) = 0\nx - 5/7 = 0\nx - -3 = 0\nx - -8/9 = 0\nx = 5/7\nx = -3\nx = -8/9"} {"input": "Solve x^2 + 19/6x + 5/3 = 0", "output": "x^2 + 19/6x + 5/3 = 0\n(x - -5/2)(x - -2/3) = 0\nx - -5/2 = 0 or x - -2/3 = 0\nx = -5/2\nx = -2/3"} {"input": "Solve quickly: x^3 - 10/3x^2 + 16/9x = 0", "output": "x^3 - 10/3x^2 + 16/9x = 0\n(x - 8/3)(x - 0)(x - 2/3) = 0\nx - 8/3 = 0\nx - 0 = 0\nx - 2/3 = 0\nx = 8/3\nx = 0\nx = 2/3"} {"input": "Solve simultaneously:\n7x + 10y = 9\n10x + 2y = -23/35", "output": "7x + 10y = 9\n10x + 2y = -23/35\n\nUsing elimination\n10*(7x + 10y = 9)\n7*(10x + 2y = -23/35)\n70x + 100y = 90\n70x + 14y = -23/5\nSubtract equations\n86y = 473/5\ny = 473/5/86\ny = 11/10\n\nSubstitute y\n7x + 10(11/10) = 9\n7x = -2\nx = -2/7\nx = -2/7"} {"input": "Solve the equations:\n6x + 9y = 20\n7x + 7y = 70/3", "output": "6x + 9y = 20\n7x + 7y = 70/3\n\nUsing elimination\n7*(6x + 9y = 20)\n6*(7x + 7y = 70/3)\n42x + 63y = 140\n42x + 42y = 140\nSubtract equations\n21y = 0\ny = 0/21\ny = 0\n\nSubstitute y\n6x + 9(0) = 20\n6x = 20\nx = 20/6\nx = 10/3"} {"input": "Determine x in x^2 - 59/90x - 22/45 = 0", "output": "x^2 - 59/90x - 22/45 = 0\n(x - 11/10)(x - -4/9) = 0\nx - 11/10 = 0 or x - -4/9 = 0\nx = 11/10\nx = -4/9"} {"input": "Compute the solution of x^2 + 10/3x + 17/12 = 0", "output": "x^2 + 10/3x + 17/12 = 0\n(x - -1/2)(x - -17/6) = 0\nx - -1/2 = 0 or x - -17/6 = 0\nx = -1/2\nx = -17/6"} {"input": "Solve simultaneously:\n2x + 5y = 46\n9x + 2y = 166", "output": "2x + 5y = 46\n9x + 2y = 166\n\nUsing elimination\n9*(2x + 5y = 46)\n2*(9x + 2y = 166)\n18x + 45y = 414\n18x + 4y = 332\nSubtract equations\n41y = 82\ny = 82/41\ny = 2\n\nSubstitute y\n2x + 5(2) = 46\n2x = 36\nx = 36/2\nx = 18"} {"input": "Find the solution to x^3 + 297/28x^2 + 755/28x - 57/14 = 0", "output": "x^3 + 297/28x^2 + 755/28x - 57/14 = 0\n(x - -6)(x - 1/7)(x - -19/4) = 0\nx - -6 = 0\nx - 1/7 = 0\nx - -19/4 = 0\nx = -6\nx = 1/7\nx = -19/4"} {"input": "Find x in x^2 - 125/7x - 300/7 = 0", "output": "x^2 - 125/7x - 300/7 = 0\n(x - -15/7)(x - 20) = 0\nx - -15/7 = 0 or x - 20 = 0\nx = -15/7\nx = 20"} {"input": "Find the solution to x^2 - 11/7x = 0", "output": "x^2 - 11/7x = 0\n(x - 0)(x - 11/7) = 0\nx - 0 = 0 or x - 11/7 = 0\nx = 0\nx = 11/7"} {"input": "Find the solution to x^2 - 17/3x + 22/3 = 0", "output": "x^2 - 17/3x + 22/3 = 0\n(x - 2)(x - 11/3) = 0\nx - 2 = 0 or x - 11/3 = 0\nx = 2\nx = 11/3"} {"input": "Solve the system:\n1x + 1y = 53/4\n7x + 10y = 169/2", "output": "1x + 1y = 53/4\n7x + 10y = 169/2\n\nUsing elimination\n7*(1x + 1y = 53/4)\n1*(7x + 10y = 169/2)\n7x + 7y = 371/4\n7x + 10y = 169/2\nSubtract equations\n-3y = 33/4\ny = 33/4/-3\ny = -11/4\n\nSubstitute y\n1x + 1(-11/4) = 53/4\n1x = 16\nx = 16/1\nx = 16"} {"input": "Solve x^3 - 5x^2 + 3/4x + 63/4 = 0", "output": "x^3 - 5x^2 + 3/4x + 63/4 = 0\n(x - 3)(x - 7/2)(x - -3/2) = 0\nx - 3 = 0\nx - 7/2 = 0\nx - -3/2 = 0\nx = 3\nx = 7/2\nx = -3/2"} {"input": "Solve 5x - 95/4 = 0", "output": "5x - 95/4 = 0\n5x = 95/4\nx = 95/4 / 5\nx = 19/4"} {"input": "Find x for x^2 - 134/35x + 17/5 = 0", "output": "x^2 - 134/35x + 17/5 = 0\n(x - 7/5)(x - 17/7) = 0\nx - 7/5 = 0 or x - 17/7 = 0\nx = 7/5\nx = 17/7"} {"input": "Compute the solution of 2x - 26/7 = 0", "output": "2x - 26/7 = 0\n2x = 26/7\nx = 26/7 / 2\nx = 13/7"} {"input": "What value of x satisfies x^3 - 84/5x^2 - 209/5x = 0", "output": "x^3 - 84/5x^2 - 209/5x = 0\n(x - -11/5)(x - 19)(x - 0) = 0\nx - -11/5 = 0\nx - 19 = 0\nx - 0 = 0\nx = -11/5\nx = 19\nx = 0"} {"input": "Solve the equation x^3 + 7x^2 + 275/36x - 425/36 = 0", "output": "x^3 + 7x^2 + 275/36x - 425/36 = 0\n(x - -5)(x - 5/6)(x - -17/6) = 0\nx - -5 = 0\nx - 5/6 = 0\nx - -17/6 = 0\nx = -5\nx = 5/6\nx = -17/6"} {"input": "Solve quickly: 5x + 25/8 = 0", "output": "5x + 25/8 = 0\n5x = -25/8\nx = -25/8 / 5\nx = -5/8"} {"input": "Find the solution to x^2 + 32/15x + 11/20 = 0", "output": "x^2 + 32/15x + 11/20 = 0\n(x - -3/10)(x - -11/6) = 0\nx - -3/10 = 0 or x - -11/6 = 0\nx = -3/10\nx = -11/6"} {"input": "Find x for 4x + 12 = 0", "output": "4x + 12 = 0\n4x = -12\nx = -12 / 4\nx = -3"} {"input": "Solve quickly: x^2 + 31/9x + 76/27 = 0", "output": "x^2 + 31/9x + 76/27 = 0\n(x - -19/9)(x - -4/3) = 0\nx - -19/9 = 0 or x - -4/3 = 0\nx = -19/9\nx = -4/3"} {"input": "What value of x satisfies x^2 + 7/10x - 13/5 = 0", "output": "x^2 + 7/10x - 13/5 = 0\n(x - -2)(x - 13/10) = 0\nx - -2 = 0 or x - 13/10 = 0\nx = -2\nx = 13/10"} {"input": "Compute the solution of x^2 + 21/2x + 55/2 = 0", "output": "x^2 + 21/2x + 55/2 = 0\n(x - -5)(x - -11/2) = 0\nx - -5 = 0 or x - -11/2 = 0\nx = -5\nx = -11/2"} {"input": "Find the solution to 1x + 17/7 = 0", "output": "1x + 17/7 = 0\n1x = -17/7\nx = -17/7 / 1\nx = -17/7"} {"input": "Solve quickly: x^3 + 77/24x^2 - 305/48x - 475/24 = 0", "output": "x^3 + 77/24x^2 - 305/48x - 475/24 = 0\n(x - -19/8)(x - 5/2)(x - -10/3) = 0\nx - -19/8 = 0\nx - 5/2 = 0\nx - -10/3 = 0\nx = -19/8\nx = 5/2\nx = -10/3"} {"input": "Solve the equations:\n8x + 10y = 808/15\n10x + 4y = 32/3", "output": "8x + 10y = 808/15\n10x + 4y = 32/3\n\nUsing elimination\n10*(8x + 10y = 808/15)\n8*(10x + 4y = 32/3)\n80x + 100y = 1616/3\n80x + 32y = 256/3\nSubtract equations\n68y = 1360/3\ny = 1360/3/68\ny = 20/3\n\nSubstitute y\n8x + 10(20/3) = 808/15\n8x = -64/5\nx = -64/5/8\nx = -8/5"} {"input": "Solve the system:\n1x + 9y = 144/5\n6x + 6y = 48/5", "output": "1x + 9y = 144/5\n6x + 6y = 48/5\n\nUsing elimination\n6*(1x + 9y = 144/5)\n1*(6x + 6y = 48/5)\n6x + 54y = 864/5\n6x + 6y = 48/5\nSubtract equations\n48y = 816/5\ny = 816/5/48\ny = 17/5\n\nSubstitute y\n1x + 9(17/5) = 144/5\n1x = -9/5\nx = -9/5/1\nx = -9/5"} {"input": "Solve the equation x^3 - 33/8x^2 + 31/32x + 195/32 = 0", "output": "x^3 - 33/8x^2 + 31/32x + 195/32 = 0\n(x - 15/8)(x - -1)(x - 13/4) = 0\nx - 15/8 = 0\nx - -1 = 0\nx - 13/4 = 0\nx = 15/8\nx = -1\nx = 13/4"} {"input": "Solve the equations:\n7x + 2y = -32/5\n9x + 10y = -134/5", "output": "7x + 2y = -32/5\n9x + 10y = -134/5\n\nUsing elimination\n9*(7x + 2y = -32/5)\n7*(9x + 10y = -134/5)\n63x + 18y = -288/5\n63x + 70y = -938/5\nSubtract equations\n-52y = 130\ny = 130/-52\ny = -5/2\n\nSubstitute y\n7x + 2(-5/2) = -32/5\n7x = -7/5\nx = -7/5/7\nx = -1/5"} {"input": "Solve simultaneously:\n5x + 8y = -117\n4x + 3y = -213/5", "output": "5x + 8y = -117\n4x + 3y = -213/5\n\nUsing elimination\n4*(5x + 8y = -117)\n5*(4x + 3y = -213/5)\n20x + 32y = -468\n20x + 15y = -213\nSubtract equations\n17y = -255\ny = -255/17\ny = -15\n\nSubstitute y\n5x + 8(-15) = -117\n5x = 3\nx = 3/5\nx = 3/5"} {"input": "Solve the equation x^2 - 22/5x + 8/5 = 0", "output": "x^2 - 22/5x + 8/5 = 0\n(x - 2/5)(x - 4) = 0\nx - 2/5 = 0 or x - 4 = 0\nx = 2/5\nx = 4"} {"input": "Find x and y such that\n6x + 10y = -6\n9x + 2y = -19/5", "output": "6x + 10y = -6\n9x + 2y = -19/5\n\nUsing elimination\n9*(6x + 10y = -6)\n6*(9x + 2y = -19/5)\n54x + 90y = -54\n54x + 12y = -114/5\nSubtract equations\n78y = -156/5\ny = -156/5/78\ny = -2/5\n\nSubstitute y\n6x + 10(-2/5) = -6\n6x = -2\nx = -2/6\nx = -1/3"} {"input": "Find x in x^3 - 102/7x^2 + 333/7x + 162/7 = 0", "output": "x^3 - 102/7x^2 + 333/7x + 162/7 = 0\n(x - 9)(x - 6)(x - -3/7) = 0\nx - 9 = 0\nx - 6 = 0\nx - -3/7 = 0\nx = 9\nx = 6\nx = -3/7"} {"input": "Find x in 2x - 20/7 = 0", "output": "2x - 20/7 = 0\n2x = 20/7\nx = 20/7 / 2\nx = 10/7"} {"input": "Find x and y such that\n7x + 4y = 101/2\n6x + 6y = 51", "output": "7x + 4y = 101/2\n6x + 6y = 51\n\nUsing elimination\n6*(7x + 4y = 101/2)\n7*(6x + 6y = 51)\n42x + 24y = 303\n42x + 42y = 357\nSubtract equations\n-18y = -54\ny = -54/-18\ny = 3\n\nSubstitute y\n7x + 4(3) = 101/2\n7x = 77/2\nx = 77/2/7\nx = 11/2"} {"input": "Solve quickly: x^2 + 2x + 1 = 0", "output": "x^2 + 2x + 1 = 0\n(x - -1)(x - -1) = 0\nx - -1 = 0 or x - -1 = 0\nx = -1\nx = -1"} {"input": "Determine x in x^3 + 29/10x^2 - 12/5x - 63/10 = 0", "output": "x^3 + 29/10x^2 - 12/5x - 63/10 = 0\n(x - -3)(x - -7/5)(x - 3/2) = 0\nx - -3 = 0\nx - -7/5 = 0\nx - 3/2 = 0\nx = -3\nx = -7/5\nx = 3/2"} {"input": "Find x for 8x - 72 = 0", "output": "8x - 72 = 0\n8x = 72\nx = 72 / 8\nx = 9"} {"input": "Solve simultaneously:\n6x + 5y = 63/2\n3x + 4y = 27", "output": "6x + 5y = 63/2\n3x + 4y = 27\n\nUsing elimination\n3*(6x + 5y = 63/2)\n6*(3x + 4y = 27)\n18x + 15y = 189/2\n18x + 24y = 162\nSubtract equations\n-9y = -135/2\ny = -135/2/-9\ny = 15/2\n\nSubstitute y\n6x + 5(15/2) = 63/2\n6x = -6\nx = -6/6\nx = -1"} {"input": "Find x in x^3 - 15/4x^2 - 139/64x + 1365/128 = 0", "output": "x^3 - 15/4x^2 - 139/64x + 1365/128 = 0\n(x - 7/2)(x - 15/8)(x - -13/8) = 0\nx - 7/2 = 0\nx - 15/8 = 0\nx - -13/8 = 0\nx = 7/2\nx = 15/8\nx = -13/8"} {"input": "Compute the solution of 4x - 80 = 0", "output": "4x - 80 = 0\n4x = 80\nx = 80 / 4\nx = 20"} {"input": "What value of x satisfies x^2 + 22/5x - 91/5 = 0", "output": "x^2 + 22/5x - 91/5 = 0\n(x - 13/5)(x - -7) = 0\nx - 13/5 = 0 or x - -7 = 0\nx = 13/5\nx = -7"} {"input": "Solve the equations:\n2x + 8y = 38/9\n9x + 7y = -1/3", "output": "2x + 8y = 38/9\n9x + 7y = -1/3\n\nUsing elimination\n9*(2x + 8y = 38/9)\n2*(9x + 7y = -1/3)\n18x + 72y = 38\n18x + 14y = -2/3\nSubtract equations\n58y = 116/3\ny = 116/3/58\ny = 2/3\n\nSubstitute y\n2x + 8(2/3) = 38/9\n2x = -10/9\nx = -10/9/2\nx = -5/9"} {"input": "Find x for 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "What value of x satisfies x^3 - 21/4x^2 + 9/8x + 135/8 = 0", "output": "x^3 - 21/4x^2 + 9/8x + 135/8 = 0\n(x - -3/2)(x - 3)(x - 15/4) = 0\nx - -3/2 = 0\nx - 3 = 0\nx - 15/4 = 0\nx = -3/2\nx = 3\nx = 15/4"} {"input": "Find x in 2x - 22/5 = 0", "output": "2x - 22/5 = 0\n2x = 22/5\nx = 22/5 / 2\nx = 11/5"} {"input": "Solve quickly: 7x + 56 = 0", "output": "7x + 56 = 0\n7x = -56\nx = -56 / 7\nx = -8"} {"input": "Solve the equation 3x + 33/8 = 0", "output": "3x + 33/8 = 0\n3x = -33/8\nx = -33/8 / 3\nx = -11/8"} {"input": "Determine x in 3x - 18 = 0", "output": "3x - 18 = 0\n3x = 18\nx = 18 / 3\nx = 6"} {"input": "Find x for x^2 + 16/3x + 20/3 = 0", "output": "x^2 + 16/3x + 20/3 = 0\n(x - -2)(x - -10/3) = 0\nx - -2 = 0 or x - -10/3 = 0\nx = -2\nx = -10/3"} {"input": "Solve simultaneously:\n9x + 8y = 41/2\n2x + 9y = 1/24", "output": "9x + 8y = 41/2\n2x + 9y = 1/24\n\nUsing elimination\n2*(9x + 8y = 41/2)\n9*(2x + 9y = 1/24)\n18x + 16y = 41\n18x + 81y = 3/8\nSubtract equations\n-65y = 325/8\ny = 325/8/-65\ny = -5/8\n\nSubstitute y\n9x + 8(-5/8) = 41/2\n9x = 51/2\nx = 51/2/9\nx = 17/6"} {"input": "Solve x^3 + 4x^2 + 1x - 6 = 0", "output": "x^3 + 4x^2 + 1x - 6 = 0\n(x - 1)(x - -2)(x - -3) = 0\nx - 1 = 0\nx - -2 = 0\nx - -3 = 0\nx = 1\nx = -2\nx = -3"} {"input": "Solve the equations:\n9x + 10y = -88\n5x + 3y = -31", "output": "9x + 10y = -88\n5x + 3y = -31\n\nUsing elimination\n5*(9x + 10y = -88)\n9*(5x + 3y = -31)\n45x + 50y = -440\n45x + 27y = -279\nSubtract equations\n23y = -161\ny = -161/23\ny = -7\n\nSubstitute y\n9x + 10(-7) = -88\n9x = -18\nx = -18/9\nx = -2"} {"input": "Solve the system:\n5x + 5y = 179/14\n9x + 3y = 1251/70", "output": "5x + 5y = 179/14\n9x + 3y = 1251/70\n\nUsing elimination\n9*(5x + 5y = 179/14)\n5*(9x + 3y = 1251/70)\n45x + 45y = 1611/14\n45x + 15y = 1251/14\nSubtract equations\n30y = 180/7\ny = 180/7/30\ny = 6/7\n\nSubstitute y\n5x + 5(6/7) = 179/14\n5x = 17/2\nx = 17/2/5\nx = 17/10"} {"input": "Find x in x^2 - 26/9x - 1/3 = 0", "output": "x^2 - 26/9x - 1/3 = 0\n(x - -1/9)(x - 3) = 0\nx - -1/9 = 0 or x - 3 = 0\nx = -1/9\nx = 3"} {"input": "What value of x satisfies x^2 - 2/5x - 24/5 = 0", "output": "x^2 - 2/5x - 24/5 = 0\n(x - 12/5)(x - -2) = 0\nx - 12/5 = 0 or x - -2 = 0\nx = 12/5\nx = -2"} {"input": "Solve the equations:\n10x + 4y = 188/7\n8x + 4y = 160/7", "output": "10x + 4y = 188/7\n8x + 4y = 160/7\n\nUsing elimination\n8*(10x + 4y = 188/7)\n10*(8x + 4y = 160/7)\n80x + 32y = 1504/7\n80x + 40y = 1600/7\nSubtract equations\n-8y = -96/7\ny = -96/7/-8\ny = 12/7\n\nSubstitute y\n10x + 4(12/7) = 188/7\n10x = 20\nx = 20/10\nx = 2"} {"input": "Find the solution to 10x - 36 = 0", "output": "10x - 36 = 0\n10x = 36\nx = 36 / 10\nx = 18/5"} {"input": "Find x in x^3 + 19/2x^2 - 153/2x + 90 = 0", "output": "x^3 + 19/2x^2 - 153/2x + 90 = 0\n(x - -15)(x - 4)(x - 3/2) = 0\nx - -15 = 0\nx - 4 = 0\nx - 3/2 = 0\nx = -15\nx = 4\nx = 3/2"} {"input": "What value of x satisfies x^2 + 1/2x - 15/2 = 0", "output": "x^2 + 1/2x - 15/2 = 0\n(x - -3)(x - 5/2) = 0\nx - -3 = 0 or x - 5/2 = 0\nx = -3\nx = 5/2"} {"input": "Compute the solution of x^2 - 41/7x + 52/7 = 0", "output": "x^2 - 41/7x + 52/7 = 0\n(x - 4)(x - 13/7) = 0\nx - 4 = 0 or x - 13/7 = 0\nx = 4\nx = 13/7"} {"input": "Find x for x^2 + 15/2x + 27/2 = 0", "output": "x^2 + 15/2x + 27/2 = 0\n(x - -3)(x - -9/2) = 0\nx - -3 = 0 or x - -9/2 = 0\nx = -3\nx = -9/2"} {"input": "Find the solution to 10x - 95/2 = 0", "output": "10x - 95/2 = 0\n10x = 95/2\nx = 95/2 / 10\nx = 19/4"} {"input": "Find x for 10x - 35/4 = 0", "output": "10x - 35/4 = 0\n10x = 35/4\nx = 35/4 / 10\nx = 7/8"} {"input": "Solve the equation x^2 + 10x + 221/9 = 0", "output": "x^2 + 10x + 221/9 = 0\n(x - -17/3)(x - -13/3) = 0\nx - -17/3 = 0 or x - -13/3 = 0\nx = -17/3\nx = -13/3"} {"input": "What value of x satisfies x^3 - 74/45x^2 + 11/15x - 4/45 = 0", "output": "x^3 - 74/45x^2 + 11/15x - 4/45 = 0\n(x - 4/9)(x - 1/5)(x - 1) = 0\nx - 4/9 = 0\nx - 1/5 = 0\nx - 1 = 0\nx = 4/9\nx = 1/5\nx = 1"} {"input": "Solve quickly: 6x + 14 = 0", "output": "6x + 14 = 0\n6x = -14\nx = -14 / 6\nx = -7/3"} {"input": "Solve the system:\n2x + 9y = 114/5\n1x + 7y = 47/5", "output": "2x + 9y = 114/5\n1x + 7y = 47/5\n\nUsing elimination\n1*(2x + 9y = 114/5)\n2*(1x + 7y = 47/5)\n2x + 9y = 114/5\n2x + 14y = 94/5\nSubtract equations\n-5y = 4\ny = 4/-5\ny = -4/5\n\nSubstitute y\n2x + 9(-4/5) = 114/5\n2x = 30\nx = 30/2\nx = 15"} {"input": "Solve the equation x^2 + 2/3x - 8/9 = 0", "output": "x^2 + 2/3x - 8/9 = 0\n(x - -4/3)(x - 2/3) = 0\nx - -4/3 = 0 or x - 2/3 = 0\nx = -4/3\nx = 2/3"} {"input": "Solve x^2 - 61/20x + 9/5 = 0", "output": "x^2 - 61/20x + 9/5 = 0\n(x - 9/4)(x - 4/5) = 0\nx - 9/4 = 0 or x - 4/5 = 0\nx = 9/4\nx = 4/5"} {"input": "Find x in x^3 + 83/21x^2 - 2/7x - 8/21 = 0", "output": "x^3 + 83/21x^2 - 2/7x - 8/21 = 0\n(x - -2/7)(x - -4)(x - 1/3) = 0\nx - -2/7 = 0\nx - -4 = 0\nx - 1/3 = 0\nx = -2/7\nx = -4\nx = 1/3"} {"input": "What value of x satisfies x^3 - 35/6x^2 + 59/6x - 5 = 0", "output": "x^3 - 35/6x^2 + 59/6x - 5 = 0\n(x - 3/2)(x - 10/3)(x - 1) = 0\nx - 3/2 = 0\nx - 10/3 = 0\nx - 1 = 0\nx = 3/2\nx = 10/3\nx = 1"} {"input": "Solve the equations:\n1x + 5y = 47\n1x + 3y = 29", "output": "1x + 5y = 47\n1x + 3y = 29\n\nUsing elimination\n1*(1x + 5y = 47)\n1*(1x + 3y = 29)\n1x + 5y = 47\n1x + 3y = 29\nSubtract equations\n2y = 18\ny = 18/2\ny = 9\n\nSubstitute y\n1x + 5(9) = 47\n1x = 2\nx = 2/1\nx = 2"} {"input": "Solve simultaneously:\n6x + 3y = 183/7\n2x + 10y = 106/7", "output": "6x + 3y = 183/7\n2x + 10y = 106/7\n\nUsing elimination\n2*(6x + 3y = 183/7)\n6*(2x + 10y = 106/7)\n12x + 6y = 366/7\n12x + 60y = 636/7\nSubtract equations\n-54y = -270/7\ny = -270/7/-54\ny = 5/7\n\nSubstitute y\n6x + 3(5/7) = 183/7\n6x = 24\nx = 24/6\nx = 4"} {"input": "Solve the equation x^2 + 9/10x - 7/10 = 0", "output": "x^2 + 9/10x - 7/10 = 0\n(x - -7/5)(x - 1/2) = 0\nx - -7/5 = 0 or x - 1/2 = 0\nx = -7/5\nx = 1/2"} {"input": "Find the solution to x^2 - 33/7x + 20/7 = 0", "output": "x^2 - 33/7x + 20/7 = 0\n(x - 4)(x - 5/7) = 0\nx - 4 = 0 or x - 5/7 = 0\nx = 4\nx = 5/7"} {"input": "Compute the solution of x^2 + 32/9x - 65/9 = 0", "output": "x^2 + 32/9x - 65/9 = 0\n(x - 13/9)(x - -5) = 0\nx - 13/9 = 0 or x - -5 = 0\nx = 13/9\nx = -5"} {"input": "Solve the equation 4x + 38/5 = 0", "output": "4x + 38/5 = 0\n4x = -38/5\nx = -38/5 / 4\nx = -19/10"} {"input": "Find x in 7x - 133/3 = 0", "output": "7x - 133/3 = 0\n7x = 133/3\nx = 133/3 / 7\nx = 19/3"} {"input": "Compute the solution of x^3 + 21/5x^2 + 104/25x + 84/125 = 0", "output": "x^3 + 21/5x^2 + 104/25x + 84/125 = 0\n(x - -14/5)(x - -1/5)(x - -6/5) = 0\nx - -14/5 = 0\nx - -1/5 = 0\nx - -6/5 = 0\nx = -14/5\nx = -1/5\nx = -6/5"} {"input": "Solve x^2 + 17/3x + 14/3 = 0", "output": "x^2 + 17/3x + 14/3 = 0\n(x - -1)(x - -14/3) = 0\nx - -1 = 0 or x - -14/3 = 0\nx = -1\nx = -14/3"} {"input": "Solve the equation x^2 + 29/2x - 15/2 = 0", "output": "x^2 + 29/2x - 15/2 = 0\n(x - 1/2)(x - -15) = 0\nx - 1/2 = 0 or x - -15 = 0\nx = 1/2\nx = -15"} {"input": "Solve the equations:\n4x + 1y = 11\n4x + 8y = 60", "output": "4x + 1y = 11\n4x + 8y = 60\n\nUsing elimination\n4*(4x + 1y = 11)\n4*(4x + 8y = 60)\n16x + 4y = 44\n16x + 32y = 240\nSubtract equations\n-28y = -196\ny = -196/-28\ny = 7\n\nSubstitute y\n4x + 1(7) = 11\n4x = 4\nx = 4/4\nx = 1"} {"input": "Solve simultaneously:\n4x + 7y = -348/5\n4x + 5y = -248/5", "output": "4x + 7y = -348/5\n4x + 5y = -248/5\n\nUsing elimination\n4*(4x + 7y = -348/5)\n4*(4x + 5y = -248/5)\n16x + 28y = -1392/5\n16x + 20y = -992/5\nSubtract equations\n8y = -80\ny = -80/8\ny = -10\n\nSubstitute y\n4x + 7(-10) = -348/5\n4x = 2/5\nx = 2/5/4\nx = 1/10"} {"input": "Solve the equations:\n3x + 2y = 61/7\n6x + 8y = 262/7", "output": "3x + 2y = 61/7\n6x + 8y = 262/7\n\nUsing elimination\n6*(3x + 2y = 61/7)\n3*(6x + 8y = 262/7)\n18x + 12y = 366/7\n18x + 24y = 786/7\nSubtract equations\n-12y = -60\ny = -60/-12\ny = 5\n\nSubstitute y\n3x + 2(5) = 61/7\n3x = -9/7\nx = -9/7/3\nx = -3/7"} {"input": "Solve simultaneously:\n10x + 9y = -163/10\n1x + 10y = -8", "output": "10x + 9y = -163/10\n1x + 10y = -8\n\nUsing elimination\n1*(10x + 9y = -163/10)\n10*(1x + 10y = -8)\n10x + 9y = -163/10\n10x + 100y = -80\nSubtract equations\n-91y = 637/10\ny = 637/10/-91\ny = -7/10\n\nSubstitute y\n10x + 9(-7/10) = -163/10\n10x = -10\nx = -10/10\nx = -1"} {"input": "Find x for 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Compute the solution of x^2 - 25/6x + 13/3 = 0", "output": "x^2 - 25/6x + 13/3 = 0\n(x - 2)(x - 13/6) = 0\nx - 2 = 0 or x - 13/6 = 0\nx = 2\nx = 13/6"} {"input": "Solve the equation x^3 + 5/6x^2 - 22/3x + 10/3 = 0", "output": "x^3 + 5/6x^2 - 22/3x + 10/3 = 0\n(x - -10/3)(x - 1/2)(x - 2) = 0\nx - -10/3 = 0\nx - 1/2 = 0\nx - 2 = 0\nx = -10/3\nx = 1/2\nx = 2"} {"input": "Determine x in 9x + 27/10 = 0", "output": "9x + 27/10 = 0\n9x = -27/10\nx = -27/10 / 9\nx = -3/10"} {"input": "Determine x in x^3 - 339/35x^2 - 162/5x + 1944/35 = 0", "output": "x^3 - 339/35x^2 - 162/5x + 1944/35 = 0\n(x - 9/7)(x - 12)(x - -18/5) = 0\nx - 9/7 = 0\nx - 12 = 0\nx - -18/5 = 0\nx = 9/7\nx = 12\nx = -18/5"} {"input": "Find x in 7x - 35/4 = 0", "output": "7x - 35/4 = 0\n7x = 35/4\nx = 35/4 / 7\nx = 5/4"} {"input": "Determine x in x^3 + 41/30x^2 - 347/150x + 2/5 = 0", "output": "x^3 + 41/30x^2 - 347/150x + 2/5 = 0\n(x - 5/6)(x - 1/5)(x - -12/5) = 0\nx - 5/6 = 0\nx - 1/5 = 0\nx - -12/5 = 0\nx = 5/6\nx = 1/5\nx = -12/5"} {"input": "Solve 9x - 10 = 0", "output": "9x - 10 = 0\n9x = 10\nx = 10 / 9\nx = 10/9"} {"input": "Find the solution to 5x + 100 = 0", "output": "5x + 100 = 0\n5x = -100\nx = -100 / 5\nx = -20"} {"input": "Solve x^2 + 34/7x - 48/7 = 0", "output": "x^2 + 34/7x - 48/7 = 0\n(x - -6)(x - 8/7) = 0\nx - -6 = 0 or x - 8/7 = 0\nx = -6\nx = 8/7"} {"input": "Solve x^2 - 5x + 4 = 0", "output": "x^2 - 5x + 4 = 0\n(x - 4)(x - 1) = 0\nx - 4 = 0 or x - 1 = 0\nx = 4\nx = 1"} {"input": "Solve the equation x^2 + 23/14x + 3/14 = 0", "output": "x^2 + 23/14x + 3/14 = 0\n(x - -1/7)(x - -3/2) = 0\nx - -1/7 = 0 or x - -3/2 = 0\nx = -1/7\nx = -3/2"} {"input": "Find x for x^2 + 27/10x + 38/25 = 0", "output": "x^2 + 27/10x + 38/25 = 0\n(x - -4/5)(x - -19/10) = 0\nx - -4/5 = 0 or x - -19/10 = 0\nx = -4/5\nx = -19/10"} {"input": "Solve simultaneously:\n10x + 10y = -205/9\n2x + 1y = -73/18", "output": "10x + 10y = -205/9\n2x + 1y = -73/18\n\nUsing elimination\n2*(10x + 10y = -205/9)\n10*(2x + 1y = -73/18)\n20x + 20y = -410/9\n20x + 10y = -365/9\nSubtract equations\n10y = -5\ny = -5/10\ny = -1/2\n\nSubstitute y\n10x + 10(-1/2) = -205/9\n10x = -160/9\nx = -160/9/10\nx = -16/9"} {"input": "Compute the solution of x^2 + 47/3x + 10 = 0", "output": "x^2 + 47/3x + 10 = 0\n(x - -15)(x - -2/3) = 0\nx - -15 = 0 or x - -2/3 = 0\nx = -15\nx = -2/3"} {"input": "What value of x satisfies x^3 - 151/7x^2 + 32x - 80/7 = 0", "output": "x^3 - 151/7x^2 + 32x - 80/7 = 0\n(x - 1)(x - 20)(x - 4/7) = 0\nx - 1 = 0\nx - 20 = 0\nx - 4/7 = 0\nx = 1\nx = 20\nx = 4/7"} {"input": "Find x for x^3 - 8x^2 + 1251/100x - 153/50 = 0", "output": "x^3 - 8x^2 + 1251/100x - 153/50 = 0\n(x - 3/10)(x - 6)(x - 17/10) = 0\nx - 3/10 = 0\nx - 6 = 0\nx - 17/10 = 0\nx = 3/10\nx = 6\nx = 17/10"} {"input": "Find the solution to 9x + 36/5 = 0", "output": "9x + 36/5 = 0\n9x = -36/5\nx = -36/5 / 9\nx = -4/5"} {"input": "Determine x in 5x - 3 = 0", "output": "5x - 3 = 0\n5x = 3\nx = 3 / 5\nx = 3/5"} {"input": "Find x in x^2 + 26/15x + 8/15 = 0", "output": "x^2 + 26/15x + 8/15 = 0\n(x - -2/5)(x - -4/3) = 0\nx - -2/5 = 0 or x - -4/3 = 0\nx = -2/5\nx = -4/3"} {"input": "Compute the solution of 9x + 36/7 = 0", "output": "9x + 36/7 = 0\n9x = -36/7\nx = -36/7 / 9\nx = -4/7"} {"input": "Solve the equation x^3 + 37/12x^2 + 1/3x - 17/16 = 0", "output": "x^3 + 37/12x^2 + 1/3x - 17/16 = 0\n(x - -17/6)(x - 1/2)(x - -3/4) = 0\nx - -17/6 = 0\nx - 1/2 = 0\nx - -3/4 = 0\nx = -17/6\nx = 1/2\nx = -3/4"} {"input": "Compute the solution of x^2 + 1/2x - 3/2 = 0", "output": "x^2 + 1/2x - 3/2 = 0\n(x - -3/2)(x - 1) = 0\nx - -3/2 = 0 or x - 1 = 0\nx = -3/2\nx = 1"} {"input": "Solve quickly: 4x + 16/7 = 0", "output": "4x + 16/7 = 0\n4x = -16/7\nx = -16/7 / 4\nx = -4/7"} {"input": "Determine x in 5x + 45/4 = 0", "output": "5x + 45/4 = 0\n5x = -45/4\nx = -45/4 / 5\nx = -9/4"} {"input": "Find x for x^2 + 21/4x + 49/8 = 0", "output": "x^2 + 21/4x + 49/8 = 0\n(x - -7/2)(x - -7/4) = 0\nx - -7/2 = 0 or x - -7/4 = 0\nx = -7/2\nx = -7/4"} {"input": "Solve simultaneously:\n6x + 9y = 21\n6x + 3y = 33", "output": "6x + 9y = 21\n6x + 3y = 33\n\nUsing elimination\n6*(6x + 9y = 21)\n6*(6x + 3y = 33)\n36x + 54y = 126\n36x + 18y = 198\nSubtract equations\n36y = -72\ny = -72/36\ny = -2\n\nSubstitute y\n6x + 9(-2) = 21\n6x = 39\nx = 39/6\nx = 13/2"} {"input": "Find x for x^3 - 353/30x^2 + 239/30x + 77/15 = 0", "output": "x^3 - 353/30x^2 + 239/30x + 77/15 = 0\n(x - 11)(x - 7/6)(x - -2/5) = 0\nx - 11 = 0\nx - 7/6 = 0\nx - -2/5 = 0\nx = 11\nx = 7/6\nx = -2/5"} {"input": "Solve simultaneously:\n6x + 9y = -40/7\n8x + 6y = -304/21", "output": "6x + 9y = -40/7\n8x + 6y = -304/21\n\nUsing elimination\n8*(6x + 9y = -40/7)\n6*(8x + 6y = -304/21)\n48x + 72y = -320/7\n48x + 36y = -608/7\nSubtract equations\n36y = 288/7\ny = 288/7/36\ny = 8/7\n\nSubstitute y\n6x + 9(8/7) = -40/7\n6x = -16\nx = -16/6\nx = -8/3"} {"input": "Solve 3x + 15 = 0", "output": "3x + 15 = 0\n3x = -15\nx = -15 / 3\nx = -5"} {"input": "Find x for 6x - 3 = 0", "output": "6x - 3 = 0\n6x = 3\nx = 3 / 6\nx = 1/2"} {"input": "Find x and y such that\n1x + 4y = 1/5\n6x + 8y = -18/5", "output": "1x + 4y = 1/5\n6x + 8y = -18/5\n\nUsing elimination\n6*(1x + 4y = 1/5)\n1*(6x + 8y = -18/5)\n6x + 24y = 6/5\n6x + 8y = -18/5\nSubtract equations\n16y = 24/5\ny = 24/5/16\ny = 3/10\n\nSubstitute y\n1x + 4(3/10) = 1/5\n1x = -1\nx = -1/1\nx = -1"} {"input": "Solve simultaneously:\n2x + 10y = 44\n1x + 6y = 23", "output": "2x + 10y = 44\n1x + 6y = 23\n\nUsing elimination\n1*(2x + 10y = 44)\n2*(1x + 6y = 23)\n2x + 10y = 44\n2x + 12y = 46\nSubtract equations\n-2y = -2\ny = -2/-2\ny = 1\n\nSubstitute y\n2x + 10(1) = 44\n2x = 34\nx = 34/2\nx = 17"} {"input": "Compute the solution of x^2 - 23/20x + 9/40 = 0", "output": "x^2 - 23/20x + 9/40 = 0\n(x - 1/4)(x - 9/10) = 0\nx - 1/4 = 0 or x - 9/10 = 0\nx = 1/4\nx = 9/10"} {"input": "Solve the system:\n9x + 7y = -9/2\n4x + 2y = -7", "output": "9x + 7y = -9/2\n4x + 2y = -7\n\nUsing elimination\n4*(9x + 7y = -9/2)\n9*(4x + 2y = -7)\n36x + 28y = -18\n36x + 18y = -63\nSubtract equations\n10y = 45\ny = 45/10\ny = 9/2\n\nSubstitute y\n9x + 7(9/2) = -9/2\n9x = -36\nx = -36/9\nx = -4"} {"input": "Find x for 7x + 7/2 = 0", "output": "7x + 7/2 = 0\n7x = -7/2\nx = -7/2 / 7\nx = -1/2"} {"input": "Solve simultaneously:\n3x + 1y = -177/35\n8x + 3y = -447/35", "output": "3x + 1y = -177/35\n8x + 3y = -447/35\n\nUsing elimination\n8*(3x + 1y = -177/35)\n3*(8x + 3y = -447/35)\n24x + 8y = -1416/35\n24x + 9y = -1341/35\nSubtract equations\n-1y = -15/7\ny = -15/7/-1\ny = 15/7\n\nSubstitute y\n3x + 1(15/7) = -177/35\n3x = -36/5\nx = -36/5/3\nx = -12/5"} {"input": "Determine x in x^2 - 2/5x - 7/5 = 0", "output": "x^2 - 2/5x - 7/5 = 0\n(x - -1)(x - 7/5) = 0\nx - -1 = 0 or x - 7/5 = 0\nx = -1\nx = 7/5"} {"input": "Find x for x^3 - 109/21x^2 + 560/81x - 400/567 = 0", "output": "x^3 - 109/21x^2 + 560/81x - 400/567 = 0\n(x - 20/9)(x - 1/9)(x - 20/7) = 0\nx - 20/9 = 0\nx - 1/9 = 0\nx - 20/7 = 0\nx = 20/9\nx = 1/9\nx = 20/7"} {"input": "Find x in 5x + 1 = 0", "output": "5x + 1 = 0\n5x = -1\nx = -1 / 5\nx = -1/5"} {"input": "Find x and y such that\n7x + 5y = 157/9\n9x + 3y = 11", "output": "7x + 5y = 157/9\n9x + 3y = 11\n\nUsing elimination\n9*(7x + 5y = 157/9)\n7*(9x + 3y = 11)\n63x + 45y = 157\n63x + 21y = 77\nSubtract equations\n24y = 80\ny = 80/24\ny = 10/3\n\nSubstitute y\n7x + 5(10/3) = 157/9\n7x = 7/9\nx = 7/9/7\nx = 1/9"} {"input": "Compute the solution of x^3 - 23/10x^2 - 837/50x + 81/5 = 0", "output": "x^3 - 23/10x^2 - 837/50x + 81/5 = 0\n(x - 5)(x - 9/10)(x - -18/5) = 0\nx - 5 = 0\nx - 9/10 = 0\nx - -18/5 = 0\nx = 5\nx = 9/10\nx = -18/5"} {"input": "Find x and y such that\n10x + 10y = -1030/21\n8x + 6y = -242/7", "output": "10x + 10y = -1030/21\n8x + 6y = -242/7\n\nUsing elimination\n8*(10x + 10y = -1030/21)\n10*(8x + 6y = -242/7)\n80x + 80y = -8240/21\n80x + 60y = -2420/7\nSubtract equations\n20y = -140/3\ny = -140/3/20\ny = -7/3\n\nSubstitute y\n10x + 10(-7/3) = -1030/21\n10x = -180/7\nx = -180/7/10\nx = -18/7"} {"input": "Find the solution to x^3 - 5/6x^2 - 41/2x - 56/3 = 0", "output": "x^3 - 5/6x^2 - 41/2x - 56/3 = 0\n(x - 16/3)(x - -1)(x - -7/2) = 0\nx - 16/3 = 0\nx - -1 = 0\nx - -7/2 = 0\nx = 16/3\nx = -1\nx = -7/2"} {"input": "What value of x satisfies 9x - 63/5 = 0", "output": "9x - 63/5 = 0\n9x = 63/5\nx = 63/5 / 9\nx = 7/5"} {"input": "Solve simultaneously:\n3x + 9y = 621/56\n10x + 10y = 265/28", "output": "3x + 9y = 621/56\n10x + 10y = 265/28\n\nUsing elimination\n10*(3x + 9y = 621/56)\n3*(10x + 10y = 265/28)\n30x + 90y = 3105/28\n30x + 30y = 795/28\nSubtract equations\n60y = 165/2\ny = 165/2/60\ny = 11/8\n\nSubstitute y\n3x + 9(11/8) = 621/56\n3x = -9/7\nx = -9/7/3\nx = -3/7"} {"input": "Solve the equation x^2 - 67/30x - 7/30 = 0", "output": "x^2 - 67/30x - 7/30 = 0\n(x - -1/10)(x - 7/3) = 0\nx - -1/10 = 0 or x - 7/3 = 0\nx = -1/10\nx = 7/3"} {"input": "Solve quickly: x^3 - 77/10x^2 + 25/2x - 11/5 = 0", "output": "x^3 - 77/10x^2 + 25/2x - 11/5 = 0\n(x - 2)(x - 1/5)(x - 11/2) = 0\nx - 2 = 0\nx - 1/5 = 0\nx - 11/2 = 0\nx = 2\nx = 1/5\nx = 11/2"} {"input": "Solve the equations:\n10x + 1y = -86/7\n2x + 10y = 120/7", "output": "10x + 1y = -86/7\n2x + 10y = 120/7\n\nUsing elimination\n2*(10x + 1y = -86/7)\n10*(2x + 10y = 120/7)\n20x + 2y = -172/7\n20x + 100y = 1200/7\nSubtract equations\n-98y = -196\ny = -196/-98\ny = 2\n\nSubstitute y\n10x + 1(2) = -86/7\n10x = -100/7\nx = -100/7/10\nx = -10/7"} {"input": "Compute the solution of x^2 - 2x + 3/4 = 0", "output": "x^2 - 2x + 3/4 = 0\n(x - 1/2)(x - 3/2) = 0\nx - 1/2 = 0 or x - 3/2 = 0\nx = 1/2\nx = 3/2"} {"input": "Solve simultaneously:\n2x + 8y = -34\n4x + 2y = -12", "output": "2x + 8y = -34\n4x + 2y = -12\n\nUsing elimination\n4*(2x + 8y = -34)\n2*(4x + 2y = -12)\n8x + 32y = -136\n8x + 4y = -24\nSubtract equations\n28y = -112\ny = -112/28\ny = -4\n\nSubstitute y\n2x + 8(-4) = -34\n2x = -2\nx = -2/2\nx = -1"} {"input": "Solve the equation x^2 + 19/6x - 85/6 = 0", "output": "x^2 + 19/6x - 85/6 = 0\n(x - 5/2)(x - -17/3) = 0\nx - 5/2 = 0 or x - -17/3 = 0\nx = 5/2\nx = -17/3"} {"input": "Solve x^2 + 9/10x - 19/10 = 0", "output": "x^2 + 9/10x - 19/10 = 0\n(x - -19/10)(x - 1) = 0\nx - -19/10 = 0 or x - 1 = 0\nx = -19/10\nx = 1"} {"input": "Solve the equations:\n2x + 7y = -159/8\n9x + 6y = -243/4", "output": "2x + 7y = -159/8\n9x + 6y = -243/4\n\nUsing elimination\n9*(2x + 7y = -159/8)\n2*(9x + 6y = -243/4)\n18x + 63y = -1431/8\n18x + 12y = -243/2\nSubtract equations\n51y = -459/8\ny = -459/8/51\ny = -9/8\n\nSubstitute y\n2x + 7(-9/8) = -159/8\n2x = -12\nx = -12/2\nx = -6"} {"input": "Find the solution to x^3 - 28/9x^2 - 361/27x - 170/27 = 0", "output": "x^3 - 28/9x^2 - 361/27x - 170/27 = 0\n(x - -2)(x - -5/9)(x - 17/3) = 0\nx - -2 = 0\nx - -5/9 = 0\nx - 17/3 = 0\nx = -2\nx = -5/9\nx = 17/3"} {"input": "Find x for x^3 + 55/18x^2 + 7/3x = 0", "output": "x^3 + 55/18x^2 + 7/3x = 0\n(x - -14/9)(x - 0)(x - -3/2) = 0\nx - -14/9 = 0\nx - 0 = 0\nx - -3/2 = 0\nx = -14/9\nx = 0\nx = -3/2"} {"input": "Find x and y such that\n6x + 1y = 187/15\n10x + 4y = 32/3", "output": "6x + 1y = 187/15\n10x + 4y = 32/3\n\nUsing elimination\n10*(6x + 1y = 187/15)\n6*(10x + 4y = 32/3)\n60x + 10y = 374/3\n60x + 24y = 64\nSubtract equations\n-14y = 182/3\ny = 182/3/-14\ny = -13/3\n\nSubstitute y\n6x + 1(-13/3) = 187/15\n6x = 84/5\nx = 84/5/6\nx = 14/5"} {"input": "Solve the equations:\n4x + 7y = -13\n3x + 6y = -21/2", "output": "4x + 7y = -13\n3x + 6y = -21/2\n\nUsing elimination\n3*(4x + 7y = -13)\n4*(3x + 6y = -21/2)\n12x + 21y = -39\n12x + 24y = -42\nSubtract equations\n-3y = 3\ny = 3/-3\ny = -1\n\nSubstitute y\n4x + 7(-1) = -13\n4x = -6\nx = -6/4\nx = -3/2"} {"input": "Solve x^2 + 4/35x - 3/7 = 0", "output": "x^2 + 4/35x - 3/7 = 0\n(x - -5/7)(x - 3/5) = 0\nx - -5/7 = 0 or x - 3/5 = 0\nx = -5/7\nx = 3/5"} {"input": "Solve x^2 + 23/3x + 34/3 = 0", "output": "x^2 + 23/3x + 34/3 = 0\n(x - -17/3)(x - -2) = 0\nx - -17/3 = 0 or x - -2 = 0\nx = -17/3\nx = -2"} {"input": "Solve the equation x^2 + 44/7x - 96/7 = 0", "output": "x^2 + 44/7x - 96/7 = 0\n(x - 12/7)(x - -8) = 0\nx - 12/7 = 0 or x - -8 = 0\nx = 12/7\nx = -8"} {"input": "Solve simultaneously:\n10x + 6y = -79/2\n7x + 2y = -93/4", "output": "10x + 6y = -79/2\n7x + 2y = -93/4\n\nUsing elimination\n7*(10x + 6y = -79/2)\n10*(7x + 2y = -93/4)\n70x + 42y = -553/2\n70x + 20y = -465/2\nSubtract equations\n22y = -44\ny = -44/22\ny = -2\n\nSubstitute y\n10x + 6(-2) = -79/2\n10x = -55/2\nx = -55/2/10\nx = -11/4"} {"input": "Solve quickly: x^2 - 1/2x - 5/18 = 0", "output": "x^2 - 1/2x - 5/18 = 0\n(x - -1/3)(x - 5/6) = 0\nx - -1/3 = 0 or x - 5/6 = 0\nx = -1/3\nx = 5/6"} {"input": "Solve the equations:\n9x + 2y = 19\n1x + 3y = 7/2", "output": "9x + 2y = 19\n1x + 3y = 7/2\n\nUsing elimination\n1*(9x + 2y = 19)\n9*(1x + 3y = 7/2)\n9x + 2y = 19\n9x + 27y = 63/2\nSubtract equations\n-25y = -25/2\ny = -25/2/-25\ny = 1/2\n\nSubstitute y\n9x + 2(1/2) = 19\n9x = 18\nx = 18/9\nx = 2"} {"input": "What value of x satisfies x^3 + 283/210x^2 - 369/70x - 104/15 = 0", "output": "x^3 + 283/210x^2 - 369/70x - 104/15 = 0\n(x - 16/7)(x - -13/10)(x - -7/3) = 0\nx - 16/7 = 0\nx - -13/10 = 0\nx - -7/3 = 0\nx = 16/7\nx = -13/10\nx = -7/3"} {"input": "Solve quickly: 3x - 21/4 = 0", "output": "3x - 21/4 = 0\n3x = 21/4\nx = 21/4 / 3\nx = 7/4"} {"input": "Compute the solution of 6x + 15/2 = 0", "output": "6x + 15/2 = 0\n6x = -15/2\nx = -15/2 / 6\nx = -5/4"} {"input": "Find the solution to x^2 + 89/14x - 255/14 = 0", "output": "x^2 + 89/14x - 255/14 = 0\n(x - 15/7)(x - -17/2) = 0\nx - 15/7 = 0 or x - -17/2 = 0\nx = 15/7\nx = -17/2"} {"input": "Compute the solution of x^2 + 65/8x - 51/16 = 0", "output": "x^2 + 65/8x - 51/16 = 0\n(x - 3/8)(x - -17/2) = 0\nx - 3/8 = 0 or x - -17/2 = 0\nx = 3/8\nx = -17/2"} {"input": "Determine x in x^2 - 22/35x - 153/35 = 0", "output": "x^2 - 22/35x - 153/35 = 0\n(x - -9/5)(x - 17/7) = 0\nx - -9/5 = 0 or x - 17/7 = 0\nx = -9/5\nx = 17/7"} {"input": "Compute the solution of 7x + 133/2 = 0", "output": "7x + 133/2 = 0\n7x = -133/2\nx = -133/2 / 7\nx = -19/2"} {"input": "Find x and y such that\n6x + 6y = 17/2\n6x + 5y = 37/4", "output": "6x + 6y = 17/2\n6x + 5y = 37/4\n\nUsing elimination\n6*(6x + 6y = 17/2)\n6*(6x + 5y = 37/4)\n36x + 36y = 51\n36x + 30y = 111/2\nSubtract equations\n6y = -9/2\ny = -9/2/6\ny = -3/4\n\nSubstitute y\n6x + 6(-3/4) = 17/2\n6x = 13\nx = 13/6\nx = 13/6"} {"input": "Find the solution to x^2 + 89/5x - 18/5 = 0", "output": "x^2 + 89/5x - 18/5 = 0\n(x - 1/5)(x - -18) = 0\nx - 1/5 = 0 or x - -18 = 0\nx = 1/5\nx = -18"} {"input": "Solve the equations:\n7x + 8y = 46\n4x + 4y = 20", "output": "7x + 8y = 46\n4x + 4y = 20\n\nUsing elimination\n4*(7x + 8y = 46)\n7*(4x + 4y = 20)\n28x + 32y = 184\n28x + 28y = 140\nSubtract equations\n4y = 44\ny = 44/4\ny = 11\n\nSubstitute y\n7x + 8(11) = 46\n7x = -42\nx = -42/7\nx = -6"} {"input": "Determine x in 3x + 10 = 0", "output": "3x + 10 = 0\n3x = -10\nx = -10 / 3\nx = -10/3"} {"input": "Solve x^2 - 157/30x + 19/3 = 0", "output": "x^2 - 157/30x + 19/3 = 0\n(x - 19/10)(x - 10/3) = 0\nx - 19/10 = 0 or x - 10/3 = 0\nx = 19/10\nx = 10/3"} {"input": "Compute the solution of 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Solve the equations:\n3x + 6y = -13/3\n3x + 1y = -8/3", "output": "3x + 6y = -13/3\n3x + 1y = -8/3\n\nUsing elimination\n3*(3x + 6y = -13/3)\n3*(3x + 1y = -8/3)\n9x + 18y = -13\n9x + 3y = -8\nSubtract equations\n15y = -5\ny = -5/15\ny = -1/3\n\nSubstitute y\n3x + 6(-1/3) = -13/3\n3x = -7/3\nx = -7/3/3\nx = -7/9"} {"input": "Find x for 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Solve quickly: 7x + 20 = 0", "output": "7x + 20 = 0\n7x = -20\nx = -20 / 7\nx = -20/7"} {"input": "Find x and y such that\n10x + 4y = 87/2\n5x + 6y = 121/4", "output": "10x + 4y = 87/2\n5x + 6y = 121/4\n\nUsing elimination\n5*(10x + 4y = 87/2)\n10*(5x + 6y = 121/4)\n50x + 20y = 435/2\n50x + 60y = 605/2\nSubtract equations\n-40y = -85\ny = -85/-40\ny = 17/8\n\nSubstitute y\n10x + 4(17/8) = 87/2\n10x = 35\nx = 35/10\nx = 7/2"} {"input": "Solve the system:\n5x + 7y = 97/72\n4x + 4y = -35/18", "output": "5x + 7y = 97/72\n4x + 4y = -35/18\n\nUsing elimination\n4*(5x + 7y = 97/72)\n5*(4x + 4y = -35/18)\n20x + 28y = 97/18\n20x + 20y = -175/18\nSubtract equations\n8y = 136/9\ny = 136/9/8\ny = 17/9\n\nSubstitute y\n5x + 7(17/9) = 97/72\n5x = -95/8\nx = -95/8/5\nx = -19/8"} {"input": "Solve the equation x^3 - 399/40x^2 + 1597/80x - 21/2 = 0", "output": "x^3 - 399/40x^2 + 1597/80x - 21/2 = 0\n(x - 8/5)(x - 7/8)(x - 15/2) = 0\nx - 8/5 = 0\nx - 7/8 = 0\nx - 15/2 = 0\nx = 8/5\nx = 7/8\nx = 15/2"} {"input": "Solve simultaneously:\n1x + 2y = -74/5\n3x + 7y = -219/5", "output": "1x + 2y = -74/5\n3x + 7y = -219/5\n\nUsing elimination\n3*(1x + 2y = -74/5)\n1*(3x + 7y = -219/5)\n3x + 6y = -222/5\n3x + 7y = -219/5\nSubtract equations\n-1y = -3/5\ny = -3/5/-1\ny = 3/5\n\nSubstitute y\n1x + 2(3/5) = -74/5\n1x = -16\nx = -16/1\nx = -16"} {"input": "What value of x satisfies x^2 + 149/90x + 11/18 = 0", "output": "x^2 + 149/90x + 11/18 = 0\n(x - -5/9)(x - -11/10) = 0\nx - -5/9 = 0 or x - -11/10 = 0\nx = -5/9\nx = -11/10"} {"input": "What value of x satisfies 8x = 0", "output": "8x = 0\n8x = 0\nx = 0 / 8\nx = 0"} {"input": "Solve the equations:\n2x + 10y = 407/35\n5x + 6y = 103/14", "output": "2x + 10y = 407/35\n5x + 6y = 103/14\n\nUsing elimination\n5*(2x + 10y = 407/35)\n2*(5x + 6y = 103/14)\n10x + 50y = 407/7\n10x + 12y = 103/7\nSubtract equations\n38y = 304/7\ny = 304/7/38\ny = 8/7\n\nSubstitute y\n2x + 10(8/7) = 407/35\n2x = 1/5\nx = 1/5/2\nx = 1/10"} {"input": "Find x in x^3 + 191/36x^2 + 4769/576x + 1805/576 = 0", "output": "x^3 + 191/36x^2 + 4769/576x + 1805/576 = 0\n(x - -19/8)(x - -19/8)(x - -5/9) = 0\nx - -19/8 = 0\nx - -19/8 = 0\nx - -5/9 = 0\nx = -19/8\nx = -19/8\nx = -5/9"} {"input": "Determine x in x^2 - 6/5x = 0", "output": "x^2 - 6/5x = 0\n(x - 0)(x - 6/5) = 0\nx - 0 = 0 or x - 6/5 = 0\nx = 0\nx = 6/5"} {"input": "What value of x satisfies x^2 - 121/12x + 95/4 = 0", "output": "x^2 - 121/12x + 95/4 = 0\n(x - 15/4)(x - 19/3) = 0\nx - 15/4 = 0 or x - 19/3 = 0\nx = 15/4\nx = 19/3"} {"input": "Find x and y such that\n8x + 6y = 26\n7x + 9y = 19", "output": "8x + 6y = 26\n7x + 9y = 19\n\nUsing elimination\n7*(8x + 6y = 26)\n8*(7x + 9y = 19)\n56x + 42y = 182\n56x + 72y = 152\nSubtract equations\n-30y = 30\ny = 30/-30\ny = -1\n\nSubstitute y\n8x + 6(-1) = 26\n8x = 32\nx = 32/8\nx = 4"} {"input": "What value of x satisfies x^3 - 193/60x^2 + 101/30x - 91/80 = 0", "output": "x^3 - 193/60x^2 + 101/30x - 91/80 = 0\n(x - 3/4)(x - 7/6)(x - 13/10) = 0\nx - 3/4 = 0\nx - 7/6 = 0\nx - 13/10 = 0\nx = 3/4\nx = 7/6\nx = 13/10"} {"input": "Solve quickly: 6x - 28 = 0", "output": "6x - 28 = 0\n6x = 28\nx = 28 / 6\nx = 14/3"} {"input": "Solve the equation x^3 + 170/9x^2 - 712/27x - 2240/27 = 0", "output": "x^3 + 170/9x^2 - 712/27x - 2240/27 = 0\n(x - 8/3)(x - -14/9)(x - -20) = 0\nx - 8/3 = 0\nx - -14/9 = 0\nx - -20 = 0\nx = 8/3\nx = -14/9\nx = -20"} {"input": "What value of x satisfies x^2 - 3x - 10 = 0", "output": "x^2 - 3x - 10 = 0\n(x - -2)(x - 5) = 0\nx - -2 = 0 or x - 5 = 0\nx = -2\nx = 5"} {"input": "Solve the equation x^3 - 14/3x^2 - 155/12x + 275/6 = 0", "output": "x^3 - 14/3x^2 - 155/12x + 275/6 = 0\n(x - 11/2)(x - 5/2)(x - -10/3) = 0\nx - 11/2 = 0\nx - 5/2 = 0\nx - -10/3 = 0\nx = 11/2\nx = 5/2\nx = -10/3"} {"input": "Solve quickly: 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "What value of x satisfies x^2 - 55/6x + 21 = 0", "output": "x^2 - 55/6x + 21 = 0\n(x - 14/3)(x - 9/2) = 0\nx - 14/3 = 0 or x - 9/2 = 0\nx = 14/3\nx = 9/2"} {"input": "Find x for 10x - 120 = 0", "output": "10x - 120 = 0\n10x = 120\nx = 120 / 10\nx = 12"} {"input": "Compute the solution of x^3 - 37/15x^2 - 166/75x + 112/25 = 0", "output": "x^3 - 37/15x^2 - 166/75x + 112/25 = 0\n(x - 6/5)(x - -7/5)(x - 8/3) = 0\nx - 6/5 = 0\nx - -7/5 = 0\nx - 8/3 = 0\nx = 6/5\nx = -7/5\nx = 8/3"} {"input": "Solve the system:\n7x + 2y = -129/7\n3x + 4y = -27/7", "output": "7x + 2y = -129/7\n3x + 4y = -27/7\n\nUsing elimination\n3*(7x + 2y = -129/7)\n7*(3x + 4y = -27/7)\n21x + 6y = -387/7\n21x + 28y = -27\nSubtract equations\n-22y = -198/7\ny = -198/7/-22\ny = 9/7\n\nSubstitute y\n7x + 2(9/7) = -129/7\n7x = -21\nx = -21/7\nx = -3"} {"input": "Solve the equations:\n8x + 9y = 421/35\n4x + 8y = 298/35", "output": "8x + 9y = 421/35\n4x + 8y = 298/35\n\nUsing elimination\n4*(8x + 9y = 421/35)\n8*(4x + 8y = 298/35)\n32x + 36y = 1684/35\n32x + 64y = 2384/35\nSubtract equations\n-28y = -20\ny = -20/-28\ny = 5/7\n\nSubstitute y\n8x + 9(5/7) = 421/35\n8x = 28/5\nx = 28/5/8\nx = 7/10"} {"input": "Compute the solution of x^2 - 1/6x - 5/2 = 0", "output": "x^2 - 1/6x - 5/2 = 0\n(x - -3/2)(x - 5/3) = 0\nx - -3/2 = 0 or x - 5/3 = 0\nx = -3/2\nx = 5/3"} {"input": "Solve 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve simultaneously:\n5x + 7y = 79/9\n2x + 3y = 10/3", "output": "5x + 7y = 79/9\n2x + 3y = 10/3\n\nUsing elimination\n2*(5x + 7y = 79/9)\n5*(2x + 3y = 10/3)\n10x + 14y = 158/9\n10x + 15y = 50/3\nSubtract equations\n-1y = 8/9\ny = 8/9/-1\ny = -8/9\n\nSubstitute y\n5x + 7(-8/9) = 79/9\n5x = 15\nx = 15/5\nx = 3"} {"input": "Determine x in x^2 + 121/24x - 85/24 = 0", "output": "x^2 + 121/24x - 85/24 = 0\n(x - 5/8)(x - -17/3) = 0\nx - 5/8 = 0 or x - -17/3 = 0\nx = 5/8\nx = -17/3"} {"input": "Find x for x^2 + 73/35x + 18/35 = 0", "output": "x^2 + 73/35x + 18/35 = 0\n(x - -9/5)(x - -2/7) = 0\nx - -9/5 = 0 or x - -2/7 = 0\nx = -9/5\nx = -2/7"} {"input": "Determine x in x^3 - 11/4x^2 - 237/2x + 90 = 0", "output": "x^3 - 11/4x^2 - 237/2x + 90 = 0\n(x - -10)(x - 3/4)(x - 12) = 0\nx - -10 = 0\nx - 3/4 = 0\nx - 12 = 0\nx = -10\nx = 3/4\nx = 12"} {"input": "Compute the solution of 9x + 42 = 0", "output": "9x + 42 = 0\n9x = -42\nx = -42 / 9\nx = -14/3"} {"input": "Solve the equation x^3 - 73/12x^2 - 1/3x + 95/3 = 0", "output": "x^3 - 73/12x^2 - 1/3x + 95/3 = 0\n(x - 19/4)(x - -2)(x - 10/3) = 0\nx - 19/4 = 0\nx - -2 = 0\nx - 10/3 = 0\nx = 19/4\nx = -2\nx = 10/3"} {"input": "Find x in 9x - 63 = 0", "output": "9x - 63 = 0\n9x = 63\nx = 63 / 9\nx = 7"} {"input": "Find x in 8x - 112/9 = 0", "output": "8x - 112/9 = 0\n8x = 112/9\nx = 112/9 / 8\nx = 14/9"} {"input": "Find the solution to x^2 - 43/15x + 8/15 = 0", "output": "x^2 - 43/15x + 8/15 = 0\n(x - 1/5)(x - 8/3) = 0\nx - 1/5 = 0 or x - 8/3 = 0\nx = 1/5\nx = 8/3"} {"input": "Find the solution to x^3 - 281/45x^2 + 88/9x - 16/5 = 0", "output": "x^3 - 281/45x^2 + 88/9x - 16/5 = 0\n(x - 4)(x - 4/9)(x - 9/5) = 0\nx - 4 = 0\nx - 4/9 = 0\nx - 9/5 = 0\nx = 4\nx = 4/9\nx = 9/5"} {"input": "Solve simultaneously:\n7x + 4y = 749/40\n10x + 8y = 599/20", "output": "7x + 4y = 749/40\n10x + 8y = 599/20\n\nUsing elimination\n10*(7x + 4y = 749/40)\n7*(10x + 8y = 599/20)\n70x + 40y = 749/4\n70x + 56y = 4193/20\nSubtract equations\n-16y = -112/5\ny = -112/5/-16\ny = 7/5\n\nSubstitute y\n7x + 4(7/5) = 749/40\n7x = 105/8\nx = 105/8/7\nx = 15/8"} {"input": "Find x for 6x + 60 = 0", "output": "6x + 60 = 0\n6x = -60\nx = -60 / 6\nx = -10"} {"input": "Solve the equation x^2 + 25/12x + 7/12 = 0", "output": "x^2 + 25/12x + 7/12 = 0\n(x - -7/4)(x - -1/3) = 0\nx - -7/4 = 0 or x - -1/3 = 0\nx = -7/4\nx = -1/3"} {"input": "Solve 5x + 5/8 = 0", "output": "5x + 5/8 = 0\n5x = -5/8\nx = -5/8 / 5\nx = -1/8"} {"input": "Find x in 9x - 153/7 = 0", "output": "9x - 153/7 = 0\n9x = 153/7\nx = 153/7 / 9\nx = 17/7"} {"input": "Find x for x^3 + 53/10x^2 + 11/5x - 12 = 0", "output": "x^3 + 53/10x^2 + 11/5x - 12 = 0\n(x - -5/2)(x - 6/5)(x - -4) = 0\nx - -5/2 = 0\nx - 6/5 = 0\nx - -4 = 0\nx = -5/2\nx = 6/5\nx = -4"} {"input": "What value of x satisfies x^2 + 22/15x - 56/15 = 0", "output": "x^2 + 22/15x - 56/15 = 0\n(x - -14/5)(x - 4/3) = 0\nx - -14/5 = 0 or x - 4/3 = 0\nx = -14/5\nx = 4/3"} {"input": "Find x and y such that\n4x + 10y = 160/9\n2x + 1y = 16/9", "output": "4x + 10y = 160/9\n2x + 1y = 16/9\n\nUsing elimination\n2*(4x + 10y = 160/9)\n4*(2x + 1y = 16/9)\n8x + 20y = 320/9\n8x + 4y = 64/9\nSubtract equations\n16y = 256/9\ny = 256/9/16\ny = 16/9\n\nSubstitute y\n4x + 10(16/9) = 160/9\n4x = 0\nx = 0/4\nx = 0"} {"input": "What value of x satisfies 6x - 9 = 0", "output": "6x - 9 = 0\n6x = 9\nx = 9 / 6\nx = 3/2"} {"input": "Solve the equation x^3 - 73/14x^2 - 81/14x + 45/7 = 0", "output": "x^3 - 73/14x^2 - 81/14x + 45/7 = 0\n(x - -3/2)(x - 5/7)(x - 6) = 0\nx - -3/2 = 0\nx - 5/7 = 0\nx - 6 = 0\nx = -3/2\nx = 5/7\nx = 6"} {"input": "Solve the system:\n8x + 1y = 143\n4x + 4y = 12", "output": "8x + 1y = 143\n4x + 4y = 12\n\nUsing elimination\n4*(8x + 1y = 143)\n8*(4x + 4y = 12)\n32x + 4y = 572\n32x + 32y = 96\nSubtract equations\n-28y = 476\ny = 476/-28\ny = -17\n\nSubstitute y\n8x + 1(-17) = 143\n8x = 160\nx = 160/8\nx = 20"} {"input": "Solve quickly: 6x - 72 = 0", "output": "6x - 72 = 0\n6x = 72\nx = 72 / 6\nx = 12"} {"input": "Find x for x^3 + 23/8x^2 - 79/16x - 77/8 = 0", "output": "x^3 + 23/8x^2 - 79/16x - 77/8 = 0\n(x - -7/2)(x - -11/8)(x - 2) = 0\nx - -7/2 = 0\nx - -11/8 = 0\nx - 2 = 0\nx = -7/2\nx = -11/8\nx = 2"} {"input": "What value of x satisfies x^3 - 57/14x^2 + 18/7x + 27/14 = 0", "output": "x^3 - 57/14x^2 + 18/7x + 27/14 = 0\n(x - -3/7)(x - 3)(x - 3/2) = 0\nx - -3/7 = 0\nx - 3 = 0\nx - 3/2 = 0\nx = -3/7\nx = 3\nx = 3/2"} {"input": "Determine x in 1x + 6/7 = 0", "output": "1x + 6/7 = 0\n1x = -6/7\nx = -6/7 / 1\nx = -6/7"} {"input": "Find x and y such that\n1x + 9y = 16\n6x + 8y = -10/9", "output": "1x + 9y = 16\n6x + 8y = -10/9\n\nUsing elimination\n6*(1x + 9y = 16)\n1*(6x + 8y = -10/9)\n6x + 54y = 96\n6x + 8y = -10/9\nSubtract equations\n46y = 874/9\ny = 874/9/46\ny = 19/9\n\nSubstitute y\n1x + 9(19/9) = 16\n1x = -3\nx = -3/1\nx = -3"} {"input": "Solve simultaneously:\n1x + 1y = 47/20\n9x + 1y = -177/20", "output": "1x + 1y = 47/20\n9x + 1y = -177/20\n\nUsing elimination\n9*(1x + 1y = 47/20)\n1*(9x + 1y = -177/20)\n9x + 9y = 423/20\n9x + 1y = -177/20\nSubtract equations\n8y = 30\ny = 30/8\ny = 15/4\n\nSubstitute y\n1x + 1(15/4) = 47/20\n1x = -7/5\nx = -7/5/1\nx = -7/5"} {"input": "Find the solution to x^3 + 17/4x^2 - 35/64x - 99/16 = 0", "output": "x^3 + 17/4x^2 - 35/64x - 99/16 = 0\n(x - -11/8)(x - 9/8)(x - -4) = 0\nx - -11/8 = 0\nx - 9/8 = 0\nx - -4 = 0\nx = -11/8\nx = 9/8\nx = -4"} {"input": "Solve the equations:\n3x + 2y = -17/8\n10x + 9y = -47/4", "output": "3x + 2y = -17/8\n10x + 9y = -47/4\n\nUsing elimination\n10*(3x + 2y = -17/8)\n3*(10x + 9y = -47/4)\n30x + 20y = -85/4\n30x + 27y = -141/4\nSubtract equations\n-7y = 14\ny = 14/-7\ny = -2\n\nSubstitute y\n3x + 2(-2) = -17/8\n3x = 15/8\nx = 15/8/3\nx = 5/8"} {"input": "Compute the solution of x^3 - 148/9x^2 + 569/27x + 80/9 = 0", "output": "x^3 - 148/9x^2 + 569/27x + 80/9 = 0\n(x - 15)(x - -1/3)(x - 16/9) = 0\nx - 15 = 0\nx - -1/3 = 0\nx - 16/9 = 0\nx = 15\nx = -1/3\nx = 16/9"} {"input": "Find x for x^3 - 197/63x^2 - 1052/567x + 76/9 = 0", "output": "x^3 - 197/63x^2 - 1052/567x + 76/9 = 0\n(x - 19/9)(x - 18/7)(x - -14/9) = 0\nx - 19/9 = 0\nx - 18/7 = 0\nx - -14/9 = 0\nx = 19/9\nx = 18/7\nx = -14/9"} {"input": "Find x for x^2 - 115/18x - 13/18 = 0", "output": "x^2 - 115/18x - 13/18 = 0\n(x - 13/2)(x - -1/9) = 0\nx - 13/2 = 0 or x - -1/9 = 0\nx = 13/2\nx = -1/9"} {"input": "Solve simultaneously:\n10x + 2y = 143/4\n9x + 9y = 603/8", "output": "10x + 2y = 143/4\n9x + 9y = 603/8\n\nUsing elimination\n9*(10x + 2y = 143/4)\n10*(9x + 9y = 603/8)\n90x + 18y = 1287/4\n90x + 90y = 3015/4\nSubtract equations\n-72y = -432\ny = -432/-72\ny = 6\n\nSubstitute y\n10x + 2(6) = 143/4\n10x = 95/4\nx = 95/4/10\nx = 19/8"} {"input": "Solve simultaneously:\n9x + 4y = 93/10\n1x + 5y = 147/10", "output": "9x + 4y = 93/10\n1x + 5y = 147/10\n\nUsing elimination\n1*(9x + 4y = 93/10)\n9*(1x + 5y = 147/10)\n9x + 4y = 93/10\n9x + 45y = 1323/10\nSubtract equations\n-41y = -123\ny = -123/-41\ny = 3\n\nSubstitute y\n9x + 4(3) = 93/10\n9x = -27/10\nx = -27/10/9\nx = -3/10"} {"input": "Solve the system:\n9x + 1y = -33\n2x + 10y = 154/3", "output": "9x + 1y = -33\n2x + 10y = 154/3\n\nUsing elimination\n2*(9x + 1y = -33)\n9*(2x + 10y = 154/3)\n18x + 2y = -66\n18x + 90y = 462\nSubtract equations\n-88y = -528\ny = -528/-88\ny = 6\n\nSubstitute y\n9x + 1(6) = -33\n9x = -39\nx = -39/9\nx = -13/3"} {"input": "Find x for x^2 + 56/9x + 80/9 = 0", "output": "x^2 + 56/9x + 80/9 = 0\n(x - -4)(x - -20/9) = 0\nx - -4 = 0 or x - -20/9 = 0\nx = -4\nx = -20/9"} {"input": "Compute the solution of x^3 + 46/9x^2 + 59/9x + 2/3 = 0", "output": "x^3 + 46/9x^2 + 59/9x + 2/3 = 0\n(x - -2)(x - -1/9)(x - -3) = 0\nx - -2 = 0\nx - -1/9 = 0\nx - -3 = 0\nx = -2\nx = -1/9\nx = -3"} {"input": "Compute the solution of 7x - 98 = 0", "output": "7x - 98 = 0\n7x = 98\nx = 98 / 7\nx = 14"} {"input": "Compute the solution of x^2 - 59/15x - 112/15 = 0", "output": "x^2 - 59/15x - 112/15 = 0\n(x - 16/3)(x - -7/5) = 0\nx - 16/3 = 0 or x - -7/5 = 0\nx = 16/3\nx = -7/5"} {"input": "Solve the system:\n7x + 10y = 355/8\n8x + 10y = 45", "output": "7x + 10y = 355/8\n8x + 10y = 45\n\nUsing elimination\n8*(7x + 10y = 355/8)\n7*(8x + 10y = 45)\n56x + 80y = 355\n56x + 70y = 315\nSubtract equations\n10y = 40\ny = 40/10\ny = 4\n\nSubstitute y\n7x + 10(4) = 355/8\n7x = 35/8\nx = 35/8/7\nx = 5/8"} {"input": "Solve the equation x^3 + 5/2x^2 - 107/16x + 51/16 = 0", "output": "x^3 + 5/2x^2 - 107/16x + 51/16 = 0\n(x - 1)(x - -17/4)(x - 3/4) = 0\nx - 1 = 0\nx - -17/4 = 0\nx - 3/4 = 0\nx = 1\nx = -17/4\nx = 3/4"} {"input": "Find x for x^2 + 6/5x + 8/25 = 0", "output": "x^2 + 6/5x + 8/25 = 0\n(x - -4/5)(x - -2/5) = 0\nx - -4/5 = 0 or x - -2/5 = 0\nx = -4/5\nx = -2/5"} {"input": "Solve quickly: 3x - 9 = 0", "output": "3x - 9 = 0\n3x = 9\nx = 9 / 3\nx = 3"} {"input": "Solve the equation x^3 - 110/63x^2 - 32/21x + 128/63 = 0", "output": "x^3 - 110/63x^2 - 32/21x + 128/63 = 0\n(x - 8/9)(x - -8/7)(x - 2) = 0\nx - 8/9 = 0\nx - -8/7 = 0\nx - 2 = 0\nx = 8/9\nx = -8/7\nx = 2"} {"input": "Find the solution to 2x + 19/5 = 0", "output": "2x + 19/5 = 0\n2x = -19/5\nx = -19/5 / 2\nx = -19/10"} {"input": "Find x in x^2 + 1/2x - 1/2 = 0", "output": "x^2 + 1/2x - 1/2 = 0\n(x - 1/2)(x - -1) = 0\nx - 1/2 = 0 or x - -1 = 0\nx = 1/2\nx = -1"} {"input": "Compute the solution of 1x - 16 = 0", "output": "1x - 16 = 0\n1x = 16\nx = 16 / 1\nx = 16"} {"input": "Solve simultaneously:\n6x + 6y = 57\n10x + 4y = 35", "output": "6x + 6y = 57\n10x + 4y = 35\n\nUsing elimination\n10*(6x + 6y = 57)\n6*(10x + 4y = 35)\n60x + 60y = 570\n60x + 24y = 210\nSubtract equations\n36y = 360\ny = 360/36\ny = 10\n\nSubstitute y\n6x + 6(10) = 57\n6x = -3\nx = -3/6\nx = -1/2"} {"input": "Find x in x^3 - 4/7x^2 - 97/63x - 10/21 = 0", "output": "x^3 - 4/7x^2 - 97/63x - 10/21 = 0\n(x - 5/3)(x - -2/3)(x - -3/7) = 0\nx - 5/3 = 0\nx - -2/3 = 0\nx - -3/7 = 0\nx = 5/3\nx = -2/3\nx = -3/7"} {"input": "Solve quickly: x^2 - 17/5x - 78/5 = 0", "output": "x^2 - 17/5x - 78/5 = 0\n(x - -13/5)(x - 6) = 0\nx - -13/5 = 0 or x - 6 = 0\nx = -13/5\nx = 6"} {"input": "Find the solution to x^2 + 1x - 60/49 = 0", "output": "x^2 + 1x - 60/49 = 0\n(x - 5/7)(x - -12/7) = 0\nx - 5/7 = 0 or x - -12/7 = 0\nx = 5/7\nx = -12/7"} {"input": "Find x and y such that\n6x + 2y = -82/3\n1x + 9y = -32", "output": "6x + 2y = -82/3\n1x + 9y = -32\n\nUsing elimination\n1*(6x + 2y = -82/3)\n6*(1x + 9y = -32)\n6x + 2y = -82/3\n6x + 54y = -192\nSubtract equations\n-52y = 494/3\ny = 494/3/-52\ny = -19/6\n\nSubstitute y\n6x + 2(-19/6) = -82/3\n6x = -21\nx = -21/6\nx = -7/2"} {"input": "Compute the solution of x^2 + 11x - 60 = 0", "output": "x^2 + 11x - 60 = 0\n(x - 4)(x - -15) = 0\nx - 4 = 0 or x - -15 = 0\nx = 4\nx = -15"} {"input": "Find the solution to x^3 + 5/24x^2 - 59/24x + 5/4 = 0", "output": "x^3 + 5/24x^2 - 59/24x + 5/4 = 0\n(x - 2/3)(x - 1)(x - -15/8) = 0\nx - 2/3 = 0\nx - 1 = 0\nx - -15/8 = 0\nx = 2/3\nx = 1\nx = -15/8"} {"input": "Solve the equation 7x + 84 = 0", "output": "7x + 84 = 0\n7x = -84\nx = -84 / 7\nx = -12"} {"input": "Solve the system:\n10x + 8y = -146\n1x + 9y = -103/2", "output": "10x + 8y = -146\n1x + 9y = -103/2\n\nUsing elimination\n1*(10x + 8y = -146)\n10*(1x + 9y = -103/2)\n10x + 8y = -146\n10x + 90y = -515\nSubtract equations\n-82y = 369\ny = 369/-82\ny = -9/2\n\nSubstitute y\n10x + 8(-9/2) = -146\n10x = -110\nx = -110/10\nx = -11"} {"input": "Solve quickly: x^2 + 13/10x - 3/10 = 0", "output": "x^2 + 13/10x - 3/10 = 0\n(x - 1/5)(x - -3/2) = 0\nx - 1/5 = 0 or x - -3/2 = 0\nx = 1/5\nx = -3/2"} {"input": "Solve quickly: x^2 - 3x - 4 = 0", "output": "x^2 - 3x - 4 = 0\n(x - 4)(x - -1) = 0\nx - 4 = 0 or x - -1 = 0\nx = 4\nx = -1"} {"input": "Determine x in 4x + 24 = 0", "output": "4x + 24 = 0\n4x = -24\nx = -24 / 4\nx = -6"} {"input": "Solve 6x + 114/5 = 0", "output": "6x + 114/5 = 0\n6x = -114/5\nx = -114/5 / 6\nx = -19/5"} {"input": "Solve the equations:\n7x + 4y = -59/5\n6x + 4y = -42/5", "output": "7x + 4y = -59/5\n6x + 4y = -42/5\n\nUsing elimination\n6*(7x + 4y = -59/5)\n7*(6x + 4y = -42/5)\n42x + 24y = -354/5\n42x + 28y = -294/5\nSubtract equations\n-4y = -12\ny = -12/-4\ny = 3\n\nSubstitute y\n7x + 4(3) = -59/5\n7x = -119/5\nx = -119/5/7\nx = -17/5"} {"input": "Solve the equation x^3 - 7/5x^2 - 53/25x + 63/25 = 0", "output": "x^3 - 7/5x^2 - 53/25x + 63/25 = 0\n(x - -7/5)(x - 9/5)(x - 1) = 0\nx - -7/5 = 0\nx - 9/5 = 0\nx - 1 = 0\nx = -7/5\nx = 9/5\nx = 1"} {"input": "Solve the equation 7x + 140/9 = 0", "output": "7x + 140/9 = 0\n7x = -140/9\nx = -140/9 / 7\nx = -20/9"} {"input": "Solve quickly: x^2 + 49/5x + 221/20 = 0", "output": "x^2 + 49/5x + 221/20 = 0\n(x - -13/10)(x - -17/2) = 0\nx - -13/10 = 0 or x - -17/2 = 0\nx = -13/10\nx = -17/2"} {"input": "Solve the equation x^2 + 35/12x + 3/2 = 0", "output": "x^2 + 35/12x + 3/2 = 0\n(x - -9/4)(x - -2/3) = 0\nx - -9/4 = 0 or x - -2/3 = 0\nx = -9/4\nx = -2/3"} {"input": "Find x for 5x - 85/8 = 0", "output": "5x - 85/8 = 0\n5x = 85/8\nx = 85/8 / 5\nx = 17/8"} {"input": "Solve simultaneously:\n1x + 7y = -188/7\n5x + 8y = -184/7", "output": "1x + 7y = -188/7\n5x + 8y = -184/7\n\nUsing elimination\n5*(1x + 7y = -188/7)\n1*(5x + 8y = -184/7)\n5x + 35y = -940/7\n5x + 8y = -184/7\nSubtract equations\n27y = -108\ny = -108/27\ny = -4\n\nSubstitute y\n1x + 7(-4) = -188/7\n1x = 8/7\nx = 8/7/1\nx = 8/7"} {"input": "Find x in x^2 + 30/7x + 32/7 = 0", "output": "x^2 + 30/7x + 32/7 = 0\n(x - -2)(x - -16/7) = 0\nx - -2 = 0 or x - -16/7 = 0\nx = -2\nx = -16/7"} {"input": "Compute the solution of 10x - 25/2 = 0", "output": "10x - 25/2 = 0\n10x = 25/2\nx = 25/2 / 10\nx = 5/4"} {"input": "Solve x^3 - 7/8x^2 - 19/32x + 15/32 = 0", "output": "x^3 - 7/8x^2 - 19/32x + 15/32 = 0\n(x - 5/8)(x - 1)(x - -3/4) = 0\nx - 5/8 = 0\nx - 1 = 0\nx - -3/4 = 0\nx = 5/8\nx = 1\nx = -3/4"} {"input": "Find x in x^3 + 194/15x^2 - 769/15x - 176/5 = 0", "output": "x^3 + 194/15x^2 - 769/15x - 176/5 = 0\n(x - 11/3)(x - -16)(x - -3/5) = 0\nx - 11/3 = 0\nx - -16 = 0\nx - -3/5 = 0\nx = 11/3\nx = -16\nx = -3/5"} {"input": "Solve the equations:\n9x + 5y = -89/3\n3x + 10y = 137/3", "output": "9x + 5y = -89/3\n3x + 10y = 137/3\n\nUsing elimination\n3*(9x + 5y = -89/3)\n9*(3x + 10y = 137/3)\n27x + 15y = -89\n27x + 90y = 411\nSubtract equations\n-75y = -500\ny = -500/-75\ny = 20/3\n\nSubstitute y\n9x + 5(20/3) = -89/3\n9x = -63\nx = -63/9\nx = -7"} {"input": "Find x and y such that\n7x + 3y = -27\n4x + 6y = -24", "output": "7x + 3y = -27\n4x + 6y = -24\n\nUsing elimination\n4*(7x + 3y = -27)\n7*(4x + 6y = -24)\n28x + 12y = -108\n28x + 42y = -168\nSubtract equations\n-30y = 60\ny = 60/-30\ny = -2\n\nSubstitute y\n7x + 3(-2) = -27\n7x = -21\nx = -21/7\nx = -3"} {"input": "Find the solution to x^3 - 11/3x^2 + 1/12x + 19/4 = 0", "output": "x^3 - 11/3x^2 + 1/12x + 19/4 = 0\n(x - 3/2)(x - 19/6)(x - -1) = 0\nx - 3/2 = 0\nx - 19/6 = 0\nx - -1 = 0\nx = 3/2\nx = 19/6\nx = -1"} {"input": "Solve simultaneously:\n10x + 3y = 176/5\n8x + 1y = 152/5", "output": "10x + 3y = 176/5\n8x + 1y = 152/5\n\nUsing elimination\n8*(10x + 3y = 176/5)\n10*(8x + 1y = 152/5)\n80x + 24y = 1408/5\n80x + 10y = 304\nSubtract equations\n14y = -112/5\ny = -112/5/14\ny = -8/5\n\nSubstitute y\n10x + 3(-8/5) = 176/5\n10x = 40\nx = 40/10\nx = 4"} {"input": "Solve the system:\n5x + 10y = -75/2\n2x + 1y = -6", "output": "5x + 10y = -75/2\n2x + 1y = -6\n\nUsing elimination\n2*(5x + 10y = -75/2)\n5*(2x + 1y = -6)\n10x + 20y = -75\n10x + 5y = -30\nSubtract equations\n15y = -45\ny = -45/15\ny = -3\n\nSubstitute y\n5x + 10(-3) = -75/2\n5x = -15/2\nx = -15/2/5\nx = -3/2"} {"input": "Find x and y such that\n10x + 6y = -121\n5x + 8y = -53", "output": "10x + 6y = -121\n5x + 8y = -53\n\nUsing elimination\n5*(10x + 6y = -121)\n10*(5x + 8y = -53)\n50x + 30y = -605\n50x + 80y = -530\nSubtract equations\n-50y = -75\ny = -75/-50\ny = 3/2\n\nSubstitute y\n10x + 6(3/2) = -121\n10x = -130\nx = -130/10\nx = -13"} {"input": "Compute the solution of x^2 - 1/8x = 0", "output": "x^2 - 1/8x = 0\n(x - 1/8)(x - 0) = 0\nx - 1/8 = 0 or x - 0 = 0\nx = 1/8\nx = 0"} {"input": "Find x in x^2 - 8x + 7 = 0", "output": "x^2 - 8x + 7 = 0\n(x - 7)(x - 1) = 0\nx - 7 = 0 or x - 1 = 0\nx = 7\nx = 1"} {"input": "Solve the equation 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve the equation 9x + 27 = 0", "output": "9x + 27 = 0\n9x = -27\nx = -27 / 9\nx = -3"} {"input": "Solve x^3 - 203/45x^2 - 56/27x + 1664/135 = 0", "output": "x^3 - 203/45x^2 - 56/27x + 1664/135 = 0\n(x - 16/9)(x - -8/5)(x - 13/3) = 0\nx - 16/9 = 0\nx - -8/5 = 0\nx - 13/3 = 0\nx = 16/9\nx = -8/5\nx = 13/3"} {"input": "What value of x satisfies x^2 - 7/4x - 9/8 = 0", "output": "x^2 - 7/4x - 9/8 = 0\n(x - 9/4)(x - -1/2) = 0\nx - 9/4 = 0 or x - -1/2 = 0\nx = 9/4\nx = -1/2"} {"input": "Solve simultaneously:\n2x + 10y = 191/3\n8x + 9y = 79", "output": "2x + 10y = 191/3\n8x + 9y = 79\n\nUsing elimination\n8*(2x + 10y = 191/3)\n2*(8x + 9y = 79)\n16x + 80y = 1528/3\n16x + 18y = 158\nSubtract equations\n62y = 1054/3\ny = 1054/3/62\ny = 17/3\n\nSubstitute y\n2x + 10(17/3) = 191/3\n2x = 7\nx = 7/2\nx = 7/2"} {"input": "Find the solution to x^3 + 21/2x^2 + 49/2x + 15 = 0", "output": "x^3 + 21/2x^2 + 49/2x + 15 = 0\n(x - -1)(x - -2)(x - -15/2) = 0\nx - -1 = 0\nx - -2 = 0\nx - -15/2 = 0\nx = -1\nx = -2\nx = -15/2"} {"input": "Solve quickly: 9x - 81/2 = 0", "output": "9x - 81/2 = 0\n9x = 81/2\nx = 81/2 / 9\nx = 9/2"} {"input": "Solve x^2 - 29/15x + 4/5 = 0", "output": "x^2 - 29/15x + 4/5 = 0\n(x - 3/5)(x - 4/3) = 0\nx - 3/5 = 0 or x - 4/3 = 0\nx = 3/5\nx = 4/3"} {"input": "Find the solution to 8x + 8 = 0", "output": "8x + 8 = 0\n8x = -8\nx = -8 / 8\nx = -1"} {"input": "Compute the solution of x^2 + 55/18x + 50/27 = 0", "output": "x^2 + 55/18x + 50/27 = 0\n(x - -20/9)(x - -5/6) = 0\nx - -20/9 = 0 or x - -5/6 = 0\nx = -20/9\nx = -5/6"} {"input": "Find x in 1x + 5/2 = 0", "output": "1x + 5/2 = 0\n1x = -5/2\nx = -5/2 / 1\nx = -5/2"} {"input": "Determine x in 9x - 27 = 0", "output": "9x - 27 = 0\n9x = 27\nx = 27 / 9\nx = 3"} {"input": "Find x for 1x + 9/5 = 0", "output": "1x + 9/5 = 0\n1x = -9/5\nx = -9/5 / 1\nx = -9/5"} {"input": "Compute the solution of x^3 + 49/4x^2 + 3x = 0", "output": "x^3 + 49/4x^2 + 3x = 0\n(x - -1/4)(x - 0)(x - -12) = 0\nx - -1/4 = 0\nx - 0 = 0\nx - -12 = 0\nx = -1/4\nx = 0\nx = -12"} {"input": "Find x for x^2 - 23/10x + 28/25 = 0", "output": "x^2 - 23/10x + 28/25 = 0\n(x - 7/10)(x - 8/5) = 0\nx - 7/10 = 0 or x - 8/5 = 0\nx = 7/10\nx = 8/5"} {"input": "Solve the equation 10x = 0", "output": "10x = 0\n10x = 0\nx = 0 / 10\nx = 0"} {"input": "Determine x in x^3 - 14/15x^2 - 49/15x = 0", "output": "x^3 - 14/15x^2 - 49/15x = 0\n(x - 7/3)(x - 0)(x - -7/5) = 0\nx - 7/3 = 0\nx - 0 = 0\nx - -7/5 = 0\nx = 7/3\nx = 0\nx = -7/5"} {"input": "What value of x satisfies x^2 + 5/3x - 13/12 = 0", "output": "x^2 + 5/3x - 13/12 = 0\n(x - 1/2)(x - -13/6) = 0\nx - 1/2 = 0 or x - -13/6 = 0\nx = 1/2\nx = -13/6"} {"input": "Find x in 5x - 80/7 = 0", "output": "5x - 80/7 = 0\n5x = 80/7\nx = 80/7 / 5\nx = 16/7"} {"input": "Find x in x^2 + 11x = 0", "output": "x^2 + 11x = 0\n(x - -11)(x - 0) = 0\nx - -11 = 0 or x - 0 = 0\nx = -11\nx = 0"} {"input": "Find x for x^2 + 3/5x - 14/5 = 0", "output": "x^2 + 3/5x - 14/5 = 0\n(x - -2)(x - 7/5) = 0\nx - -2 = 0 or x - 7/5 = 0\nx = -2\nx = 7/5"} {"input": "Solve the equations:\n2x + 10y = 13/4\n6x + 9y = -111/8", "output": "2x + 10y = 13/4\n6x + 9y = -111/8\n\nUsing elimination\n6*(2x + 10y = 13/4)\n2*(6x + 9y = -111/8)\n12x + 60y = 39/2\n12x + 18y = -111/4\nSubtract equations\n42y = 189/4\ny = 189/4/42\ny = 9/8\n\nSubstitute y\n2x + 10(9/8) = 13/4\n2x = -8\nx = -8/2\nx = -4"} {"input": "Compute the solution of x^2 - 47/9x + 44/9 = 0", "output": "x^2 - 47/9x + 44/9 = 0\n(x - 4)(x - 11/9) = 0\nx - 4 = 0 or x - 11/9 = 0\nx = 4\nx = 11/9"} {"input": "Find the solution to x^3 - 59/20x^2 - 96/25x + 63/20 = 0", "output": "x^3 - 59/20x^2 - 96/25x + 63/20 = 0\n(x - -7/5)(x - 3/5)(x - 15/4) = 0\nx - -7/5 = 0\nx - 3/5 = 0\nx - 15/4 = 0\nx = -7/5\nx = 3/5\nx = 15/4"} {"input": "Find the solution to x^3 + 35/3x^2 + 107/12x - 665/6 = 0", "output": "x^3 + 35/3x^2 + 107/12x - 665/6 = 0\n(x - -19/2)(x - -14/3)(x - 5/2) = 0\nx - -19/2 = 0\nx - -14/3 = 0\nx - 5/2 = 0\nx = -19/2\nx = -14/3\nx = 5/2"} {"input": "Solve the equations:\n3x + 9y = -66/5\n1x + 10y = -57/5", "output": "3x + 9y = -66/5\n1x + 10y = -57/5\n\nUsing elimination\n1*(3x + 9y = -66/5)\n3*(1x + 10y = -57/5)\n3x + 9y = -66/5\n3x + 30y = -171/5\nSubtract equations\n-21y = 21\ny = 21/-21\ny = -1\n\nSubstitute y\n3x + 9(-1) = -66/5\n3x = -21/5\nx = -21/5/3\nx = -7/5"} {"input": "Find x and y such that\n6x + 5y = 190/63\n4x + 4y = 80/63", "output": "6x + 5y = 190/63\n4x + 4y = 80/63\n\nUsing elimination\n4*(6x + 5y = 190/63)\n6*(4x + 4y = 80/63)\n24x + 20y = 760/63\n24x + 24y = 160/21\nSubtract equations\n-4y = 40/9\ny = 40/9/-4\ny = -10/9\n\nSubstitute y\n6x + 5(-10/9) = 190/63\n6x = 60/7\nx = 60/7/6\nx = 10/7"} {"input": "Find x and y such that\n5x + 9y = 22\n5x + 7y = 18", "output": "5x + 9y = 22\n5x + 7y = 18\n\nUsing elimination\n5*(5x + 9y = 22)\n5*(5x + 7y = 18)\n25x + 45y = 110\n25x + 35y = 90\nSubtract equations\n10y = 20\ny = 20/10\ny = 2\n\nSubstitute y\n5x + 9(2) = 22\n5x = 4\nx = 4/5\nx = 4/5"} {"input": "Solve simultaneously:\n4x + 9y = 27\n6x + 7y = 21", "output": "4x + 9y = 27\n6x + 7y = 21\n\nUsing elimination\n6*(4x + 9y = 27)\n4*(6x + 7y = 21)\n24x + 54y = 162\n24x + 28y = 84\nSubtract equations\n26y = 78\ny = 78/26\ny = 3\n\nSubstitute y\n4x + 9(3) = 27\n4x = 0\nx = 0/4\nx = 0"} {"input": "Find the solution to 5x - 80 = 0", "output": "5x - 80 = 0\n5x = 80\nx = 80 / 5\nx = 16"} {"input": "Solve quickly: x^3 - 334/35x^2 + 1259/140x - 153/140 = 0", "output": "x^3 - 334/35x^2 + 1259/140x - 153/140 = 0\n(x - 1/7)(x - 9/10)(x - 17/2) = 0\nx - 1/7 = 0\nx - 9/10 = 0\nx - 17/2 = 0\nx = 1/7\nx = 9/10\nx = 17/2"} {"input": "Find x in x^3 - 71/6x^2 + 119/3x - 245/6 = 0", "output": "x^3 - 71/6x^2 + 119/3x - 245/6 = 0\n(x - 5/2)(x - 7)(x - 7/3) = 0\nx - 5/2 = 0\nx - 7 = 0\nx - 7/3 = 0\nx = 5/2\nx = 7\nx = 7/3"} {"input": "Solve x^3 + 73/9x^2 + 12x - 160/9 = 0", "output": "x^3 + 73/9x^2 + 12x - 160/9 = 0\n(x - -4)(x - 8/9)(x - -5) = 0\nx - -4 = 0\nx - 8/9 = 0\nx - -5 = 0\nx = -4\nx = 8/9\nx = -5"} {"input": "Solve simultaneously:\n4x + 1y = -364/45\n9x + 8y = -183/5", "output": "4x + 1y = -364/45\n9x + 8y = -183/5\n\nUsing elimination\n9*(4x + 1y = -364/45)\n4*(9x + 8y = -183/5)\n36x + 9y = -364/5\n36x + 32y = -732/5\nSubtract equations\n-23y = 368/5\ny = 368/5/-23\ny = -16/5\n\nSubstitute y\n4x + 1(-16/5) = -364/45\n4x = -44/9\nx = -44/9/4\nx = -11/9"} {"input": "Solve x^2 + 1/4x - 7/2 = 0", "output": "x^2 + 1/4x - 7/2 = 0\n(x - 7/4)(x - -2) = 0\nx - 7/4 = 0 or x - -2 = 0\nx = 7/4\nx = -2"} {"input": "Find x in x^2 + 10/9x - 77/27 = 0", "output": "x^2 + 10/9x - 77/27 = 0\n(x - 11/9)(x - -7/3) = 0\nx - 11/9 = 0 or x - -7/3 = 0\nx = 11/9\nx = -7/3"} {"input": "Find x and y such that\n7x + 3y = 9/10\n3x + 10y = 76/5", "output": "7x + 3y = 9/10\n3x + 10y = 76/5\n\nUsing elimination\n3*(7x + 3y = 9/10)\n7*(3x + 10y = 76/5)\n21x + 9y = 27/10\n21x + 70y = 532/5\nSubtract equations\n-61y = -1037/10\ny = -1037/10/-61\ny = 17/10\n\nSubstitute y\n7x + 3(17/10) = 9/10\n7x = -21/5\nx = -21/5/7\nx = -3/5"} {"input": "Find x in x^2 + 11x + 28 = 0", "output": "x^2 + 11x + 28 = 0\n(x - -4)(x - -7) = 0\nx - -4 = 0 or x - -7 = 0\nx = -4\nx = -7"} {"input": "Solve 2x - 3 = 0", "output": "2x - 3 = 0\n2x = 3\nx = 3 / 2\nx = 3/2"} {"input": "Solve x^3 + 153/8x^2 + 229/8x - 255/2 = 0", "output": "x^3 + 153/8x^2 + 229/8x - 255/2 = 0\n(x - 15/8)(x - -4)(x - -17) = 0\nx - 15/8 = 0\nx - -4 = 0\nx - -17 = 0\nx = 15/8\nx = -4\nx = -17"} {"input": "Solve simultaneously:\n5x + 3y = -53/28\n5x + 1y = -151/28", "output": "5x + 3y = -53/28\n5x + 1y = -151/28\n\nUsing elimination\n5*(5x + 3y = -53/28)\n5*(5x + 1y = -151/28)\n25x + 15y = -265/28\n25x + 5y = -755/28\nSubtract equations\n10y = 35/2\ny = 35/2/10\ny = 7/4\n\nSubstitute y\n5x + 3(7/4) = -53/28\n5x = -50/7\nx = -50/7/5\nx = -10/7"} {"input": "Solve the system:\n7x + 3y = -187/6\n10x + 3y = -271/6", "output": "7x + 3y = -187/6\n10x + 3y = -271/6\n\nUsing elimination\n10*(7x + 3y = -187/6)\n7*(10x + 3y = -271/6)\n70x + 30y = -935/3\n70x + 21y = -1897/6\nSubtract equations\n9y = 9/2\ny = 9/2/9\ny = 1/2\n\nSubstitute y\n7x + 3(1/2) = -187/6\n7x = -98/3\nx = -98/3/7\nx = -14/3"} {"input": "Find the solution to x^3 - 31/3x^2 - 48x - 140/3 = 0", "output": "x^3 - 31/3x^2 - 48x - 140/3 = 0\n(x - -5/3)(x - 14)(x - -2) = 0\nx - -5/3 = 0\nx - 14 = 0\nx - -2 = 0\nx = -5/3\nx = 14\nx = -2"} {"input": "Determine x in x^3 - 102/5x^2 + 621/25x + 836/25 = 0", "output": "x^3 - 102/5x^2 + 621/25x + 836/25 = 0\n(x - 19)(x - -4/5)(x - 11/5) = 0\nx - 19 = 0\nx - -4/5 = 0\nx - 11/5 = 0\nx = 19\nx = -4/5\nx = 11/5"} {"input": "Find x in 2x + 16/9 = 0", "output": "2x + 16/9 = 0\n2x = -16/9\nx = -16/9 / 2\nx = -8/9"} {"input": "Find x for x^2 - 11x = 0", "output": "x^2 - 11x = 0\n(x - 11)(x - 0) = 0\nx - 11 = 0 or x - 0 = 0\nx = 11\nx = 0"} {"input": "Solve the equation x^3 + 23/28x^2 - 747/56x + 405/28 = 0", "output": "x^3 + 23/28x^2 - 747/56x + 405/28 = 0\n(x - 10/7)(x - -9/2)(x - 9/4) = 0\nx - 10/7 = 0\nx - -9/2 = 0\nx - 9/4 = 0\nx = 10/7\nx = -9/2\nx = 9/4"} {"input": "Solve the equation 1x - 5/8 = 0", "output": "1x - 5/8 = 0\n1x = 5/8\nx = 5/8 / 1\nx = 5/8"} {"input": "Compute the solution of 4x - 4 = 0", "output": "4x - 4 = 0\n4x = 4\nx = 4 / 4\nx = 1"} {"input": "Solve simultaneously:\n5x + 9y = 44\n9x + 4y = 91/5", "output": "5x + 9y = 44\n9x + 4y = 91/5\n\nUsing elimination\n9*(5x + 9y = 44)\n5*(9x + 4y = 91/5)\n45x + 81y = 396\n45x + 20y = 91\nSubtract equations\n61y = 305\ny = 305/61\ny = 5\n\nSubstitute y\n5x + 9(5) = 44\n5x = -1\nx = -1/5\nx = -1/5"} {"input": "Solve simultaneously:\n9x + 3y = 135/8\n9x + 9y = 225/8", "output": "9x + 3y = 135/8\n9x + 9y = 225/8\n\nUsing elimination\n9*(9x + 3y = 135/8)\n9*(9x + 9y = 225/8)\n81x + 27y = 1215/8\n81x + 81y = 2025/8\nSubtract equations\n-54y = -405/4\ny = -405/4/-54\ny = 15/8\n\nSubstitute y\n9x + 3(15/8) = 135/8\n9x = 45/4\nx = 45/4/9\nx = 5/4"} {"input": "What value of x satisfies x^3 + 293/36x^2 - 187/18x - 95/4 = 0", "output": "x^3 + 293/36x^2 - 187/18x - 95/4 = 0\n(x - 19/9)(x - -5/4)(x - -9) = 0\nx - 19/9 = 0\nx - -5/4 = 0\nx - -9 = 0\nx = 19/9\nx = -5/4\nx = -9"} {"input": "Solve 10x + 8 = 0", "output": "10x + 8 = 0\n10x = -8\nx = -8 / 10\nx = -4/5"} {"input": "Find x for 3x - 21/8 = 0", "output": "3x - 21/8 = 0\n3x = 21/8\nx = 21/8 / 3\nx = 7/8"} {"input": "Find x and y such that\n2x + 6y = -5/3\n10x + 10y = 35/3", "output": "2x + 6y = -5/3\n10x + 10y = 35/3\n\nUsing elimination\n10*(2x + 6y = -5/3)\n2*(10x + 10y = 35/3)\n20x + 60y = -50/3\n20x + 20y = 70/3\nSubtract equations\n40y = -40\ny = -40/40\ny = -1\n\nSubstitute y\n2x + 6(-1) = -5/3\n2x = 13/3\nx = 13/3/2\nx = 13/6"} {"input": "Solve the system:\n6x + 2y = 64/5\n3x + 5y = 52/5", "output": "6x + 2y = 64/5\n3x + 5y = 52/5\n\nUsing elimination\n3*(6x + 2y = 64/5)\n6*(3x + 5y = 52/5)\n18x + 6y = 192/5\n18x + 30y = 312/5\nSubtract equations\n-24y = -24\ny = -24/-24\ny = 1\n\nSubstitute y\n6x + 2(1) = 64/5\n6x = 54/5\nx = 54/5/6\nx = 9/5"} {"input": "What value of x satisfies 10x - 5/2 = 0", "output": "10x - 5/2 = 0\n10x = 5/2\nx = 5/2 / 10\nx = 1/4"} {"input": "What value of x satisfies 2x + 18 = 0", "output": "2x + 18 = 0\n2x = -18\nx = -18 / 2\nx = -9"} {"input": "What value of x satisfies x^2 - 21x + 38 = 0", "output": "x^2 - 21x + 38 = 0\n(x - 19)(x - 2) = 0\nx - 19 = 0 or x - 2 = 0\nx = 19\nx = 2"} {"input": "Find the solution to 6x + 102/5 = 0", "output": "6x + 102/5 = 0\n6x = -102/5\nx = -102/5 / 6\nx = -17/5"} {"input": "Solve the equation x^3 + 23/5x^2 - 2/5x - 56/5 = 0", "output": "x^3 + 23/5x^2 - 2/5x - 56/5 = 0\n(x - -2)(x - -4)(x - 7/5) = 0\nx - -2 = 0\nx - -4 = 0\nx - 7/5 = 0\nx = -2\nx = -4\nx = 7/5"} {"input": "Solve the equation x^3 - 21/4x^2 - 42x - 55 = 0", "output": "x^3 - 21/4x^2 - 42x - 55 = 0\n(x - 10)(x - -11/4)(x - -2) = 0\nx - 10 = 0\nx - -11/4 = 0\nx - -2 = 0\nx = 10\nx = -11/4\nx = -2"} {"input": "Solve the system:\n8x + 10y = 124/7\n7x + 2y = 176/7", "output": "8x + 10y = 124/7\n7x + 2y = 176/7\n\nUsing elimination\n7*(8x + 10y = 124/7)\n8*(7x + 2y = 176/7)\n56x + 70y = 124\n56x + 16y = 1408/7\nSubtract equations\n54y = -540/7\ny = -540/7/54\ny = -10/7\n\nSubstitute y\n8x + 10(-10/7) = 124/7\n8x = 32\nx = 32/8\nx = 4"} {"input": "Find x in x^2 - 1/2x - 15/2 = 0", "output": "x^2 - 1/2x - 15/2 = 0\n(x - -5/2)(x - 3) = 0\nx - -5/2 = 0 or x - 3 = 0\nx = -5/2\nx = 3"} {"input": "Solve simultaneously:\n1x + 6y = 31/2\n4x + 10y = 114/5", "output": "1x + 6y = 31/2\n4x + 10y = 114/5\n\nUsing elimination\n4*(1x + 6y = 31/2)\n1*(4x + 10y = 114/5)\n4x + 24y = 62\n4x + 10y = 114/5\nSubtract equations\n14y = 196/5\ny = 196/5/14\ny = 14/5\n\nSubstitute y\n1x + 6(14/5) = 31/2\n1x = -13/10\nx = -13/10/1\nx = -13/10"} {"input": "Solve quickly: 6x - 3/5 = 0", "output": "6x - 3/5 = 0\n6x = 3/5\nx = 3/5 / 6\nx = 1/10"} {"input": "Solve the equation x^2 - 23/8x - 117/16 = 0", "output": "x^2 - 23/8x - 117/16 = 0\n(x - 9/2)(x - -13/8) = 0\nx - 9/2 = 0 or x - -13/8 = 0\nx = 9/2\nx = -13/8"} {"input": "Solve quickly: x^2 + 11/2x - 3 = 0", "output": "x^2 + 11/2x - 3 = 0\n(x - -6)(x - 1/2) = 0\nx - -6 = 0 or x - 1/2 = 0\nx = -6\nx = 1/2"} {"input": "Solve the equation x^2 + 49/8x - 165/16 = 0", "output": "x^2 + 49/8x - 165/16 = 0\n(x - 11/8)(x - -15/2) = 0\nx - 11/8 = 0 or x - -15/2 = 0\nx = 11/8\nx = -15/2"} {"input": "Find x for x^3 - 37/56x^2 - 159/224x - 27/224 = 0", "output": "x^3 - 37/56x^2 - 159/224x - 27/224 = 0\n(x - 9/7)(x - -1/4)(x - -3/8) = 0\nx - 9/7 = 0\nx - -1/4 = 0\nx - -3/8 = 0\nx = 9/7\nx = -1/4\nx = -3/8"} {"input": "Compute the solution of 5x - 65 = 0", "output": "5x - 65 = 0\n5x = 65\nx = 65 / 5\nx = 13"} {"input": "Solve the system:\n9x + 2y = 123/7\n3x + 4y = 81/7", "output": "9x + 2y = 123/7\n3x + 4y = 81/7\n\nUsing elimination\n3*(9x + 2y = 123/7)\n9*(3x + 4y = 81/7)\n27x + 6y = 369/7\n27x + 36y = 729/7\nSubtract equations\n-30y = -360/7\ny = -360/7/-30\ny = 12/7\n\nSubstitute y\n9x + 2(12/7) = 123/7\n9x = 99/7\nx = 99/7/9\nx = 11/7"} {"input": "Find x in x^2 + 22/7x + 3/7 = 0", "output": "x^2 + 22/7x + 3/7 = 0\n(x - -1/7)(x - -3) = 0\nx - -1/7 = 0 or x - -3 = 0\nx = -1/7\nx = -3"} {"input": "Solve simultaneously:\n3x + 5y = -109/7\n7x + 7y = -33", "output": "3x + 5y = -109/7\n7x + 7y = -33\n\nUsing elimination\n7*(3x + 5y = -109/7)\n3*(7x + 7y = -33)\n21x + 35y = -109\n21x + 21y = -99\nSubtract equations\n14y = -10\ny = -10/14\ny = -5/7\n\nSubstitute y\n3x + 5(-5/7) = -109/7\n3x = -12\nx = -12/3\nx = -4"} {"input": "Find x in x^2 + 116/21x + 160/21 = 0", "output": "x^2 + 116/21x + 160/21 = 0\n(x - -8/3)(x - -20/7) = 0\nx - -8/3 = 0 or x - -20/7 = 0\nx = -8/3\nx = -20/7"} {"input": "Determine x in x^2 - 1/14x - 85/14 = 0", "output": "x^2 - 1/14x - 85/14 = 0\n(x - -17/7)(x - 5/2) = 0\nx - -17/7 = 0 or x - 5/2 = 0\nx = -17/7\nx = 5/2"} {"input": "Solve 10x + 55/3 = 0", "output": "10x + 55/3 = 0\n10x = -55/3\nx = -55/3 / 10\nx = -11/6"} {"input": "Determine x in 7x - 1 = 0", "output": "7x - 1 = 0\n7x = 1\nx = 1 / 7\nx = 1/7"} {"input": "Determine x in 2x + 32 = 0", "output": "2x + 32 = 0\n2x = -32\nx = -32 / 2\nx = -16"} {"input": "Solve quickly: 4x + 8/3 = 0", "output": "4x + 8/3 = 0\n4x = -8/3\nx = -8/3 / 4\nx = -2/3"} {"input": "Compute the solution of x^2 - 16/3x - 4 = 0", "output": "x^2 - 16/3x - 4 = 0\n(x - -2/3)(x - 6) = 0\nx - -2/3 = 0 or x - 6 = 0\nx = -2/3\nx = 6"} {"input": "Solve the equations:\n3x + 9y = -69/2\n5x + 2y = -37/2", "output": "3x + 9y = -69/2\n5x + 2y = -37/2\n\nUsing elimination\n5*(3x + 9y = -69/2)\n3*(5x + 2y = -37/2)\n15x + 45y = -345/2\n15x + 6y = -111/2\nSubtract equations\n39y = -117\ny = -117/39\ny = -3\n\nSubstitute y\n3x + 9(-3) = -69/2\n3x = -15/2\nx = -15/2/3\nx = -5/2"} {"input": "Find x for x^3 + 17/4x^2 + 33/8x + 9/8 = 0", "output": "x^3 + 17/4x^2 + 33/8x + 9/8 = 0\n(x - -1/2)(x - -3/4)(x - -3) = 0\nx - -1/2 = 0\nx - -3/4 = 0\nx - -3 = 0\nx = -1/2\nx = -3/4\nx = -3"} {"input": "Compute the solution of x^3 - 9/4x^2 - 23/8x + 15/8 = 0", "output": "x^3 - 9/4x^2 - 23/8x + 15/8 = 0\n(x - -5/4)(x - 3)(x - 1/2) = 0\nx - -5/4 = 0\nx - 3 = 0\nx - 1/2 = 0\nx = -5/4\nx = 3\nx = 1/2"} {"input": "Find x in 8x - 68/3 = 0", "output": "8x - 68/3 = 0\n8x = 68/3\nx = 68/3 / 8\nx = 17/6"} {"input": "Find x and y such that\n8x + 3y = 18\n4x + 3y = 18", "output": "8x + 3y = 18\n4x + 3y = 18\n\nUsing elimination\n4*(8x + 3y = 18)\n8*(4x + 3y = 18)\n32x + 12y = 72\n32x + 24y = 144\nSubtract equations\n-12y = -72\ny = -72/-12\ny = 6\n\nSubstitute y\n8x + 3(6) = 18\n8x = 0\nx = 0/8\nx = 0"} {"input": "Solve the equations:\n1x + 2y = 17/9\n4x + 9y = 9", "output": "1x + 2y = 17/9\n4x + 9y = 9\n\nUsing elimination\n4*(1x + 2y = 17/9)\n1*(4x + 9y = 9)\n4x + 8y = 68/9\n4x + 9y = 9\nSubtract equations\n-1y = -13/9\ny = -13/9/-1\ny = 13/9\n\nSubstitute y\n1x + 2(13/9) = 17/9\n1x = -1\nx = -1/1\nx = -1"} {"input": "Solve the system:\n3x + 7y = -37/2\n10x + 7y = -22", "output": "3x + 7y = -37/2\n10x + 7y = -22\n\nUsing elimination\n10*(3x + 7y = -37/2)\n3*(10x + 7y = -22)\n30x + 70y = -185\n30x + 21y = -66\nSubtract equations\n49y = -119\ny = -119/49\ny = -17/7\n\nSubstitute y\n3x + 7(-17/7) = -37/2\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Determine x in 1x + 1/2 = 0", "output": "1x + 1/2 = 0\n1x = -1/2\nx = -1/2 / 1\nx = -1/2"} {"input": "What value of x satisfies x^2 + 43/35x - 2/7 = 0", "output": "x^2 + 43/35x - 2/7 = 0\n(x - -10/7)(x - 1/5) = 0\nx - -10/7 = 0 or x - 1/5 = 0\nx = -10/7\nx = 1/5"} {"input": "Solve the equations:\n8x + 3y = 8\n6x + 1y = 13/3", "output": "8x + 3y = 8\n6x + 1y = 13/3\n\nUsing elimination\n6*(8x + 3y = 8)\n8*(6x + 1y = 13/3)\n48x + 18y = 48\n48x + 8y = 104/3\nSubtract equations\n10y = 40/3\ny = 40/3/10\ny = 4/3\n\nSubstitute y\n8x + 3(4/3) = 8\n8x = 4\nx = 4/8\nx = 1/2"} {"input": "Solve the equations:\n4x + 8y = -97\n3x + 5y = -243/4", "output": "4x + 8y = -97\n3x + 5y = -243/4\n\nUsing elimination\n3*(4x + 8y = -97)\n4*(3x + 5y = -243/4)\n12x + 24y = -291\n12x + 20y = -243\nSubtract equations\n4y = -48\ny = -48/4\ny = -12\n\nSubstitute y\n4x + 8(-12) = -97\n4x = -1\nx = -1/4\nx = -1/4"} {"input": "Compute the solution of 5x - 85 = 0", "output": "5x - 85 = 0\n5x = 85\nx = 85 / 5\nx = 17"} {"input": "Solve x^2 + 2x - 15 = 0", "output": "x^2 + 2x - 15 = 0\n(x - -5)(x - 3) = 0\nx - -5 = 0 or x - 3 = 0\nx = -5\nx = 3"} {"input": "Determine x in 8x + 48 = 0", "output": "8x + 48 = 0\n8x = -48\nx = -48 / 8\nx = -6"} {"input": "Solve simultaneously:\n6x + 10y = 273/5\n3x + 3y = 153/10", "output": "6x + 10y = 273/5\n3x + 3y = 153/10\n\nUsing elimination\n3*(6x + 10y = 273/5)\n6*(3x + 3y = 153/10)\n18x + 30y = 819/5\n18x + 18y = 459/5\nSubtract equations\n12y = 72\ny = 72/12\ny = 6\n\nSubstitute y\n6x + 10(6) = 273/5\n6x = -27/5\nx = -27/5/6\nx = -9/10"} {"input": "Solve quickly: 6x - 36 = 0", "output": "6x - 36 = 0\n6x = 36\nx = 36 / 6\nx = 6"} {"input": "Determine x in 1x + 5/2 = 0", "output": "1x + 5/2 = 0\n1x = -5/2\nx = -5/2 / 1\nx = -5/2"} {"input": "Solve the system:\n10x + 2y = 26\n9x + 9y = 9", "output": "10x + 2y = 26\n9x + 9y = 9\n\nUsing elimination\n9*(10x + 2y = 26)\n10*(9x + 9y = 9)\n90x + 18y = 234\n90x + 90y = 90\nSubtract equations\n-72y = 144\ny = 144/-72\ny = -2\n\nSubstitute y\n10x + 2(-2) = 26\n10x = 30\nx = 30/10\nx = 3"} {"input": "Solve 6x - 66/7 = 0", "output": "6x - 66/7 = 0\n6x = 66/7\nx = 66/7 / 6\nx = 11/7"} {"input": "Solve the equation 3x + 1 = 0", "output": "3x + 1 = 0\n3x = -1\nx = -1 / 3\nx = -1/3"} {"input": "Find the solution to 8x + 40 = 0", "output": "8x + 40 = 0\n8x = -40\nx = -40 / 8\nx = -5"} {"input": "Solve the equations:\n10x + 2y = 46\n8x + 3y = 48", "output": "10x + 2y = 46\n8x + 3y = 48\n\nUsing elimination\n8*(10x + 2y = 46)\n10*(8x + 3y = 48)\n80x + 16y = 368\n80x + 30y = 480\nSubtract equations\n-14y = -112\ny = -112/-14\ny = 8\n\nSubstitute y\n10x + 2(8) = 46\n10x = 30\nx = 30/10\nx = 3"} {"input": "Solve the system:\n2x + 5y = -301/4\n10x + 5y = -305/4", "output": "2x + 5y = -301/4\n10x + 5y = -305/4\n\nUsing elimination\n10*(2x + 5y = -301/4)\n2*(10x + 5y = -305/4)\n20x + 50y = -1505/2\n20x + 10y = -305/2\nSubtract equations\n40y = -600\ny = -600/40\ny = -15\n\nSubstitute y\n2x + 5(-15) = -301/4\n2x = -1/4\nx = -1/4/2\nx = -1/8"} {"input": "Solve 1x - 7 = 0", "output": "1x - 7 = 0\n1x = 7\nx = 7 / 1\nx = 7"} {"input": "What value of x satisfies x^2 + 178/21x + 95/7 = 0", "output": "x^2 + 178/21x + 95/7 = 0\n(x - -15/7)(x - -19/3) = 0\nx - -15/7 = 0 or x - -19/3 = 0\nx = -15/7\nx = -19/3"} {"input": "Solve the equation x^2 - 29/10x + 9/5 = 0", "output": "x^2 - 29/10x + 9/5 = 0\n(x - 2)(x - 9/10) = 0\nx - 2 = 0 or x - 9/10 = 0\nx = 2\nx = 9/10"} {"input": "Find x in x^3 + 101/14x^2 + 199/14x + 38/7 = 0", "output": "x^3 + 101/14x^2 + 199/14x + 38/7 = 0\n(x - -1/2)(x - -19/7)(x - -4) = 0\nx - -1/2 = 0\nx - -19/7 = 0\nx - -4 = 0\nx = -1/2\nx = -19/7\nx = -4"} {"input": "Solve the system:\n9x + 8y = 97/10\n3x + 3y = 37/10", "output": "9x + 8y = 97/10\n3x + 3y = 37/10\n\nUsing elimination\n3*(9x + 8y = 97/10)\n9*(3x + 3y = 37/10)\n27x + 24y = 291/10\n27x + 27y = 333/10\nSubtract equations\n-3y = -21/5\ny = -21/5/-3\ny = 7/5\n\nSubstitute y\n9x + 8(7/5) = 97/10\n9x = -3/2\nx = -3/2/9\nx = -1/6"} {"input": "Find x in x^2 + 114/7x + 32 = 0", "output": "x^2 + 114/7x + 32 = 0\n(x - -14)(x - -16/7) = 0\nx - -14 = 0 or x - -16/7 = 0\nx = -14\nx = -16/7"} {"input": "Find the solution to x^2 - 35/6x + 25/3 = 0", "output": "x^2 - 35/6x + 25/3 = 0\n(x - 5/2)(x - 10/3) = 0\nx - 5/2 = 0 or x - 10/3 = 0\nx = 5/2\nx = 10/3"} {"input": "Solve simultaneously:\n6x + 8y = -141/4\n10x + 2y = -99/4", "output": "6x + 8y = -141/4\n10x + 2y = -99/4\n\nUsing elimination\n10*(6x + 8y = -141/4)\n6*(10x + 2y = -99/4)\n60x + 80y = -705/2\n60x + 12y = -297/2\nSubtract equations\n68y = -204\ny = -204/68\ny = -3\n\nSubstitute y\n6x + 8(-3) = -141/4\n6x = -45/4\nx = -45/4/6\nx = -15/8"} {"input": "Solve the system:\n9x + 9y = 129/2\n6x + 7y = 259/6", "output": "9x + 9y = 129/2\n6x + 7y = 259/6\n\nUsing elimination\n6*(9x + 9y = 129/2)\n9*(6x + 7y = 259/6)\n54x + 54y = 387\n54x + 63y = 777/2\nSubtract equations\n-9y = -3/2\ny = -3/2/-9\ny = 1/6\n\nSubstitute y\n9x + 9(1/6) = 129/2\n9x = 63\nx = 63/9\nx = 7"} {"input": "Determine x in x^3 + 80/9x^2 - 1811/81x + 770/81 = 0", "output": "x^3 + 80/9x^2 - 1811/81x + 770/81 = 0\n(x - -11)(x - 5/9)(x - 14/9) = 0\nx - -11 = 0\nx - 5/9 = 0\nx - 14/9 = 0\nx = -11\nx = 5/9\nx = 14/9"} {"input": "Find the solution to x^2 + 31/4x + 55/4 = 0", "output": "x^2 + 31/4x + 55/4 = 0\n(x - -5)(x - -11/4) = 0\nx - -5 = 0 or x - -11/4 = 0\nx = -5\nx = -11/4"} {"input": "Find x and y such that\n1x + 10y = 41/2\n4x + 2y = 145/2", "output": "1x + 10y = 41/2\n4x + 2y = 145/2\n\nUsing elimination\n4*(1x + 10y = 41/2)\n1*(4x + 2y = 145/2)\n4x + 40y = 82\n4x + 2y = 145/2\nSubtract equations\n38y = 19/2\ny = 19/2/38\ny = 1/4\n\nSubstitute y\n1x + 10(1/4) = 41/2\n1x = 18\nx = 18/1\nx = 18"} {"input": "What value of x satisfies 2x - 2/3 = 0", "output": "2x - 2/3 = 0\n2x = 2/3\nx = 2/3 / 2\nx = 1/3"} {"input": "Solve x^3 + 25/4x^2 - 19/4x - 55 = 0", "output": "x^3 + 25/4x^2 - 19/4x - 55 = 0\n(x - 11/4)(x - -5)(x - -4) = 0\nx - 11/4 = 0\nx - -5 = 0\nx - -4 = 0\nx = 11/4\nx = -5\nx = -4"} {"input": "Find x in x^3 + 113/8x^2 + 183/8x - 63/2 = 0", "output": "x^3 + 113/8x^2 + 183/8x - 63/2 = 0\n(x - -3)(x - 7/8)(x - -12) = 0\nx - -3 = 0\nx - 7/8 = 0\nx - -12 = 0\nx = -3\nx = 7/8\nx = -12"} {"input": "Solve simultaneously:\n8x + 5y = -94/9\n5x + 2y = -199/36", "output": "8x + 5y = -94/9\n5x + 2y = -199/36\n\nUsing elimination\n5*(8x + 5y = -94/9)\n8*(5x + 2y = -199/36)\n40x + 25y = -470/9\n40x + 16y = -398/9\nSubtract equations\n9y = -8\ny = -8/9\ny = -8/9\n\nSubstitute y\n8x + 5(-8/9) = -94/9\n8x = -6\nx = -6/8\nx = -3/4"} {"input": "Find x in x^2 + 83/5x + 182/5 = 0", "output": "x^2 + 83/5x + 182/5 = 0\n(x - -14)(x - -13/5) = 0\nx - -14 = 0 or x - -13/5 = 0\nx = -14\nx = -13/5"} {"input": "Find x for 2x - 17 = 0", "output": "2x - 17 = 0\n2x = 17\nx = 17 / 2\nx = 17/2"} {"input": "Solve the system:\n8x + 8y = 32\n9x + 1y = 116", "output": "8x + 8y = 32\n9x + 1y = 116\n\nUsing elimination\n9*(8x + 8y = 32)\n8*(9x + 1y = 116)\n72x + 72y = 288\n72x + 8y = 928\nSubtract equations\n64y = -640\ny = -640/64\ny = -10\n\nSubstitute y\n8x + 8(-10) = 32\n8x = 112\nx = 112/8\nx = 14"} {"input": "What value of x satisfies 3x - 19/3 = 0", "output": "3x - 19/3 = 0\n3x = 19/3\nx = 19/3 / 3\nx = 19/9"} {"input": "Solve the equations:\n5x + 10y = -130/3\n10x + 4y = -172/3", "output": "5x + 10y = -130/3\n10x + 4y = -172/3\n\nUsing elimination\n10*(5x + 10y = -130/3)\n5*(10x + 4y = -172/3)\n50x + 100y = -1300/3\n50x + 20y = -860/3\nSubtract equations\n80y = -440/3\ny = -440/3/80\ny = -11/6\n\nSubstitute y\n5x + 10(-11/6) = -130/3\n5x = -25\nx = -25/5\nx = -5"} {"input": "What value of x satisfies x^2 + 1/8x - 3/16 = 0", "output": "x^2 + 1/8x - 3/16 = 0\n(x - -1/2)(x - 3/8) = 0\nx - -1/2 = 0 or x - 3/8 = 0\nx = -1/2\nx = 3/8"} {"input": "What value of x satisfies x^2 - 52/9x + 140/27 = 0", "output": "x^2 - 52/9x + 140/27 = 0\n(x - 10/9)(x - 14/3) = 0\nx - 10/9 = 0 or x - 14/3 = 0\nx = 10/9\nx = 14/3"} {"input": "What value of x satisfies x^3 - 25/8x^2 - 83/32x + 665/64 = 0", "output": "x^3 - 25/8x^2 - 83/32x + 665/64 = 0\n(x - 5/2)(x - 19/8)(x - -7/4) = 0\nx - 5/2 = 0\nx - 19/8 = 0\nx - -7/4 = 0\nx = 5/2\nx = 19/8\nx = -7/4"} {"input": "Solve x^2 - 1/2x - 3/2 = 0", "output": "x^2 - 1/2x - 3/2 = 0\n(x - 3/2)(x - -1) = 0\nx - 3/2 = 0 or x - -1 = 0\nx = 3/2\nx = -1"} {"input": "Solve the system:\n9x + 2y = -153\n7x + 4y = -119", "output": "9x + 2y = -153\n7x + 4y = -119\n\nUsing elimination\n7*(9x + 2y = -153)\n9*(7x + 4y = -119)\n63x + 14y = -1071\n63x + 36y = -1071\nSubtract equations\n-22y = 0\ny = 0/-22\ny = 0\n\nSubstitute y\n9x + 2(0) = -153\n9x = -153\nx = -153/9\nx = -17"} {"input": "Solve the equation 10x + 16 = 0", "output": "10x + 16 = 0\n10x = -16\nx = -16 / 10\nx = -8/5"} {"input": "Solve the equations:\n2x + 4y = 94/5\n10x + 4y = 774/5", "output": "2x + 4y = 94/5\n10x + 4y = 774/5\n\nUsing elimination\n10*(2x + 4y = 94/5)\n2*(10x + 4y = 774/5)\n20x + 40y = 188\n20x + 8y = 1548/5\nSubtract equations\n32y = -608/5\ny = -608/5/32\ny = -19/5\n\nSubstitute y\n2x + 4(-19/5) = 94/5\n2x = 34\nx = 34/2\nx = 17"} {"input": "Solve x^3 + 1/2x^2 - 243/2x - 342 = 0", "output": "x^3 + 1/2x^2 - 243/2x - 342 = 0\n(x - -3)(x - 12)(x - -19/2) = 0\nx - -3 = 0\nx - 12 = 0\nx - -19/2 = 0\nx = -3\nx = 12\nx = -19/2"} {"input": "Solve simultaneously:\n1x + 3y = -31/5\n6x + 1y = 18/5", "output": "1x + 3y = -31/5\n6x + 1y = 18/5\n\nUsing elimination\n6*(1x + 3y = -31/5)\n1*(6x + 1y = 18/5)\n6x + 18y = -186/5\n6x + 1y = 18/5\nSubtract equations\n17y = -204/5\ny = -204/5/17\ny = -12/5\n\nSubstitute y\n1x + 3(-12/5) = -31/5\n1x = 1\nx = 1/1\nx = 1"} {"input": "Solve quickly: x^3 - 1/2x^2 - 239/16x + 357/16 = 0", "output": "x^3 - 1/2x^2 - 239/16x + 357/16 = 0\n(x - 7/4)(x - 3)(x - -17/4) = 0\nx - 7/4 = 0\nx - 3 = 0\nx - -17/4 = 0\nx = 7/4\nx = 3\nx = -17/4"} {"input": "Determine x in 10x + 140 = 0", "output": "10x + 140 = 0\n10x = -140\nx = -140 / 10\nx = -14"} {"input": "Determine x in 3x - 12 = 0", "output": "3x - 12 = 0\n3x = 12\nx = 12 / 3\nx = 4"} {"input": "Find x and y such that\n10x + 3y = 85/2\n2x + 3y = 113/2", "output": "10x + 3y = 85/2\n2x + 3y = 113/2\n\nUsing elimination\n2*(10x + 3y = 85/2)\n10*(2x + 3y = 113/2)\n20x + 6y = 85\n20x + 30y = 565\nSubtract equations\n-24y = -480\ny = -480/-24\ny = 20\n\nSubstitute y\n10x + 3(20) = 85/2\n10x = -35/2\nx = -35/2/10\nx = -7/4"} {"input": "Solve the equations:\n9x + 1y = -335/2\n3x + 7y = -65/2", "output": "9x + 1y = -335/2\n3x + 7y = -65/2\n\nUsing elimination\n3*(9x + 1y = -335/2)\n9*(3x + 7y = -65/2)\n27x + 3y = -1005/2\n27x + 63y = -585/2\nSubtract equations\n-60y = -210\ny = -210/-60\ny = 7/2\n\nSubstitute y\n9x + 1(7/2) = -335/2\n9x = -171\nx = -171/9\nx = -19"} {"input": "Find x in x^3 + 155/7x^2 + 300/7x = 0", "output": "x^3 + 155/7x^2 + 300/7x = 0\n(x - 0)(x - -15/7)(x - -20) = 0\nx - 0 = 0\nx - -15/7 = 0\nx - -20 = 0\nx = 0\nx = -15/7\nx = -20"} {"input": "Find the solution to 8x - 16/3 = 0", "output": "8x - 16/3 = 0\n8x = 16/3\nx = 16/3 / 8\nx = 2/3"} {"input": "Solve 9x + 63/5 = 0", "output": "9x + 63/5 = 0\n9x = -63/5\nx = -63/5 / 9\nx = -7/5"} {"input": "Determine x in 10x - 45/2 = 0", "output": "10x - 45/2 = 0\n10x = 45/2\nx = 45/2 / 10\nx = 9/4"} {"input": "Solve the equation x^3 + 11/7x^2 - 312/49x - 540/49 = 0", "output": "x^3 + 11/7x^2 - 312/49x - 540/49 = 0\n(x - -15/7)(x - -2)(x - 18/7) = 0\nx - -15/7 = 0\nx - -2 = 0\nx - 18/7 = 0\nx = -15/7\nx = -2\nx = 18/7"} {"input": "Find the solution to x^3 + 37/6x^2 - 137/18x - 770/27 = 0", "output": "x^3 + 37/6x^2 - 137/18x - 770/27 = 0\n(x - 7/3)(x - -20/3)(x - -11/6) = 0\nx - 7/3 = 0\nx - -20/3 = 0\nx - -11/6 = 0\nx = 7/3\nx = -20/3\nx = -11/6"} {"input": "Find x in x^3 - 19/120x^2 - 233/30x + 4199/480 = 0", "output": "x^3 - 19/120x^2 - 233/30x + 4199/480 = 0\n(x - -19/6)(x - 17/10)(x - 13/8) = 0\nx - -19/6 = 0\nx - 17/10 = 0\nx - 13/8 = 0\nx = -19/6\nx = 17/10\nx = 13/8"} {"input": "Solve the equations:\n2x + 4y = 79/5\n9x + 10y = 91/2", "output": "2x + 4y = 79/5\n9x + 10y = 91/2\n\nUsing elimination\n9*(2x + 4y = 79/5)\n2*(9x + 10y = 91/2)\n18x + 36y = 711/5\n18x + 20y = 91\nSubtract equations\n16y = 256/5\ny = 256/5/16\ny = 16/5\n\nSubstitute y\n2x + 4(16/5) = 79/5\n2x = 3\nx = 3/2\nx = 3/2"} {"input": "Solve quickly: x^2 + 8/5x - 4/5 = 0", "output": "x^2 + 8/5x - 4/5 = 0\n(x - 2/5)(x - -2) = 0\nx - 2/5 = 0 or x - -2 = 0\nx = 2/5\nx = -2"} {"input": "Solve quickly: 3x - 39/5 = 0", "output": "3x - 39/5 = 0\n3x = 39/5\nx = 39/5 / 3\nx = 13/5"} {"input": "Determine x in x^3 - 191/10x^2 + 141/10x + 513/5 = 0", "output": "x^3 - 191/10x^2 + 141/10x + 513/5 = 0\n(x - -19/10)(x - 18)(x - 3) = 0\nx - -19/10 = 0\nx - 18 = 0\nx - 3 = 0\nx = -19/10\nx = 18\nx = 3"} {"input": "Find the solution to x^3 - 37/12x^2 + 37/12x - 1 = 0", "output": "x^3 - 37/12x^2 + 37/12x - 1 = 0\n(x - 4/3)(x - 1)(x - 3/4) = 0\nx - 4/3 = 0\nx - 1 = 0\nx - 3/4 = 0\nx = 4/3\nx = 1\nx = 3/4"} {"input": "Find x in x^2 + 55/12x + 25/6 = 0", "output": "x^2 + 55/12x + 25/6 = 0\n(x - -5/4)(x - -10/3) = 0\nx - -5/4 = 0 or x - -10/3 = 0\nx = -5/4\nx = -10/3"} {"input": "Determine x in x^3 - 52/35x^2 - 108/35x + 144/35 = 0", "output": "x^3 - 52/35x^2 - 108/35x + 144/35 = 0\n(x - -12/7)(x - 6/5)(x - 2) = 0\nx - -12/7 = 0\nx - 6/5 = 0\nx - 2 = 0\nx = -12/7\nx = 6/5\nx = 2"} {"input": "Compute the solution of x^3 + 85/21x^2 - 64/3x - 304/7 = 0", "output": "x^3 + 85/21x^2 - 64/3x - 304/7 = 0\n(x - -12/7)(x - -19/3)(x - 4) = 0\nx - -12/7 = 0\nx - -19/3 = 0\nx - 4 = 0\nx = -12/7\nx = -19/3\nx = 4"} {"input": "What value of x satisfies x^2 + 1x + 12/49 = 0", "output": "x^2 + 1x + 12/49 = 0\n(x - -4/7)(x - -3/7) = 0\nx - -4/7 = 0 or x - -3/7 = 0\nx = -4/7\nx = -3/7"} {"input": "Find x for x^2 - 10x + 21 = 0", "output": "x^2 - 10x + 21 = 0\n(x - 7)(x - 3) = 0\nx - 7 = 0 or x - 3 = 0\nx = 7\nx = 3"} {"input": "Solve 4x + 76/3 = 0", "output": "4x + 76/3 = 0\n4x = -76/3\nx = -76/3 / 4\nx = -19/3"} {"input": "Find x for x^3 + 227/35x^2 - 1154/35x + 152/7 = 0", "output": "x^3 + 227/35x^2 - 1154/35x + 152/7 = 0\n(x - -10)(x - 19/7)(x - 4/5) = 0\nx - -10 = 0\nx - 19/7 = 0\nx - 4/5 = 0\nx = -10\nx = 19/7\nx = 4/5"} {"input": "Determine x in x^3 + 31/12x^2 - 75/8x - 27/8 = 0", "output": "x^3 + 31/12x^2 - 75/8x - 27/8 = 0\n(x - -9/2)(x - -1/3)(x - 9/4) = 0\nx - -9/2 = 0\nx - -1/3 = 0\nx - 9/4 = 0\nx = -9/2\nx = -1/3\nx = 9/4"} {"input": "Solve x^2 - 10/9x - 17/3 = 0", "output": "x^2 - 10/9x - 17/3 = 0\n(x - -17/9)(x - 3) = 0\nx - -17/9 = 0 or x - 3 = 0\nx = -17/9\nx = 3"} {"input": "Determine x in x^2 - 7/2x - 36 = 0", "output": "x^2 - 7/2x - 36 = 0\n(x - -9/2)(x - 8) = 0\nx - -9/2 = 0 or x - 8 = 0\nx = -9/2\nx = 8"} {"input": "Determine x in 3x - 27/7 = 0", "output": "3x - 27/7 = 0\n3x = 27/7\nx = 27/7 / 3\nx = 9/7"} {"input": "Solve the equation x^3 - 101/90x^2 - 133/90x = 0", "output": "x^3 - 101/90x^2 - 133/90x = 0\n(x - -7/9)(x - 0)(x - 19/10) = 0\nx - -7/9 = 0\nx - 0 = 0\nx - 19/10 = 0\nx = -7/9\nx = 0\nx = 19/10"} {"input": "Find the solution to x^3 - 57/5x^2 + 38x - 168/5 = 0", "output": "x^3 - 57/5x^2 + 38x - 168/5 = 0\n(x - 4)(x - 6)(x - 7/5) = 0\nx - 4 = 0\nx - 6 = 0\nx - 7/5 = 0\nx = 4\nx = 6\nx = 7/5"} {"input": "Find x for x^2 - 13/8x - 105/16 = 0", "output": "x^2 - 13/8x - 105/16 = 0\n(x - 7/2)(x - -15/8) = 0\nx - 7/2 = 0 or x - -15/8 = 0\nx = 7/2\nx = -15/8"} {"input": "Solve x^3 + 11/2x^2 - 40/9x - 350/9 = 0", "output": "x^3 + 11/2x^2 - 40/9x - 350/9 = 0\n(x - 5/2)(x - -10/3)(x - -14/3) = 0\nx - 5/2 = 0\nx - -10/3 = 0\nx - -14/3 = 0\nx = 5/2\nx = -10/3\nx = -14/3"} {"input": "Find x in 2x + 10 = 0", "output": "2x + 10 = 0\n2x = -10\nx = -10 / 2\nx = -5"} {"input": "Solve simultaneously:\n8x + 4y = 73\n10x + 8y = 545/4", "output": "8x + 4y = 73\n10x + 8y = 545/4\n\nUsing elimination\n10*(8x + 4y = 73)\n8*(10x + 8y = 545/4)\n80x + 40y = 730\n80x + 64y = 1090\nSubtract equations\n-24y = -360\ny = -360/-24\ny = 15\n\nSubstitute y\n8x + 4(15) = 73\n8x = 13\nx = 13/8\nx = 13/8"} {"input": "Solve quickly: x^2 + 5x = 0", "output": "x^2 + 5x = 0\n(x - 0)(x - -5) = 0\nx - 0 = 0 or x - -5 = 0\nx = 0\nx = -5"} {"input": "Solve the system:\n5x + 9y = 1/4\n5x + 3y = 131/12", "output": "5x + 9y = 1/4\n5x + 3y = 131/12\n\nUsing elimination\n5*(5x + 9y = 1/4)\n5*(5x + 3y = 131/12)\n25x + 45y = 5/4\n25x + 15y = 655/12\nSubtract equations\n30y = -160/3\ny = -160/3/30\ny = -16/9\n\nSubstitute y\n5x + 9(-16/9) = 1/4\n5x = 65/4\nx = 65/4/5\nx = 13/4"} {"input": "Determine x in 6x + 54/5 = 0", "output": "6x + 54/5 = 0\n6x = -54/5\nx = -54/5 / 6\nx = -9/5"} {"input": "Find the solution to x^3 - 154/15x^2 + 287/15x - 8 = 0", "output": "x^3 - 154/15x^2 + 287/15x - 8 = 0\n(x - 5/3)(x - 8)(x - 3/5) = 0\nx - 5/3 = 0\nx - 8 = 0\nx - 3/5 = 0\nx = 5/3\nx = 8\nx = 3/5"} {"input": "Solve simultaneously:\n10x + 2y = -31/4\n4x + 2y = -1/4", "output": "10x + 2y = -31/4\n4x + 2y = -1/4\n\nUsing elimination\n4*(10x + 2y = -31/4)\n10*(4x + 2y = -1/4)\n40x + 8y = -31\n40x + 20y = -5/2\nSubtract equations\n-12y = -57/2\ny = -57/2/-12\ny = 19/8\n\nSubstitute y\n10x + 2(19/8) = -31/4\n10x = -25/2\nx = -25/2/10\nx = -5/4"} {"input": "Solve the equations:\n5x + 9y = 41/9\n3x + 3y = 5/3", "output": "5x + 9y = 41/9\n3x + 3y = 5/3\n\nUsing elimination\n3*(5x + 9y = 41/9)\n5*(3x + 3y = 5/3)\n15x + 27y = 41/3\n15x + 15y = 25/3\nSubtract equations\n12y = 16/3\ny = 16/3/12\ny = 4/9\n\nSubstitute y\n5x + 9(4/9) = 41/9\n5x = 5/9\nx = 5/9/5\nx = 1/9"} {"input": "Solve the equations:\n3x + 9y = -477/4\n6x + 4y = -85/2", "output": "3x + 9y = -477/4\n6x + 4y = -85/2\n\nUsing elimination\n6*(3x + 9y = -477/4)\n3*(6x + 4y = -85/2)\n18x + 54y = -1431/2\n18x + 12y = -255/2\nSubtract equations\n42y = -588\ny = -588/42\ny = -14\n\nSubstitute y\n3x + 9(-14) = -477/4\n3x = 27/4\nx = 27/4/3\nx = 9/4"} {"input": "Solve the equation x^3 - 383/40x^2 + 1057/80x - 49/10 = 0", "output": "x^3 - 383/40x^2 + 1057/80x - 49/10 = 0\n(x - 7/8)(x - 7/10)(x - 8) = 0\nx - 7/8 = 0\nx - 7/10 = 0\nx - 8 = 0\nx = 7/8\nx = 7/10\nx = 8"} {"input": "Solve x^3 + 5/9x^2 = 0", "output": "x^3 + 5/9x^2 = 0\n(x - 0)(x - -5/9)(x - 0) = 0\nx - 0 = 0\nx - -5/9 = 0\nx - 0 = 0\nx = 0\nx = -5/9\nx = 0"} {"input": "Determine x in x^3 + 185/21x^2 + 422/21x + 272/21 = 0", "output": "x^3 + 185/21x^2 + 422/21x + 272/21 = 0\n(x - -2)(x - -17/3)(x - -8/7) = 0\nx - -2 = 0\nx - -17/3 = 0\nx - -8/7 = 0\nx = -2\nx = -17/3\nx = -8/7"} {"input": "Solve quickly: x^2 + 13/6x - 22/3 = 0", "output": "x^2 + 13/6x - 22/3 = 0\n(x - 11/6)(x - -4) = 0\nx - 11/6 = 0 or x - -4 = 0\nx = 11/6\nx = -4"} {"input": "Solve quickly: x^2 + 101/24x + 35/12 = 0", "output": "x^2 + 101/24x + 35/12 = 0\n(x - -10/3)(x - -7/8) = 0\nx - -10/3 = 0 or x - -7/8 = 0\nx = -10/3\nx = -7/8"} {"input": "Find the solution to 1x - 15 = 0", "output": "1x - 15 = 0\n1x = 15\nx = 15 / 1\nx = 15"} {"input": "Determine x in 3x - 3/10 = 0", "output": "3x - 3/10 = 0\n3x = 3/10\nx = 3/10 / 3\nx = 1/10"} {"input": "Find the solution to 4x + 26/3 = 0", "output": "4x + 26/3 = 0\n4x = -26/3\nx = -26/3 / 4\nx = -13/6"} {"input": "Find x in x^2 - 31/5x - 72/5 = 0", "output": "x^2 - 31/5x - 72/5 = 0\n(x - 8)(x - -9/5) = 0\nx - 8 = 0 or x - -9/5 = 0\nx = 8\nx = -9/5"} {"input": "Solve the equation 2x + 32/5 = 0", "output": "2x + 32/5 = 0\n2x = -32/5\nx = -32/5 / 2\nx = -16/5"} {"input": "Compute the solution of 4x - 32/5 = 0", "output": "4x - 32/5 = 0\n4x = 32/5\nx = 32/5 / 4\nx = 8/5"} {"input": "Solve the system:\n1x + 9y = 181/3\n1x + 6y = 118/3", "output": "1x + 9y = 181/3\n1x + 6y = 118/3\n\nUsing elimination\n1*(1x + 9y = 181/3)\n1*(1x + 6y = 118/3)\n1x + 9y = 181/3\n1x + 6y = 118/3\nSubtract equations\n3y = 21\ny = 21/3\ny = 7\n\nSubstitute y\n1x + 9(7) = 181/3\n1x = -8/3\nx = -8/3/1\nx = -8/3"} {"input": "Find x in x^3 - 181/120x^2 - 221/240x + 7/16 = 0", "output": "x^3 - 181/120x^2 - 221/240x + 7/16 = 0\n(x - -7/10)(x - 15/8)(x - 1/3) = 0\nx - -7/10 = 0\nx - 15/8 = 0\nx - 1/3 = 0\nx = -7/10\nx = 15/8\nx = 1/3"} {"input": "Compute the solution of 2x + 2 = 0", "output": "2x + 2 = 0\n2x = -2\nx = -2 / 2\nx = -1"} {"input": "Solve quickly: x^2 - 1/30x - 7/5 = 0", "output": "x^2 - 1/30x - 7/5 = 0\n(x - -7/6)(x - 6/5) = 0\nx - -7/6 = 0 or x - 6/5 = 0\nx = -7/6\nx = 6/5"} {"input": "Find the solution to x^3 + 129/10x^2 + 389/10x + 171/5 = 0", "output": "x^3 + 129/10x^2 + 389/10x + 171/5 = 0\n(x - -9)(x - -19/10)(x - -2) = 0\nx - -9 = 0\nx - -19/10 = 0\nx - -2 = 0\nx = -9\nx = -19/10\nx = -2"} {"input": "Find x in 1x + 1/4 = 0", "output": "1x + 1/4 = 0\n1x = -1/4\nx = -1/4 / 1\nx = -1/4"} {"input": "Solve simultaneously:\n5x + 4y = -101/4\n9x + 9y = -225/4", "output": "5x + 4y = -101/4\n9x + 9y = -225/4\n\nUsing elimination\n9*(5x + 4y = -101/4)\n5*(9x + 9y = -225/4)\n45x + 36y = -909/4\n45x + 45y = -1125/4\nSubtract equations\n-9y = 54\ny = 54/-9\ny = -6\n\nSubstitute y\n5x + 4(-6) = -101/4\n5x = -5/4\nx = -5/4/5\nx = -1/4"} {"input": "Solve the system:\n7x + 3y = -12\n6x + 6y = -72/7", "output": "7x + 3y = -12\n6x + 6y = -72/7\n\nUsing elimination\n6*(7x + 3y = -12)\n7*(6x + 6y = -72/7)\n42x + 18y = -72\n42x + 42y = -72\nSubtract equations\n-24y = 0\ny = 0/-24\ny = 0\n\nSubstitute y\n7x + 3(0) = -12\n7x = -12\nx = -12/7\nx = -12/7"} {"input": "Solve the equation x^2 + 5/2x - 7/2 = 0", "output": "x^2 + 5/2x - 7/2 = 0\n(x - 1)(x - -7/2) = 0\nx - 1 = 0 or x - -7/2 = 0\nx = 1\nx = -7/2"} {"input": "Solve the equations:\n1x + 5y = -39/14\n6x + 7y = -73/14", "output": "1x + 5y = -39/14\n6x + 7y = -73/14\n\nUsing elimination\n6*(1x + 5y = -39/14)\n1*(6x + 7y = -73/14)\n6x + 30y = -117/7\n6x + 7y = -73/14\nSubtract equations\n23y = -23/2\ny = -23/2/23\ny = -1/2\n\nSubstitute y\n1x + 5(-1/2) = -39/14\n1x = -2/7\nx = -2/7/1\nx = -2/7"} {"input": "Find the solution to 3x - 27/4 = 0", "output": "3x - 27/4 = 0\n3x = 27/4\nx = 27/4 / 3\nx = 9/4"} {"input": "Solve simultaneously:\n1x + 2y = -83/15\n9x + 6y = -119/5", "output": "1x + 2y = -83/15\n9x + 6y = -119/5\n\nUsing elimination\n9*(1x + 2y = -83/15)\n1*(9x + 6y = -119/5)\n9x + 18y = -249/5\n9x + 6y = -119/5\nSubtract equations\n12y = -26\ny = -26/12\ny = -13/6\n\nSubstitute y\n1x + 2(-13/6) = -83/15\n1x = -6/5\nx = -6/5/1\nx = -6/5"} {"input": "Find x for x^3 + 67/6x^2 + 39/2x = 0", "output": "x^3 + 67/6x^2 + 39/2x = 0\n(x - 0)(x - -13/6)(x - -9) = 0\nx - 0 = 0\nx - -13/6 = 0\nx - -9 = 0\nx = 0\nx = -13/6\nx = -9"} {"input": "Solve quickly: 8x - 18 = 0", "output": "8x - 18 = 0\n8x = 18\nx = 18 / 8\nx = 9/4"} {"input": "Find x and y such that\n5x + 5y = 69\n4x + 3y = 211/5", "output": "5x + 5y = 69\n4x + 3y = 211/5\n\nUsing elimination\n4*(5x + 5y = 69)\n5*(4x + 3y = 211/5)\n20x + 20y = 276\n20x + 15y = 211\nSubtract equations\n5y = 65\ny = 65/5\ny = 13\n\nSubstitute y\n5x + 5(13) = 69\n5x = 4\nx = 4/5\nx = 4/5"} {"input": "Solve quickly: x^3 + 121/8x^2 + 223/8x + 13/4 = 0", "output": "x^3 + 121/8x^2 + 223/8x + 13/4 = 0\n(x - -1/8)(x - -2)(x - -13) = 0\nx - -1/8 = 0\nx - -2 = 0\nx - -13 = 0\nx = -1/8\nx = -2\nx = -13"} {"input": "Solve the equations:\n2x + 2y = 418/35\n7x + 4y = 1193/35", "output": "2x + 2y = 418/35\n7x + 4y = 1193/35\n\nUsing elimination\n7*(2x + 2y = 418/35)\n2*(7x + 4y = 1193/35)\n14x + 14y = 418/5\n14x + 8y = 2386/35\nSubtract equations\n6y = 108/7\ny = 108/7/6\ny = 18/7\n\nSubstitute y\n2x + 2(18/7) = 418/35\n2x = 34/5\nx = 34/5/2\nx = 17/5"} {"input": "Solve the equation x^2 + 1/2x - 1/2 = 0", "output": "x^2 + 1/2x - 1/2 = 0\n(x - -1)(x - 1/2) = 0\nx - -1 = 0 or x - 1/2 = 0\nx = -1\nx = 1/2"} {"input": "Solve x^2 - 3x - 10 = 0", "output": "x^2 - 3x - 10 = 0\n(x - 5)(x - -2) = 0\nx - 5 = 0 or x - -2 = 0\nx = 5\nx = -2"} {"input": "Solve simultaneously:\n5x + 4y = 22/5\n7x + 10y = 0", "output": "5x + 4y = 22/5\n7x + 10y = 0\n\nUsing elimination\n7*(5x + 4y = 22/5)\n5*(7x + 10y = 0)\n35x + 28y = 154/5\n35x + 50y = 0\nSubtract equations\n-22y = 154/5\ny = 154/5/-22\ny = -7/5\n\nSubstitute y\n5x + 4(-7/5) = 22/5\n5x = 10\nx = 10/5\nx = 2"} {"input": "Solve x^2 + 33/8x + 35/16 = 0", "output": "x^2 + 33/8x + 35/16 = 0\n(x - -5/8)(x - -7/2) = 0\nx - -5/8 = 0 or x - -7/2 = 0\nx = -5/8\nx = -7/2"} {"input": "Compute the solution of 10x - 180/7 = 0", "output": "10x - 180/7 = 0\n10x = 180/7\nx = 180/7 / 10\nx = 18/7"} {"input": "Find the solution to x^2 - 6/35x - 8/35 = 0", "output": "x^2 - 6/35x - 8/35 = 0\n(x - -2/5)(x - 4/7) = 0\nx - -2/5 = 0 or x - 4/7 = 0\nx = -2/5\nx = 4/7"} {"input": "Solve quickly: 7x + 21/2 = 0", "output": "7x + 21/2 = 0\n7x = -21/2\nx = -21/2 / 7\nx = -3/2"} {"input": "Find x for 5x - 90/7 = 0", "output": "5x - 90/7 = 0\n5x = 90/7\nx = 90/7 / 5\nx = 18/7"} {"input": "Find x for x^2 - 39/5x + 54/5 = 0", "output": "x^2 - 39/5x + 54/5 = 0\n(x - 6)(x - 9/5) = 0\nx - 6 = 0 or x - 9/5 = 0\nx = 6\nx = 9/5"} {"input": "Solve simultaneously:\n5x + 1y = -19/12\n8x + 4y = 5/3", "output": "5x + 1y = -19/12\n8x + 4y = 5/3\n\nUsing elimination\n8*(5x + 1y = -19/12)\n5*(8x + 4y = 5/3)\n40x + 8y = -38/3\n40x + 20y = 25/3\nSubtract equations\n-12y = -21\ny = -21/-12\ny = 7/4\n\nSubstitute y\n5x + 1(7/4) = -19/12\n5x = -10/3\nx = -10/3/5\nx = -2/3"} {"input": "What value of x satisfies x^3 + 14/3x^2 + 67/12x + 7/4 = 0", "output": "x^3 + 14/3x^2 + 67/12x + 7/4 = 0\n(x - -3)(x - -7/6)(x - -1/2) = 0\nx - -3 = 0\nx - -7/6 = 0\nx - -1/2 = 0\nx = -3\nx = -7/6\nx = -1/2"} {"input": "Find the solution to x^2 - 23/20x - 7/20 = 0", "output": "x^2 - 23/20x - 7/20 = 0\n(x - 7/5)(x - -1/4) = 0\nx - 7/5 = 0 or x - -1/4 = 0\nx = 7/5\nx = -1/4"} {"input": "Find x and y such that\n10x + 5y = 99\n7x + 2y = 333/5", "output": "10x + 5y = 99\n7x + 2y = 333/5\n\nUsing elimination\n7*(10x + 5y = 99)\n10*(7x + 2y = 333/5)\n70x + 35y = 693\n70x + 20y = 666\nSubtract equations\n15y = 27\ny = 27/15\ny = 9/5\n\nSubstitute y\n10x + 5(9/5) = 99\n10x = 90\nx = 90/10\nx = 9"} {"input": "Find x in 3x + 3/2 = 0", "output": "3x + 3/2 = 0\n3x = -3/2\nx = -3/2 / 3\nx = -1/2"} {"input": "Find x in x^3 + 49/10x^2 + 27/10x - 18/5 = 0", "output": "x^3 + 49/10x^2 + 27/10x - 18/5 = 0\n(x - 3/5)(x - -3/2)(x - -4) = 0\nx - 3/5 = 0\nx - -3/2 = 0\nx - -4 = 0\nx = 3/5\nx = -3/2\nx = -4"} {"input": "What value of x satisfies x^2 - 61/40x + 9/20 = 0", "output": "x^2 - 61/40x + 9/20 = 0\n(x - 9/8)(x - 2/5) = 0\nx - 9/8 = 0 or x - 2/5 = 0\nx = 9/8\nx = 2/5"} {"input": "Solve simultaneously:\n3x + 10y = 8\n8x + 4y = -52/5", "output": "3x + 10y = 8\n8x + 4y = -52/5\n\nUsing elimination\n8*(3x + 10y = 8)\n3*(8x + 4y = -52/5)\n24x + 80y = 64\n24x + 12y = -156/5\nSubtract equations\n68y = 476/5\ny = 476/5/68\ny = 7/5\n\nSubstitute y\n3x + 10(7/5) = 8\n3x = -6\nx = -6/3\nx = -2"} {"input": "Find x in x^2 + 61/15x - 136/15 = 0", "output": "x^2 + 61/15x - 136/15 = 0\n(x - -17/3)(x - 8/5) = 0\nx - -17/3 = 0 or x - 8/5 = 0\nx = -17/3\nx = 8/5"} {"input": "Solve 5x + 45/2 = 0", "output": "5x + 45/2 = 0\n5x = -45/2\nx = -45/2 / 5\nx = -9/2"} {"input": "Solve quickly: x^2 + 7/9x - 98/27 = 0", "output": "x^2 + 7/9x - 98/27 = 0\n(x - 14/9)(x - -7/3) = 0\nx - 14/9 = 0 or x - -7/3 = 0\nx = 14/9\nx = -7/3"} {"input": "Solve quickly: x^2 + 1/4x - 55/8 = 0", "output": "x^2 + 1/4x - 55/8 = 0\n(x - 5/2)(x - -11/4) = 0\nx - 5/2 = 0 or x - -11/4 = 0\nx = 5/2\nx = -11/4"} {"input": "Solve 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Find x and y such that\n8x + 6y = 134/5\n5x + 4y = 19", "output": "8x + 6y = 134/5\n5x + 4y = 19\n\nUsing elimination\n5*(8x + 6y = 134/5)\n8*(5x + 4y = 19)\n40x + 30y = 134\n40x + 32y = 152\nSubtract equations\n-2y = -18\ny = -18/-2\ny = 9\n\nSubstitute y\n8x + 6(9) = 134/5\n8x = -136/5\nx = -136/5/8\nx = -17/5"} {"input": "Solve x^2 + 76/9x - 5 = 0", "output": "x^2 + 76/9x - 5 = 0\n(x - 5/9)(x - -9) = 0\nx - 5/9 = 0 or x - -9 = 0\nx = 5/9\nx = -9"} {"input": "Find x and y such that\n2x + 1y = -79/10\n9x + 10y = -107/4", "output": "2x + 1y = -79/10\n9x + 10y = -107/4\n\nUsing elimination\n9*(2x + 1y = -79/10)\n2*(9x + 10y = -107/4)\n18x + 9y = -711/10\n18x + 20y = -107/2\nSubtract equations\n-11y = -88/5\ny = -88/5/-11\ny = 8/5\n\nSubstitute y\n2x + 1(8/5) = -79/10\n2x = -19/2\nx = -19/2/2\nx = -19/4"} {"input": "Solve x^3 + 257/15x^2 + 496/15x + 16 = 0", "output": "x^3 + 257/15x^2 + 496/15x + 16 = 0\n(x - -4/5)(x - -4/3)(x - -15) = 0\nx - -4/5 = 0\nx - -4/3 = 0\nx - -15 = 0\nx = -4/5\nx = -4/3\nx = -15"} {"input": "Find x for x^2 - 35/8x + 143/32 = 0", "output": "x^2 - 35/8x + 143/32 = 0\n(x - 11/4)(x - 13/8) = 0\nx - 11/4 = 0 or x - 13/8 = 0\nx = 11/4\nx = 13/8"} {"input": "Compute the solution of x^2 - 9/8x - 45/8 = 0", "output": "x^2 - 9/8x - 45/8 = 0\n(x - -15/8)(x - 3) = 0\nx - -15/8 = 0 or x - 3 = 0\nx = -15/8\nx = 3"} {"input": "Find x and y such that\n3x + 1y = 4\n4x + 7y = 39/2", "output": "3x + 1y = 4\n4x + 7y = 39/2\n\nUsing elimination\n4*(3x + 1y = 4)\n3*(4x + 7y = 39/2)\n12x + 4y = 16\n12x + 21y = 117/2\nSubtract equations\n-17y = -85/2\ny = -85/2/-17\ny = 5/2\n\nSubstitute y\n3x + 1(5/2) = 4\n3x = 3/2\nx = 3/2/3\nx = 1/2"} {"input": "Find x and y such that\n1x + 2y = -13/6\n7x + 6y = 7/2", "output": "1x + 2y = -13/6\n7x + 6y = 7/2\n\nUsing elimination\n7*(1x + 2y = -13/6)\n1*(7x + 6y = 7/2)\n7x + 14y = -91/6\n7x + 6y = 7/2\nSubtract equations\n8y = -56/3\ny = -56/3/8\ny = -7/3\n\nSubstitute y\n1x + 2(-7/3) = -13/6\n1x = 5/2\nx = 5/2/1\nx = 5/2"} {"input": "Compute the solution of x^3 + 41/15x^2 + 33/20x = 0", "output": "x^3 + 41/15x^2 + 33/20x = 0\n(x - -11/6)(x - -9/10)(x - 0) = 0\nx - -11/6 = 0\nx - -9/10 = 0\nx - 0 = 0\nx = -11/6\nx = -9/10\nx = 0"} {"input": "Solve the equation x^3 + 67/6x^2 - 227/6x + 77/3 = 0", "output": "x^3 + 67/6x^2 - 227/6x + 77/3 = 0\n(x - 1)(x - 11/6)(x - -14) = 0\nx - 1 = 0\nx - 11/6 = 0\nx - -14 = 0\nx = 1\nx = 11/6\nx = -14"} {"input": "Find x and y such that\n9x + 7y = -165/2\n3x + 5y = -87/2", "output": "9x + 7y = -165/2\n3x + 5y = -87/2\n\nUsing elimination\n3*(9x + 7y = -165/2)\n9*(3x + 5y = -87/2)\n27x + 21y = -495/2\n27x + 45y = -783/2\nSubtract equations\n-24y = 144\ny = 144/-24\ny = -6\n\nSubstitute y\n9x + 7(-6) = -165/2\n9x = -81/2\nx = -81/2/9\nx = -9/2"} {"input": "Solve simultaneously:\n4x + 5y = 1/3\n2x + 4y = 5/3", "output": "4x + 5y = 1/3\n2x + 4y = 5/3\n\nUsing elimination\n2*(4x + 5y = 1/3)\n4*(2x + 4y = 5/3)\n8x + 10y = 2/3\n8x + 16y = 20/3\nSubtract equations\n-6y = -6\ny = -6/-6\ny = 1\n\nSubstitute y\n4x + 5(1) = 1/3\n4x = -14/3\nx = -14/3/4\nx = -7/6"} {"input": "Solve the equations:\n10x + 3y = -9\n7x + 1y = -19/10", "output": "10x + 3y = -9\n7x + 1y = -19/10\n\nUsing elimination\n7*(10x + 3y = -9)\n10*(7x + 1y = -19/10)\n70x + 21y = -63\n70x + 10y = -19\nSubtract equations\n11y = -44\ny = -44/11\ny = -4\n\nSubstitute y\n10x + 3(-4) = -9\n10x = 3\nx = 3/10\nx = 3/10"} {"input": "Find the solution to x^3 - 3/8x^2 = 0", "output": "x^3 - 3/8x^2 = 0\n(x - 0)(x - 0)(x - 3/8) = 0\nx - 0 = 0\nx - 0 = 0\nx - 3/8 = 0\nx = 0\nx = 0\nx = 3/8"} {"input": "Solve 2x - 8/5 = 0", "output": "2x - 8/5 = 0\n2x = 8/5\nx = 8/5 / 2\nx = 4/5"} {"input": "Find x and y such that\n8x + 9y = 177\n7x + 1y = 38", "output": "8x + 9y = 177\n7x + 1y = 38\n\nUsing elimination\n7*(8x + 9y = 177)\n8*(7x + 1y = 38)\n56x + 63y = 1239\n56x + 8y = 304\nSubtract equations\n55y = 935\ny = 935/55\ny = 17\n\nSubstitute y\n8x + 9(17) = 177\n8x = 24\nx = 24/8\nx = 3"} {"input": "Find x in 7x + 49/9 = 0", "output": "7x + 49/9 = 0\n7x = -49/9\nx = -49/9 / 7\nx = -7/9"} {"input": "What value of x satisfies 2x + 2 = 0", "output": "2x + 2 = 0\n2x = -2\nx = -2 / 2\nx = -1"} {"input": "Solve the equation 6x + 15 = 0", "output": "6x + 15 = 0\n6x = -15\nx = -15 / 6\nx = -5/2"} {"input": "Solve 4x - 16/5 = 0", "output": "4x - 16/5 = 0\n4x = 16/5\nx = 16/5 / 4\nx = 4/5"} {"input": "What value of x satisfies 10x + 35/2 = 0", "output": "10x + 35/2 = 0\n10x = -35/2\nx = -35/2 / 10\nx = -7/4"} {"input": "Compute the solution of 1x + 5/4 = 0", "output": "1x + 5/4 = 0\n1x = -5/4\nx = -5/4 / 1\nx = -5/4"} {"input": "Solve the equation x^3 + 10x^2 + 11/9x - 70 = 0", "output": "x^3 + 10x^2 + 11/9x - 70 = 0\n(x - -10/3)(x - 7/3)(x - -9) = 0\nx - -10/3 = 0\nx - 7/3 = 0\nx - -9 = 0\nx = -10/3\nx = 7/3\nx = -9"} {"input": "Compute the solution of x^2 - 54/7x - 160/7 = 0", "output": "x^2 - 54/7x - 160/7 = 0\n(x - 10)(x - -16/7) = 0\nx - 10 = 0 or x - -16/7 = 0\nx = 10\nx = -16/7"} {"input": "Solve the system:\n5x + 4y = -619/20\n2x + 6y = -203/10", "output": "5x + 4y = -619/20\n2x + 6y = -203/10\n\nUsing elimination\n2*(5x + 4y = -619/20)\n5*(2x + 6y = -203/10)\n10x + 8y = -619/10\n10x + 30y = -203/2\nSubtract equations\n-22y = 198/5\ny = 198/5/-22\ny = -9/5\n\nSubstitute y\n5x + 4(-9/5) = -619/20\n5x = -95/4\nx = -95/4/5\nx = -19/4"} {"input": "Find x in 6x + 34 = 0", "output": "6x + 34 = 0\n6x = -34\nx = -34 / 6\nx = -17/3"} {"input": "Find x and y such that\n2x + 9y = -79/2\n3x + 6y = -137/4", "output": "2x + 9y = -79/2\n3x + 6y = -137/4\n\nUsing elimination\n3*(2x + 9y = -79/2)\n2*(3x + 6y = -137/4)\n6x + 27y = -237/2\n6x + 12y = -137/2\nSubtract equations\n15y = -50\ny = -50/15\ny = -10/3\n\nSubstitute y\n2x + 9(-10/3) = -79/2\n2x = -19/2\nx = -19/2/2\nx = -19/4"} {"input": "Solve the equations:\n1x + 6y = 348/35\n7x + 2y = -12/5", "output": "1x + 6y = 348/35\n7x + 2y = -12/5\n\nUsing elimination\n7*(1x + 6y = 348/35)\n1*(7x + 2y = -12/5)\n7x + 42y = 348/5\n7x + 2y = -12/5\nSubtract equations\n40y = 72\ny = 72/40\ny = 9/5\n\nSubstitute y\n1x + 6(9/5) = 348/35\n1x = -6/7\nx = -6/7/1\nx = -6/7"} {"input": "Find x in x^3 + 209/84x^2 - 83/12x + 17/7 = 0", "output": "x^3 + 209/84x^2 - 83/12x + 17/7 = 0\n(x - 4/3)(x - 3/7)(x - -17/4) = 0\nx - 4/3 = 0\nx - 3/7 = 0\nx - -17/4 = 0\nx = 4/3\nx = 3/7\nx = -17/4"} {"input": "Solve 10x - 5 = 0", "output": "10x - 5 = 0\n10x = 5\nx = 5 / 10\nx = 1/2"} {"input": "Compute the solution of x^3 + 49/2x^2 + 107x + 95/2 = 0", "output": "x^3 + 49/2x^2 + 107x + 95/2 = 0\n(x - -5)(x - -1/2)(x - -19) = 0\nx - -5 = 0\nx - -1/2 = 0\nx - -19 = 0\nx = -5\nx = -1/2\nx = -19"} {"input": "Solve quickly: x^3 + 29/20x^2 - 199/20x + 663/80 = 0", "output": "x^3 + 29/20x^2 - 199/20x + 663/80 = 0\n(x - -17/4)(x - 13/10)(x - 3/2) = 0\nx - -17/4 = 0\nx - 13/10 = 0\nx - 3/2 = 0\nx = -17/4\nx = 13/10\nx = 3/2"} {"input": "Solve quickly: x^2 + 63/10x + 22/5 = 0", "output": "x^2 + 63/10x + 22/5 = 0\n(x - -4/5)(x - -11/2) = 0\nx - -4/5 = 0 or x - -11/2 = 0\nx = -4/5\nx = -11/2"} {"input": "Solve the equations:\n3x + 4y = -217/30\n6x + 7y = -182/15", "output": "3x + 4y = -217/30\n6x + 7y = -182/15\n\nUsing elimination\n6*(3x + 4y = -217/30)\n3*(6x + 7y = -182/15)\n18x + 24y = -217/5\n18x + 21y = -182/5\nSubtract equations\n3y = -7\ny = -7/3\ny = -7/3\n\nSubstitute y\n3x + 4(-7/3) = -217/30\n3x = 21/10\nx = 21/10/3\nx = 7/10"} {"input": "Find x and y such that\n3x + 6y = -113\n10x + 9y = -536/3", "output": "3x + 6y = -113\n10x + 9y = -536/3\n\nUsing elimination\n10*(3x + 6y = -113)\n3*(10x + 9y = -536/3)\n30x + 60y = -1130\n30x + 27y = -536\nSubtract equations\n33y = -594\ny = -594/33\ny = -18\n\nSubstitute y\n3x + 6(-18) = -113\n3x = -5\nx = -5/3\nx = -5/3"} {"input": "Determine x in 10x + 40/7 = 0", "output": "10x + 40/7 = 0\n10x = -40/7\nx = -40/7 / 10\nx = -4/7"} {"input": "Find x and y such that\n9x + 8y = -98/5\n2x + 6y = -64/5", "output": "9x + 8y = -98/5\n2x + 6y = -64/5\n\nUsing elimination\n2*(9x + 8y = -98/5)\n9*(2x + 6y = -64/5)\n18x + 16y = -196/5\n18x + 54y = -576/5\nSubtract equations\n-38y = 76\ny = 76/-38\ny = -2\n\nSubstitute y\n9x + 8(-2) = -98/5\n9x = -18/5\nx = -18/5/9\nx = -2/5"} {"input": "Solve the equation x^2 - 8x - 17/4 = 0", "output": "x^2 - 8x - 17/4 = 0\n(x - -1/2)(x - 17/2) = 0\nx - -1/2 = 0 or x - 17/2 = 0\nx = -1/2\nx = 17/2"} {"input": "Solve x^3 - 41/20x^2 - 1/2x + 6/5 = 0", "output": "x^3 - 41/20x^2 - 1/2x + 6/5 = 0\n(x - -3/4)(x - 4/5)(x - 2) = 0\nx - -3/4 = 0\nx - 4/5 = 0\nx - 2 = 0\nx = -3/4\nx = 4/5\nx = 2"} {"input": "Solve simultaneously:\n5x + 7y = 217/8\n4x + 6y = 89/4", "output": "5x + 7y = 217/8\n4x + 6y = 89/4\n\nUsing elimination\n4*(5x + 7y = 217/8)\n5*(4x + 6y = 89/4)\n20x + 28y = 217/2\n20x + 30y = 445/4\nSubtract equations\n-2y = -11/4\ny = -11/4/-2\ny = 11/8\n\nSubstitute y\n5x + 7(11/8) = 217/8\n5x = 35/2\nx = 35/2/5\nx = 7/2"} {"input": "Solve x^2 - 5/2x - 26 = 0", "output": "x^2 - 5/2x - 26 = 0\n(x - -4)(x - 13/2) = 0\nx - -4 = 0 or x - 13/2 = 0\nx = -4\nx = 13/2"} {"input": "Compute the solution of 2x - 1/2 = 0", "output": "2x - 1/2 = 0\n2x = 1/2\nx = 1/2 / 2\nx = 1/4"} {"input": "Find x and y such that\n3x + 3y = 27/2\n5x + 2y = 30", "output": "3x + 3y = 27/2\n5x + 2y = 30\n\nUsing elimination\n5*(3x + 3y = 27/2)\n3*(5x + 2y = 30)\n15x + 15y = 135/2\n15x + 6y = 90\nSubtract equations\n9y = -45/2\ny = -45/2/9\ny = -5/2\n\nSubstitute y\n3x + 3(-5/2) = 27/2\n3x = 21\nx = 21/3\nx = 7"} {"input": "Find x in x^3 + 514/45x^2 + 349/15x + 66/5 = 0", "output": "x^3 + 514/45x^2 + 349/15x + 66/5 = 0\n(x - -11/9)(x - -9)(x - -6/5) = 0\nx - -11/9 = 0\nx - -9 = 0\nx - -6/5 = 0\nx = -11/9\nx = -9\nx = -6/5"} {"input": "Solve the system:\n6x + 4y = 100/7\n4x + 5y = 83/7", "output": "6x + 4y = 100/7\n4x + 5y = 83/7\n\nUsing elimination\n4*(6x + 4y = 100/7)\n6*(4x + 5y = 83/7)\n24x + 16y = 400/7\n24x + 30y = 498/7\nSubtract equations\n-14y = -14\ny = -14/-14\ny = 1\n\nSubstitute y\n6x + 4(1) = 100/7\n6x = 72/7\nx = 72/7/6\nx = 12/7"} {"input": "Determine x in 10x - 35/2 = 0", "output": "10x - 35/2 = 0\n10x = 35/2\nx = 35/2 / 10\nx = 7/4"} {"input": "Solve the equations:\n6x + 2y = -8/9\n2x + 6y = -8/3", "output": "6x + 2y = -8/9\n2x + 6y = -8/3\n\nUsing elimination\n2*(6x + 2y = -8/9)\n6*(2x + 6y = -8/3)\n12x + 4y = -16/9\n12x + 36y = -16\nSubtract equations\n-32y = 128/9\ny = 128/9/-32\ny = -4/9\n\nSubstitute y\n6x + 2(-4/9) = -8/9\n6x = 0\nx = 0/6\nx = 0"} {"input": "What value of x satisfies x^2 + 13/18x - 10/3 = 0", "output": "x^2 + 13/18x - 10/3 = 0\n(x - 3/2)(x - -20/9) = 0\nx - 3/2 = 0 or x - -20/9 = 0\nx = 3/2\nx = -20/9"} {"input": "Solve x^2 + 36/5x + 36/5 = 0", "output": "x^2 + 36/5x + 36/5 = 0\n(x - -6/5)(x - -6) = 0\nx - -6/5 = 0 or x - -6 = 0\nx = -6/5\nx = -6"} {"input": "Find x in x^3 - 59/3x^2 + 38/3x = 0", "output": "x^3 - 59/3x^2 + 38/3x = 0\n(x - 0)(x - 19)(x - 2/3) = 0\nx - 0 = 0\nx - 19 = 0\nx - 2/3 = 0\nx = 0\nx = 19\nx = 2/3"} {"input": "Find x in 1x - 17/3 = 0", "output": "1x - 17/3 = 0\n1x = 17/3\nx = 17/3 / 1\nx = 17/3"} {"input": "Compute the solution of 2x + 6 = 0", "output": "2x + 6 = 0\n2x = -6\nx = -6 / 2\nx = -3"} {"input": "Find the solution to x^2 + 7/6x - 1/2 = 0", "output": "x^2 + 7/6x - 1/2 = 0\n(x - 1/3)(x - -3/2) = 0\nx - 1/3 = 0 or x - -3/2 = 0\nx = 1/3\nx = -3/2"} {"input": "Find the solution to x^2 - 1x + 4/25 = 0", "output": "x^2 - 1x + 4/25 = 0\n(x - 1/5)(x - 4/5) = 0\nx - 1/5 = 0 or x - 4/5 = 0\nx = 1/5\nx = 4/5"} {"input": "Solve simultaneously:\n3x + 1y = -13/2\n1x + 1y = -5/2", "output": "3x + 1y = -13/2\n1x + 1y = -5/2\n\nUsing elimination\n1*(3x + 1y = -13/2)\n3*(1x + 1y = -5/2)\n3x + 1y = -13/2\n3x + 3y = -15/2\nSubtract equations\n-2y = 1\ny = 1/-2\ny = -1/2\n\nSubstitute y\n3x + 1(-1/2) = -13/2\n3x = -6\nx = -6/3\nx = -2"} {"input": "What value of x satisfies x^2 - 13/18x - 35/27 = 0", "output": "x^2 - 13/18x - 35/27 = 0\n(x - -5/6)(x - 14/9) = 0\nx - -5/6 = 0 or x - 14/9 = 0\nx = -5/6\nx = 14/9"} {"input": "Solve simultaneously:\n5x + 10y = -33\n9x + 4y = 18/5", "output": "5x + 10y = -33\n9x + 4y = 18/5\n\nUsing elimination\n9*(5x + 10y = -33)\n5*(9x + 4y = 18/5)\n45x + 90y = -297\n45x + 20y = 18\nSubtract equations\n70y = -315\ny = -315/70\ny = -9/2\n\nSubstitute y\n5x + 10(-9/2) = -33\n5x = 12\nx = 12/5\nx = 12/5"} {"input": "Find x for 5x - 25 = 0", "output": "5x - 25 = 0\n5x = 25\nx = 25 / 5\nx = 5"} {"input": "Find x in x^2 + 7/24x - 5/24 = 0", "output": "x^2 + 7/24x - 5/24 = 0\n(x - 1/3)(x - -5/8) = 0\nx - 1/3 = 0 or x - -5/8 = 0\nx = 1/3\nx = -5/8"} {"input": "What value of x satisfies x^2 + 55/6x + 50/3 = 0", "output": "x^2 + 55/6x + 50/3 = 0\n(x - -20/3)(x - -5/2) = 0\nx - -20/3 = 0 or x - -5/2 = 0\nx = -20/3\nx = -5/2"} {"input": "Solve simultaneously:\n4x + 8y = -169/6\n10x + 7y = -481/12", "output": "4x + 8y = -169/6\n10x + 7y = -481/12\n\nUsing elimination\n10*(4x + 8y = -169/6)\n4*(10x + 7y = -481/12)\n40x + 80y = -845/3\n40x + 28y = -481/3\nSubtract equations\n52y = -364/3\ny = -364/3/52\ny = -7/3\n\nSubstitute y\n4x + 8(-7/3) = -169/6\n4x = -19/2\nx = -19/2/4\nx = -19/8"} {"input": "What value of x satisfies x^2 + 11/8x - 19/8 = 0", "output": "x^2 + 11/8x - 19/8 = 0\n(x - -19/8)(x - 1) = 0\nx - -19/8 = 0 or x - 1 = 0\nx = -19/8\nx = 1"} {"input": "Determine x in x^2 - 109/24x - 51/8 = 0", "output": "x^2 - 109/24x - 51/8 = 0\n(x - 17/3)(x - -9/8) = 0\nx - 17/3 = 0 or x - -9/8 = 0\nx = 17/3\nx = -9/8"} {"input": "Find x in 7x + 105/8 = 0", "output": "7x + 105/8 = 0\n7x = -105/8\nx = -105/8 / 7\nx = -15/8"} {"input": "Solve quickly: x^3 + 131/42x^2 - 11/7x - 5/6 = 0", "output": "x^3 + 131/42x^2 - 11/7x - 5/6 = 0\n(x - -1/3)(x - -7/2)(x - 5/7) = 0\nx - -1/3 = 0\nx - -7/2 = 0\nx - 5/7 = 0\nx = -1/3\nx = -7/2\nx = 5/7"} {"input": "What value of x satisfies x^2 + 1/20x - 3/40 = 0", "output": "x^2 + 1/20x - 3/40 = 0\n(x - -3/10)(x - 1/4) = 0\nx - -3/10 = 0 or x - 1/4 = 0\nx = -3/10\nx = 1/4"} {"input": "Solve quickly: x^3 + 625/36x^2 - 1025/18x - 250/3 = 0", "output": "x^3 + 625/36x^2 - 1025/18x - 250/3 = 0\n(x - -10/9)(x - 15/4)(x - -20) = 0\nx - -10/9 = 0\nx - 15/4 = 0\nx - -20 = 0\nx = -10/9\nx = 15/4\nx = -20"} {"input": "What value of x satisfies x^3 + 54/7x^2 + 2097/112x + 405/28 = 0", "output": "x^3 + 54/7x^2 + 2097/112x + 405/28 = 0\n(x - -15/4)(x - -9/4)(x - -12/7) = 0\nx - -15/4 = 0\nx - -9/4 = 0\nx - -12/7 = 0\nx = -15/4\nx = -9/4\nx = -12/7"} {"input": "Solve x^2 - 7/2x + 3 = 0", "output": "x^2 - 7/2x + 3 = 0\n(x - 2)(x - 3/2) = 0\nx - 2 = 0 or x - 3/2 = 0\nx = 2\nx = 3/2"} {"input": "Find x and y such that\n7x + 6y = -140\n8x + 2y = -446/3", "output": "7x + 6y = -140\n8x + 2y = -446/3\n\nUsing elimination\n8*(7x + 6y = -140)\n7*(8x + 2y = -446/3)\n56x + 48y = -1120\n56x + 14y = -3122/3\nSubtract equations\n34y = -238/3\ny = -238/3/34\ny = -7/3\n\nSubstitute y\n7x + 6(-7/3) = -140\n7x = -126\nx = -126/7\nx = -18"} {"input": "Find x in x^2 + 23/2x + 15 = 0", "output": "x^2 + 23/2x + 15 = 0\n(x - -10)(x - -3/2) = 0\nx - -10 = 0 or x - -3/2 = 0\nx = -10\nx = -3/2"} {"input": "Find x for x^2 - 1/10x - 3/10 = 0", "output": "x^2 - 1/10x - 3/10 = 0\n(x - 3/5)(x - -1/2) = 0\nx - 3/5 = 0 or x - -1/2 = 0\nx = 3/5\nx = -1/2"} {"input": "Compute the solution of x^3 + 7/12x^2 - 203/12x - 17/3 = 0", "output": "x^3 + 7/12x^2 - 203/12x - 17/3 = 0\n(x - -17/4)(x - -1/3)(x - 4) = 0\nx - -17/4 = 0\nx - -1/3 = 0\nx - 4 = 0\nx = -17/4\nx = -1/3\nx = 4"} {"input": "What value of x satisfies x^3 - 493/28x^2 - 184/7x - 95/28 = 0", "output": "x^3 - 493/28x^2 - 184/7x - 95/28 = 0\n(x - -5/4)(x - -1/7)(x - 19) = 0\nx - -5/4 = 0\nx - -1/7 = 0\nx - 19 = 0\nx = -5/4\nx = -1/7\nx = 19"} {"input": "Determine x in x^2 + 172/9x + 323/9 = 0", "output": "x^2 + 172/9x + 323/9 = 0\n(x - -19/9)(x - -17) = 0\nx - -19/9 = 0 or x - -17 = 0\nx = -19/9\nx = -17"} {"input": "Solve quickly: x^2 + 32/3x + 256/9 = 0", "output": "x^2 + 32/3x + 256/9 = 0\n(x - -16/3)(x - -16/3) = 0\nx - -16/3 = 0 or x - -16/3 = 0\nx = -16/3\nx = -16/3"} {"input": "Compute the solution of 2x - 4/3 = 0", "output": "2x - 4/3 = 0\n2x = 4/3\nx = 4/3 / 2\nx = 2/3"} {"input": "Solve the equations:\n5x + 10y = -10/3\n10x + 5y = -85/6", "output": "5x + 10y = -10/3\n10x + 5y = -85/6\n\nUsing elimination\n10*(5x + 10y = -10/3)\n5*(10x + 5y = -85/6)\n50x + 100y = -100/3\n50x + 25y = -425/6\nSubtract equations\n75y = 75/2\ny = 75/2/75\ny = 1/2\n\nSubstitute y\n5x + 10(1/2) = -10/3\n5x = -25/3\nx = -25/3/5\nx = -5/3"} {"input": "Compute the solution of x^3 - 103/9x^2 + 941/36x - 85/9 = 0", "output": "x^3 - 103/9x^2 + 941/36x - 85/9 = 0\n(x - 5/2)(x - 17/2)(x - 4/9) = 0\nx - 5/2 = 0\nx - 17/2 = 0\nx - 4/9 = 0\nx = 5/2\nx = 17/2\nx = 4/9"} {"input": "What value of x satisfies x^3 + 6/5x^2 + 1/20x - 33/500 = 0", "output": "x^3 + 6/5x^2 + 1/20x - 33/500 = 0\n(x - -11/10)(x - 1/5)(x - -3/10) = 0\nx - -11/10 = 0\nx - 1/5 = 0\nx - -3/10 = 0\nx = -11/10\nx = 1/5\nx = -3/10"} {"input": "Determine x in 1x - 4/3 = 0", "output": "1x - 4/3 = 0\n1x = 4/3\nx = 4/3 / 1\nx = 4/3"} {"input": "Compute the solution of 2x - 14 = 0", "output": "2x - 14 = 0\n2x = 14\nx = 14 / 2\nx = 7"} {"input": "Find x and y such that\n2x + 5y = -163/9\n8x + 3y = -193/9", "output": "2x + 5y = -163/9\n8x + 3y = -193/9\n\nUsing elimination\n8*(2x + 5y = -163/9)\n2*(8x + 3y = -193/9)\n16x + 40y = -1304/9\n16x + 6y = -386/9\nSubtract equations\n34y = -102\ny = -102/34\ny = -3\n\nSubstitute y\n2x + 5(-3) = -163/9\n2x = -28/9\nx = -28/9/2\nx = -14/9"} {"input": "Find the solution to x^2 - 37/20x - 63/10 = 0", "output": "x^2 - 37/20x - 63/10 = 0\n(x - -7/4)(x - 18/5) = 0\nx - -7/4 = 0 or x - 18/5 = 0\nx = -7/4\nx = 18/5"} {"input": "Solve x^2 + 26/3x - 95 = 0", "output": "x^2 + 26/3x - 95 = 0\n(x - -15)(x - 19/3) = 0\nx - -15 = 0 or x - 19/3 = 0\nx = -15\nx = 19/3"} {"input": "Compute the solution of x^3 + 143/18x^2 + 340/27x + 50/9 = 0", "output": "x^3 + 143/18x^2 + 340/27x + 50/9 = 0\n(x - -6)(x - -10/9)(x - -5/6) = 0\nx - -6 = 0\nx - -10/9 = 0\nx - -5/6 = 0\nx = -6\nx = -10/9\nx = -5/6"} {"input": "Find the solution to x^2 + 59/10x - 3/5 = 0", "output": "x^2 + 59/10x - 3/5 = 0\n(x - 1/10)(x - -6) = 0\nx - 1/10 = 0 or x - -6 = 0\nx = 1/10\nx = -6"} {"input": "Solve 9x - 54 = 0", "output": "9x - 54 = 0\n9x = 54\nx = 54 / 9\nx = 6"} {"input": "Solve quickly: 6x - 3 = 0", "output": "6x - 3 = 0\n6x = 3\nx = 3 / 6\nx = 1/2"} {"input": "Find x for x^3 - 22/35x^2 - 167/35x + 34/35 = 0", "output": "x^3 - 22/35x^2 - 167/35x + 34/35 = 0\n(x - 17/7)(x - -2)(x - 1/5) = 0\nx - 17/7 = 0\nx - -2 = 0\nx - 1/5 = 0\nx = 17/7\nx = -2\nx = 1/5"} {"input": "Compute the solution of x^3 + 13x^2 - 741/25x + 27/5 = 0", "output": "x^3 + 13x^2 - 741/25x + 27/5 = 0\n(x - -15)(x - 1/5)(x - 9/5) = 0\nx - -15 = 0\nx - 1/5 = 0\nx - 9/5 = 0\nx = -15\nx = 1/5\nx = 9/5"} {"input": "Solve the system:\n8x + 9y = -64/7\n1x + 2y = -15/7", "output": "8x + 9y = -64/7\n1x + 2y = -15/7\n\nUsing elimination\n1*(8x + 9y = -64/7)\n8*(1x + 2y = -15/7)\n8x + 9y = -64/7\n8x + 16y = -120/7\nSubtract equations\n-7y = 8\ny = 8/-7\ny = -8/7\n\nSubstitute y\n8x + 9(-8/7) = -64/7\n8x = 8/7\nx = 8/7/8\nx = 1/7"} {"input": "Solve quickly: x^2 + 37/9x + 70/27 = 0", "output": "x^2 + 37/9x + 70/27 = 0\n(x - -7/9)(x - -10/3) = 0\nx - -7/9 = 0 or x - -10/3 = 0\nx = -7/9\nx = -10/3"} {"input": "Solve quickly: 9x - 63/5 = 0", "output": "9x - 63/5 = 0\n9x = 63/5\nx = 63/5 / 9\nx = 7/5"} {"input": "Solve x^2 + 4/3x + 1/3 = 0", "output": "x^2 + 4/3x + 1/3 = 0\n(x - -1/3)(x - -1) = 0\nx - -1/3 = 0 or x - -1 = 0\nx = -1/3\nx = -1"} {"input": "Find x in x^3 + 137/30x^2 - 28/3x - 22/5 = 0", "output": "x^3 + 137/30x^2 - 28/3x - 22/5 = 0\n(x - -6)(x - -2/5)(x - 11/6) = 0\nx - -6 = 0\nx - -2/5 = 0\nx - 11/6 = 0\nx = -6\nx = -2/5\nx = 11/6"} {"input": "Solve the system:\n4x + 8y = 62/3\n8x + 8y = 92/3", "output": "4x + 8y = 62/3\n8x + 8y = 92/3\n\nUsing elimination\n8*(4x + 8y = 62/3)\n4*(8x + 8y = 92/3)\n32x + 64y = 496/3\n32x + 32y = 368/3\nSubtract equations\n32y = 128/3\ny = 128/3/32\ny = 4/3\n\nSubstitute y\n4x + 8(4/3) = 62/3\n4x = 10\nx = 10/4\nx = 5/2"} {"input": "Find the solution to 7x + 63/4 = 0", "output": "7x + 63/4 = 0\n7x = -63/4\nx = -63/4 / 7\nx = -9/4"} {"input": "Determine x in 8x - 112/9 = 0", "output": "8x - 112/9 = 0\n8x = 112/9\nx = 112/9 / 8\nx = 14/9"} {"input": "Find x in x^3 + 1x^2 - 35/4x = 0", "output": "x^3 + 1x^2 - 35/4x = 0\n(x - 5/2)(x - -7/2)(x - 0) = 0\nx - 5/2 = 0\nx - -7/2 = 0\nx - 0 = 0\nx = 5/2\nx = -7/2\nx = 0"} {"input": "Solve the system:\n3x + 5y = -333/20\n8x + 6y = -279/10", "output": "3x + 5y = -333/20\n8x + 6y = -279/10\n\nUsing elimination\n8*(3x + 5y = -333/20)\n3*(8x + 6y = -279/10)\n24x + 40y = -666/5\n24x + 18y = -837/10\nSubtract equations\n22y = -99/2\ny = -99/2/22\ny = -9/4\n\nSubstitute y\n3x + 5(-9/4) = -333/20\n3x = -27/5\nx = -27/5/3\nx = -9/5"} {"input": "Solve x^2 + 31/6x + 7/3 = 0", "output": "x^2 + 31/6x + 7/3 = 0\n(x - -1/2)(x - -14/3) = 0\nx - -1/2 = 0 or x - -14/3 = 0\nx = -1/2\nx = -14/3"} {"input": "Find x for x^3 - 53/21x^2 - 974/147x + 816/49 = 0", "output": "x^3 - 53/21x^2 - 974/147x + 816/49 = 0\n(x - 8/3)(x - 17/7)(x - -18/7) = 0\nx - 8/3 = 0\nx - 17/7 = 0\nx - -18/7 = 0\nx = 8/3\nx = 17/7\nx = -18/7"} {"input": "Find x for 7x + 77/5 = 0", "output": "7x + 77/5 = 0\n7x = -77/5\nx = -77/5 / 7\nx = -11/5"} {"input": "Solve the equations:\n5x + 1y = -13/3\n8x + 2y = -142/15", "output": "5x + 1y = -13/3\n8x + 2y = -142/15\n\nUsing elimination\n8*(5x + 1y = -13/3)\n5*(8x + 2y = -142/15)\n40x + 8y = -104/3\n40x + 10y = -142/3\nSubtract equations\n-2y = 38/3\ny = 38/3/-2\ny = -19/3\n\nSubstitute y\n5x + 1(-19/3) = -13/3\n5x = 2\nx = 2/5\nx = 2/5"} {"input": "What value of x satisfies 4x + 1/2 = 0", "output": "4x + 1/2 = 0\n4x = -1/2\nx = -1/2 / 4\nx = -1/8"} {"input": "Solve quickly: x^2 - 23/3x + 14/3 = 0", "output": "x^2 - 23/3x + 14/3 = 0\n(x - 2/3)(x - 7) = 0\nx - 2/3 = 0 or x - 7 = 0\nx = 2/3\nx = 7"} {"input": "Find the solution to x^3 + 53/9x^2 - 166/27x - 520/81 = 0", "output": "x^3 + 53/9x^2 - 166/27x - 520/81 = 0\n(x - -2/3)(x - -20/3)(x - 13/9) = 0\nx - -2/3 = 0\nx - -20/3 = 0\nx - 13/9 = 0\nx = -2/3\nx = -20/3\nx = 13/9"} {"input": "Solve quickly: x^3 + 81/20x^2 + 91/20x + 9/10 = 0", "output": "x^3 + 81/20x^2 + 91/20x + 9/10 = 0\n(x - -2)(x - -1/4)(x - -9/5) = 0\nx - -2 = 0\nx - -1/4 = 0\nx - -9/5 = 0\nx = -2\nx = -1/4\nx = -9/5"} {"input": "Solve the system:\n1x + 7y = 37\n5x + 10y = 60", "output": "1x + 7y = 37\n5x + 10y = 60\n\nUsing elimination\n5*(1x + 7y = 37)\n1*(5x + 10y = 60)\n5x + 35y = 185\n5x + 10y = 60\nSubtract equations\n25y = 125\ny = 125/25\ny = 5\n\nSubstitute y\n1x + 7(5) = 37\n1x = 2\nx = 2/1\nx = 2"} {"input": "Find x in 8x - 96/5 = 0", "output": "8x - 96/5 = 0\n8x = 96/5\nx = 96/5 / 8\nx = 12/5"} {"input": "What value of x satisfies x^3 + 23/3x^2 - 556/81x - 2720/81 = 0", "output": "x^3 + 23/3x^2 - 556/81x - 2720/81 = 0\n(x - 20/9)(x - -8)(x - -17/9) = 0\nx - 20/9 = 0\nx - -8 = 0\nx - -17/9 = 0\nx = 20/9\nx = -8\nx = -17/9"} {"input": "Determine x in x^3 - 41/2x^2 + 1001/9x - 3211/18 = 0", "output": "x^3 - 41/2x^2 + 1001/9x - 3211/18 = 0\n(x - 13/3)(x - 19/6)(x - 13) = 0\nx - 13/3 = 0\nx - 19/6 = 0\nx - 13 = 0\nx = 13/3\nx = 19/6\nx = 13"} {"input": "Determine x in x^3 + 153/7x^2 + 258/7x - 40/7 = 0", "output": "x^3 + 153/7x^2 + 258/7x - 40/7 = 0\n(x - -20)(x - -2)(x - 1/7) = 0\nx - -20 = 0\nx - -2 = 0\nx - 1/7 = 0\nx = -20\nx = -2\nx = 1/7"} {"input": "Solve quickly: x^2 - 16x + 48 = 0", "output": "x^2 - 16x + 48 = 0\n(x - 4)(x - 12) = 0\nx - 4 = 0 or x - 12 = 0\nx = 4\nx = 12"} {"input": "Solve quickly: x^2 + 29/15x - 52/5 = 0", "output": "x^2 + 29/15x - 52/5 = 0\n(x - -13/3)(x - 12/5) = 0\nx - -13/3 = 0 or x - 12/5 = 0\nx = -13/3\nx = 12/5"} {"input": "Solve simultaneously:\n3x + 1y = 559/10\n10x + 1y = 1889/10", "output": "3x + 1y = 559/10\n10x + 1y = 1889/10\n\nUsing elimination\n10*(3x + 1y = 559/10)\n3*(10x + 1y = 1889/10)\n30x + 10y = 559\n30x + 3y = 5667/10\nSubtract equations\n7y = -77/10\ny = -77/10/7\ny = -11/10\n\nSubstitute y\n3x + 1(-11/10) = 559/10\n3x = 57\nx = 57/3\nx = 19"} {"input": "Determine x in x^2 + 41/8x + 165/32 = 0", "output": "x^2 + 41/8x + 165/32 = 0\n(x - -11/8)(x - -15/4) = 0\nx - -11/8 = 0 or x - -15/4 = 0\nx = -11/8\nx = -15/4"} {"input": "Find the solution to x^3 + 10/3x^2 - 8/3x = 0", "output": "x^3 + 10/3x^2 - 8/3x = 0\n(x - -4)(x - 0)(x - 2/3) = 0\nx - -4 = 0\nx - 0 = 0\nx - 2/3 = 0\nx = -4\nx = 0\nx = 2/3"} {"input": "Solve simultaneously:\n7x + 4y = -19/6\n3x + 10y = 83/6", "output": "7x + 4y = -19/6\n3x + 10y = 83/6\n\nUsing elimination\n3*(7x + 4y = -19/6)\n7*(3x + 10y = 83/6)\n21x + 12y = -19/2\n21x + 70y = 581/6\nSubtract equations\n-58y = -319/3\ny = -319/3/-58\ny = 11/6\n\nSubstitute y\n7x + 4(11/6) = -19/6\n7x = -21/2\nx = -21/2/7\nx = -3/2"} {"input": "Find x for x^2 - 71/15x + 14/3 = 0", "output": "x^2 - 71/15x + 14/3 = 0\n(x - 10/3)(x - 7/5) = 0\nx - 10/3 = 0 or x - 7/5 = 0\nx = 10/3\nx = 7/5"} {"input": "What value of x satisfies x^3 - 8/3x^2 - 20/3x + 16/3 = 0", "output": "x^3 - 8/3x^2 - 20/3x + 16/3 = 0\n(x - -2)(x - 4)(x - 2/3) = 0\nx - -2 = 0\nx - 4 = 0\nx - 2/3 = 0\nx = -2\nx = 4\nx = 2/3"} {"input": "Solve quickly: x^2 - 7/2x - 9/2 = 0", "output": "x^2 - 7/2x - 9/2 = 0\n(x - 9/2)(x - -1) = 0\nx - 9/2 = 0 or x - -1 = 0\nx = 9/2\nx = -1"} {"input": "Find the solution to 3x + 9 = 0", "output": "3x + 9 = 0\n3x = -9\nx = -9 / 3\nx = -3"} {"input": "Solve the equation x^3 - 1/2x^2 = 0", "output": "x^3 - 1/2x^2 = 0\n(x - 1/2)(x - 0)(x - 0) = 0\nx - 1/2 = 0\nx - 0 = 0\nx - 0 = 0\nx = 1/2\nx = 0\nx = 0"} {"input": "Solve the system:\n1x + 7y = 201/10\n9x + 4y = 521/5", "output": "1x + 7y = 201/10\n9x + 4y = 521/5\n\nUsing elimination\n9*(1x + 7y = 201/10)\n1*(9x + 4y = 521/5)\n9x + 63y = 1809/10\n9x + 4y = 521/5\nSubtract equations\n59y = 767/10\ny = 767/10/59\ny = 13/10\n\nSubstitute y\n1x + 7(13/10) = 201/10\n1x = 11\nx = 11/1\nx = 11"} {"input": "Solve x^2 + 23/4x - 39/8 = 0", "output": "x^2 + 23/4x - 39/8 = 0\n(x - 3/4)(x - -13/2) = 0\nx - 3/4 = 0 or x - -13/2 = 0\nx = 3/4\nx = -13/2"} {"input": "Determine x in x^3 + 8/3x^2 - 11/4x - 21/4 = 0", "output": "x^3 + 8/3x^2 - 11/4x - 21/4 = 0\n(x - -7/6)(x - -3)(x - 3/2) = 0\nx - -7/6 = 0\nx - -3 = 0\nx - 3/2 = 0\nx = -7/6\nx = -3\nx = 3/2"} {"input": "What value of x satisfies x^3 + 85/42x^2 - 122/21x + 11/14 = 0", "output": "x^3 + 85/42x^2 - 122/21x + 11/14 = 0\n(x - 3/2)(x - -11/3)(x - 1/7) = 0\nx - 3/2 = 0\nx - -11/3 = 0\nx - 1/7 = 0\nx = 3/2\nx = -11/3\nx = 1/7"} {"input": "Find the solution to 7x - 7 = 0", "output": "7x - 7 = 0\n7x = 7\nx = 7 / 7\nx = 1"} {"input": "Solve quickly: 4x - 8/3 = 0", "output": "4x - 8/3 = 0\n4x = 8/3\nx = 8/3 / 4\nx = 2/3"} {"input": "Solve quickly: x^2 - 128/35x + 16/7 = 0", "output": "x^2 - 128/35x + 16/7 = 0\n(x - 4/5)(x - 20/7) = 0\nx - 4/5 = 0 or x - 20/7 = 0\nx = 4/5\nx = 20/7"} {"input": "What value of x satisfies x^3 - 5x^2 - 52/9x - 4/3 = 0", "output": "x^3 - 5x^2 - 52/9x - 4/3 = 0\n(x - -1/3)(x - -2/3)(x - 6) = 0\nx - -1/3 = 0\nx - -2/3 = 0\nx - 6 = 0\nx = -1/3\nx = -2/3\nx = 6"} {"input": "Solve the equation x^2 - 19x + 78 = 0", "output": "x^2 - 19x + 78 = 0\n(x - 13)(x - 6) = 0\nx - 13 = 0 or x - 6 = 0\nx = 13\nx = 6"} {"input": "Compute the solution of 6x + 90/7 = 0", "output": "6x + 90/7 = 0\n6x = -90/7\nx = -90/7 / 6\nx = -15/7"} {"input": "Solve the system:\n2x + 8y = -44/3\n7x + 2y = -37/3", "output": "2x + 8y = -44/3\n7x + 2y = -37/3\n\nUsing elimination\n7*(2x + 8y = -44/3)\n2*(7x + 2y = -37/3)\n14x + 56y = -308/3\n14x + 4y = -74/3\nSubtract equations\n52y = -78\ny = -78/52\ny = -3/2\n\nSubstitute y\n2x + 8(-3/2) = -44/3\n2x = -8/3\nx = -8/3/2\nx = -4/3"} {"input": "Solve quickly: x^3 - 163/10x^2 + 647/10x + 68/5 = 0", "output": "x^3 - 163/10x^2 + 647/10x + 68/5 = 0\n(x - 17/2)(x - 8)(x - -1/5) = 0\nx - 17/2 = 0\nx - 8 = 0\nx - -1/5 = 0\nx = 17/2\nx = 8\nx = -1/5"} {"input": "Determine x in 10x - 70/9 = 0", "output": "10x - 70/9 = 0\n10x = 70/9\nx = 70/9 / 10\nx = 7/9"} {"input": "Solve the system:\n3x + 7y = 7/2\n6x + 4y = 7", "output": "3x + 7y = 7/2\n6x + 4y = 7\n\nUsing elimination\n6*(3x + 7y = 7/2)\n3*(6x + 4y = 7)\n18x + 42y = 21\n18x + 12y = 21\nSubtract equations\n30y = 0\ny = 0/30\ny = 0\n\nSubstitute y\n3x + 7(0) = 7/2\n3x = 7/2\nx = 7/2/3\nx = 7/6"} {"input": "Solve quickly: x^3 - 43/4x^2 + 61/4x + 9/2 = 0", "output": "x^3 - 43/4x^2 + 61/4x + 9/2 = 0\n(x - 9)(x - -1/4)(x - 2) = 0\nx - 9 = 0\nx - -1/4 = 0\nx - 2 = 0\nx = 9\nx = -1/4\nx = 2"} {"input": "Solve the system:\n5x + 10y = 75/2\n9x + 2y = -25/2", "output": "5x + 10y = 75/2\n9x + 2y = -25/2\n\nUsing elimination\n9*(5x + 10y = 75/2)\n5*(9x + 2y = -25/2)\n45x + 90y = 675/2\n45x + 10y = -125/2\nSubtract equations\n80y = 400\ny = 400/80\ny = 5\n\nSubstitute y\n5x + 10(5) = 75/2\n5x = -25/2\nx = -25/2/5\nx = -5/2"} {"input": "Solve simultaneously:\n9x + 7y = -125/7\n4x + 1y = -26/7", "output": "9x + 7y = -125/7\n4x + 1y = -26/7\n\nUsing elimination\n4*(9x + 7y = -125/7)\n9*(4x + 1y = -26/7)\n36x + 28y = -500/7\n36x + 9y = -234/7\nSubtract equations\n19y = -38\ny = -38/19\ny = -2\n\nSubstitute y\n9x + 7(-2) = -125/7\n9x = -27/7\nx = -27/7/9\nx = -3/7"} {"input": "Solve the equation x^3 + 182/15x^2 + 3584/75x + 1536/25 = 0", "output": "x^3 + 182/15x^2 + 3584/75x + 1536/25 = 0\n(x - -18/5)(x - -16/5)(x - -16/3) = 0\nx - -18/5 = 0\nx - -16/5 = 0\nx - -16/3 = 0\nx = -18/5\nx = -16/5\nx = -16/3"} {"input": "Find the solution to x^2 - 39/10x + 7/2 = 0", "output": "x^2 - 39/10x + 7/2 = 0\n(x - 7/5)(x - 5/2) = 0\nx - 7/5 = 0 or x - 5/2 = 0\nx = 7/5\nx = 5/2"} {"input": "Find x and y such that\n4x + 3y = 79/6\n7x + 5y = 133/6", "output": "4x + 3y = 79/6\n7x + 5y = 133/6\n\nUsing elimination\n7*(4x + 3y = 79/6)\n4*(7x + 5y = 133/6)\n28x + 21y = 553/6\n28x + 20y = 266/3\nSubtract equations\n1y = 7/2\ny = 7/2/1\ny = 7/2\n\nSubstitute y\n4x + 3(7/2) = 79/6\n4x = 8/3\nx = 8/3/4\nx = 2/3"} {"input": "Solve the equation 2x - 10 = 0", "output": "2x - 10 = 0\n2x = 10\nx = 10 / 2\nx = 5"} {"input": "Solve the equation 10x - 14 = 0", "output": "10x - 14 = 0\n10x = 14\nx = 14 / 10\nx = 7/5"} {"input": "Solve the equations:\n10x + 7y = -203/6\n10x + 2y = -79/3", "output": "10x + 7y = -203/6\n10x + 2y = -79/3\n\nUsing elimination\n10*(10x + 7y = -203/6)\n10*(10x + 2y = -79/3)\n100x + 70y = -1015/3\n100x + 20y = -790/3\nSubtract equations\n50y = -75\ny = -75/50\ny = -3/2\n\nSubstitute y\n10x + 7(-3/2) = -203/6\n10x = -70/3\nx = -70/3/10\nx = -7/3"} {"input": "Find x in x^3 - 95/14x^2 + 1391/112x - 169/56 = 0", "output": "x^3 - 95/14x^2 + 1391/112x - 169/56 = 0\n(x - 13/4)(x - 2/7)(x - 13/4) = 0\nx - 13/4 = 0\nx - 2/7 = 0\nx - 13/4 = 0\nx = 13/4\nx = 2/7\nx = 13/4"} {"input": "Compute the solution of x^2 - 107/70x + 33/70 = 0", "output": "x^2 - 107/70x + 33/70 = 0\n(x - 11/10)(x - 3/7) = 0\nx - 11/10 = 0 or x - 3/7 = 0\nx = 11/10\nx = 3/7"} {"input": "Solve x^2 - 13/5x + 6/5 = 0", "output": "x^2 - 13/5x + 6/5 = 0\n(x - 3/5)(x - 2) = 0\nx - 3/5 = 0 or x - 2 = 0\nx = 3/5\nx = 2"} {"input": "Find x and y such that\n2x + 9y = -80/7\n3x + 10y = -78/7", "output": "2x + 9y = -80/7\n3x + 10y = -78/7\n\nUsing elimination\n3*(2x + 9y = -80/7)\n2*(3x + 10y = -78/7)\n6x + 27y = -240/7\n6x + 20y = -156/7\nSubtract equations\n7y = -12\ny = -12/7\ny = -12/7\n\nSubstitute y\n2x + 9(-12/7) = -80/7\n2x = 4\nx = 4/2\nx = 2"} {"input": "Solve the equation x^2 - 5/6x - 25/18 = 0", "output": "x^2 - 5/6x - 25/18 = 0\n(x - -5/6)(x - 5/3) = 0\nx - -5/6 = 0 or x - 5/3 = 0\nx = -5/6\nx = 5/3"} {"input": "Find x and y such that\n6x + 10y = -38/7\n8x + 9y = 10/7", "output": "6x + 10y = -38/7\n8x + 9y = 10/7\n\nUsing elimination\n8*(6x + 10y = -38/7)\n6*(8x + 9y = 10/7)\n48x + 80y = -304/7\n48x + 54y = 60/7\nSubtract equations\n26y = -52\ny = -52/26\ny = -2\n\nSubstitute y\n6x + 10(-2) = -38/7\n6x = 102/7\nx = 102/7/6\nx = 17/7"} {"input": "Determine x in x^2 - 33/10x - 19/10 = 0", "output": "x^2 - 33/10x - 19/10 = 0\n(x - -1/2)(x - 19/5) = 0\nx - -1/2 = 0 or x - 19/5 = 0\nx = -1/2\nx = 19/5"} {"input": "What value of x satisfies 3x - 9 = 0", "output": "3x - 9 = 0\n3x = 9\nx = 9 / 3\nx = 3"} {"input": "Compute the solution of x^3 - 41/36x^2 - 5/36x = 0", "output": "x^3 - 41/36x^2 - 5/36x = 0\n(x - 5/4)(x - -1/9)(x - 0) = 0\nx - 5/4 = 0\nx - -1/9 = 0\nx - 0 = 0\nx = 5/4\nx = -1/9\nx = 0"} {"input": "Find the solution to x^2 + 7/2x + 3 = 0", "output": "x^2 + 7/2x + 3 = 0\n(x - -2)(x - -3/2) = 0\nx - -2 = 0 or x - -3/2 = 0\nx = -2\nx = -3/2"} {"input": "Find x for x^3 + 13/5x^2 - 13/5x - 21/5 = 0", "output": "x^3 + 13/5x^2 - 13/5x - 21/5 = 0\n(x - -1)(x - 7/5)(x - -3) = 0\nx - -1 = 0\nx - 7/5 = 0\nx - -3 = 0\nx = -1\nx = 7/5\nx = -3"} {"input": "Find the solution to 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Compute the solution of 1x - 1/2 = 0", "output": "1x - 1/2 = 0\n1x = 1/2\nx = 1/2 / 1\nx = 1/2"} {"input": "Find x in x^2 - 26/7x + 24/7 = 0", "output": "x^2 - 26/7x + 24/7 = 0\n(x - 12/7)(x - 2) = 0\nx - 12/7 = 0 or x - 2 = 0\nx = 12/7\nx = 2"} {"input": "What value of x satisfies x^3 + 11/2x^2 + 15/2x = 0", "output": "x^3 + 11/2x^2 + 15/2x = 0\n(x - 0)(x - -3)(x - -5/2) = 0\nx - 0 = 0\nx - -3 = 0\nx - -5/2 = 0\nx = 0\nx = -3\nx = -5/2"} {"input": "Find x in x^3 - 14/5x^2 + 32/25x + 128/125 = 0", "output": "x^3 - 14/5x^2 + 32/25x + 128/125 = 0\n(x - -2/5)(x - 8/5)(x - 8/5) = 0\nx - -2/5 = 0\nx - 8/5 = 0\nx - 8/5 = 0\nx = -2/5\nx = 8/5\nx = 8/5"} {"input": "Find the solution to 1x - 1/2 = 0", "output": "1x - 1/2 = 0\n1x = 1/2\nx = 1/2 / 1\nx = 1/2"} {"input": "Solve the equations:\n4x + 7y = 31/5\n4x + 4y = 34/5", "output": "4x + 7y = 31/5\n4x + 4y = 34/5\n\nUsing elimination\n4*(4x + 7y = 31/5)\n4*(4x + 4y = 34/5)\n16x + 28y = 124/5\n16x + 16y = 136/5\nSubtract equations\n12y = -12/5\ny = -12/5/12\ny = -1/5\n\nSubstitute y\n4x + 7(-1/5) = 31/5\n4x = 38/5\nx = 38/5/4\nx = 19/10"} {"input": "Compute the solution of 5x - 5/8 = 0", "output": "5x - 5/8 = 0\n5x = 5/8\nx = 5/8 / 5\nx = 1/8"} {"input": "Compute the solution of 10x - 25/2 = 0", "output": "10x - 25/2 = 0\n10x = 25/2\nx = 25/2 / 10\nx = 5/4"} {"input": "Compute the solution of x^3 + 7/2x^2 + 17/9x - 35/18 = 0", "output": "x^3 + 7/2x^2 + 17/9x - 35/18 = 0\n(x - -7/3)(x - -5/3)(x - 1/2) = 0\nx - -7/3 = 0\nx - -5/3 = 0\nx - 1/2 = 0\nx = -7/3\nx = -5/3\nx = 1/2"} {"input": "Find x in 6x + 33/2 = 0", "output": "6x + 33/2 = 0\n6x = -33/2\nx = -33/2 / 6\nx = -11/4"} {"input": "Solve the equation 3x + 24 = 0", "output": "3x + 24 = 0\n3x = -24\nx = -24 / 3\nx = -8"} {"input": "What value of x satisfies x^2 - 115/36x + 91/36 = 0", "output": "x^2 - 115/36x + 91/36 = 0\n(x - 7/4)(x - 13/9) = 0\nx - 7/4 = 0 or x - 13/9 = 0\nx = 7/4\nx = 13/9"} {"input": "Find x for 6x - 40/3 = 0", "output": "6x - 40/3 = 0\n6x = 40/3\nx = 40/3 / 6\nx = 20/9"} {"input": "Solve x^2 + 19/5x + 14/5 = 0", "output": "x^2 + 19/5x + 14/5 = 0\n(x - -14/5)(x - -1) = 0\nx - -14/5 = 0 or x - -1 = 0\nx = -14/5\nx = -1"} {"input": "Find the solution to 3x - 9/2 = 0", "output": "3x - 9/2 = 0\n3x = 9/2\nx = 9/2 / 3\nx = 3/2"} {"input": "Solve the system:\n7x + 9y = 87/2\n2x + 5y = 47/3", "output": "7x + 9y = 87/2\n2x + 5y = 47/3\n\nUsing elimination\n2*(7x + 9y = 87/2)\n7*(2x + 5y = 47/3)\n14x + 18y = 87\n14x + 35y = 329/3\nSubtract equations\n-17y = -68/3\ny = -68/3/-17\ny = 4/3\n\nSubstitute y\n7x + 9(4/3) = 87/2\n7x = 63/2\nx = 63/2/7\nx = 9/2"} {"input": "What value of x satisfies 6x + 33 = 0", "output": "6x + 33 = 0\n6x = -33\nx = -33 / 6\nx = -11/2"} {"input": "Find x and y such that\n8x + 2y = -127/10\n10x + 6y = -37/2", "output": "8x + 2y = -127/10\n10x + 6y = -37/2\n\nUsing elimination\n10*(8x + 2y = -127/10)\n8*(10x + 6y = -37/2)\n80x + 20y = -127\n80x + 48y = -148\nSubtract equations\n-28y = 21\ny = 21/-28\ny = -3/4\n\nSubstitute y\n8x + 2(-3/4) = -127/10\n8x = -56/5\nx = -56/5/8\nx = -7/5"} {"input": "Solve simultaneously:\n7x + 10y = 391/10\n9x + 2y = 177/10", "output": "7x + 10y = 391/10\n9x + 2y = 177/10\n\nUsing elimination\n9*(7x + 10y = 391/10)\n7*(9x + 2y = 177/10)\n63x + 90y = 3519/10\n63x + 14y = 1239/10\nSubtract equations\n76y = 228\ny = 228/76\ny = 3\n\nSubstitute y\n7x + 10(3) = 391/10\n7x = 91/10\nx = 91/10/7\nx = 13/10"} {"input": "What value of x satisfies 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "Solve the equations:\n5x + 1y = -59/8\n9x + 1y = -119/8", "output": "5x + 1y = -59/8\n9x + 1y = -119/8\n\nUsing elimination\n9*(5x + 1y = -59/8)\n5*(9x + 1y = -119/8)\n45x + 9y = -531/8\n45x + 5y = -595/8\nSubtract equations\n4y = 8\ny = 8/4\ny = 2\n\nSubstitute y\n5x + 1(2) = -59/8\n5x = -75/8\nx = -75/8/5\nx = -15/8"} {"input": "Solve the system:\n2x + 8y = 48/5\n3x + 3y = 9", "output": "2x + 8y = 48/5\n3x + 3y = 9\n\nUsing elimination\n3*(2x + 8y = 48/5)\n2*(3x + 3y = 9)\n6x + 24y = 144/5\n6x + 6y = 18\nSubtract equations\n18y = 54/5\ny = 54/5/18\ny = 3/5\n\nSubstitute y\n2x + 8(3/5) = 48/5\n2x = 24/5\nx = 24/5/2\nx = 12/5"} {"input": "Find the solution to x^3 + 9/10x^2 - 61/10x + 3/5 = 0", "output": "x^3 + 9/10x^2 - 61/10x + 3/5 = 0\n(x - 1/10)(x - -3)(x - 2) = 0\nx - 1/10 = 0\nx - -3 = 0\nx - 2 = 0\nx = 1/10\nx = -3\nx = 2"} {"input": "Compute the solution of x^3 + 83/42x^2 - 229/42x - 65/21 = 0", "output": "x^3 + 83/42x^2 - 229/42x - 65/21 = 0\n(x - 13/7)(x - -1/2)(x - -10/3) = 0\nx - 13/7 = 0\nx - -1/2 = 0\nx - -10/3 = 0\nx = 13/7\nx = -1/2\nx = -10/3"} {"input": "Determine x in 4x + 24 = 0", "output": "4x + 24 = 0\n4x = -24\nx = -24 / 4\nx = -6"} {"input": "Solve x^3 + 9/8x^2 - 4x - 9/2 = 0", "output": "x^3 + 9/8x^2 - 4x - 9/2 = 0\n(x - 2)(x - -9/8)(x - -2) = 0\nx - 2 = 0\nx - -9/8 = 0\nx - -2 = 0\nx = 2\nx = -9/8\nx = -2"} {"input": "Solve 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Find x in x^3 + 35/3x^2 + 631/36x - 1235/12 = 0", "output": "x^3 + 35/3x^2 + 631/36x - 1235/12 = 0\n(x - -19/3)(x - -15/2)(x - 13/6) = 0\nx - -19/3 = 0\nx - -15/2 = 0\nx - 13/6 = 0\nx = -19/3\nx = -15/2\nx = 13/6"} {"input": "What value of x satisfies x^2 - 59/12x + 6 = 0", "output": "x^2 - 59/12x + 6 = 0\n(x - 8/3)(x - 9/4) = 0\nx - 8/3 = 0 or x - 9/4 = 0\nx = 8/3\nx = 9/4"} {"input": "Compute the solution of x^3 - 19/3x^2 - 302/3x - 280/3 = 0", "output": "x^3 - 19/3x^2 - 302/3x - 280/3 = 0\n(x - 14)(x - -20/3)(x - -1) = 0\nx - 14 = 0\nx - -20/3 = 0\nx - -1 = 0\nx = 14\nx = -20/3\nx = -1"} {"input": "What value of x satisfies 6x + 32 = 0", "output": "6x + 32 = 0\n6x = -32\nx = -32 / 6\nx = -16/3"} {"input": "Solve 7x - 91/6 = 0", "output": "7x - 91/6 = 0\n7x = 91/6\nx = 91/6 / 7\nx = 13/6"} {"input": "Find x in x^3 + 28/3x^2 + 19/9x - 616/9 = 0", "output": "x^3 + 28/3x^2 + 19/9x - 616/9 = 0\n(x - -11/3)(x - 7/3)(x - -8) = 0\nx - -11/3 = 0\nx - 7/3 = 0\nx - -8 = 0\nx = -11/3\nx = 7/3\nx = -8"} {"input": "Solve the equation x^3 + 15/4x^2 - 351/8x + 243/8 = 0", "output": "x^3 + 15/4x^2 - 351/8x + 243/8 = 0\n(x - 3/4)(x - -9)(x - 9/2) = 0\nx - 3/4 = 0\nx - -9 = 0\nx - 9/2 = 0\nx = 3/4\nx = -9\nx = 9/2"} {"input": "Solve the system:\n9x + 3y = -145/6\n2x + 1y = -50/9", "output": "9x + 3y = -145/6\n2x + 1y = -50/9\n\nUsing elimination\n2*(9x + 3y = -145/6)\n9*(2x + 1y = -50/9)\n18x + 6y = -145/3\n18x + 9y = -50\nSubtract equations\n-3y = 5/3\ny = 5/3/-3\ny = -5/9\n\nSubstitute y\n9x + 3(-5/9) = -145/6\n9x = -45/2\nx = -45/2/9\nx = -5/2"} {"input": "Find the solution to x^3 - 61/12x^2 + 149/24x - 5/4 = 0", "output": "x^3 - 61/12x^2 + 149/24x - 5/4 = 0\n(x - 10/3)(x - 1/4)(x - 3/2) = 0\nx - 10/3 = 0\nx - 1/4 = 0\nx - 3/2 = 0\nx = 10/3\nx = 1/4\nx = 3/2"} {"input": "Determine x in 1x + 5/3 = 0", "output": "1x + 5/3 = 0\n1x = -5/3\nx = -5/3 / 1\nx = -5/3"} {"input": "Find x in x^3 + 6/7x^2 - 37/7x + 24/7 = 0", "output": "x^3 + 6/7x^2 - 37/7x + 24/7 = 0\n(x - 1)(x - 8/7)(x - -3) = 0\nx - 1 = 0\nx - 8/7 = 0\nx - -3 = 0\nx = 1\nx = 8/7\nx = -3"} {"input": "Solve quickly: x^3 - 1/8x^2 - 269/400x + 9/40 = 0", "output": "x^3 - 1/8x^2 - 269/400x + 9/40 = 0\n(x - 5/8)(x - -9/10)(x - 2/5) = 0\nx - 5/8 = 0\nx - -9/10 = 0\nx - 2/5 = 0\nx = 5/8\nx = -9/10\nx = 2/5"} {"input": "What value of x satisfies x^2 + 25x + 136 = 0", "output": "x^2 + 25x + 136 = 0\n(x - -17)(x - -8) = 0\nx - -17 = 0 or x - -8 = 0\nx = -17\nx = -8"} {"input": "Solve x^3 - 45/28x^2 - 375/56x + 125/14 = 0", "output": "x^3 - 45/28x^2 - 375/56x + 125/14 = 0\n(x - -5/2)(x - 20/7)(x - 5/4) = 0\nx - -5/2 = 0\nx - 20/7 = 0\nx - 5/4 = 0\nx = -5/2\nx = 20/7\nx = 5/4"} {"input": "Solve quickly: x^3 + 203/12x^2 + 287/24x - 130/3 = 0", "output": "x^3 + 203/12x^2 + 287/24x - 130/3 = 0\n(x - -13/6)(x - 5/4)(x - -16) = 0\nx - -13/6 = 0\nx - 5/4 = 0\nx - -16 = 0\nx = -13/6\nx = 5/4\nx = -16"} {"input": "Solve x^3 + 121/45x^2 + 31/36x - 221/180 = 0", "output": "x^3 + 121/45x^2 + 31/36x - 221/180 = 0\n(x - -17/9)(x - 1/2)(x - -13/10) = 0\nx - -17/9 = 0\nx - 1/2 = 0\nx - -13/10 = 0\nx = -17/9\nx = 1/2\nx = -13/10"} {"input": "Find the solution to x^2 - 11/7x - 6/7 = 0", "output": "x^2 - 11/7x - 6/7 = 0\n(x - -3/7)(x - 2) = 0\nx - -3/7 = 0 or x - 2 = 0\nx = -3/7\nx = 2"} {"input": "Find x for 3x + 7 = 0", "output": "3x + 7 = 0\n3x = -7\nx = -7 / 3\nx = -7/3"} {"input": "Determine x in x^3 - 31/10x^2 - 651/10x + 108 = 0", "output": "x^3 - 31/10x^2 - 651/10x + 108 = 0\n(x - 9)(x - 8/5)(x - -15/2) = 0\nx - 9 = 0\nx - 8/5 = 0\nx - -15/2 = 0\nx = 9\nx = 8/5\nx = -15/2"} {"input": "Determine x in x^3 + 23/6x^2 - 35/9x - 4 = 0", "output": "x^3 + 23/6x^2 - 35/9x - 4 = 0\n(x - -2/3)(x - 4/3)(x - -9/2) = 0\nx - -2/3 = 0\nx - 4/3 = 0\nx - -9/2 = 0\nx = -2/3\nx = 4/3\nx = -9/2"} {"input": "Find x for x^2 + 29/5x - 88/5 = 0", "output": "x^2 + 29/5x - 88/5 = 0\n(x - 11/5)(x - -8) = 0\nx - 11/5 = 0 or x - -8 = 0\nx = 11/5\nx = -8"} {"input": "Find the solution to 2x - 11/3 = 0", "output": "2x - 11/3 = 0\n2x = 11/3\nx = 11/3 / 2\nx = 11/6"} {"input": "Find x for x^3 - 103/20x^2 + 17/4x + 7/5 = 0", "output": "x^3 - 103/20x^2 + 17/4x + 7/5 = 0\n(x - -1/4)(x - 7/5)(x - 4) = 0\nx - -1/4 = 0\nx - 7/5 = 0\nx - 4 = 0\nx = -1/4\nx = 7/5\nx = 4"} {"input": "Solve 9x + 1 = 0", "output": "9x + 1 = 0\n9x = -1\nx = -1 / 9\nx = -1/9"} {"input": "Solve the equation 9x - 63/8 = 0", "output": "9x - 63/8 = 0\n9x = 63/8\nx = 63/8 / 9\nx = 7/8"} {"input": "Solve 6x + 48/5 = 0", "output": "6x + 48/5 = 0\n6x = -48/5\nx = -48/5 / 6\nx = -8/5"} {"input": "Find the solution to x^3 - 23/5x^2 + 146/25x - 56/25 = 0", "output": "x^3 - 23/5x^2 + 146/25x - 56/25 = 0\n(x - 1)(x - 4/5)(x - 14/5) = 0\nx - 1 = 0\nx - 4/5 = 0\nx - 14/5 = 0\nx = 1\nx = 4/5\nx = 14/5"} {"input": "Find x for 9x + 15 = 0", "output": "9x + 15 = 0\n9x = -15\nx = -15 / 9\nx = -5/3"} {"input": "Solve the equation 6x + 108/7 = 0", "output": "6x + 108/7 = 0\n6x = -108/7\nx = -108/7 / 6\nx = -18/7"} {"input": "Find x and y such that\n3x + 6y = -73/7\n5x + 9y = -332/21", "output": "3x + 6y = -73/7\n5x + 9y = -332/21\n\nUsing elimination\n5*(3x + 6y = -73/7)\n3*(5x + 9y = -332/21)\n15x + 30y = -365/7\n15x + 27y = -332/7\nSubtract equations\n3y = -33/7\ny = -33/7/3\ny = -11/7\n\nSubstitute y\n3x + 6(-11/7) = -73/7\n3x = -1\nx = -1/3\nx = -1/3"} {"input": "Find the solution to x^2 + 80/7x + 153/7 = 0", "output": "x^2 + 80/7x + 153/7 = 0\n(x - -17/7)(x - -9) = 0\nx - -17/7 = 0 or x - -9 = 0\nx = -17/7\nx = -9"} {"input": "Determine x in x^2 - 10x + 24 = 0", "output": "x^2 - 10x + 24 = 0\n(x - 4)(x - 6) = 0\nx - 4 = 0 or x - 6 = 0\nx = 4\nx = 6"} {"input": "Solve the system:\n9x + 10y = -321/4\n3x + 4y = -27", "output": "9x + 10y = -321/4\n3x + 4y = -27\n\nUsing elimination\n3*(9x + 10y = -321/4)\n9*(3x + 4y = -27)\n27x + 30y = -963/4\n27x + 36y = -243\nSubtract equations\n-6y = 9/4\ny = 9/4/-6\ny = -3/8\n\nSubstitute y\n9x + 10(-3/8) = -321/4\n9x = -153/2\nx = -153/2/9\nx = -17/2"} {"input": "Find x for 3x + 33/5 = 0", "output": "3x + 33/5 = 0\n3x = -33/5\nx = -33/5 / 3\nx = -11/5"} {"input": "Find the solution to 6x + 18/5 = 0", "output": "6x + 18/5 = 0\n6x = -18/5\nx = -18/5 / 6\nx = -3/5"} {"input": "Compute the solution of 7x + 91/8 = 0", "output": "7x + 91/8 = 0\n7x = -91/8\nx = -91/8 / 7\nx = -13/8"} {"input": "Solve the system:\n8x + 8y = 276/5\n10x + 3y = 34", "output": "8x + 8y = 276/5\n10x + 3y = 34\n\nUsing elimination\n10*(8x + 8y = 276/5)\n8*(10x + 3y = 34)\n80x + 80y = 552\n80x + 24y = 272\nSubtract equations\n56y = 280\ny = 280/56\ny = 5\n\nSubstitute y\n8x + 8(5) = 276/5\n8x = 76/5\nx = 76/5/8\nx = 19/10"} {"input": "Determine x in 8x - 12 = 0", "output": "8x - 12 = 0\n8x = 12\nx = 12 / 8\nx = 3/2"} {"input": "Determine x in x^3 - 381/35x^2 + 198/35x + 32 = 0", "output": "x^3 - 381/35x^2 + 198/35x + 32 = 0\n(x - -7/5)(x - 10)(x - 16/7) = 0\nx - -7/5 = 0\nx - 10 = 0\nx - 16/7 = 0\nx = -7/5\nx = 10\nx = 16/7"} {"input": "Solve the equation x^3 - 7/2x^2 - 153/4x + 495/8 = 0", "output": "x^3 - 7/2x^2 - 153/4x + 495/8 = 0\n(x - 3/2)(x - 15/2)(x - -11/2) = 0\nx - 3/2 = 0\nx - 15/2 = 0\nx - -11/2 = 0\nx = 3/2\nx = 15/2\nx = -11/2"} {"input": "Compute the solution of x^2 + 17/8x + 9/8 = 0", "output": "x^2 + 17/8x + 9/8 = 0\n(x - -1)(x - -9/8) = 0\nx - -1 = 0 or x - -9/8 = 0\nx = -1\nx = -9/8"} {"input": "What value of x satisfies 9x - 117/5 = 0", "output": "9x - 117/5 = 0\n9x = 117/5\nx = 117/5 / 9\nx = 13/5"} {"input": "Find x and y such that\n2x + 5y = 67/10\n1x + 7y = 83/10", "output": "2x + 5y = 67/10\n1x + 7y = 83/10\n\nUsing elimination\n1*(2x + 5y = 67/10)\n2*(1x + 7y = 83/10)\n2x + 5y = 67/10\n2x + 14y = 83/5\nSubtract equations\n-9y = -99/10\ny = -99/10/-9\ny = 11/10\n\nSubstitute y\n2x + 5(11/10) = 67/10\n2x = 6/5\nx = 6/5/2\nx = 3/5"} {"input": "Solve the equations:\n6x + 3y = 20\n1x + 10y = 67/3", "output": "6x + 3y = 20\n1x + 10y = 67/3\n\nUsing elimination\n1*(6x + 3y = 20)\n6*(1x + 10y = 67/3)\n6x + 3y = 20\n6x + 60y = 134\nSubtract equations\n-57y = -114\ny = -114/-57\ny = 2\n\nSubstitute y\n6x + 3(2) = 20\n6x = 14\nx = 14/6\nx = 7/3"} {"input": "Determine x in x^2 - 15/2x + 14 = 0", "output": "x^2 - 15/2x + 14 = 0\n(x - 7/2)(x - 4) = 0\nx - 7/2 = 0 or x - 4 = 0\nx = 7/2\nx = 4"} {"input": "Find x in x^3 + 395/126x^2 - 43/63x - 715/126 = 0", "output": "x^3 + 395/126x^2 - 43/63x - 715/126 = 0\n(x - -13/7)(x - 11/9)(x - -5/2) = 0\nx - -13/7 = 0\nx - 11/9 = 0\nx - -5/2 = 0\nx = -13/7\nx = 11/9\nx = -5/2"} {"input": "Find the solution to x^2 + 13/4x + 5/2 = 0", "output": "x^2 + 13/4x + 5/2 = 0\n(x - -2)(x - -5/4) = 0\nx - -2 = 0 or x - -5/4 = 0\nx = -2\nx = -5/4"} {"input": "Find x and y such that\n5x + 1y = -47/8\n5x + 2y = -11/2", "output": "5x + 1y = -47/8\n5x + 2y = -11/2\n\nUsing elimination\n5*(5x + 1y = -47/8)\n5*(5x + 2y = -11/2)\n25x + 5y = -235/8\n25x + 10y = -55/2\nSubtract equations\n-5y = -15/8\ny = -15/8/-5\ny = 3/8\n\nSubstitute y\n5x + 1(3/8) = -47/8\n5x = -25/4\nx = -25/4/5\nx = -5/4"} {"input": "Find x in 8x - 112/3 = 0", "output": "8x - 112/3 = 0\n8x = 112/3\nx = 112/3 / 8\nx = 14/3"} {"input": "Find x in x^2 + 137/24x + 95/12 = 0", "output": "x^2 + 137/24x + 95/12 = 0\n(x - -19/8)(x - -10/3) = 0\nx - -19/8 = 0 or x - -10/3 = 0\nx = -19/8\nx = -10/3"} {"input": "Find the solution to x^2 - 27/2x + 81/2 = 0", "output": "x^2 - 27/2x + 81/2 = 0\n(x - 9)(x - 9/2) = 0\nx - 9 = 0 or x - 9/2 = 0\nx = 9\nx = 9/2"} {"input": "Find the solution to x^3 + 121/60x^2 - 161/30x + 6/5 = 0", "output": "x^3 + 121/60x^2 - 161/30x + 6/5 = 0\n(x - 1/4)(x - 4/3)(x - -18/5) = 0\nx - 1/4 = 0\nx - 4/3 = 0\nx - -18/5 = 0\nx = 1/4\nx = 4/3\nx = -18/5"} {"input": "Determine x in x^3 - 110/9x^2 + 233/9x + 28 = 0", "output": "x^3 - 110/9x^2 + 233/9x + 28 = 0\n(x - -7/9)(x - 4)(x - 9) = 0\nx - -7/9 = 0\nx - 4 = 0\nx - 9 = 0\nx = -7/9\nx = 4\nx = 9"} {"input": "What value of x satisfies 10x - 80/3 = 0", "output": "10x - 80/3 = 0\n10x = 80/3\nx = 80/3 / 10\nx = 8/3"} {"input": "Solve the equations:\n7x + 9y = -279/2\n6x + 1y = 8", "output": "7x + 9y = -279/2\n6x + 1y = 8\n\nUsing elimination\n6*(7x + 9y = -279/2)\n7*(6x + 1y = 8)\n42x + 54y = -837\n42x + 7y = 56\nSubtract equations\n47y = -893\ny = -893/47\ny = -19\n\nSubstitute y\n7x + 9(-19) = -279/2\n7x = 63/2\nx = 63/2/7\nx = 9/2"} {"input": "Solve 9x + 21/2 = 0", "output": "9x + 21/2 = 0\n9x = -21/2\nx = -21/2 / 9\nx = -7/6"} {"input": "Find x for x^2 - 121/63x - 10/21 = 0", "output": "x^2 - 121/63x - 10/21 = 0\n(x - -2/9)(x - 15/7) = 0\nx - -2/9 = 0 or x - 15/7 = 0\nx = -2/9\nx = 15/7"} {"input": "Find x for x^2 + 110/9x + 200/9 = 0", "output": "x^2 + 110/9x + 200/9 = 0\n(x - -10)(x - -20/9) = 0\nx - -10 = 0 or x - -20/9 = 0\nx = -10\nx = -20/9"} {"input": "Solve quickly: 8x + 16/9 = 0", "output": "8x + 16/9 = 0\n8x = -16/9\nx = -16/9 / 8\nx = -2/9"} {"input": "Solve simultaneously:\n8x + 5y = 50\n1x + 7y = 191/2", "output": "8x + 5y = 50\n1x + 7y = 191/2\n\nUsing elimination\n1*(8x + 5y = 50)\n8*(1x + 7y = 191/2)\n8x + 5y = 50\n8x + 56y = 764\nSubtract equations\n-51y = -714\ny = -714/-51\ny = 14\n\nSubstitute y\n8x + 5(14) = 50\n8x = -20\nx = -20/8\nx = -5/2"} {"input": "Compute the solution of x^3 - 50/3x^2 - 79/3x + 42 = 0", "output": "x^3 - 50/3x^2 - 79/3x + 42 = 0\n(x - 1)(x - 18)(x - -7/3) = 0\nx - 1 = 0\nx - 18 = 0\nx - -7/3 = 0\nx = 1\nx = 18\nx = -7/3"} {"input": "Solve quickly: 5x + 50 = 0", "output": "5x + 50 = 0\n5x = -50\nx = -50 / 5\nx = -10"} {"input": "What value of x satisfies 4x - 44 = 0", "output": "4x - 44 = 0\n4x = 44\nx = 44 / 4\nx = 11"} {"input": "Compute the solution of x^3 - 41/9x^2 - 1297/36x + 85/4 = 0", "output": "x^3 - 41/9x^2 - 1297/36x + 85/4 = 0\n(x - 17/2)(x - 5/9)(x - -9/2) = 0\nx - 17/2 = 0\nx - 5/9 = 0\nx - -9/2 = 0\nx = 17/2\nx = 5/9\nx = -9/2"} {"input": "Solve x^3 + 1/3x^2 - 34/3x + 40/3 = 0", "output": "x^3 + 1/3x^2 - 34/3x + 40/3 = 0\n(x - 2)(x - -4)(x - 5/3) = 0\nx - 2 = 0\nx - -4 = 0\nx - 5/3 = 0\nx = 2\nx = -4\nx = 5/3"} {"input": "Compute the solution of 9x + 81/5 = 0", "output": "9x + 81/5 = 0\n9x = -81/5\nx = -81/5 / 9\nx = -9/5"} {"input": "Find x for 2x - 16/5 = 0", "output": "2x - 16/5 = 0\n2x = 16/5\nx = 16/5 / 2\nx = 8/5"} {"input": "Solve the equation x^3 + 59/24x^2 - 23/2x - 117/8 = 0", "output": "x^3 + 59/24x^2 - 23/2x - 117/8 = 0\n(x - -13/3)(x - 3)(x - -9/8) = 0\nx - -13/3 = 0\nx - 3 = 0\nx - -9/8 = 0\nx = -13/3\nx = 3\nx = -9/8"} {"input": "Solve the equations:\n4x + 7y = 197/7\n9x + 7y = 277/7", "output": "4x + 7y = 197/7\n9x + 7y = 277/7\n\nUsing elimination\n9*(4x + 7y = 197/7)\n4*(9x + 7y = 277/7)\n36x + 63y = 1773/7\n36x + 28y = 1108/7\nSubtract equations\n35y = 95\ny = 95/35\ny = 19/7\n\nSubstitute y\n4x + 7(19/7) = 197/7\n4x = 64/7\nx = 64/7/4\nx = 16/7"} {"input": "Find the solution to 7x - 21/2 = 0", "output": "7x - 21/2 = 0\n7x = 21/2\nx = 21/2 / 7\nx = 3/2"} {"input": "Find x in x^3 + 23/2x^2 + 10x - 225/2 = 0", "output": "x^3 + 23/2x^2 + 10x - 225/2 = 0\n(x - -9)(x - 5/2)(x - -5) = 0\nx - -9 = 0\nx - 5/2 = 0\nx - -5 = 0\nx = -9\nx = 5/2\nx = -5"} {"input": "Find x in x^3 - 419/120x^2 + 145/48x - 13/40 = 0", "output": "x^3 - 419/120x^2 + 145/48x - 13/40 = 0\n(x - 13/6)(x - 6/5)(x - 1/8) = 0\nx - 13/6 = 0\nx - 6/5 = 0\nx - 1/8 = 0\nx = 13/6\nx = 6/5\nx = 1/8"} {"input": "Solve the equation 10x - 1 = 0", "output": "10x - 1 = 0\n10x = 1\nx = 1 / 10\nx = 1/10"} {"input": "Solve 4x - 68/5 = 0", "output": "4x - 68/5 = 0\n4x = 68/5\nx = 68/5 / 4\nx = 17/5"} {"input": "Compute the solution of 3x + 27/5 = 0", "output": "3x + 27/5 = 0\n3x = -27/5\nx = -27/5 / 3\nx = -9/5"} {"input": "Solve the equation x^2 - 25/4 = 0", "output": "x^2 - 25/4 = 0\n(x - 5/2)(x - -5/2) = 0\nx - 5/2 = 0 or x - -5/2 = 0\nx = 5/2\nx = -5/2"} {"input": "Solve the equation x^3 - 43/70x^2 - 264/35x - 459/70 = 0", "output": "x^3 - 43/70x^2 - 264/35x - 459/70 = 0\n(x - -9/7)(x - 17/5)(x - -3/2) = 0\nx - -9/7 = 0\nx - 17/5 = 0\nx - -3/2 = 0\nx = -9/7\nx = 17/5\nx = -3/2"} {"input": "Compute the solution of x^3 - 449/42x^2 + 632/21x - 130/7 = 0", "output": "x^3 - 449/42x^2 + 632/21x - 130/7 = 0\n(x - 6/7)(x - 13/2)(x - 10/3) = 0\nx - 6/7 = 0\nx - 13/2 = 0\nx - 10/3 = 0\nx = 6/7\nx = 13/2\nx = 10/3"} {"input": "Find the solution to x^3 + 109/60x^2 - 123/40x - 133/24 = 0", "output": "x^3 + 109/60x^2 - 123/40x - 133/24 = 0\n(x - 7/4)(x - -5/3)(x - -19/10) = 0\nx - 7/4 = 0\nx - -5/3 = 0\nx - -19/10 = 0\nx = 7/4\nx = -5/3\nx = -19/10"} {"input": "Solve the system:\n5x + 10y = 45/2\n9x + 5y = 71/4", "output": "5x + 10y = 45/2\n9x + 5y = 71/4\n\nUsing elimination\n9*(5x + 10y = 45/2)\n5*(9x + 5y = 71/4)\n45x + 90y = 405/2\n45x + 25y = 355/4\nSubtract equations\n65y = 455/4\ny = 455/4/65\ny = 7/4\n\nSubstitute y\n5x + 10(7/4) = 45/2\n5x = 5\nx = 5/5\nx = 1"} {"input": "Compute the solution of x^2 - 13x - 14 = 0", "output": "x^2 - 13x - 14 = 0\n(x - 14)(x - -1) = 0\nx - 14 = 0 or x - -1 = 0\nx = 14\nx = -1"} {"input": "Find the solution to 4x + 20 = 0", "output": "4x + 20 = 0\n4x = -20\nx = -20 / 4\nx = -5"} {"input": "Solve the system:\n7x + 6y = 9/8\n7x + 7y = 7/8", "output": "7x + 6y = 9/8\n7x + 7y = 7/8\n\nUsing elimination\n7*(7x + 6y = 9/8)\n7*(7x + 7y = 7/8)\n49x + 42y = 63/8\n49x + 49y = 49/8\nSubtract equations\n-7y = 7/4\ny = 7/4/-7\ny = -1/4\n\nSubstitute y\n7x + 6(-1/4) = 9/8\n7x = 21/8\nx = 21/8/7\nx = 3/8"} {"input": "Find the solution to x^2 - 3/7x - 88/49 = 0", "output": "x^2 - 3/7x - 88/49 = 0\n(x - -8/7)(x - 11/7) = 0\nx - -8/7 = 0 or x - 11/7 = 0\nx = -8/7\nx = 11/7"} {"input": "Solve the system:\n2x + 4y = 0\n5x + 4y = -6", "output": "2x + 4y = 0\n5x + 4y = -6\n\nUsing elimination\n5*(2x + 4y = 0)\n2*(5x + 4y = -6)\n10x + 20y = 0\n10x + 8y = -12\nSubtract equations\n12y = 12\ny = 12/12\ny = 1\n\nSubstitute y\n2x + 4(1) = 0\n2x = -4\nx = -4/2\nx = -2"} {"input": "Solve the system:\n8x + 5y = 28\n10x + 9y = 46", "output": "8x + 5y = 28\n10x + 9y = 46\n\nUsing elimination\n10*(8x + 5y = 28)\n8*(10x + 9y = 46)\n80x + 50y = 280\n80x + 72y = 368\nSubtract equations\n-22y = -88\ny = -88/-22\ny = 4\n\nSubstitute y\n8x + 5(4) = 28\n8x = 8\nx = 8/8\nx = 1"} {"input": "Solve x^3 + 21/4x^2 + 1/2x - 15/4 = 0", "output": "x^3 + 21/4x^2 + 1/2x - 15/4 = 0\n(x - -1)(x - 3/4)(x - -5) = 0\nx - -1 = 0\nx - 3/4 = 0\nx - -5 = 0\nx = -1\nx = 3/4\nx = -5"} {"input": "Solve simultaneously:\n7x + 4y = -209/2\n10x + 6y = -595/4", "output": "7x + 4y = -209/2\n10x + 6y = -595/4\n\nUsing elimination\n10*(7x + 4y = -209/2)\n7*(10x + 6y = -595/4)\n70x + 40y = -1045\n70x + 42y = -4165/4\nSubtract equations\n-2y = -15/4\ny = -15/4/-2\ny = 15/8\n\nSubstitute y\n7x + 4(15/8) = -209/2\n7x = -112\nx = -112/7\nx = -16"} {"input": "Find x for x^2 - 11/12x - 5/12 = 0", "output": "x^2 - 11/12x - 5/12 = 0\n(x - -1/3)(x - 5/4) = 0\nx - -1/3 = 0 or x - 5/4 = 0\nx = -1/3\nx = 5/4"} {"input": "Compute the solution of 6x + 114/5 = 0", "output": "6x + 114/5 = 0\n6x = -114/5\nx = -114/5 / 6\nx = -19/5"} {"input": "Solve the equation x^3 - 97/30x^2 + 59/30x - 1/3 = 0", "output": "x^3 - 97/30x^2 + 59/30x - 1/3 = 0\n(x - 5/2)(x - 2/5)(x - 1/3) = 0\nx - 5/2 = 0\nx - 2/5 = 0\nx - 1/3 = 0\nx = 5/2\nx = 2/5\nx = 1/3"} {"input": "Solve the system:\n7x + 8y = 64/3\n10x + 8y = 67/3", "output": "7x + 8y = 64/3\n10x + 8y = 67/3\n\nUsing elimination\n10*(7x + 8y = 64/3)\n7*(10x + 8y = 67/3)\n70x + 80y = 640/3\n70x + 56y = 469/3\nSubtract equations\n24y = 57\ny = 57/24\ny = 19/8\n\nSubstitute y\n7x + 8(19/8) = 64/3\n7x = 7/3\nx = 7/3/7\nx = 1/3"} {"input": "Find the solution to 10x - 24 = 0", "output": "10x - 24 = 0\n10x = 24\nx = 24 / 10\nx = 12/5"} {"input": "Find the solution to x^3 - 118/21x^2 + 104/21x + 128/21 = 0", "output": "x^3 - 118/21x^2 + 104/21x + 128/21 = 0\n(x - 16/7)(x - 4)(x - -2/3) = 0\nx - 16/7 = 0\nx - 4 = 0\nx - -2/3 = 0\nx = 16/7\nx = 4\nx = -2/3"} {"input": "Find x and y such that\n4x + 9y = 11/6\n1x + 6y = 7/3", "output": "4x + 9y = 11/6\n1x + 6y = 7/3\n\nUsing elimination\n1*(4x + 9y = 11/6)\n4*(1x + 6y = 7/3)\n4x + 9y = 11/6\n4x + 24y = 28/3\nSubtract equations\n-15y = -15/2\ny = -15/2/-15\ny = 1/2\n\nSubstitute y\n4x + 9(1/2) = 11/6\n4x = -8/3\nx = -8/3/4\nx = -2/3"} {"input": "Find x and y such that\n7x + 3y = 25\n2x + 3y = 95/7", "output": "7x + 3y = 25\n2x + 3y = 95/7\n\nUsing elimination\n2*(7x + 3y = 25)\n7*(2x + 3y = 95/7)\n14x + 6y = 50\n14x + 21y = 95\nSubtract equations\n-15y = -45\ny = -45/-15\ny = 3\n\nSubstitute y\n7x + 3(3) = 25\n7x = 16\nx = 16/7\nx = 16/7"} {"input": "Find x for 2x + 5 = 0", "output": "2x + 5 = 0\n2x = -5\nx = -5 / 2\nx = -5/2"} {"input": "Solve the equation x^2 - 29/6x - 5/6 = 0", "output": "x^2 - 29/6x - 5/6 = 0\n(x - 5)(x - -1/6) = 0\nx - 5 = 0 or x - -1/6 = 0\nx = 5\nx = -1/6"} {"input": "Find x for x^2 - 16/15x - 7/15 = 0", "output": "x^2 - 16/15x - 7/15 = 0\n(x - -1/3)(x - 7/5) = 0\nx - -1/3 = 0 or x - 7/5 = 0\nx = -1/3\nx = 7/5"} {"input": "Solve the system:\n9x + 9y = 378/5\n2x + 5y = 12", "output": "9x + 9y = 378/5\n2x + 5y = 12\n\nUsing elimination\n2*(9x + 9y = 378/5)\n9*(2x + 5y = 12)\n18x + 18y = 756/5\n18x + 45y = 108\nSubtract equations\n-27y = 216/5\ny = 216/5/-27\ny = -8/5\n\nSubstitute y\n9x + 9(-8/5) = 378/5\n9x = 90\nx = 90/9\nx = 10"} {"input": "Find x for x^2 + 13/5x + 6/5 = 0", "output": "x^2 + 13/5x + 6/5 = 0\n(x - -2)(x - -3/5) = 0\nx - -2 = 0 or x - -3/5 = 0\nx = -2\nx = -3/5"} {"input": "Solve the equation x^2 - 7/10x + 1/10 = 0", "output": "x^2 - 7/10x + 1/10 = 0\n(x - 1/2)(x - 1/5) = 0\nx - 1/2 = 0 or x - 1/5 = 0\nx = 1/2\nx = 1/5"} {"input": "What value of x satisfies 6x + 6 = 0", "output": "6x + 6 = 0\n6x = -6\nx = -6 / 6\nx = -1"} {"input": "What value of x satisfies x^3 + 239/35x^2 - 352/35x - 192/35 = 0", "output": "x^3 + 239/35x^2 - 352/35x - 192/35 = 0\n(x - 8/5)(x - -8)(x - -3/7) = 0\nx - 8/5 = 0\nx - -8 = 0\nx - -3/7 = 0\nx = 8/5\nx = -8\nx = -3/7"} {"input": "Solve x^3 + 1/2x^2 - 71/16x - 63/16 = 0", "output": "x^3 + 1/2x^2 - 71/16x - 63/16 = 0\n(x - 9/4)(x - -7/4)(x - -1) = 0\nx - 9/4 = 0\nx - -7/4 = 0\nx - -1 = 0\nx = 9/4\nx = -7/4\nx = -1"} {"input": "Find x for 2x + 10 = 0", "output": "2x + 10 = 0\n2x = -10\nx = -10 / 2\nx = -5"} {"input": "Find x for 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Solve the equation x^3 + 11/4x^2 + 29/64x - 133/128 = 0", "output": "x^3 + 11/4x^2 + 29/64x - 133/128 = 0\n(x - 1/2)(x - -19/8)(x - -7/8) = 0\nx - 1/2 = 0\nx - -19/8 = 0\nx - -7/8 = 0\nx = 1/2\nx = -19/8\nx = -7/8"} {"input": "What value of x satisfies x^2 + 41/4x + 45/4 = 0", "output": "x^2 + 41/4x + 45/4 = 0\n(x - -9)(x - -5/4) = 0\nx - -9 = 0 or x - -5/4 = 0\nx = -9\nx = -5/4"} {"input": "Find the solution to 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "Solve x^3 + 415/84x^2 + 91/12x + 7/2 = 0", "output": "x^3 + 415/84x^2 + 91/12x + 7/2 = 0\n(x - -6/7)(x - -7/4)(x - -7/3) = 0\nx - -6/7 = 0\nx - -7/4 = 0\nx - -7/3 = 0\nx = -6/7\nx = -7/4\nx = -7/3"} {"input": "Find the solution to 6x - 42/5 = 0", "output": "6x - 42/5 = 0\n6x = 42/5\nx = 42/5 / 6\nx = 7/5"} {"input": "Solve the equation 8x - 48/7 = 0", "output": "8x - 48/7 = 0\n8x = 48/7\nx = 48/7 / 8\nx = 6/7"} {"input": "Solve x^3 + 379/90x^2 + 89/18x + 5/3 = 0", "output": "x^3 + 379/90x^2 + 89/18x + 5/3 = 0\n(x - -10/9)(x - -5/2)(x - -3/5) = 0\nx - -10/9 = 0\nx - -5/2 = 0\nx - -3/5 = 0\nx = -10/9\nx = -5/2\nx = -3/5"} {"input": "Find x for x^2 - 32/5x + 12/5 = 0", "output": "x^2 - 32/5x + 12/5 = 0\n(x - 2/5)(x - 6) = 0\nx - 2/5 = 0 or x - 6 = 0\nx = 2/5\nx = 6"} {"input": "Find x in 1x - 17 = 0", "output": "1x - 17 = 0\n1x = 17\nx = 17 / 1\nx = 17"} {"input": "Find x and y such that\n9x + 6y = 165/4\n8x + 4y = 71/2", "output": "9x + 6y = 165/4\n8x + 4y = 71/2\n\nUsing elimination\n8*(9x + 6y = 165/4)\n9*(8x + 4y = 71/2)\n72x + 48y = 330\n72x + 36y = 639/2\nSubtract equations\n12y = 21/2\ny = 21/2/12\ny = 7/8\n\nSubstitute y\n9x + 6(7/8) = 165/4\n9x = 36\nx = 36/9\nx = 4"} {"input": "Determine x in x^3 - 7/10x^2 - 61/2x - 234/5 = 0", "output": "x^3 - 7/10x^2 - 61/2x - 234/5 = 0\n(x - -9/5)(x - 13/2)(x - -4) = 0\nx - -9/5 = 0\nx - 13/2 = 0\nx - -4 = 0\nx = -9/5\nx = 13/2\nx = -4"} {"input": "Find x and y such that\n5x + 4y = 75/4\n7x + 7y = 105/4", "output": "5x + 4y = 75/4\n7x + 7y = 105/4\n\nUsing elimination\n7*(5x + 4y = 75/4)\n5*(7x + 7y = 105/4)\n35x + 28y = 525/4\n35x + 35y = 525/4\nSubtract equations\n-7y = 0\ny = 0/-7\ny = 0\n\nSubstitute y\n5x + 4(0) = 75/4\n5x = 75/4\nx = 75/4/5\nx = 15/4"} {"input": "What value of x satisfies 9x + 45 = 0", "output": "9x + 45 = 0\n9x = -45\nx = -45 / 9\nx = -5"} {"input": "Solve the equation x^2 - 6/5x - 13/4 = 0", "output": "x^2 - 6/5x - 13/4 = 0\n(x - -13/10)(x - 5/2) = 0\nx - -13/10 = 0 or x - 5/2 = 0\nx = -13/10\nx = 5/2"} {"input": "Solve the equations:\n7x + 8y = 215/9\n10x + 8y = 230/9", "output": "7x + 8y = 215/9\n10x + 8y = 230/9\n\nUsing elimination\n10*(7x + 8y = 215/9)\n7*(10x + 8y = 230/9)\n70x + 80y = 2150/9\n70x + 56y = 1610/9\nSubtract equations\n24y = 60\ny = 60/24\ny = 5/2\n\nSubstitute y\n7x + 8(5/2) = 215/9\n7x = 35/9\nx = 35/9/7\nx = 5/9"} {"input": "Solve simultaneously:\n10x + 7y = -58/3\n4x + 9y = 14/3", "output": "10x + 7y = -58/3\n4x + 9y = 14/3\n\nUsing elimination\n4*(10x + 7y = -58/3)\n10*(4x + 9y = 14/3)\n40x + 28y = -232/3\n40x + 90y = 140/3\nSubtract equations\n-62y = -124\ny = -124/-62\ny = 2\n\nSubstitute y\n10x + 7(2) = -58/3\n10x = -100/3\nx = -100/3/10\nx = -10/3"} {"input": "Solve quickly: 7x + 98/3 = 0", "output": "7x + 98/3 = 0\n7x = -98/3\nx = -98/3 / 7\nx = -14/3"} {"input": "Solve quickly: 8x - 88/9 = 0", "output": "8x - 88/9 = 0\n8x = 88/9\nx = 88/9 / 8\nx = 11/9"} {"input": "Solve the equations:\n8x + 9y = 909/14\n2x + 3y = 327/14", "output": "8x + 9y = 909/14\n2x + 3y = 327/14\n\nUsing elimination\n2*(8x + 9y = 909/14)\n8*(2x + 3y = 327/14)\n16x + 18y = 909/7\n16x + 24y = 1308/7\nSubtract equations\n-6y = -57\ny = -57/-6\ny = 19/2\n\nSubstitute y\n8x + 9(19/2) = 909/14\n8x = -144/7\nx = -144/7/8\nx = -18/7"} {"input": "What value of x satisfies x^3 + 3/10x^2 - 41/80x - 21/160 = 0", "output": "x^3 + 3/10x^2 - 41/80x - 21/160 = 0\n(x - -1/4)(x - -3/4)(x - 7/10) = 0\nx - -1/4 = 0\nx - -3/4 = 0\nx - 7/10 = 0\nx = -1/4\nx = -3/4\nx = 7/10"} {"input": "Determine x in x^3 + 1/8x^2 - 505/144x + 143/72 = 0", "output": "x^3 + 1/8x^2 - 505/144x + 143/72 = 0\n(x - -13/6)(x - 2/3)(x - 11/8) = 0\nx - -13/6 = 0\nx - 2/3 = 0\nx - 11/8 = 0\nx = -13/6\nx = 2/3\nx = 11/8"} {"input": "Compute the solution of x^2 + 33/10x + 13/5 = 0", "output": "x^2 + 33/10x + 13/5 = 0\n(x - -2)(x - -13/10) = 0\nx - -2 = 0 or x - -13/10 = 0\nx = -2\nx = -13/10"} {"input": "Solve x^2 - 43/35x - 102/35 = 0", "output": "x^2 - 43/35x - 102/35 = 0\n(x - 17/7)(x - -6/5) = 0\nx - 17/7 = 0 or x - -6/5 = 0\nx = 17/7\nx = -6/5"} {"input": "Solve quickly: x^3 + 171/40x^2 + 491/160x + 51/160 = 0", "output": "x^3 + 171/40x^2 + 491/160x + 51/160 = 0\n(x - -1/8)(x - -3/4)(x - -17/5) = 0\nx - -1/8 = 0\nx - -3/4 = 0\nx - -17/5 = 0\nx = -1/8\nx = -3/4\nx = -17/5"} {"input": "Solve the system:\n8x + 3y = 41/5\n10x + 8y = 23", "output": "8x + 3y = 41/5\n10x + 8y = 23\n\nUsing elimination\n10*(8x + 3y = 41/5)\n8*(10x + 8y = 23)\n80x + 30y = 82\n80x + 64y = 184\nSubtract equations\n-34y = -102\ny = -102/-34\ny = 3\n\nSubstitute y\n8x + 3(3) = 41/5\n8x = -4/5\nx = -4/5/8\nx = -1/10"} {"input": "Find x for x^2 - 11/3x - 20/3 = 0", "output": "x^2 - 11/3x - 20/3 = 0\n(x - -4/3)(x - 5) = 0\nx - -4/3 = 0 or x - 5 = 0\nx = -4/3\nx = 5"} {"input": "Find x in x^3 - 29/42x^2 - 1111/126x - 484/63 = 0", "output": "x^3 - 29/42x^2 - 1111/126x - 484/63 = 0\n(x - -8/7)(x - 11/3)(x - -11/6) = 0\nx - -8/7 = 0\nx - 11/3 = 0\nx - -11/6 = 0\nx = -8/7\nx = 11/3\nx = -11/6"} {"input": "Solve the equation x^2 - 3x - 70 = 0", "output": "x^2 - 3x - 70 = 0\n(x - -7)(x - 10) = 0\nx - -7 = 0 or x - 10 = 0\nx = -7\nx = 10"} {"input": "Find x in x^2 - 61/70x - 39/70 = 0", "output": "x^2 - 61/70x - 39/70 = 0\n(x - -3/7)(x - 13/10) = 0\nx - -3/7 = 0 or x - 13/10 = 0\nx = -3/7\nx = 13/10"} {"input": "Find x for x^3 + 2x^2 - 5/4x = 0", "output": "x^3 + 2x^2 - 5/4x = 0\n(x - 0)(x - 1/2)(x - -5/2) = 0\nx - 0 = 0\nx - 1/2 = 0\nx - -5/2 = 0\nx = 0\nx = 1/2\nx = -5/2"} {"input": "Solve quickly: x^2 - 25/12x + 11/24 = 0", "output": "x^2 - 25/12x + 11/24 = 0\n(x - 1/4)(x - 11/6) = 0\nx - 1/4 = 0 or x - 11/6 = 0\nx = 1/4\nx = 11/6"} {"input": "Solve x^3 + 11/2x^2 - 65/2x - 154 = 0", "output": "x^3 + 11/2x^2 - 65/2x - 154 = 0\n(x - -4)(x - -7)(x - 11/2) = 0\nx - -4 = 0\nx - -7 = 0\nx - 11/2 = 0\nx = -4\nx = -7\nx = 11/2"} {"input": "Solve quickly: x^3 - 1/14x^2 - 541/350x + 18/25 = 0", "output": "x^3 - 1/14x^2 - 541/350x + 18/25 = 0\n(x - -7/5)(x - 4/7)(x - 9/10) = 0\nx - -7/5 = 0\nx - 4/7 = 0\nx - 9/10 = 0\nx = -7/5\nx = 4/7\nx = 9/10"} {"input": "Compute the solution of x^3 + 359/35x^2 + 781/35x - 17/5 = 0", "output": "x^3 + 359/35x^2 + 781/35x - 17/5 = 0\n(x - -17/5)(x - 1/7)(x - -7) = 0\nx - -17/5 = 0\nx - 1/7 = 0\nx - -7 = 0\nx = -17/5\nx = 1/7\nx = -7"} {"input": "Solve quickly: x^3 + 4/3x^2 - 15x + 50/3 = 0", "output": "x^3 + 4/3x^2 - 15x + 50/3 = 0\n(x - -5)(x - 2)(x - 5/3) = 0\nx - -5 = 0\nx - 2 = 0\nx - 5/3 = 0\nx = -5\nx = 2\nx = 5/3"} {"input": "Find x for 7x + 42/5 = 0", "output": "7x + 42/5 = 0\n7x = -42/5\nx = -42/5 / 7\nx = -6/5"} {"input": "Solve the equation x^2 - 160/9x + 256/9 = 0", "output": "x^2 - 160/9x + 256/9 = 0\n(x - 16)(x - 16/9) = 0\nx - 16 = 0 or x - 16/9 = 0\nx = 16\nx = 16/9"} {"input": "Find the solution to x^3 + 121/72x^2 - 45/16x - 275/144 = 0", "output": "x^3 + 121/72x^2 - 45/16x - 275/144 = 0\n(x - -5/9)(x - 11/8)(x - -5/2) = 0\nx - -5/9 = 0\nx - 11/8 = 0\nx - -5/2 = 0\nx = -5/9\nx = 11/8\nx = -5/2"} {"input": "Find x for x^3 + 23/10x^2 + 1/2x - 1/5 = 0", "output": "x^3 + 23/10x^2 + 1/2x - 1/5 = 0\n(x - -1/2)(x - -2)(x - 1/5) = 0\nx - -1/2 = 0\nx - -2 = 0\nx - 1/5 = 0\nx = -1/2\nx = -2\nx = 1/5"} {"input": "Solve the system:\n9x + 6y = -69/7\n8x + 10y = -192/7", "output": "9x + 6y = -69/7\n8x + 10y = -192/7\n\nUsing elimination\n8*(9x + 6y = -69/7)\n9*(8x + 10y = -192/7)\n72x + 48y = -552/7\n72x + 90y = -1728/7\nSubtract equations\n-42y = 168\ny = 168/-42\ny = -4\n\nSubstitute y\n9x + 6(-4) = -69/7\n9x = 99/7\nx = 99/7/9\nx = 11/7"} {"input": "Find the solution to x^2 + 47/12x + 5/8 = 0", "output": "x^2 + 47/12x + 5/8 = 0\n(x - -15/4)(x - -1/6) = 0\nx - -15/4 = 0 or x - -1/6 = 0\nx = -15/4\nx = -1/6"} {"input": "Solve 8x + 12 = 0", "output": "8x + 12 = 0\n8x = -12\nx = -12 / 8\nx = -3/2"} {"input": "Find x in x^3 - 47/4x^2 - 37/2x + 117/4 = 0", "output": "x^3 - 47/4x^2 - 37/2x + 117/4 = 0\n(x - 13)(x - 1)(x - -9/4) = 0\nx - 13 = 0\nx - 1 = 0\nx - -9/4 = 0\nx = 13\nx = 1\nx = -9/4"} {"input": "Find x in x^3 - 27/7x^2 - 120/7x + 400/7 = 0", "output": "x^3 - 27/7x^2 - 120/7x + 400/7 = 0\n(x - -4)(x - 5)(x - 20/7) = 0\nx - -4 = 0\nx - 5 = 0\nx - 20/7 = 0\nx = -4\nx = 5\nx = 20/7"} {"input": "What value of x satisfies x^3 + 277/84x^2 - 131/84x - 39/7 = 0", "output": "x^3 + 277/84x^2 - 131/84x - 39/7 = 0\n(x - 9/7)(x - -4/3)(x - -13/4) = 0\nx - 9/7 = 0\nx - -4/3 = 0\nx - -13/4 = 0\nx = 9/7\nx = -4/3\nx = -13/4"} {"input": "What value of x satisfies x^3 - 37/4x^2 + 17/8x + 63 = 0", "output": "x^3 - 37/4x^2 + 17/8x + 63 = 0\n(x - 8)(x - 7/2)(x - -9/4) = 0\nx - 8 = 0\nx - 7/2 = 0\nx - -9/4 = 0\nx = 8\nx = 7/2\nx = -9/4"} {"input": "Solve quickly: x^3 - 29/40x^2 - 131/40x + 3 = 0", "output": "x^3 - 29/40x^2 - 131/40x + 3 = 0\n(x - 8/5)(x - 1)(x - -15/8) = 0\nx - 8/5 = 0\nx - 1 = 0\nx - -15/8 = 0\nx = 8/5\nx = 1\nx = -15/8"} {"input": "Solve simultaneously:\n2x + 1y = -23/6\n7x + 2y = -101/12", "output": "2x + 1y = -23/6\n7x + 2y = -101/12\n\nUsing elimination\n7*(2x + 1y = -23/6)\n2*(7x + 2y = -101/12)\n14x + 7y = -161/6\n14x + 4y = -101/6\nSubtract equations\n3y = -10\ny = -10/3\ny = -10/3\n\nSubstitute y\n2x + 1(-10/3) = -23/6\n2x = -1/2\nx = -1/2/2\nx = -1/4"} {"input": "Compute the solution of 5x + 35 = 0", "output": "5x + 35 = 0\n5x = -35\nx = -35 / 5\nx = -7"} {"input": "Find x for x^2 + 16/3x - 19/3 = 0", "output": "x^2 + 16/3x - 19/3 = 0\n(x - 1)(x - -19/3) = 0\nx - 1 = 0 or x - -19/3 = 0\nx = 1\nx = -19/3"} {"input": "Find x in 9x + 108 = 0", "output": "9x + 108 = 0\n9x = -108\nx = -108 / 9\nx = -12"} {"input": "Determine x in 7x + 21/5 = 0", "output": "7x + 21/5 = 0\n7x = -21/5\nx = -21/5 / 7\nx = -3/5"} {"input": "Solve the system:\n3x + 5y = -31/2\n10x + 2y = 43/3", "output": "3x + 5y = -31/2\n10x + 2y = 43/3\n\nUsing elimination\n10*(3x + 5y = -31/2)\n3*(10x + 2y = 43/3)\n30x + 50y = -155\n30x + 6y = 43\nSubtract equations\n44y = -198\ny = -198/44\ny = -9/2\n\nSubstitute y\n3x + 5(-9/2) = -31/2\n3x = 7\nx = 7/3\nx = 7/3"} {"input": "Find the solution to 4x - 8 = 0", "output": "4x - 8 = 0\n4x = 8\nx = 8 / 4\nx = 2"} {"input": "Find x in x^3 - 27/4x^2 + 853/72x - 187/36 = 0", "output": "x^3 - 27/4x^2 + 853/72x - 187/36 = 0\n(x - 2/3)(x - 17/4)(x - 11/6) = 0\nx - 2/3 = 0\nx - 17/4 = 0\nx - 11/6 = 0\nx = 2/3\nx = 17/4\nx = 11/6"} {"input": "Solve the equation x^3 + 52/3x^2 + 299/3x + 190 = 0", "output": "x^3 + 52/3x^2 + 299/3x + 190 = 0\n(x - -6)(x - -19/3)(x - -5) = 0\nx - -6 = 0\nx - -19/3 = 0\nx - -5 = 0\nx = -6\nx = -19/3\nx = -5"} {"input": "Compute the solution of x^3 - 116/21x^2 - 247/21x + 10 = 0", "output": "x^3 - 116/21x^2 - 247/21x + 10 = 0\n(x - -15/7)(x - 7)(x - 2/3) = 0\nx - -15/7 = 0\nx - 7 = 0\nx - 2/3 = 0\nx = -15/7\nx = 7\nx = 2/3"} {"input": "Solve the system:\n7x + 6y = -1/8\n9x + 3y = -39/8", "output": "7x + 6y = -1/8\n9x + 3y = -39/8\n\nUsing elimination\n9*(7x + 6y = -1/8)\n7*(9x + 3y = -39/8)\n63x + 54y = -9/8\n63x + 21y = -273/8\nSubtract equations\n33y = 33\ny = 33/33\ny = 1\n\nSubstitute y\n7x + 6(1) = -1/8\n7x = -49/8\nx = -49/8/7\nx = -7/8"} {"input": "Find x and y such that\n9x + 3y = -119/2\n1x + 1y = -47/6", "output": "9x + 3y = -119/2\n1x + 1y = -47/6\n\nUsing elimination\n1*(9x + 3y = -119/2)\n9*(1x + 1y = -47/6)\n9x + 3y = -119/2\n9x + 9y = -141/2\nSubtract equations\n-6y = 11\ny = 11/-6\ny = -11/6\n\nSubstitute y\n9x + 3(-11/6) = -119/2\n9x = -54\nx = -54/9\nx = -6"} {"input": "Solve the equations:\n4x + 9y = 48\n10x + 4y = 83", "output": "4x + 9y = 48\n10x + 4y = 83\n\nUsing elimination\n10*(4x + 9y = 48)\n4*(10x + 4y = 83)\n40x + 90y = 480\n40x + 16y = 332\nSubtract equations\n74y = 148\ny = 148/74\ny = 2\n\nSubstitute y\n4x + 9(2) = 48\n4x = 30\nx = 30/4\nx = 15/2"} {"input": "Determine x in x^2 - 81/56x - 81/28 = 0", "output": "x^2 - 81/56x - 81/28 = 0\n(x - -9/8)(x - 18/7) = 0\nx - -9/8 = 0 or x - 18/7 = 0\nx = -9/8\nx = 18/7"} {"input": "Solve the system:\n5x + 2y = 19/14\n5x + 9y = -37/14", "output": "5x + 2y = 19/14\n5x + 9y = -37/14\n\nUsing elimination\n5*(5x + 2y = 19/14)\n5*(5x + 9y = -37/14)\n25x + 10y = 95/14\n25x + 45y = -185/14\nSubtract equations\n-35y = 20\ny = 20/-35\ny = -4/7\n\nSubstitute y\n5x + 2(-4/7) = 19/14\n5x = 5/2\nx = 5/2/5\nx = 1/2"} {"input": "Solve the system:\n5x + 7y = 51\n9x + 2y = -18/5", "output": "5x + 7y = 51\n9x + 2y = -18/5\n\nUsing elimination\n9*(5x + 7y = 51)\n5*(9x + 2y = -18/5)\n45x + 63y = 459\n45x + 10y = -18\nSubtract equations\n53y = 477\ny = 477/53\ny = 9\n\nSubstitute y\n5x + 7(9) = 51\n5x = -12\nx = -12/5\nx = -12/5"} {"input": "Find x and y such that\n3x + 7y = -75/8\n6x + 3y = -51/8", "output": "3x + 7y = -75/8\n6x + 3y = -51/8\n\nUsing elimination\n6*(3x + 7y = -75/8)\n3*(6x + 3y = -51/8)\n18x + 42y = -225/4\n18x + 9y = -153/8\nSubtract equations\n33y = -297/8\ny = -297/8/33\ny = -9/8\n\nSubstitute y\n3x + 7(-9/8) = -75/8\n3x = -3/2\nx = -3/2/3\nx = -1/2"} {"input": "Find x for x^2 - 1/5x - 3/20 = 0", "output": "x^2 - 1/5x - 3/20 = 0\n(x - -3/10)(x - 1/2) = 0\nx - -3/10 = 0 or x - 1/2 = 0\nx = -3/10\nx = 1/2"} {"input": "Determine x in x^2 - 1 = 0", "output": "x^2 - 1 = 0\n(x - 1)(x - -1) = 0\nx - 1 = 0 or x - -1 = 0\nx = 1\nx = -1"} {"input": "Find x in x^3 + 814/105x^2 + 112/15x + 32/21 = 0", "output": "x^3 + 814/105x^2 + 112/15x + 32/21 = 0\n(x - -4/5)(x - -20/3)(x - -2/7) = 0\nx - -4/5 = 0\nx - -20/3 = 0\nx - -2/7 = 0\nx = -4/5\nx = -20/3\nx = -2/7"} {"input": "Solve the system:\n10x + 7y = 467/9\n9x + 10y = 80", "output": "10x + 7y = 467/9\n9x + 10y = 80\n\nUsing elimination\n9*(10x + 7y = 467/9)\n10*(9x + 10y = 80)\n90x + 63y = 467\n90x + 100y = 800\nSubtract equations\n-37y = -333\ny = -333/-37\ny = 9\n\nSubstitute y\n10x + 7(9) = 467/9\n10x = -100/9\nx = -100/9/10\nx = -10/9"} {"input": "Compute the solution of x^2 - 128/9x - 35/3 = 0", "output": "x^2 - 128/9x - 35/3 = 0\n(x - 15)(x - -7/9) = 0\nx - 15 = 0 or x - -7/9 = 0\nx = 15\nx = -7/9"} {"input": "Determine x in x^2 - 81/4 = 0", "output": "x^2 - 81/4 = 0\n(x - 9/2)(x - -9/2) = 0\nx - 9/2 = 0 or x - -9/2 = 0\nx = 9/2\nx = -9/2"} {"input": "Solve x^2 + 19/5x - 66/5 = 0", "output": "x^2 + 19/5x - 66/5 = 0\n(x - 11/5)(x - -6) = 0\nx - 11/5 = 0 or x - -6 = 0\nx = 11/5\nx = -6"} {"input": "Find the solution to x^2 + 2/5x - 39/5 = 0", "output": "x^2 + 2/5x - 39/5 = 0\n(x - -3)(x - 13/5) = 0\nx - -3 = 0 or x - 13/5 = 0\nx = -3\nx = 13/5"} {"input": "Find the solution to x^3 + 145/18x^2 + 473/27x + 605/54 = 0", "output": "x^3 + 145/18x^2 + 473/27x + 605/54 = 0\n(x - -5)(x - -11/6)(x - -11/9) = 0\nx - -5 = 0\nx - -11/6 = 0\nx - -11/9 = 0\nx = -5\nx = -11/6\nx = -11/9"} {"input": "Find x and y such that\n2x + 4y = 6\n3x + 3y = 15/2", "output": "2x + 4y = 6\n3x + 3y = 15/2\n\nUsing elimination\n3*(2x + 4y = 6)\n2*(3x + 3y = 15/2)\n6x + 12y = 18\n6x + 6y = 15\nSubtract equations\n6y = 3\ny = 3/6\ny = 1/2\n\nSubstitute y\n2x + 4(1/2) = 6\n2x = 4\nx = 4/2\nx = 2"} {"input": "Solve the equations:\n9x + 6y = 75/2\n1x + 2y = 21/2", "output": "9x + 6y = 75/2\n1x + 2y = 21/2\n\nUsing elimination\n1*(9x + 6y = 75/2)\n9*(1x + 2y = 21/2)\n9x + 6y = 75/2\n9x + 18y = 189/2\nSubtract equations\n-12y = -57\ny = -57/-12\ny = 19/4\n\nSubstitute y\n9x + 6(19/4) = 75/2\n9x = 9\nx = 9/9\nx = 1"} {"input": "Find x and y such that\n8x + 5y = -259/18\n7x + 5y = -221/18", "output": "8x + 5y = -259/18\n7x + 5y = -221/18\n\nUsing elimination\n7*(8x + 5y = -259/18)\n8*(7x + 5y = -221/18)\n56x + 35y = -1813/18\n56x + 40y = -884/9\nSubtract equations\n-5y = -5/2\ny = -5/2/-5\ny = 1/2\n\nSubstitute y\n8x + 5(1/2) = -259/18\n8x = -152/9\nx = -152/9/8\nx = -19/9"} {"input": "What value of x satisfies x^3 - 22/21x^2 + 13/84x + 5/84 = 0", "output": "x^3 - 22/21x^2 + 13/84x + 5/84 = 0\n(x - 5/7)(x - 1/2)(x - -1/6) = 0\nx - 5/7 = 0\nx - 1/2 = 0\nx - -1/6 = 0\nx = 5/7\nx = 1/2\nx = -1/6"} {"input": "Compute the solution of x^3 + 4/35x^2 - 143/35x - 16/5 = 0", "output": "x^3 + 4/35x^2 - 143/35x - 16/5 = 0\n(x - -7/5)(x - -1)(x - 16/7) = 0\nx - -7/5 = 0\nx - -1 = 0\nx - 16/7 = 0\nx = -7/5\nx = -1\nx = 16/7"} {"input": "Find the solution to x^2 + 23/7x - 20/7 = 0", "output": "x^2 + 23/7x - 20/7 = 0\n(x - -4)(x - 5/7) = 0\nx - -4 = 0 or x - 5/7 = 0\nx = -4\nx = 5/7"} {"input": "Compute the solution of x^2 + 37/10x + 21/10 = 0", "output": "x^2 + 37/10x + 21/10 = 0\n(x - -7/10)(x - -3) = 0\nx - -7/10 = 0 or x - -3 = 0\nx = -7/10\nx = -3"} {"input": "Solve quickly: x^2 - 43/6x - 5/2 = 0", "output": "x^2 - 43/6x - 5/2 = 0\n(x - 15/2)(x - -1/3) = 0\nx - 15/2 = 0 or x - -1/3 = 0\nx = 15/2\nx = -1/3"} {"input": "Find the solution to x^2 + 17/3x - 56/3 = 0", "output": "x^2 + 17/3x - 56/3 = 0\n(x - -8)(x - 7/3) = 0\nx - -8 = 0 or x - 7/3 = 0\nx = -8\nx = 7/3"} {"input": "Find x for x^3 - 377/30x^2 + 98/3x - 51/10 = 0", "output": "x^3 - 377/30x^2 + 98/3x - 51/10 = 0\n(x - 17/5)(x - 1/6)(x - 9) = 0\nx - 17/5 = 0\nx - 1/6 = 0\nx - 9 = 0\nx = 17/5\nx = 1/6\nx = 9"} {"input": "What value of x satisfies x^3 + 37/30x^2 - 137/15x - 76/5 = 0", "output": "x^3 + 37/30x^2 - 137/15x - 76/5 = 0\n(x - 19/6)(x - -2)(x - -12/5) = 0\nx - 19/6 = 0\nx - -2 = 0\nx - -12/5 = 0\nx = 19/6\nx = -2\nx = -12/5"} {"input": "Solve the equations:\n6x + 4y = -65\n3x + 7y = -235/2", "output": "6x + 4y = -65\n3x + 7y = -235/2\n\nUsing elimination\n3*(6x + 4y = -65)\n6*(3x + 7y = -235/2)\n18x + 12y = -195\n18x + 42y = -705\nSubtract equations\n-30y = 510\ny = 510/-30\ny = -17\n\nSubstitute y\n6x + 4(-17) = -65\n6x = 3\nx = 3/6\nx = 1/2"} {"input": "Solve x^3 - 9/10x^2 - 21/10x - 1/5 = 0", "output": "x^3 - 9/10x^2 - 21/10x - 1/5 = 0\n(x - -1/10)(x - -1)(x - 2) = 0\nx - -1/10 = 0\nx - -1 = 0\nx - 2 = 0\nx = -1/10\nx = -1\nx = 2"} {"input": "Find x for x^3 + 61/40x^2 - 247/160x - 77/32 = 0", "output": "x^3 + 61/40x^2 - 247/160x - 77/32 = 0\n(x - -7/5)(x - 5/4)(x - -11/8) = 0\nx - -7/5 = 0\nx - 5/4 = 0\nx - -11/8 = 0\nx = -7/5\nx = 5/4\nx = -11/8"} {"input": "Find x in 7x - 15 = 0", "output": "7x - 15 = 0\n7x = 15\nx = 15 / 7\nx = 15/7"} {"input": "Determine x in x^3 - 169/280x^2 - 17/40x + 3/14 = 0", "output": "x^3 - 169/280x^2 - 17/40x + 3/14 = 0\n(x - -5/8)(x - 3/7)(x - 4/5) = 0\nx - -5/8 = 0\nx - 3/7 = 0\nx - 4/5 = 0\nx = -5/8\nx = 3/7\nx = 4/5"} {"input": "Determine x in x^3 - 1/45x^2 - 158/135x + 16/45 = 0", "output": "x^3 - 1/45x^2 - 158/135x + 16/45 = 0\n(x - 8/9)(x - 1/3)(x - -6/5) = 0\nx - 8/9 = 0\nx - 1/3 = 0\nx - -6/5 = 0\nx = 8/9\nx = 1/3\nx = -6/5"} {"input": "Find x in x^2 + 18/7x + 11/7 = 0", "output": "x^2 + 18/7x + 11/7 = 0\n(x - -1)(x - -11/7) = 0\nx - -1 = 0 or x - -11/7 = 0\nx = -1\nx = -11/7"} {"input": "Solve x^2 + 53/4x + 323/8 = 0", "output": "x^2 + 53/4x + 323/8 = 0\n(x - -17/2)(x - -19/4) = 0\nx - -17/2 = 0 or x - -19/4 = 0\nx = -17/2\nx = -19/4"} {"input": "Solve the equation 3x + 57/2 = 0", "output": "3x + 57/2 = 0\n3x = -57/2\nx = -57/2 / 3\nx = -19/2"} {"input": "Solve quickly: x^2 + 1/21x - 152/21 = 0", "output": "x^2 + 1/21x - 152/21 = 0\n(x - 8/3)(x - -19/7) = 0\nx - 8/3 = 0 or x - -19/7 = 0\nx = 8/3\nx = -19/7"} {"input": "Find x for x^2 - 5/56x - 38/7 = 0", "output": "x^2 - 5/56x - 38/7 = 0\n(x - 19/8)(x - -16/7) = 0\nx - 19/8 = 0 or x - -16/7 = 0\nx = 19/8\nx = -16/7"} {"input": "Compute the solution of 4x - 10/3 = 0", "output": "4x - 10/3 = 0\n4x = 10/3\nx = 10/3 / 4\nx = 5/6"} {"input": "Find x and y such that\n9x + 10y = 940/7\n6x + 4y = 328/7", "output": "9x + 10y = 940/7\n6x + 4y = 328/7\n\nUsing elimination\n6*(9x + 10y = 940/7)\n9*(6x + 4y = 328/7)\n54x + 60y = 5640/7\n54x + 36y = 2952/7\nSubtract equations\n24y = 384\ny = 384/24\ny = 16\n\nSubstitute y\n9x + 10(16) = 940/7\n9x = -180/7\nx = -180/7/9\nx = -20/7"} {"input": "Find x and y such that\n10x + 8y = -179/6\n3x + 5y = -97/12", "output": "10x + 8y = -179/6\n3x + 5y = -97/12\n\nUsing elimination\n3*(10x + 8y = -179/6)\n10*(3x + 5y = -97/12)\n30x + 24y = -179/2\n30x + 50y = -485/6\nSubtract equations\n-26y = -26/3\ny = -26/3/-26\ny = 1/3\n\nSubstitute y\n10x + 8(1/3) = -179/6\n10x = -65/2\nx = -65/2/10\nx = -13/4"} {"input": "Solve simultaneously:\n8x + 7y = 46\n1x + 1y = 51/8", "output": "8x + 7y = 46\n1x + 1y = 51/8\n\nUsing elimination\n1*(8x + 7y = 46)\n8*(1x + 1y = 51/8)\n8x + 7y = 46\n8x + 8y = 51\nSubtract equations\n-1y = -5\ny = -5/-1\ny = 5\n\nSubstitute y\n8x + 7(5) = 46\n8x = 11\nx = 11/8\nx = 11/8"} {"input": "Find the solution to x^2 - 4x + 4 = 0", "output": "x^2 - 4x + 4 = 0\n(x - 2)(x - 2) = 0\nx - 2 = 0 or x - 2 = 0\nx = 2\nx = 2"} {"input": "Find the solution to x^3 + 37/6x^2 - 92/3x + 19/2 = 0", "output": "x^3 + 37/6x^2 - 92/3x + 19/2 = 0\n(x - 3)(x - -19/2)(x - 1/3) = 0\nx - 3 = 0\nx - -19/2 = 0\nx - 1/3 = 0\nx = 3\nx = -19/2\nx = 1/3"} {"input": "Find x in x^2 - 94/21x + 80/21 = 0", "output": "x^2 - 94/21x + 80/21 = 0\n(x - 10/3)(x - 8/7) = 0\nx - 10/3 = 0 or x - 8/7 = 0\nx = 10/3\nx = 8/7"} {"input": "Solve 5x - 85/6 = 0", "output": "5x - 85/6 = 0\n5x = 85/6\nx = 85/6 / 5\nx = 17/6"} {"input": "Solve 6x - 3/5 = 0", "output": "6x - 3/5 = 0\n6x = 3/5\nx = 3/5 / 6\nx = 1/10"} {"input": "Find the solution to x^3 - 321/40x^2 - 383/20x - 6 = 0", "output": "x^3 - 321/40x^2 - 383/20x - 6 = 0\n(x - 10)(x - -3/8)(x - -8/5) = 0\nx - 10 = 0\nx - -3/8 = 0\nx - -8/5 = 0\nx = 10\nx = -3/8\nx = -8/5"} {"input": "Solve 9x + 153/4 = 0", "output": "9x + 153/4 = 0\n9x = -153/4\nx = -153/4 / 9\nx = -17/4"} {"input": "Solve simultaneously:\n5x + 1y = -477/56\n8x + 2y = -93/7", "output": "5x + 1y = -477/56\n8x + 2y = -93/7\n\nUsing elimination\n8*(5x + 1y = -477/56)\n5*(8x + 2y = -93/7)\n40x + 8y = -477/7\n40x + 10y = -465/7\nSubtract equations\n-2y = -12/7\ny = -12/7/-2\ny = 6/7\n\nSubstitute y\n5x + 1(6/7) = -477/56\n5x = -75/8\nx = -75/8/5\nx = -15/8"} {"input": "Solve the equation x^2 - 81/7x - 34 = 0", "output": "x^2 - 81/7x - 34 = 0\n(x - 14)(x - -17/7) = 0\nx - 14 = 0 or x - -17/7 = 0\nx = 14\nx = -17/7"} {"input": "Solve the system:\n10x + 5y = 25/4\n4x + 1y = 3/2", "output": "10x + 5y = 25/4\n4x + 1y = 3/2\n\nUsing elimination\n4*(10x + 5y = 25/4)\n10*(4x + 1y = 3/2)\n40x + 20y = 25\n40x + 10y = 15\nSubtract equations\n10y = 10\ny = 10/10\ny = 1\n\nSubstitute y\n10x + 5(1) = 25/4\n10x = 5/4\nx = 5/4/10\nx = 1/8"} {"input": "Find x and y such that\n10x + 2y = 16\n2x + 6y = -26/5", "output": "10x + 2y = 16\n2x + 6y = -26/5\n\nUsing elimination\n2*(10x + 2y = 16)\n10*(2x + 6y = -26/5)\n20x + 4y = 32\n20x + 60y = -52\nSubtract equations\n-56y = 84\ny = 84/-56\ny = -3/2\n\nSubstitute y\n10x + 2(-3/2) = 16\n10x = 19\nx = 19/10\nx = 19/10"} {"input": "Find the solution to x^3 - 7/3x^2 - 6x - 8/3 = 0", "output": "x^3 - 7/3x^2 - 6x - 8/3 = 0\n(x - -1)(x - -2/3)(x - 4) = 0\nx - -1 = 0\nx - -2/3 = 0\nx - 4 = 0\nx = -1\nx = -2/3\nx = 4"} {"input": "Solve quickly: x^3 + 53/24x^2 - 77/12x + 3 = 0", "output": "x^3 + 53/24x^2 - 77/12x + 3 = 0\n(x - -4)(x - 2/3)(x - 9/8) = 0\nx - -4 = 0\nx - 2/3 = 0\nx - 9/8 = 0\nx = -4\nx = 2/3\nx = 9/8"} {"input": "Solve quickly: 2x + 9/2 = 0", "output": "2x + 9/2 = 0\n2x = -9/2\nx = -9/2 / 2\nx = -9/4"} {"input": "Find x for 9x + 45/4 = 0", "output": "9x + 45/4 = 0\n9x = -45/4\nx = -45/4 / 9\nx = -5/4"} {"input": "Solve simultaneously:\n7x + 8y = -141/5\n5x + 9y = -866/35", "output": "7x + 8y = -141/5\n5x + 9y = -866/35\n\nUsing elimination\n5*(7x + 8y = -141/5)\n7*(5x + 9y = -866/35)\n35x + 40y = -141\n35x + 63y = -866/5\nSubtract equations\n-23y = 161/5\ny = 161/5/-23\ny = -7/5\n\nSubstitute y\n7x + 8(-7/5) = -141/5\n7x = -17\nx = -17/7\nx = -17/7"} {"input": "Solve the equation x^3 - 209/30x^2 + 47/3x - 56/5 = 0", "output": "x^3 - 209/30x^2 + 47/3x - 56/5 = 0\n(x - 14/5)(x - 3/2)(x - 8/3) = 0\nx - 14/5 = 0\nx - 3/2 = 0\nx - 8/3 = 0\nx = 14/5\nx = 3/2\nx = 8/3"} {"input": "Solve the equation x^3 - 247/56x^2 + 335/56x - 18/7 = 0", "output": "x^3 - 247/56x^2 + 335/56x - 18/7 = 0\n(x - 1)(x - 16/7)(x - 9/8) = 0\nx - 1 = 0\nx - 16/7 = 0\nx - 9/8 = 0\nx = 1\nx = 16/7\nx = 9/8"} {"input": "Find the solution to x^2 - 49/8x - 323/16 = 0", "output": "x^2 - 49/8x - 323/16 = 0\n(x - 17/2)(x - -19/8) = 0\nx - 17/2 = 0 or x - -19/8 = 0\nx = 17/2\nx = -19/8"} {"input": "Find x for x^3 + 80/21x^2 - 281/21x - 340/21 = 0", "output": "x^3 + 80/21x^2 - 281/21x - 340/21 = 0\n(x - -17/3)(x - -1)(x - 20/7) = 0\nx - -17/3 = 0\nx - -1 = 0\nx - 20/7 = 0\nx = -17/3\nx = -1\nx = 20/7"} {"input": "Solve quickly: x^3 + 17/3x^2 + 10/3x = 0", "output": "x^3 + 17/3x^2 + 10/3x = 0\n(x - 0)(x - -5)(x - -2/3) = 0\nx - 0 = 0\nx - -5 = 0\nx - -2/3 = 0\nx = 0\nx = -5\nx = -2/3"} {"input": "Solve the system:\n9x + 7y = 117/4\n5x + 2y = 55/6", "output": "9x + 7y = 117/4\n5x + 2y = 55/6\n\nUsing elimination\n5*(9x + 7y = 117/4)\n9*(5x + 2y = 55/6)\n45x + 35y = 585/4\n45x + 18y = 165/2\nSubtract equations\n17y = 255/4\ny = 255/4/17\ny = 15/4\n\nSubstitute y\n9x + 7(15/4) = 117/4\n9x = 3\nx = 3/9\nx = 1/3"} {"input": "Find the solution to 4x + 32 = 0", "output": "4x + 32 = 0\n4x = -32\nx = -32 / 4\nx = -8"} {"input": "Find the solution to 8x + 36 = 0", "output": "8x + 36 = 0\n8x = -36\nx = -36 / 8\nx = -9/2"} {"input": "Find the solution to x^2 + 13/5x + 153/100 = 0", "output": "x^2 + 13/5x + 153/100 = 0\n(x - -17/10)(x - -9/10) = 0\nx - -17/10 = 0 or x - -9/10 = 0\nx = -17/10\nx = -9/10"} {"input": "Find x in x^2 + 19/3x + 10 = 0", "output": "x^2 + 19/3x + 10 = 0\n(x - -3)(x - -10/3) = 0\nx - -3 = 0 or x - -10/3 = 0\nx = -3\nx = -10/3"} {"input": "Solve quickly: x^2 + 16/9x - 80/9 = 0", "output": "x^2 + 16/9x - 80/9 = 0\n(x - -4)(x - 20/9) = 0\nx - -4 = 0 or x - 20/9 = 0\nx = -4\nx = 20/9"} {"input": "Solve simultaneously:\n10x + 3y = 94/7\n1x + 2y = 57/7", "output": "10x + 3y = 94/7\n1x + 2y = 57/7\n\nUsing elimination\n1*(10x + 3y = 94/7)\n10*(1x + 2y = 57/7)\n10x + 3y = 94/7\n10x + 20y = 570/7\nSubtract equations\n-17y = -68\ny = -68/-17\ny = 4\n\nSubstitute y\n10x + 3(4) = 94/7\n10x = 10/7\nx = 10/7/10\nx = 1/7"} {"input": "Find x for x^3 + 21/2x^2 - 57/50x - 2527/25 = 0", "output": "x^3 + 21/2x^2 - 57/50x - 2527/25 = 0\n(x - -19/2)(x - 14/5)(x - -19/5) = 0\nx - -19/2 = 0\nx - 14/5 = 0\nx - -19/5 = 0\nx = -19/2\nx = 14/5\nx = -19/5"} {"input": "Determine x in 3x - 3/8 = 0", "output": "3x - 3/8 = 0\n3x = 3/8\nx = 3/8 / 3\nx = 1/8"} {"input": "Determine x in x^2 - 29/18x + 5/9 = 0", "output": "x^2 - 29/18x + 5/9 = 0\n(x - 1/2)(x - 10/9) = 0\nx - 1/2 = 0 or x - 10/9 = 0\nx = 1/2\nx = 10/9"} {"input": "Solve the equations:\n4x + 4y = -72/35\n6x + 4y = -52/35", "output": "4x + 4y = -72/35\n6x + 4y = -52/35\n\nUsing elimination\n6*(4x + 4y = -72/35)\n4*(6x + 4y = -52/35)\n24x + 24y = -432/35\n24x + 16y = -208/35\nSubtract equations\n8y = -32/5\ny = -32/5/8\ny = -4/5\n\nSubstitute y\n4x + 4(-4/5) = -72/35\n4x = 8/7\nx = 8/7/4\nx = 2/7"} {"input": "Solve x^3 - 33/5x^2 - 327/20x + 17/10 = 0", "output": "x^3 - 33/5x^2 - 327/20x + 17/10 = 0\n(x - 17/2)(x - -2)(x - 1/10) = 0\nx - 17/2 = 0\nx - -2 = 0\nx - 1/10 = 0\nx = 17/2\nx = -2\nx = 1/10"} {"input": "Compute the solution of x^3 - 29/24x^2 + 7/24x = 0", "output": "x^3 - 29/24x^2 + 7/24x = 0\n(x - 7/8)(x - 0)(x - 1/3) = 0\nx - 7/8 = 0\nx - 0 = 0\nx - 1/3 = 0\nx = 7/8\nx = 0\nx = 1/3"} {"input": "Solve simultaneously:\n6x + 10y = -65\n3x + 8y = -34", "output": "6x + 10y = -65\n3x + 8y = -34\n\nUsing elimination\n3*(6x + 10y = -65)\n6*(3x + 8y = -34)\n18x + 30y = -195\n18x + 48y = -204\nSubtract equations\n-18y = 9\ny = 9/-18\ny = -1/2\n\nSubstitute y\n6x + 10(-1/2) = -65\n6x = -60\nx = -60/6\nx = -10"} {"input": "Find x in x^2 - 1/6x - 35/3 = 0", "output": "x^2 - 1/6x - 35/3 = 0\n(x - 7/2)(x - -10/3) = 0\nx - 7/2 = 0 or x - -10/3 = 0\nx = 7/2\nx = -10/3"} {"input": "Find x and y such that\n5x + 1y = 167/10\n10x + 9y = 453/10", "output": "5x + 1y = 167/10\n10x + 9y = 453/10\n\nUsing elimination\n10*(5x + 1y = 167/10)\n5*(10x + 9y = 453/10)\n50x + 10y = 167\n50x + 45y = 453/2\nSubtract equations\n-35y = -119/2\ny = -119/2/-35\ny = 17/10\n\nSubstitute y\n5x + 1(17/10) = 167/10\n5x = 15\nx = 15/5\nx = 3"} {"input": "Find x for x^3 + 152/7x^2 + 1712/49x + 640/49 = 0", "output": "x^3 + 152/7x^2 + 1712/49x + 640/49 = 0\n(x - -20)(x - -4/7)(x - -8/7) = 0\nx - -20 = 0\nx - -4/7 = 0\nx - -8/7 = 0\nx = -20\nx = -4/7\nx = -8/7"} {"input": "What value of x satisfies x^3 + 66/7x^2 + 521/49x - 312/49 = 0", "output": "x^3 + 66/7x^2 + 521/49x - 312/49 = 0\n(x - -8)(x - -13/7)(x - 3/7) = 0\nx - -8 = 0\nx - -13/7 = 0\nx - 3/7 = 0\nx = -8\nx = -13/7\nx = 3/7"} {"input": "Solve simultaneously:\n4x + 10y = -63/2\n2x + 8y = -543/20", "output": "4x + 10y = -63/2\n2x + 8y = -543/20\n\nUsing elimination\n2*(4x + 10y = -63/2)\n4*(2x + 8y = -543/20)\n8x + 20y = -63\n8x + 32y = -543/5\nSubtract equations\n-12y = 228/5\ny = 228/5/-12\ny = -19/5\n\nSubstitute y\n4x + 10(-19/5) = -63/2\n4x = 13/2\nx = 13/2/4\nx = 13/8"} {"input": "Find x in 10x + 170/3 = 0", "output": "10x + 170/3 = 0\n10x = -170/3\nx = -170/3 / 10\nx = -17/3"} {"input": "Solve quickly: 4x - 32/3 = 0", "output": "4x - 32/3 = 0\n4x = 32/3\nx = 32/3 / 4\nx = 8/3"} {"input": "Solve the equation x^2 + 1/3x - 10 = 0", "output": "x^2 + 1/3x - 10 = 0\n(x - -10/3)(x - 3) = 0\nx - -10/3 = 0 or x - 3 = 0\nx = -10/3\nx = 3"} {"input": "Solve 7x - 7/3 = 0", "output": "7x - 7/3 = 0\n7x = 7/3\nx = 7/3 / 7\nx = 1/3"} {"input": "Determine x in x^3 - 7/9x^2 - 14/3x + 40/9 = 0", "output": "x^3 - 7/9x^2 - 14/3x + 40/9 = 0\n(x - -20/9)(x - 1)(x - 2) = 0\nx - -20/9 = 0\nx - 1 = 0\nx - 2 = 0\nx = -20/9\nx = 1\nx = 2"} {"input": "Find x for x^3 - 10x^2 + 509/81x + 220/9 = 0", "output": "x^3 - 10x^2 + 509/81x + 220/9 = 0\n(x - -11/9)(x - 9)(x - 20/9) = 0\nx - -11/9 = 0\nx - 9 = 0\nx - 20/9 = 0\nx = -11/9\nx = 9\nx = 20/9"} {"input": "Determine x in x^3 - 17/6x^2 - 7/3x = 0", "output": "x^3 - 17/6x^2 - 7/3x = 0\n(x - 7/2)(x - -2/3)(x - 0) = 0\nx - 7/2 = 0\nx - -2/3 = 0\nx - 0 = 0\nx = 7/2\nx = -2/3\nx = 0"} {"input": "Find x for 6x - 2 = 0", "output": "6x - 2 = 0\n6x = 2\nx = 2 / 6\nx = 1/3"} {"input": "Determine x in x^2 - 46/5x + 96/5 = 0", "output": "x^2 - 46/5x + 96/5 = 0\n(x - 16/5)(x - 6) = 0\nx - 16/5 = 0 or x - 6 = 0\nx = 16/5\nx = 6"} {"input": "Compute the solution of x^2 + 67/40x - 133/80 = 0", "output": "x^2 + 67/40x - 133/80 = 0\n(x - -19/8)(x - 7/10) = 0\nx - -19/8 = 0 or x - 7/10 = 0\nx = -19/8\nx = 7/10"} {"input": "Solve quickly: x^2 - 9x - 10 = 0", "output": "x^2 - 9x - 10 = 0\n(x - -1)(x - 10) = 0\nx - -1 = 0 or x - 10 = 0\nx = -1\nx = 10"} {"input": "Find the solution to x^2 - 7/3x - 10/3 = 0", "output": "x^2 - 7/3x - 10/3 = 0\n(x - -1)(x - 10/3) = 0\nx - -1 = 0 or x - 10/3 = 0\nx = -1\nx = 10/3"} {"input": "Find x for x^2 - 146/21x + 51/7 = 0", "output": "x^2 - 146/21x + 51/7 = 0\n(x - 9/7)(x - 17/3) = 0\nx - 9/7 = 0 or x - 17/3 = 0\nx = 9/7\nx = 17/3"} {"input": "Solve the equation 2x - 16 = 0", "output": "2x - 16 = 0\n2x = 16\nx = 16 / 2\nx = 8"} {"input": "Solve quickly: x^2 + 4x = 0", "output": "x^2 + 4x = 0\n(x - 0)(x - -4) = 0\nx - 0 = 0 or x - -4 = 0\nx = 0\nx = -4"} {"input": "Solve quickly: x^2 + 117/10x + 17 = 0", "output": "x^2 + 117/10x + 17 = 0\n(x - -10)(x - -17/10) = 0\nx - -10 = 0 or x - -17/10 = 0\nx = -10\nx = -17/10"} {"input": "Find x for x^2 - 1/10x - 1/5 = 0", "output": "x^2 - 1/10x - 1/5 = 0\n(x - 1/2)(x - -2/5) = 0\nx - 1/2 = 0 or x - -2/5 = 0\nx = 1/2\nx = -2/5"} {"input": "Find x in x^3 - 62/7x^2 + 47/7x + 8/7 = 0", "output": "x^3 - 62/7x^2 + 47/7x + 8/7 = 0\n(x - 8)(x - 1)(x - -1/7) = 0\nx - 8 = 0\nx - 1 = 0\nx - -1/7 = 0\nx = 8\nx = 1\nx = -1/7"} {"input": "Find x and y such that\n9x + 4y = 77\n6x + 2y = 58", "output": "9x + 4y = 77\n6x + 2y = 58\n\nUsing elimination\n6*(9x + 4y = 77)\n9*(6x + 2y = 58)\n54x + 24y = 462\n54x + 18y = 522\nSubtract equations\n6y = -60\ny = -60/6\ny = -10\n\nSubstitute y\n9x + 4(-10) = 77\n9x = 117\nx = 117/9\nx = 13"} {"input": "What value of x satisfies x^2 - 8x - 20 = 0", "output": "x^2 - 8x - 20 = 0\n(x - 10)(x - -2) = 0\nx - 10 = 0 or x - -2 = 0\nx = 10\nx = -2"} {"input": "Solve the system:\n10x + 10y = 860/7\n10x + 1y = 41/7", "output": "10x + 10y = 860/7\n10x + 1y = 41/7\n\nUsing elimination\n10*(10x + 10y = 860/7)\n10*(10x + 1y = 41/7)\n100x + 100y = 8600/7\n100x + 10y = 410/7\nSubtract equations\n90y = 1170\ny = 1170/90\ny = 13\n\nSubstitute y\n10x + 10(13) = 860/7\n10x = -50/7\nx = -50/7/10\nx = -5/7"} {"input": "Find x in x^2 - 29/35x - 4/5 = 0", "output": "x^2 - 29/35x - 4/5 = 0\n(x - -4/7)(x - 7/5) = 0\nx - -4/7 = 0 or x - 7/5 = 0\nx = -4/7\nx = 7/5"} {"input": "Compute the solution of x^3 + 111/4x^2 + 615/4x - 475/2 = 0", "output": "x^3 + 111/4x^2 + 615/4x - 475/2 = 0\n(x - -10)(x - 5/4)(x - -19) = 0\nx - -10 = 0\nx - 5/4 = 0\nx - -19 = 0\nx = -10\nx = 5/4\nx = -19"} {"input": "Find the solution to 3x + 24/5 = 0", "output": "3x + 24/5 = 0\n3x = -24/5\nx = -24/5 / 3\nx = -8/5"} {"input": "Find the solution to x^3 + 54/5x^2 + 79/5x - 18/5 = 0", "output": "x^3 + 54/5x^2 + 79/5x - 18/5 = 0\n(x - 1/5)(x - -2)(x - -9) = 0\nx - 1/5 = 0\nx - -2 = 0\nx - -9 = 0\nx = 1/5\nx = -2\nx = -9"} {"input": "Determine x in 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Compute the solution of 5x + 35/4 = 0", "output": "5x + 35/4 = 0\n5x = -35/4\nx = -35/4 / 5\nx = -7/4"} {"input": "What value of x satisfies x^3 + 43/2x^2 + 114x + 126 = 0", "output": "x^3 + 43/2x^2 + 114x + 126 = 0\n(x - -6)(x - -14)(x - -3/2) = 0\nx - -6 = 0\nx - -14 = 0\nx - -3/2 = 0\nx = -6\nx = -14\nx = -3/2"} {"input": "Find x and y such that\n1x + 3y = 146/9\n7x + 2y = 167/9", "output": "1x + 3y = 146/9\n7x + 2y = 167/9\n\nUsing elimination\n7*(1x + 3y = 146/9)\n1*(7x + 2y = 167/9)\n7x + 21y = 1022/9\n7x + 2y = 167/9\nSubtract equations\n19y = 95\ny = 95/19\ny = 5\n\nSubstitute y\n1x + 3(5) = 146/9\n1x = 11/9\nx = 11/9/1\nx = 11/9"} {"input": "Determine x in x^2 - 17/6x + 5/3 = 0", "output": "x^2 - 17/6x + 5/3 = 0\n(x - 2)(x - 5/6) = 0\nx - 2 = 0 or x - 5/6 = 0\nx = 2\nx = 5/6"} {"input": "Solve quickly: x^3 + 9/4x^2 - 5/8x - 21/8 = 0", "output": "x^3 + 9/4x^2 - 5/8x - 21/8 = 0\n(x - 1)(x - -3/2)(x - -7/4) = 0\nx - 1 = 0\nx - -3/2 = 0\nx - -7/4 = 0\nx = 1\nx = -3/2\nx = -7/4"} {"input": "Find x and y such that\n9x + 4y = -109/12\n10x + 5y = -55/6", "output": "9x + 4y = -109/12\n10x + 5y = -55/6\n\nUsing elimination\n10*(9x + 4y = -109/12)\n9*(10x + 5y = -55/6)\n90x + 40y = -545/6\n90x + 45y = -165/2\nSubtract equations\n-5y = -25/3\ny = -25/3/-5\ny = 5/3\n\nSubstitute y\n9x + 4(5/3) = -109/12\n9x = -63/4\nx = -63/4/9\nx = -7/4"} {"input": "Find x and y such that\n9x + 4y = -46/3\n2x + 3y = -2", "output": "9x + 4y = -46/3\n2x + 3y = -2\n\nUsing elimination\n2*(9x + 4y = -46/3)\n9*(2x + 3y = -2)\n18x + 8y = -92/3\n18x + 27y = -18\nSubtract equations\n-19y = -38/3\ny = -38/3/-19\ny = 2/3\n\nSubstitute y\n9x + 4(2/3) = -46/3\n9x = -18\nx = -18/9\nx = -2"} {"input": "Solve x^2 + 63/40x - 26/5 = 0", "output": "x^2 + 63/40x - 26/5 = 0\n(x - 13/8)(x - -16/5) = 0\nx - 13/8 = 0 or x - -16/5 = 0\nx = 13/8\nx = -16/5"} {"input": "Find x and y such that\n6x + 7y = 12\n4x + 1y = 13/3", "output": "6x + 7y = 12\n4x + 1y = 13/3\n\nUsing elimination\n4*(6x + 7y = 12)\n6*(4x + 1y = 13/3)\n24x + 28y = 48\n24x + 6y = 26\nSubtract equations\n22y = 22\ny = 22/22\ny = 1\n\nSubstitute y\n6x + 7(1) = 12\n6x = 5\nx = 5/6\nx = 5/6"} {"input": "Determine x in 6x - 114 = 0", "output": "6x - 114 = 0\n6x = 114\nx = 114 / 6\nx = 19"} {"input": "Find the solution to x^2 - 121/7x + 144/7 = 0", "output": "x^2 - 121/7x + 144/7 = 0\n(x - 16)(x - 9/7) = 0\nx - 16 = 0 or x - 9/7 = 0\nx = 16\nx = 9/7"} {"input": "Find x for x^3 + 115/28x^2 + 107/28x + 5/7 = 0", "output": "x^3 + 115/28x^2 + 107/28x + 5/7 = 0\n(x - -20/7)(x - -1)(x - -1/4) = 0\nx - -20/7 = 0\nx - -1 = 0\nx - -1/4 = 0\nx = -20/7\nx = -1\nx = -1/4"} {"input": "Solve simultaneously:\n8x + 5y = 4\n10x + 9y = 16", "output": "8x + 5y = 4\n10x + 9y = 16\n\nUsing elimination\n10*(8x + 5y = 4)\n8*(10x + 9y = 16)\n80x + 50y = 40\n80x + 72y = 128\nSubtract equations\n-22y = -88\ny = -88/-22\ny = 4\n\nSubstitute y\n8x + 5(4) = 4\n8x = -16\nx = -16/8\nx = -2"} {"input": "What value of x satisfies 5x - 19/2 = 0", "output": "5x - 19/2 = 0\n5x = 19/2\nx = 19/2 / 5\nx = 19/10"} {"input": "Find x and y such that\n8x + 2y = -25\n4x + 10y = 28", "output": "8x + 2y = -25\n4x + 10y = 28\n\nUsing elimination\n4*(8x + 2y = -25)\n8*(4x + 10y = 28)\n32x + 8y = -100\n32x + 80y = 224\nSubtract equations\n-72y = -324\ny = -324/-72\ny = 9/2\n\nSubstitute y\n8x + 2(9/2) = -25\n8x = -34\nx = -34/8\nx = -17/4"} {"input": "Solve 9x - 63/5 = 0", "output": "9x - 63/5 = 0\n9x = 63/5\nx = 63/5 / 9\nx = 7/5"} {"input": "Solve x^3 - 71/9x^2 + 127/9x + 5/3 = 0", "output": "x^3 - 71/9x^2 + 127/9x + 5/3 = 0\n(x - 5)(x - -1/9)(x - 3) = 0\nx - 5 = 0\nx - -1/9 = 0\nx - 3 = 0\nx = 5\nx = -1/9\nx = 3"} {"input": "Solve the equations:\n6x + 9y = 354/5\n8x + 2y = 612/5", "output": "6x + 9y = 354/5\n8x + 2y = 612/5\n\nUsing elimination\n8*(6x + 9y = 354/5)\n6*(8x + 2y = 612/5)\n48x + 72y = 2832/5\n48x + 12y = 3672/5\nSubtract equations\n60y = -168\ny = -168/60\ny = -14/5\n\nSubstitute y\n6x + 9(-14/5) = 354/5\n6x = 96\nx = 96/6\nx = 16"} {"input": "Solve 10x - 32 = 0", "output": "10x - 32 = 0\n10x = 32\nx = 32 / 10\nx = 16/5"} {"input": "Solve the equations:\n9x + 9y = -444/7\n4x + 3y = -167/7", "output": "9x + 9y = -444/7\n4x + 3y = -167/7\n\nUsing elimination\n4*(9x + 9y = -444/7)\n9*(4x + 3y = -167/7)\n36x + 36y = -1776/7\n36x + 27y = -1503/7\nSubtract equations\n9y = -39\ny = -39/9\ny = -13/3\n\nSubstitute y\n9x + 9(-13/3) = -444/7\n9x = -171/7\nx = -171/7/9\nx = -19/7"} {"input": "Find the solution to x^3 - 36/7x^2 - 1056/49x - 512/49 = 0", "output": "x^3 - 36/7x^2 - 1056/49x - 512/49 = 0\n(x - 8)(x - -16/7)(x - -4/7) = 0\nx - 8 = 0\nx - -16/7 = 0\nx - -4/7 = 0\nx = 8\nx = -16/7\nx = -4/7"} {"input": "Compute the solution of x^3 - 23/36x^2 - 83/18x + 17/4 = 0", "output": "x^3 - 23/36x^2 - 83/18x + 17/4 = 0\n(x - -9/4)(x - 17/9)(x - 1) = 0\nx - -9/4 = 0\nx - 17/9 = 0\nx - 1 = 0\nx = -9/4\nx = 17/9\nx = 1"} {"input": "Solve 6x + 12 = 0", "output": "6x + 12 = 0\n6x = -12\nx = -12 / 6\nx = -2"} {"input": "What value of x satisfies 2x - 2/7 = 0", "output": "2x - 2/7 = 0\n2x = 2/7\nx = 2/7 / 2\nx = 1/7"} {"input": "Determine x in x^2 - 14/9x - 40/27 = 0", "output": "x^2 - 14/9x - 40/27 = 0\n(x - -2/3)(x - 20/9) = 0\nx - -2/3 = 0 or x - 20/9 = 0\nx = -2/3\nx = 20/9"} {"input": "Solve quickly: x^2 - 17/4x - 9/8 = 0", "output": "x^2 - 17/4x - 9/8 = 0\n(x - -1/4)(x - 9/2) = 0\nx - -1/4 = 0 or x - 9/2 = 0\nx = -1/4\nx = 9/2"} {"input": "Find the solution to x^2 - 1x - 3/4 = 0", "output": "x^2 - 1x - 3/4 = 0\n(x - -1/2)(x - 3/2) = 0\nx - -1/2 = 0 or x - 3/2 = 0\nx = -1/2\nx = 3/2"} {"input": "Determine x in 3x + 15/2 = 0", "output": "3x + 15/2 = 0\n3x = -15/2\nx = -15/2 / 3\nx = -5/2"} {"input": "Solve 1x - 7/6 = 0", "output": "1x - 7/6 = 0\n1x = 7/6\nx = 7/6 / 1\nx = 7/6"} {"input": "Find the solution to 7x - 21 = 0", "output": "7x - 21 = 0\n7x = 21\nx = 21 / 7\nx = 3"} {"input": "Find x in x^2 - 25/2x + 36 = 0", "output": "x^2 - 25/2x + 36 = 0\n(x - 8)(x - 9/2) = 0\nx - 8 = 0 or x - 9/2 = 0\nx = 8\nx = 9/2"} {"input": "Find the solution to x^2 + 3/2x - 136/25 = 0", "output": "x^2 + 3/2x - 136/25 = 0\n(x - -16/5)(x - 17/10) = 0\nx - -16/5 = 0 or x - 17/10 = 0\nx = -16/5\nx = 17/10"} {"input": "Find x and y such that\n9x + 7y = 761/10\n10x + 3y = 107/2", "output": "9x + 7y = 761/10\n10x + 3y = 107/2\n\nUsing elimination\n10*(9x + 7y = 761/10)\n9*(10x + 3y = 107/2)\n90x + 70y = 761\n90x + 27y = 963/2\nSubtract equations\n43y = 559/2\ny = 559/2/43\ny = 13/2\n\nSubstitute y\n9x + 7(13/2) = 761/10\n9x = 153/5\nx = 153/5/9\nx = 17/5"} {"input": "What value of x satisfies x^2 + 12/5x + 7/5 = 0", "output": "x^2 + 12/5x + 7/5 = 0\n(x - -7/5)(x - -1) = 0\nx - -7/5 = 0 or x - -1 = 0\nx = -7/5\nx = -1"} {"input": "Find x for x^3 + 32/9x^2 - 1088/27x - 1024/27 = 0", "output": "x^3 + 32/9x^2 - 1088/27x - 1024/27 = 0\n(x - 16/3)(x - -8)(x - -8/9) = 0\nx - 16/3 = 0\nx - -8 = 0\nx - -8/9 = 0\nx = 16/3\nx = -8\nx = -8/9"} {"input": "Solve quickly: 6x + 48 = 0", "output": "6x + 48 = 0\n6x = -48\nx = -48 / 6\nx = -8"} {"input": "Solve quickly: x^2 + 25/2x + 33/2 = 0", "output": "x^2 + 25/2x + 33/2 = 0\n(x - -11)(x - -3/2) = 0\nx - -11 = 0 or x - -3/2 = 0\nx = -11\nx = -3/2"} {"input": "Solve quickly: x^3 - 127/24x^2 + 33/4x - 10/3 = 0", "output": "x^3 - 127/24x^2 + 33/4x - 10/3 = 0\n(x - 2)(x - 8/3)(x - 5/8) = 0\nx - 2 = 0\nx - 8/3 = 0\nx - 5/8 = 0\nx = 2\nx = 8/3\nx = 5/8"} {"input": "Determine x in x^2 + 52/15x + 28/15 = 0", "output": "x^2 + 52/15x + 28/15 = 0\n(x - -2/3)(x - -14/5) = 0\nx - -2/3 = 0 or x - -14/5 = 0\nx = -2/3\nx = -14/5"} {"input": "Compute the solution of x^3 + 17/2x^2 + 341/16x + 221/16 = 0", "output": "x^3 + 17/2x^2 + 341/16x + 221/16 = 0\n(x - -17/4)(x - -1)(x - -13/4) = 0\nx - -17/4 = 0\nx - -1 = 0\nx - -13/4 = 0\nx = -17/4\nx = -1\nx = -13/4"} {"input": "Solve 1x - 10/3 = 0", "output": "1x - 10/3 = 0\n1x = 10/3\nx = 10/3 / 1\nx = 10/3"} {"input": "Find x and y such that\n6x + 3y = 46/3\n5x + 2y = 106/9", "output": "6x + 3y = 46/3\n5x + 2y = 106/9\n\nUsing elimination\n5*(6x + 3y = 46/3)\n6*(5x + 2y = 106/9)\n30x + 15y = 230/3\n30x + 12y = 212/3\nSubtract equations\n3y = 6\ny = 6/3\ny = 2\n\nSubstitute y\n6x + 3(2) = 46/3\n6x = 28/3\nx = 28/3/6\nx = 14/9"} {"input": "Solve the system:\n8x + 3y = 9/10\n7x + 6y = 36/5", "output": "8x + 3y = 9/10\n7x + 6y = 36/5\n\nUsing elimination\n7*(8x + 3y = 9/10)\n8*(7x + 6y = 36/5)\n56x + 21y = 63/10\n56x + 48y = 288/5\nSubtract equations\n-27y = -513/10\ny = -513/10/-27\ny = 19/10\n\nSubstitute y\n8x + 3(19/10) = 9/10\n8x = -24/5\nx = -24/5/8\nx = -3/5"} {"input": "Solve the equations:\n6x + 4y = 16\n7x + 6y = 20", "output": "6x + 4y = 16\n7x + 6y = 20\n\nUsing elimination\n7*(6x + 4y = 16)\n6*(7x + 6y = 20)\n42x + 28y = 112\n42x + 36y = 120\nSubtract equations\n-8y = -8\ny = -8/-8\ny = 1\n\nSubstitute y\n6x + 4(1) = 16\n6x = 12\nx = 12/6\nx = 2"} {"input": "Compute the solution of x^3 + 16/35x^2 - 208/175x - 128/175 = 0", "output": "x^3 + 16/35x^2 - 208/175x - 128/175 = 0\n(x - 8/7)(x - -4/5)(x - -4/5) = 0\nx - 8/7 = 0\nx - -4/5 = 0\nx - -4/5 = 0\nx = 8/7\nx = -4/5\nx = -4/5"} {"input": "Find x for x^3 + 14/15x^2 - 27x - 884/15 = 0", "output": "x^3 + 14/15x^2 - 27x - 884/15 = 0\n(x - -4)(x - -13/5)(x - 17/3) = 0\nx - -4 = 0\nx - -13/5 = 0\nx - 17/3 = 0\nx = -4\nx = -13/5\nx = 17/3"} {"input": "Solve x^3 - 14x^2 - 81x + 1134 = 0", "output": "x^3 - 14x^2 - 81x + 1134 = 0\n(x - 14)(x - -9)(x - 9) = 0\nx - 14 = 0\nx - -9 = 0\nx - 9 = 0\nx = 14\nx = -9\nx = 9"} {"input": "What value of x satisfies x^2 - 8/7x - 15/7 = 0", "output": "x^2 - 8/7x - 15/7 = 0\n(x - 15/7)(x - -1) = 0\nx - 15/7 = 0 or x - -1 = 0\nx = 15/7\nx = -1"} {"input": "Find x in 6x - 18 = 0", "output": "6x - 18 = 0\n6x = 18\nx = 18 / 6\nx = 3"} {"input": "Find x for x^2 - 5x + 21/4 = 0", "output": "x^2 - 5x + 21/4 = 0\n(x - 7/2)(x - 3/2) = 0\nx - 7/2 = 0 or x - 3/2 = 0\nx = 7/2\nx = 3/2"} {"input": "Find x in 6x + 21 = 0", "output": "6x + 21 = 0\n6x = -21\nx = -21 / 6\nx = -7/2"} {"input": "Find x and y such that\n3x + 6y = -156/7\n10x + 2y = -16/7", "output": "3x + 6y = -156/7\n10x + 2y = -16/7\n\nUsing elimination\n10*(3x + 6y = -156/7)\n3*(10x + 2y = -16/7)\n30x + 60y = -1560/7\n30x + 6y = -48/7\nSubtract equations\n54y = -216\ny = -216/54\ny = -4\n\nSubstitute y\n3x + 6(-4) = -156/7\n3x = 12/7\nx = 12/7/3\nx = 4/7"} {"input": "Find x and y such that\n3x + 5y = 19/70\n2x + 7y = 14/5", "output": "3x + 5y = 19/70\n2x + 7y = 14/5\n\nUsing elimination\n2*(3x + 5y = 19/70)\n3*(2x + 7y = 14/5)\n6x + 10y = 19/35\n6x + 21y = 42/5\nSubtract equations\n-11y = -55/7\ny = -55/7/-11\ny = 5/7\n\nSubstitute y\n3x + 5(5/7) = 19/70\n3x = -33/10\nx = -33/10/3\nx = -11/10"} {"input": "What value of x satisfies x^3 + 12/5x^2 + 173/100x + 33/100 = 0", "output": "x^3 + 12/5x^2 + 173/100x + 33/100 = 0\n(x - -1)(x - -3/10)(x - -11/10) = 0\nx - -1 = 0\nx - -3/10 = 0\nx - -11/10 = 0\nx = -1\nx = -3/10\nx = -11/10"} {"input": "Find x for x^2 - 16/9x - 11/3 = 0", "output": "x^2 - 16/9x - 11/3 = 0\n(x - -11/9)(x - 3) = 0\nx - -11/9 = 0 or x - 3 = 0\nx = -11/9\nx = 3"} {"input": "Solve the system:\n9x + 6y = 131/7\n5x + 10y = 1615/63", "output": "9x + 6y = 131/7\n5x + 10y = 1615/63\n\nUsing elimination\n5*(9x + 6y = 131/7)\n9*(5x + 10y = 1615/63)\n45x + 30y = 655/7\n45x + 90y = 1615/7\nSubtract equations\n-60y = -960/7\ny = -960/7/-60\ny = 16/7\n\nSubstitute y\n9x + 6(16/7) = 131/7\n9x = 5\nx = 5/9\nx = 5/9"} {"input": "Solve the equation 5x - 5/6 = 0", "output": "5x - 5/6 = 0\n5x = 5/6\nx = 5/6 / 5\nx = 1/6"} {"input": "Solve quickly: x^3 - 59/24x^2 - 83/24x + 35/4 = 0", "output": "x^3 - 59/24x^2 - 83/24x + 35/4 = 0\n(x - -15/8)(x - 7/3)(x - 2) = 0\nx - -15/8 = 0\nx - 7/3 = 0\nx - 2 = 0\nx = -15/8\nx = 7/3\nx = 2"} {"input": "Determine x in x^3 - 1583/504x^2 - 116/63x + 17/2 = 0", "output": "x^3 - 1583/504x^2 - 116/63x + 17/2 = 0\n(x - 18/7)(x - -14/9)(x - 17/8) = 0\nx - 18/7 = 0\nx - -14/9 = 0\nx - 17/8 = 0\nx = 18/7\nx = -14/9\nx = 17/8"} {"input": "Solve quickly: x^2 + 11/72x - 26/9 = 0", "output": "x^2 + 11/72x - 26/9 = 0\n(x - -16/9)(x - 13/8) = 0\nx - -16/9 = 0 or x - 13/8 = 0\nx = -16/9\nx = 13/8"} {"input": "Compute the solution of x^2 - 41/2x + 195/2 = 0", "output": "x^2 - 41/2x + 195/2 = 0\n(x - 13)(x - 15/2) = 0\nx - 13 = 0 or x - 15/2 = 0\nx = 13\nx = 15/2"} {"input": "Compute the solution of x^3 - 118/45x^2 - 44/75x + 56/225 = 0", "output": "x^3 - 118/45x^2 - 44/75x + 56/225 = 0\n(x - -2/5)(x - 2/9)(x - 14/5) = 0\nx - -2/5 = 0\nx - 2/9 = 0\nx - 14/5 = 0\nx = -2/5\nx = 2/9\nx = 14/5"} {"input": "What value of x satisfies x^3 - 25/9x^2 - 88/27x = 0", "output": "x^3 - 25/9x^2 - 88/27x = 0\n(x - -8/9)(x - 11/3)(x - 0) = 0\nx - -8/9 = 0\nx - 11/3 = 0\nx - 0 = 0\nx = -8/9\nx = 11/3\nx = 0"} {"input": "Compute the solution of 9x + 45/4 = 0", "output": "9x + 45/4 = 0\n9x = -45/4\nx = -45/4 / 9\nx = -5/4"} {"input": "Solve quickly: x^3 + 347/70x^2 - 19/35x - 117/10 = 0", "output": "x^3 + 347/70x^2 - 19/35x - 117/10 = 0\n(x - -9/2)(x - -13/7)(x - 7/5) = 0\nx - -9/2 = 0\nx - -13/7 = 0\nx - 7/5 = 0\nx = -9/2\nx = -13/7\nx = 7/5"} {"input": "Solve x^2 - 65/21x - 22/3 = 0", "output": "x^2 - 65/21x - 22/3 = 0\n(x - 14/3)(x - -11/7) = 0\nx - 14/3 = 0 or x - -11/7 = 0\nx = 14/3\nx = -11/7"} {"input": "Solve the equations:\n1x + 6y = 49/4\n9x + 3y = 627/8", "output": "1x + 6y = 49/4\n9x + 3y = 627/8\n\nUsing elimination\n9*(1x + 6y = 49/4)\n1*(9x + 3y = 627/8)\n9x + 54y = 441/4\n9x + 3y = 627/8\nSubtract equations\n51y = 255/8\ny = 255/8/51\ny = 5/8\n\nSubstitute y\n1x + 6(5/8) = 49/4\n1x = 17/2\nx = 17/2/1\nx = 17/2"} {"input": "Solve 10x + 75/4 = 0", "output": "10x + 75/4 = 0\n10x = -75/4\nx = -75/4 / 10\nx = -15/8"} {"input": "Compute the solution of 4x - 26/5 = 0", "output": "4x - 26/5 = 0\n4x = 26/5\nx = 26/5 / 4\nx = 13/10"} {"input": "Find x and y such that\n4x + 8y = -34\n7x + 7y = -217/4", "output": "4x + 8y = -34\n7x + 7y = -217/4\n\nUsing elimination\n7*(4x + 8y = -34)\n4*(7x + 7y = -217/4)\n28x + 56y = -238\n28x + 28y = -217\nSubtract equations\n28y = -21\ny = -21/28\ny = -3/4\n\nSubstitute y\n4x + 8(-3/4) = -34\n4x = -28\nx = -28/4\nx = -7"} {"input": "Solve x^3 + 23/70x^2 - 423/70x - 18/7 = 0", "output": "x^3 + 23/70x^2 - 423/70x - 18/7 = 0\n(x - -12/5)(x - 5/2)(x - -3/7) = 0\nx - -12/5 = 0\nx - 5/2 = 0\nx - -3/7 = 0\nx = -12/5\nx = 5/2\nx = -3/7"} {"input": "Solve quickly: x^2 - 3x - 27/4 = 0", "output": "x^2 - 3x - 27/4 = 0\n(x - -3/2)(x - 9/2) = 0\nx - -3/2 = 0 or x - 9/2 = 0\nx = -3/2\nx = 9/2"} {"input": "What value of x satisfies x^2 + 64/15x + 13/3 = 0", "output": "x^2 + 64/15x + 13/3 = 0\n(x - -13/5)(x - -5/3) = 0\nx - -13/5 = 0 or x - -5/3 = 0\nx = -13/5\nx = -5/3"} {"input": "Solve the equations:\n4x + 10y = -94/3\n4x + 7y = -67/3", "output": "4x + 10y = -94/3\n4x + 7y = -67/3\n\nUsing elimination\n4*(4x + 10y = -94/3)\n4*(4x + 7y = -67/3)\n16x + 40y = -376/3\n16x + 28y = -268/3\nSubtract equations\n12y = -36\ny = -36/12\ny = -3\n\nSubstitute y\n4x + 10(-3) = -94/3\n4x = -4/3\nx = -4/3/4\nx = -1/3"} {"input": "Solve the equation x^2 - 13/18x + 1/9 = 0", "output": "x^2 - 13/18x + 1/9 = 0\n(x - 1/2)(x - 2/9) = 0\nx - 1/2 = 0 or x - 2/9 = 0\nx = 1/2\nx = 2/9"} {"input": "Solve the equation x^3 - 8x^2 + 12x = 0", "output": "x^3 - 8x^2 + 12x = 0\n(x - 0)(x - 2)(x - 6) = 0\nx - 0 = 0\nx - 2 = 0\nx - 6 = 0\nx = 0\nx = 2\nx = 6"} {"input": "Solve quickly: x^3 + 1349/56x^2 + 722/7x + 6859/56 = 0", "output": "x^3 + 1349/56x^2 + 722/7x + 6859/56 = 0\n(x - -19/8)(x - -19)(x - -19/7) = 0\nx - -19/8 = 0\nx - -19 = 0\nx - -19/7 = 0\nx = -19/8\nx = -19\nx = -19/7"} {"input": "Solve the system:\n6x + 10y = -87\n5x + 6y = -337/6", "output": "6x + 10y = -87\n5x + 6y = -337/6\n\nUsing elimination\n5*(6x + 10y = -87)\n6*(5x + 6y = -337/6)\n30x + 50y = -435\n30x + 36y = -337\nSubtract equations\n14y = -98\ny = -98/14\ny = -7\n\nSubstitute y\n6x + 10(-7) = -87\n6x = -17\nx = -17/6\nx = -17/6"} {"input": "Determine x in x^2 + 121/72x - 17/18 = 0", "output": "x^2 + 121/72x - 17/18 = 0\n(x - -17/8)(x - 4/9) = 0\nx - -17/8 = 0 or x - 4/9 = 0\nx = -17/8\nx = 4/9"} {"input": "Solve x^3 + 13/10x^2 - 931/10x + 748/5 = 0", "output": "x^3 + 13/10x^2 - 931/10x + 748/5 = 0\n(x - 17/10)(x - 8)(x - -11) = 0\nx - 17/10 = 0\nx - 8 = 0\nx - -11 = 0\nx = 17/10\nx = 8\nx = -11"} {"input": "Solve the equations:\n5x + 1y = 197/10\n3x + 6y = 21", "output": "5x + 1y = 197/10\n3x + 6y = 21\n\nUsing elimination\n3*(5x + 1y = 197/10)\n5*(3x + 6y = 21)\n15x + 3y = 591/10\n15x + 30y = 105\nSubtract equations\n-27y = -459/10\ny = -459/10/-27\ny = 17/10\n\nSubstitute y\n5x + 1(17/10) = 197/10\n5x = 18\nx = 18/5\nx = 18/5"} {"input": "Compute the solution of x^2 + 47/6x + 26/3 = 0", "output": "x^2 + 47/6x + 26/3 = 0\n(x - -4/3)(x - -13/2) = 0\nx - -4/3 = 0 or x - -13/2 = 0\nx = -4/3\nx = -13/2"} {"input": "Solve the system:\n6x + 3y = 18\n10x + 7y = 30", "output": "6x + 3y = 18\n10x + 7y = 30\n\nUsing elimination\n10*(6x + 3y = 18)\n6*(10x + 7y = 30)\n60x + 30y = 180\n60x + 42y = 180\nSubtract equations\n-12y = 0\ny = 0/-12\ny = 0\n\nSubstitute y\n6x + 3(0) = 18\n6x = 18\nx = 18/6\nx = 3"} {"input": "Solve 8x + 80/3 = 0", "output": "8x + 80/3 = 0\n8x = -80/3\nx = -80/3 / 8\nx = -10/3"} {"input": "Solve 2x + 12 = 0", "output": "2x + 12 = 0\n2x = -12\nx = -12 / 2\nx = -6"} {"input": "Determine x in 7x + 49/10 = 0", "output": "7x + 49/10 = 0\n7x = -49/10\nx = -49/10 / 7\nx = -7/10"} {"input": "Solve the equation 9x + 57 = 0", "output": "9x + 57 = 0\n9x = -57\nx = -57 / 9\nx = -19/3"} {"input": "Compute the solution of x^3 - 29/6x^2 + 1409/192x - 57/16 = 0", "output": "x^3 - 29/6x^2 + 1409/192x - 57/16 = 0\n(x - 4/3)(x - 19/8)(x - 9/8) = 0\nx - 4/3 = 0\nx - 19/8 = 0\nx - 9/8 = 0\nx = 4/3\nx = 19/8\nx = 9/8"} {"input": "Solve the equations:\n5x + 4y = 44\n9x + 10y = 75", "output": "5x + 4y = 44\n9x + 10y = 75\n\nUsing elimination\n9*(5x + 4y = 44)\n5*(9x + 10y = 75)\n45x + 36y = 396\n45x + 50y = 375\nSubtract equations\n-14y = 21\ny = 21/-14\ny = -3/2\n\nSubstitute y\n5x + 4(-3/2) = 44\n5x = 50\nx = 50/5\nx = 10"} {"input": "Solve the equations:\n7x + 9y = 34\n4x + 1y = 7", "output": "7x + 9y = 34\n4x + 1y = 7\n\nUsing elimination\n4*(7x + 9y = 34)\n7*(4x + 1y = 7)\n28x + 36y = 136\n28x + 7y = 49\nSubtract equations\n29y = 87\ny = 87/29\ny = 3\n\nSubstitute y\n7x + 9(3) = 34\n7x = 7\nx = 7/7\nx = 1"} {"input": "Solve simultaneously:\n2x + 2y = 26/3\n4x + 1y = 58/3", "output": "2x + 2y = 26/3\n4x + 1y = 58/3\n\nUsing elimination\n4*(2x + 2y = 26/3)\n2*(4x + 1y = 58/3)\n8x + 8y = 104/3\n8x + 2y = 116/3\nSubtract equations\n6y = -4\ny = -4/6\ny = -2/3\n\nSubstitute y\n2x + 2(-2/3) = 26/3\n2x = 10\nx = 10/2\nx = 5"} {"input": "Solve x^2 + 8/5x - 17 = 0", "output": "x^2 + 8/5x - 17 = 0\n(x - -5)(x - 17/5) = 0\nx - -5 = 0 or x - 17/5 = 0\nx = -5\nx = 17/5"} {"input": "What value of x satisfies x^3 - 10/3x^2 + 1/3x + 2 = 0", "output": "x^3 - 10/3x^2 + 1/3x + 2 = 0\n(x - 1)(x - -2/3)(x - 3) = 0\nx - 1 = 0\nx - -2/3 = 0\nx - 3 = 0\nx = 1\nx = -2/3\nx = 3"} {"input": "Find x in x^2 - 27/10x + 17/10 = 0", "output": "x^2 - 27/10x + 17/10 = 0\n(x - 1)(x - 17/10) = 0\nx - 1 = 0 or x - 17/10 = 0\nx = 1\nx = 17/10"} {"input": "Solve the equation 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Solve quickly: 10x + 35/4 = 0", "output": "10x + 35/4 = 0\n10x = -35/4\nx = -35/4 / 10\nx = -7/8"} {"input": "Find x for 10x - 10 = 0", "output": "10x - 10 = 0\n10x = 10\nx = 10 / 10\nx = 1"} {"input": "Solve the equation x^3 + 257/28x^2 + 81/4x + 99/14 = 0", "output": "x^3 + 257/28x^2 + 81/4x + 99/14 = 0\n(x - -6)(x - -3/7)(x - -11/4) = 0\nx - -6 = 0\nx - -3/7 = 0\nx - -11/4 = 0\nx = -6\nx = -3/7\nx = -11/4"} {"input": "Compute the solution of x^3 + 17/8x^2 - 29/16x - 33/8 = 0", "output": "x^3 + 17/8x^2 - 29/16x - 33/8 = 0\n(x - -3/2)(x - 11/8)(x - -2) = 0\nx - -3/2 = 0\nx - 11/8 = 0\nx - -2 = 0\nx = -3/2\nx = 11/8\nx = -2"} {"input": "Determine x in x^3 + 389/36x^2 + 3553/108x + 578/27 = 0", "output": "x^3 + 389/36x^2 + 3553/108x + 578/27 = 0\n(x - -17/4)(x - -17/3)(x - -8/9) = 0\nx - -17/4 = 0\nx - -17/3 = 0\nx - -8/9 = 0\nx = -17/4\nx = -17/3\nx = -8/9"} {"input": "Solve the system:\n4x + 7y = -27/4\n10x + 7y = -183/4", "output": "4x + 7y = -27/4\n10x + 7y = -183/4\n\nUsing elimination\n10*(4x + 7y = -27/4)\n4*(10x + 7y = -183/4)\n40x + 70y = -135/2\n40x + 28y = -183\nSubtract equations\n42y = 231/2\ny = 231/2/42\ny = 11/4\n\nSubstitute y\n4x + 7(11/4) = -27/4\n4x = -26\nx = -26/4\nx = -13/2"} {"input": "What value of x satisfies x^2 + 8/7x - 12/7 = 0", "output": "x^2 + 8/7x - 12/7 = 0\n(x - -2)(x - 6/7) = 0\nx - -2 = 0 or x - 6/7 = 0\nx = -2\nx = 6/7"} {"input": "What value of x satisfies x^3 + 387/28x^2 + 209/28x - 585/14 = 0", "output": "x^3 + 387/28x^2 + 209/28x - 585/14 = 0\n(x - 10/7)(x - -13)(x - -9/4) = 0\nx - 10/7 = 0\nx - -13 = 0\nx - -9/4 = 0\nx = 10/7\nx = -13\nx = -9/4"} {"input": "Find x in x^3 - 205/63x^2 + 919/441x - 85/441 = 0", "output": "x^3 - 205/63x^2 + 919/441x - 85/441 = 0\n(x - 17/7)(x - 5/7)(x - 1/9) = 0\nx - 17/7 = 0\nx - 5/7 = 0\nx - 1/9 = 0\nx = 17/7\nx = 5/7\nx = 1/9"} {"input": "Determine x in 5x + 11 = 0", "output": "5x + 11 = 0\n5x = -11\nx = -11 / 5\nx = -11/5"} {"input": "Find x in x^2 - 17/7x + 30/49 = 0", "output": "x^2 - 17/7x + 30/49 = 0\n(x - 2/7)(x - 15/7) = 0\nx - 2/7 = 0 or x - 15/7 = 0\nx = 2/7\nx = 15/7"} {"input": "What value of x satisfies x^2 + 21/5x + 22/5 = 0", "output": "x^2 + 21/5x + 22/5 = 0\n(x - -11/5)(x - -2) = 0\nx - -11/5 = 0 or x - -2 = 0\nx = -11/5\nx = -2"} {"input": "What value of x satisfies x^2 + 25/9x + 52/27 = 0", "output": "x^2 + 25/9x + 52/27 = 0\n(x - -4/3)(x - -13/9) = 0\nx - -4/3 = 0 or x - -13/9 = 0\nx = -4/3\nx = -13/9"} {"input": "Solve the equation x^2 + 37/9x + 4/9 = 0", "output": "x^2 + 37/9x + 4/9 = 0\n(x - -1/9)(x - -4) = 0\nx - -1/9 = 0 or x - -4 = 0\nx = -1/9\nx = -4"} {"input": "Find x and y such that\n8x + 2y = -32\n10x + 4y = -43", "output": "8x + 2y = -32\n10x + 4y = -43\n\nUsing elimination\n10*(8x + 2y = -32)\n8*(10x + 4y = -43)\n80x + 20y = -320\n80x + 32y = -344\nSubtract equations\n-12y = 24\ny = 24/-12\ny = -2\n\nSubstitute y\n8x + 2(-2) = -32\n8x = -28\nx = -28/8\nx = -7/2"} {"input": "Find x and y such that\n8x + 6y = -466/5\n7x + 6y = -464/5", "output": "8x + 6y = -466/5\n7x + 6y = -464/5\n\nUsing elimination\n7*(8x + 6y = -466/5)\n8*(7x + 6y = -464/5)\n56x + 42y = -3262/5\n56x + 48y = -3712/5\nSubtract equations\n-6y = 90\ny = 90/-6\ny = -15\n\nSubstitute y\n8x + 6(-15) = -466/5\n8x = -16/5\nx = -16/5/8\nx = -2/5"} {"input": "Solve simultaneously:\n1x + 6y = -1/5\n5x + 8y = 9/2", "output": "1x + 6y = -1/5\n5x + 8y = 9/2\n\nUsing elimination\n5*(1x + 6y = -1/5)\n1*(5x + 8y = 9/2)\n5x + 30y = -1\n5x + 8y = 9/2\nSubtract equations\n22y = -11/2\ny = -11/2/22\ny = -1/4\n\nSubstitute y\n1x + 6(-1/4) = -1/5\n1x = 13/10\nx = 13/10/1\nx = 13/10"} {"input": "Find x and y such that\n10x + 7y = -143/4\n6x + 4y = -21", "output": "10x + 7y = -143/4\n6x + 4y = -21\n\nUsing elimination\n6*(10x + 7y = -143/4)\n10*(6x + 4y = -21)\n60x + 42y = -429/2\n60x + 40y = -210\nSubtract equations\n2y = -9/2\ny = -9/2/2\ny = -9/4\n\nSubstitute y\n10x + 7(-9/4) = -143/4\n10x = -20\nx = -20/10\nx = -2"} {"input": "Solve the equations:\n8x + 4y = 48/5\n3x + 2y = 24/5", "output": "8x + 4y = 48/5\n3x + 2y = 24/5\n\nUsing elimination\n3*(8x + 4y = 48/5)\n8*(3x + 2y = 24/5)\n24x + 12y = 144/5\n24x + 16y = 192/5\nSubtract equations\n-4y = -48/5\ny = -48/5/-4\ny = 12/5\n\nSubstitute y\n8x + 4(12/5) = 48/5\n8x = 0\nx = 0/8\nx = 0"} {"input": "Solve 8x + 112/5 = 0", "output": "8x + 112/5 = 0\n8x = -112/5\nx = -112/5 / 8\nx = -14/5"} {"input": "Solve x^2 - 41/8x + 5/8 = 0", "output": "x^2 - 41/8x + 5/8 = 0\n(x - 1/8)(x - 5) = 0\nx - 1/8 = 0 or x - 5 = 0\nx = 1/8\nx = 5"} {"input": "Solve the system:\n2x + 3y = 213/35\n5x + 2y = 90/7", "output": "2x + 3y = 213/35\n5x + 2y = 90/7\n\nUsing elimination\n5*(2x + 3y = 213/35)\n2*(5x + 2y = 90/7)\n10x + 15y = 213/7\n10x + 4y = 180/7\nSubtract equations\n11y = 33/7\ny = 33/7/11\ny = 3/7\n\nSubstitute y\n2x + 3(3/7) = 213/35\n2x = 24/5\nx = 24/5/2\nx = 12/5"} {"input": "Solve the system:\n5x + 2y = -17/2\n2x + 9y = -15/2", "output": "5x + 2y = -17/2\n2x + 9y = -15/2\n\nUsing elimination\n2*(5x + 2y = -17/2)\n5*(2x + 9y = -15/2)\n10x + 4y = -17\n10x + 45y = -75/2\nSubtract equations\n-41y = 41/2\ny = 41/2/-41\ny = -1/2\n\nSubstitute y\n5x + 2(-1/2) = -17/2\n5x = -15/2\nx = -15/2/5\nx = -3/2"} {"input": "Find x for x^3 + 143/40x^2 - 65/16x + 9/20 = 0", "output": "x^3 + 143/40x^2 - 65/16x + 9/20 = 0\n(x - -9/2)(x - 1/8)(x - 4/5) = 0\nx - -9/2 = 0\nx - 1/8 = 0\nx - 4/5 = 0\nx = -9/2\nx = 1/8\nx = 4/5"} {"input": "Find x in x^2 + 1x - 5/16 = 0", "output": "x^2 + 1x - 5/16 = 0\n(x - -5/4)(x - 1/4) = 0\nx - -5/4 = 0 or x - 1/4 = 0\nx = -5/4\nx = 1/4"} {"input": "Solve simultaneously:\n1x + 6y = 34/3\n6x + 6y = 3", "output": "1x + 6y = 34/3\n6x + 6y = 3\n\nUsing elimination\n6*(1x + 6y = 34/3)\n1*(6x + 6y = 3)\n6x + 36y = 68\n6x + 6y = 3\nSubtract equations\n30y = 65\ny = 65/30\ny = 13/6\n\nSubstitute y\n1x + 6(13/6) = 34/3\n1x = -5/3\nx = -5/3/1\nx = -5/3"} {"input": "Find x for x^2 + 49/10x + 51/10 = 0", "output": "x^2 + 49/10x + 51/10 = 0\n(x - -3/2)(x - -17/5) = 0\nx - -3/2 = 0 or x - -17/5 = 0\nx = -3/2\nx = -17/5"} {"input": "Find the solution to x^2 + 27/2x - 7 = 0", "output": "x^2 + 27/2x - 7 = 0\n(x - 1/2)(x - -14) = 0\nx - 1/2 = 0 or x - -14 = 0\nx = 1/2\nx = -14"} {"input": "Find x and y such that\n8x + 2y = -4\n4x + 8y = 40", "output": "8x + 2y = -4\n4x + 8y = 40\n\nUsing elimination\n4*(8x + 2y = -4)\n8*(4x + 8y = 40)\n32x + 8y = -16\n32x + 64y = 320\nSubtract equations\n-56y = -336\ny = -336/-56\ny = 6\n\nSubstitute y\n8x + 2(6) = -4\n8x = -16\nx = -16/8\nx = -2"} {"input": "Solve quickly: 10x - 36 = 0", "output": "10x - 36 = 0\n10x = 36\nx = 36 / 10\nx = 18/5"} {"input": "Find x in x^3 - 124/7x^2 + 467/7x - 494/7 = 0", "output": "x^3 - 124/7x^2 + 467/7x - 494/7 = 0\n(x - 2)(x - 19/7)(x - 13) = 0\nx - 2 = 0\nx - 19/7 = 0\nx - 13 = 0\nx = 2\nx = 19/7\nx = 13"} {"input": "Find the solution to x^3 - 6/5x^2 - 53/20x + 21/10 = 0", "output": "x^3 - 6/5x^2 - 53/20x + 21/10 = 0\n(x - -3/2)(x - 7/10)(x - 2) = 0\nx - -3/2 = 0\nx - 7/10 = 0\nx - 2 = 0\nx = -3/2\nx = 7/10\nx = 2"} {"input": "Solve the equations:\n10x + 7y = -397/9\n1x + 9y = -82/5", "output": "10x + 7y = -397/9\n1x + 9y = -82/5\n\nUsing elimination\n1*(10x + 7y = -397/9)\n10*(1x + 9y = -82/5)\n10x + 7y = -397/9\n10x + 90y = -164\nSubtract equations\n-83y = 1079/9\ny = 1079/9/-83\ny = -13/9\n\nSubstitute y\n10x + 7(-13/9) = -397/9\n10x = -34\nx = -34/10\nx = -17/5"} {"input": "Find x and y such that\n2x + 9y = -440/3\n1x + 8y = -388/3", "output": "2x + 9y = -440/3\n1x + 8y = -388/3\n\nUsing elimination\n1*(2x + 9y = -440/3)\n2*(1x + 8y = -388/3)\n2x + 9y = -440/3\n2x + 16y = -776/3\nSubtract equations\n-7y = 112\ny = 112/-7\ny = -16\n\nSubstitute y\n2x + 9(-16) = -440/3\n2x = -8/3\nx = -8/3/2\nx = -4/3"} {"input": "Determine x in 10x + 30 = 0", "output": "10x + 30 = 0\n10x = -30\nx = -30 / 10\nx = -3"} {"input": "Compute the solution of x^3 - 971/126x^2 + 2399/126x - 136/9 = 0", "output": "x^3 - 971/126x^2 + 2399/126x - 136/9 = 0\n(x - 7/2)(x - 17/7)(x - 16/9) = 0\nx - 7/2 = 0\nx - 17/7 = 0\nx - 16/9 = 0\nx = 7/2\nx = 17/7\nx = 16/9"} {"input": "Solve 4x - 26/5 = 0", "output": "4x - 26/5 = 0\n4x = 26/5\nx = 26/5 / 4\nx = 13/10"} {"input": "Find the solution to x^3 + 31/3x^2 + 379/12x + 55/2 = 0", "output": "x^3 + 31/3x^2 + 379/12x + 55/2 = 0\n(x - -3/2)(x - -11/2)(x - -10/3) = 0\nx - -3/2 = 0\nx - -11/2 = 0\nx - -10/3 = 0\nx = -3/2\nx = -11/2\nx = -10/3"} {"input": "Solve the equation 7x - 133/4 = 0", "output": "7x - 133/4 = 0\n7x = 133/4\nx = 133/4 / 7\nx = 19/4"} {"input": "Solve x^2 - 21/5x + 98/25 = 0", "output": "x^2 - 21/5x + 98/25 = 0\n(x - 7/5)(x - 14/5) = 0\nx - 7/5 = 0 or x - 14/5 = 0\nx = 7/5\nx = 14/5"} {"input": "Determine x in x^3 - 99/35x^2 - 42/5x + 104/7 = 0", "output": "x^3 - 99/35x^2 - 42/5x + 104/7 = 0\n(x - 4)(x - -13/5)(x - 10/7) = 0\nx - 4 = 0\nx - -13/5 = 0\nx - 10/7 = 0\nx = 4\nx = -13/5\nx = 10/7"} {"input": "Find the solution to x^2 - 48/5x - 4 = 0", "output": "x^2 - 48/5x - 4 = 0\n(x - -2/5)(x - 10) = 0\nx - -2/5 = 0 or x - 10 = 0\nx = -2/5\nx = 10"} {"input": "Solve the equation x^2 - 50/3x - 24 = 0", "output": "x^2 - 50/3x - 24 = 0\n(x - 18)(x - -4/3) = 0\nx - 18 = 0 or x - -4/3 = 0\nx = 18\nx = -4/3"} {"input": "What value of x satisfies x^2 - 109/30x + 7/3 = 0", "output": "x^2 - 109/30x + 7/3 = 0\n(x - 14/5)(x - 5/6) = 0\nx - 14/5 = 0 or x - 5/6 = 0\nx = 14/5\nx = 5/6"} {"input": "Find x for 8x - 28 = 0", "output": "8x - 28 = 0\n8x = 28\nx = 28 / 8\nx = 7/2"} {"input": "Solve the system:\n6x + 9y = -243/7\n2x + 5y = -121/7", "output": "6x + 9y = -243/7\n2x + 5y = -121/7\n\nUsing elimination\n2*(6x + 9y = -243/7)\n6*(2x + 5y = -121/7)\n12x + 18y = -486/7\n12x + 30y = -726/7\nSubtract equations\n-12y = 240/7\ny = 240/7/-12\ny = -20/7\n\nSubstitute y\n6x + 9(-20/7) = -243/7\n6x = -9\nx = -9/6\nx = -3/2"} {"input": "Solve the system:\n7x + 2y = -197/6\n9x + 8y = -275/6", "output": "7x + 2y = -197/6\n9x + 8y = -275/6\n\nUsing elimination\n9*(7x + 2y = -197/6)\n7*(9x + 8y = -275/6)\n63x + 18y = -591/2\n63x + 56y = -1925/6\nSubtract equations\n-38y = 76/3\ny = 76/3/-38\ny = -2/3\n\nSubstitute y\n7x + 2(-2/3) = -197/6\n7x = -63/2\nx = -63/2/7\nx = -9/2"} {"input": "Solve quickly: 7x - 70 = 0", "output": "7x - 70 = 0\n7x = 70\nx = 70 / 7\nx = 10"} {"input": "Solve the equation x^3 + 1865/252x^2 + 1103/84x + 323/126 = 0", "output": "x^3 + 1865/252x^2 + 1103/84x + 323/126 = 0\n(x - -17/7)(x - -19/4)(x - -2/9) = 0\nx - -17/7 = 0\nx - -19/4 = 0\nx - -2/9 = 0\nx = -17/7\nx = -19/4\nx = -2/9"} {"input": "Solve the equations:\n10x + 1y = -47/9\n6x + 6y = -13/3", "output": "10x + 1y = -47/9\n6x + 6y = -13/3\n\nUsing elimination\n6*(10x + 1y = -47/9)\n10*(6x + 6y = -13/3)\n60x + 6y = -94/3\n60x + 60y = -130/3\nSubtract equations\n-54y = 12\ny = 12/-54\ny = -2/9\n\nSubstitute y\n10x + 1(-2/9) = -47/9\n10x = -5\nx = -5/10\nx = -1/2"} {"input": "Compute the solution of 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Solve 10x + 6 = 0", "output": "10x + 6 = 0\n10x = -6\nx = -6 / 10\nx = -3/5"} {"input": "What value of x satisfies x^2 - 7/5x - 34/5 = 0", "output": "x^2 - 7/5x - 34/5 = 0\n(x - 17/5)(x - -2) = 0\nx - 17/5 = 0 or x - -2 = 0\nx = 17/5\nx = -2"} {"input": "Solve the equation x^2 - 67/72x + 5/24 = 0", "output": "x^2 - 67/72x + 5/24 = 0\n(x - 3/8)(x - 5/9) = 0\nx - 3/8 = 0 or x - 5/9 = 0\nx = 3/8\nx = 5/9"} {"input": "Solve x^2 - 13/3x + 4 = 0", "output": "x^2 - 13/3x + 4 = 0\n(x - 3)(x - 4/3) = 0\nx - 3 = 0 or x - 4/3 = 0\nx = 3\nx = 4/3"} {"input": "Find x and y such that\n8x + 6y = -50\n7x + 8y = -41", "output": "8x + 6y = -50\n7x + 8y = -41\n\nUsing elimination\n7*(8x + 6y = -50)\n8*(7x + 8y = -41)\n56x + 42y = -350\n56x + 64y = -328\nSubtract equations\n-22y = -22\ny = -22/-22\ny = 1\n\nSubstitute y\n8x + 6(1) = -50\n8x = -56\nx = -56/8\nx = -7"} {"input": "Solve simultaneously:\n10x + 9y = -38/7\n9x + 10y = -152/35", "output": "10x + 9y = -38/7\n9x + 10y = -152/35\n\nUsing elimination\n9*(10x + 9y = -38/7)\n10*(9x + 10y = -152/35)\n90x + 81y = -342/7\n90x + 100y = -304/7\nSubtract equations\n-19y = -38/7\ny = -38/7/-19\ny = 2/7\n\nSubstitute y\n10x + 9(2/7) = -38/7\n10x = -8\nx = -8/10\nx = -4/5"} {"input": "Solve the equations:\n1x + 3y = 169/15\n9x + 1y = 221/5", "output": "1x + 3y = 169/15\n9x + 1y = 221/5\n\nUsing elimination\n9*(1x + 3y = 169/15)\n1*(9x + 1y = 221/5)\n9x + 27y = 507/5\n9x + 1y = 221/5\nSubtract equations\n26y = 286/5\ny = 286/5/26\ny = 11/5\n\nSubstitute y\n1x + 3(11/5) = 169/15\n1x = 14/3\nx = 14/3/1\nx = 14/3"} {"input": "Solve the system:\n1x + 2y = 31/10\n8x + 9y = 103/5", "output": "1x + 2y = 31/10\n8x + 9y = 103/5\n\nUsing elimination\n8*(1x + 2y = 31/10)\n1*(8x + 9y = 103/5)\n8x + 16y = 124/5\n8x + 9y = 103/5\nSubtract equations\n7y = 21/5\ny = 21/5/7\ny = 3/5\n\nSubstitute y\n1x + 2(3/5) = 31/10\n1x = 19/10\nx = 19/10/1\nx = 19/10"} {"input": "Determine x in x^3 - 11/8x^2 - 41/16x + 21/8 = 0", "output": "x^3 - 11/8x^2 - 41/16x + 21/8 = 0\n(x - 2)(x - -3/2)(x - 7/8) = 0\nx - 2 = 0\nx - -3/2 = 0\nx - 7/8 = 0\nx = 2\nx = -3/2\nx = 7/8"} {"input": "Solve the equations:\n5x + 6y = 281/6\n1x + 4y = 247/18", "output": "5x + 6y = 281/6\n1x + 4y = 247/18\n\nUsing elimination\n1*(5x + 6y = 281/6)\n5*(1x + 4y = 247/18)\n5x + 6y = 281/6\n5x + 20y = 1235/18\nSubtract equations\n-14y = -196/9\ny = -196/9/-14\ny = 14/9\n\nSubstitute y\n5x + 6(14/9) = 281/6\n5x = 75/2\nx = 75/2/5\nx = 15/2"} {"input": "Determine x in x^2 - 26/5x - 24/5 = 0", "output": "x^2 - 26/5x - 24/5 = 0\n(x - 6)(x - -4/5) = 0\nx - 6 = 0 or x - -4/5 = 0\nx = 6\nx = -4/5"} {"input": "Find the solution to 1x - 18/7 = 0", "output": "1x - 18/7 = 0\n1x = 18/7\nx = 18/7 / 1\nx = 18/7"} {"input": "Solve the equations:\n9x + 9y = 63/2\n10x + 8y = 31", "output": "9x + 9y = 63/2\n10x + 8y = 31\n\nUsing elimination\n10*(9x + 9y = 63/2)\n9*(10x + 8y = 31)\n90x + 90y = 315\n90x + 72y = 279\nSubtract equations\n18y = 36\ny = 36/18\ny = 2\n\nSubstitute y\n9x + 9(2) = 63/2\n9x = 27/2\nx = 27/2/9\nx = 3/2"} {"input": "Solve the equation x^3 + 233/168x^2 - 10/21x - 25/42 = 0", "output": "x^3 + 233/168x^2 - 10/21x - 25/42 = 0\n(x - -10/7)(x - -5/8)(x - 2/3) = 0\nx - -10/7 = 0\nx - -5/8 = 0\nx - 2/3 = 0\nx = -10/7\nx = -5/8\nx = 2/3"} {"input": "Find x in 7x - 49/6 = 0", "output": "7x - 49/6 = 0\n7x = 49/6\nx = 49/6 / 7\nx = 7/6"} {"input": "Find x in x^3 - 59/10x^2 + 49/18x + 8/5 = 0", "output": "x^3 - 59/10x^2 + 49/18x + 8/5 = 0\n(x - -1/3)(x - 9/10)(x - 16/3) = 0\nx - -1/3 = 0\nx - 9/10 = 0\nx - 16/3 = 0\nx = -1/3\nx = 9/10\nx = 16/3"} {"input": "Solve simultaneously:\n5x + 8y = -88\n10x + 5y = -110", "output": "5x + 8y = -88\n10x + 5y = -110\n\nUsing elimination\n10*(5x + 8y = -88)\n5*(10x + 5y = -110)\n50x + 80y = -880\n50x + 25y = -550\nSubtract equations\n55y = -330\ny = -330/55\ny = -6\n\nSubstitute y\n5x + 8(-6) = -88\n5x = -40\nx = -40/5\nx = -8"} {"input": "Solve the system:\n9x + 5y = -1697/36\n1x + 5y = -473/36", "output": "9x + 5y = -1697/36\n1x + 5y = -473/36\n\nUsing elimination\n1*(9x + 5y = -1697/36)\n9*(1x + 5y = -473/36)\n9x + 5y = -1697/36\n9x + 45y = -473/4\nSubtract equations\n-40y = 640/9\ny = 640/9/-40\ny = -16/9\n\nSubstitute y\n9x + 5(-16/9) = -1697/36\n9x = -153/4\nx = -153/4/9\nx = -17/4"} {"input": "Solve simultaneously:\n3x + 7y = 88/5\n1x + 7y = 56/5", "output": "3x + 7y = 88/5\n1x + 7y = 56/5\n\nUsing elimination\n1*(3x + 7y = 88/5)\n3*(1x + 7y = 56/5)\n3x + 7y = 88/5\n3x + 21y = 168/5\nSubtract equations\n-14y = -16\ny = -16/-14\ny = 8/7\n\nSubstitute y\n3x + 7(8/7) = 88/5\n3x = 48/5\nx = 48/5/3\nx = 16/5"} {"input": "Determine x in 8x + 16 = 0", "output": "8x + 16 = 0\n8x = -16\nx = -16 / 8\nx = -2"} {"input": "Solve the system:\n10x + 3y = -49/2\n9x + 5y = -191/12", "output": "10x + 3y = -49/2\n9x + 5y = -191/12\n\nUsing elimination\n9*(10x + 3y = -49/2)\n10*(9x + 5y = -191/12)\n90x + 27y = -441/2\n90x + 50y = -955/6\nSubtract equations\n-23y = -184/3\ny = -184/3/-23\ny = 8/3\n\nSubstitute y\n10x + 3(8/3) = -49/2\n10x = -65/2\nx = -65/2/10\nx = -13/4"} {"input": "Determine x in x^2 - 2/5x - 33/20 = 0", "output": "x^2 - 2/5x - 33/20 = 0\n(x - -11/10)(x - 3/2) = 0\nx - -11/10 = 0 or x - 3/2 = 0\nx = -11/10\nx = 3/2"} {"input": "What value of x satisfies x^3 + 21/8x^2 - 27/4x - 5 = 0", "output": "x^3 + 21/8x^2 - 27/4x - 5 = 0\n(x - -5/8)(x - -4)(x - 2) = 0\nx - -5/8 = 0\nx - -4 = 0\nx - 2 = 0\nx = -5/8\nx = -4\nx = 2"} {"input": "Solve the equation 4x - 28 = 0", "output": "4x - 28 = 0\n4x = 28\nx = 28 / 4\nx = 7"} {"input": "Solve x^3 + 73/6x^2 + 95/4x - 361/24 = 0", "output": "x^3 + 73/6x^2 + 95/4x - 361/24 = 0\n(x - -19/2)(x - 1/2)(x - -19/6) = 0\nx - -19/2 = 0\nx - 1/2 = 0\nx - -19/6 = 0\nx = -19/2\nx = 1/2\nx = -19/6"} {"input": "Solve simultaneously:\n7x + 3y = -153/4\n10x + 7y = -131/2", "output": "7x + 3y = -153/4\n10x + 7y = -131/2\n\nUsing elimination\n10*(7x + 3y = -153/4)\n7*(10x + 7y = -131/2)\n70x + 30y = -765/2\n70x + 49y = -917/2\nSubtract equations\n-19y = 76\ny = 76/-19\ny = -4\n\nSubstitute y\n7x + 3(-4) = -153/4\n7x = -105/4\nx = -105/4/7\nx = -15/4"} {"input": "What value of x satisfies x^2 - 40/9x + 16/9 = 0", "output": "x^2 - 40/9x + 16/9 = 0\n(x - 4/9)(x - 4) = 0\nx - 4/9 = 0 or x - 4 = 0\nx = 4/9\nx = 4"} {"input": "Determine x in 5x + 15/4 = 0", "output": "5x + 15/4 = 0\n5x = -15/4\nx = -15/4 / 5\nx = -3/4"} {"input": "Compute the solution of x^2 + 31/5x - 28/5 = 0", "output": "x^2 + 31/5x - 28/5 = 0\n(x - -7)(x - 4/5) = 0\nx - -7 = 0 or x - 4/5 = 0\nx = -7\nx = 4/5"} {"input": "Find x for x^3 + 26/45x^2 - 1/135x - 4/135 = 0", "output": "x^3 + 26/45x^2 - 1/135x - 4/135 = 0\n(x - 1/5)(x - -1/3)(x - -4/9) = 0\nx - 1/5 = 0\nx - -1/3 = 0\nx - -4/9 = 0\nx = 1/5\nx = -1/3\nx = -4/9"} {"input": "Solve 1x + 1 = 0", "output": "1x + 1 = 0\n1x = -1\nx = -1 / 1\nx = -1"} {"input": "Solve quickly: x^3 - 16/21x^2 - 71/21x - 34/21 = 0", "output": "x^3 - 16/21x^2 - 71/21x - 34/21 = 0\n(x - -1)(x - 17/7)(x - -2/3) = 0\nx - -1 = 0\nx - 17/7 = 0\nx - -2/3 = 0\nx = -1\nx = 17/7\nx = -2/3"} {"input": "Find the solution to x^3 + 7/3x^2 - 58/3x + 16 = 0", "output": "x^3 + 7/3x^2 - 58/3x + 16 = 0\n(x - -6)(x - 1)(x - 8/3) = 0\nx - -6 = 0\nx - 1 = 0\nx - 8/3 = 0\nx = -6\nx = 1\nx = 8/3"} {"input": "Determine x in x^3 + 17/3x^2 - 103/3x - 39 = 0", "output": "x^3 + 17/3x^2 - 103/3x - 39 = 0\n(x - -9)(x - 13/3)(x - -1) = 0\nx - -9 = 0\nx - 13/3 = 0\nx - -1 = 0\nx = -9\nx = 13/3\nx = -1"} {"input": "Solve the equation 10x - 32 = 0", "output": "10x - 32 = 0\n10x = 32\nx = 32 / 10\nx = 16/5"} {"input": "Solve the equation x^2 + 4x - 32 = 0", "output": "x^2 + 4x - 32 = 0\n(x - -8)(x - 4) = 0\nx - -8 = 0 or x - 4 = 0\nx = -8\nx = 4"} {"input": "Solve the equations:\n6x + 7y = 68\n7x + 3y = 197/6", "output": "6x + 7y = 68\n7x + 3y = 197/6\n\nUsing elimination\n7*(6x + 7y = 68)\n6*(7x + 3y = 197/6)\n42x + 49y = 476\n42x + 18y = 197\nSubtract equations\n31y = 279\ny = 279/31\ny = 9\n\nSubstitute y\n6x + 7(9) = 68\n6x = 5\nx = 5/6\nx = 5/6"} {"input": "Solve quickly: 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Find x for x^2 + 118/15x + 8 = 0", "output": "x^2 + 118/15x + 8 = 0\n(x - -6/5)(x - -20/3) = 0\nx - -6/5 = 0 or x - -20/3 = 0\nx = -6/5\nx = -20/3"} {"input": "Determine x in 8x - 120 = 0", "output": "8x - 120 = 0\n8x = 120\nx = 120 / 8\nx = 15"} {"input": "Solve the equations:\n2x + 7y = -217/6\n4x + 5y = -263/6", "output": "2x + 7y = -217/6\n4x + 5y = -263/6\n\nUsing elimination\n4*(2x + 7y = -217/6)\n2*(4x + 5y = -263/6)\n8x + 28y = -434/3\n8x + 10y = -263/3\nSubtract equations\n18y = -57\ny = -57/18\ny = -19/6\n\nSubstitute y\n2x + 7(-19/6) = -217/6\n2x = -14\nx = -14/2\nx = -7"} {"input": "Solve simultaneously:\n10x + 6y = -16/7\n2x + 3y = 22/7", "output": "10x + 6y = -16/7\n2x + 3y = 22/7\n\nUsing elimination\n2*(10x + 6y = -16/7)\n10*(2x + 3y = 22/7)\n20x + 12y = -32/7\n20x + 30y = 220/7\nSubtract equations\n-18y = -36\ny = -36/-18\ny = 2\n\nSubstitute y\n10x + 6(2) = -16/7\n10x = -100/7\nx = -100/7/10\nx = -10/7"} {"input": "Solve 2x - 11/4 = 0", "output": "2x - 11/4 = 0\n2x = 11/4\nx = 11/4 / 2\nx = 11/8"} {"input": "Find x and y such that\n6x + 10y = -61/4\n4x + 4y = -15/2", "output": "6x + 10y = -61/4\n4x + 4y = -15/2\n\nUsing elimination\n4*(6x + 10y = -61/4)\n6*(4x + 4y = -15/2)\n24x + 40y = -61\n24x + 24y = -45\nSubtract equations\n16y = -16\ny = -16/16\ny = -1\n\nSubstitute y\n6x + 10(-1) = -61/4\n6x = -21/4\nx = -21/4/6\nx = -7/8"} {"input": "Compute the solution of 6x - 19 = 0", "output": "6x - 19 = 0\n6x = 19\nx = 19 / 6\nx = 19/6"} {"input": "What value of x satisfies 3x - 9/7 = 0", "output": "3x - 9/7 = 0\n3x = 9/7\nx = 9/7 / 3\nx = 3/7"} {"input": "Find the solution to x^2 - 14/9x + 16/27 = 0", "output": "x^2 - 14/9x + 16/27 = 0\n(x - 8/9)(x - 2/3) = 0\nx - 8/9 = 0 or x - 2/3 = 0\nx = 8/9\nx = 2/3"} {"input": "Find x in x^3 + 12x^2 + 29x + 18 = 0", "output": "x^3 + 12x^2 + 29x + 18 = 0\n(x - -9)(x - -2)(x - -1) = 0\nx - -9 = 0\nx - -2 = 0\nx - -1 = 0\nx = -9\nx = -2\nx = -1"} {"input": "Compute the solution of x^3 + 122/15x^2 + 19/5x - 722/15 = 0", "output": "x^3 + 122/15x^2 + 19/5x - 722/15 = 0\n(x - 2)(x - -19/5)(x - -19/3) = 0\nx - 2 = 0\nx - -19/5 = 0\nx - -19/3 = 0\nx = 2\nx = -19/5\nx = -19/3"} {"input": "Determine x in 4x - 22 = 0", "output": "4x - 22 = 0\n4x = 22\nx = 22 / 4\nx = 11/2"} {"input": "Solve simultaneously:\n6x + 4y = 67/10\n9x + 10y = 131/20", "output": "6x + 4y = 67/10\n9x + 10y = 131/20\n\nUsing elimination\n9*(6x + 4y = 67/10)\n6*(9x + 10y = 131/20)\n54x + 36y = 603/10\n54x + 60y = 393/10\nSubtract equations\n-24y = 21\ny = 21/-24\ny = -7/8\n\nSubstitute y\n6x + 4(-7/8) = 67/10\n6x = 51/5\nx = 51/5/6\nx = 17/10"} {"input": "Solve quickly: x^2 - 23/3x + 76/9 = 0", "output": "x^2 - 23/3x + 76/9 = 0\n(x - 19/3)(x - 4/3) = 0\nx - 19/3 = 0 or x - 4/3 = 0\nx = 19/3\nx = 4/3"} {"input": "Solve the equations:\n10x + 2y = -10\n9x + 1y = -43/3", "output": "10x + 2y = -10\n9x + 1y = -43/3\n\nUsing elimination\n9*(10x + 2y = -10)\n10*(9x + 1y = -43/3)\n90x + 18y = -90\n90x + 10y = -430/3\nSubtract equations\n8y = 160/3\ny = 160/3/8\ny = 20/3\n\nSubstitute y\n10x + 2(20/3) = -10\n10x = -70/3\nx = -70/3/10\nx = -7/3"} {"input": "Find x for x^2 + 7/2x + 3 = 0", "output": "x^2 + 7/2x + 3 = 0\n(x - -3/2)(x - -2) = 0\nx - -3/2 = 0 or x - -2 = 0\nx = -3/2\nx = -2"} {"input": "Compute the solution of x^2 + 22/5x - 9/20 = 0", "output": "x^2 + 22/5x - 9/20 = 0\n(x - 1/10)(x - -9/2) = 0\nx - 1/10 = 0 or x - -9/2 = 0\nx = 1/10\nx = -9/2"} {"input": "Solve quickly: x^2 + 323/72x + 361/72 = 0", "output": "x^2 + 323/72x + 361/72 = 0\n(x - -19/9)(x - -19/8) = 0\nx - -19/9 = 0 or x - -19/8 = 0\nx = -19/9\nx = -19/8"} {"input": "Find x for 4x + 14/5 = 0", "output": "4x + 14/5 = 0\n4x = -14/5\nx = -14/5 / 4\nx = -7/10"} {"input": "Find x for x^2 + 14/5x - 19/5 = 0", "output": "x^2 + 14/5x - 19/5 = 0\n(x - 1)(x - -19/5) = 0\nx - 1 = 0 or x - -19/5 = 0\nx = 1\nx = -19/5"} {"input": "Determine x in 8x - 24 = 0", "output": "8x - 24 = 0\n8x = 24\nx = 24 / 8\nx = 3"} {"input": "What value of x satisfies x^3 - 127/10x^2 + 88/5x + 121/10 = 0", "output": "x^3 - 127/10x^2 + 88/5x + 121/10 = 0\n(x - 11/5)(x - 11)(x - -1/2) = 0\nx - 11/5 = 0\nx - 11 = 0\nx - -1/2 = 0\nx = 11/5\nx = 11\nx = -1/2"} {"input": "Compute the solution of x^3 + 7/3x^2 - 245/12x + 19/2 = 0", "output": "x^3 + 7/3x^2 - 245/12x + 19/2 = 0\n(x - 19/6)(x - -6)(x - 1/2) = 0\nx - 19/6 = 0\nx - -6 = 0\nx - 1/2 = 0\nx = 19/6\nx = -6\nx = 1/2"} {"input": "Determine x in x^3 + 133/40x^2 - 281/80x - 13/4 = 0", "output": "x^3 + 133/40x^2 - 281/80x - 13/4 = 0\n(x - 13/10)(x - -5/8)(x - -4) = 0\nx - 13/10 = 0\nx - -5/8 = 0\nx - -4 = 0\nx = 13/10\nx = -5/8\nx = -4"} {"input": "Find x for 1x + 7/9 = 0", "output": "1x + 7/9 = 0\n1x = -7/9\nx = -7/9 / 1\nx = -7/9"} {"input": "Solve the system:\n4x + 6y = -106\n2x + 6y = -98", "output": "4x + 6y = -106\n2x + 6y = -98\n\nUsing elimination\n2*(4x + 6y = -106)\n4*(2x + 6y = -98)\n8x + 12y = -212\n8x + 24y = -392\nSubtract equations\n-12y = 180\ny = 180/-12\ny = -15\n\nSubstitute y\n4x + 6(-15) = -106\n4x = -16\nx = -16/4\nx = -4"} {"input": "Compute the solution of x^3 + 481/280x^2 - 97/56x - 57/140 = 0", "output": "x^3 + 481/280x^2 - 97/56x - 57/140 = 0\n(x - -19/8)(x - -1/5)(x - 6/7) = 0\nx - -19/8 = 0\nx - -1/5 = 0\nx - 6/7 = 0\nx = -19/8\nx = -1/5\nx = 6/7"} {"input": "Find x for x^2 + 2/3x - 133/3 = 0", "output": "x^2 + 2/3x - 133/3 = 0\n(x - 19/3)(x - -7) = 0\nx - 19/3 = 0 or x - -7 = 0\nx = 19/3\nx = -7"} {"input": "Determine x in x^3 + 23/5x^2 - 101/5x - 119/5 = 0", "output": "x^3 + 23/5x^2 - 101/5x - 119/5 = 0\n(x - -7)(x - 17/5)(x - -1) = 0\nx - -7 = 0\nx - 17/5 = 0\nx - -1 = 0\nx = -7\nx = 17/5\nx = -1"} {"input": "Find x and y such that\n6x + 10y = 668/21\n8x + 4y = 1076/63", "output": "6x + 10y = 668/21\n8x + 4y = 1076/63\n\nUsing elimination\n8*(6x + 10y = 668/21)\n6*(8x + 4y = 1076/63)\n48x + 80y = 5344/21\n48x + 24y = 2152/21\nSubtract equations\n56y = 152\ny = 152/56\ny = 19/7\n\nSubstitute y\n6x + 10(19/7) = 668/21\n6x = 14/3\nx = 14/3/6\nx = 7/9"} {"input": "Find x in x^3 + 29/28x^2 - 15/14x - 27/28 = 0", "output": "x^3 + 29/28x^2 - 15/14x - 27/28 = 0\n(x - -9/7)(x - 1)(x - -3/4) = 0\nx - -9/7 = 0\nx - 1 = 0\nx - -3/4 = 0\nx = -9/7\nx = 1\nx = -3/4"} {"input": "Solve x^2 + 7/8x - 9/4 = 0", "output": "x^2 + 7/8x - 9/4 = 0\n(x - 9/8)(x - -2) = 0\nx - 9/8 = 0 or x - -2 = 0\nx = 9/8\nx = -2"} {"input": "Solve the equation 3x + 24/5 = 0", "output": "3x + 24/5 = 0\n3x = -24/5\nx = -24/5 / 3\nx = -8/5"} {"input": "Determine x in x^3 - 7/120x^2 - 49/120x + 1/20 = 0", "output": "x^3 - 7/120x^2 - 49/120x + 1/20 = 0\n(x - 1/8)(x - -2/3)(x - 3/5) = 0\nx - 1/8 = 0\nx - -2/3 = 0\nx - 3/5 = 0\nx = 1/8\nx = -2/3\nx = 3/5"} {"input": "Find x in x^2 - 23/10x + 9/10 = 0", "output": "x^2 - 23/10x + 9/10 = 0\n(x - 1/2)(x - 9/5) = 0\nx - 1/2 = 0 or x - 9/5 = 0\nx = 1/2\nx = 9/5"} {"input": "Solve the equation x^2 + 22/5x + 21/5 = 0", "output": "x^2 + 22/5x + 21/5 = 0\n(x - -3)(x - -7/5) = 0\nx - -3 = 0 or x - -7/5 = 0\nx = -3\nx = -7/5"} {"input": "Find the solution to 9x - 27/4 = 0", "output": "9x - 27/4 = 0\n9x = 27/4\nx = 27/4 / 9\nx = 3/4"} {"input": "Compute the solution of x^2 - 29/4x + 51/4 = 0", "output": "x^2 - 29/4x + 51/4 = 0\n(x - 3)(x - 17/4) = 0\nx - 3 = 0 or x - 17/4 = 0\nx = 3\nx = 17/4"} {"input": "Solve 6x + 24/7 = 0", "output": "6x + 24/7 = 0\n6x = -24/7\nx = -24/7 / 6\nx = -4/7"} {"input": "Solve simultaneously:\n3x + 9y = 197/10\n8x + 5y = 167/6", "output": "3x + 9y = 197/10\n8x + 5y = 167/6\n\nUsing elimination\n8*(3x + 9y = 197/10)\n3*(8x + 5y = 167/6)\n24x + 72y = 788/5\n24x + 15y = 167/2\nSubtract equations\n57y = 741/10\ny = 741/10/57\ny = 13/10\n\nSubstitute y\n3x + 9(13/10) = 197/10\n3x = 8\nx = 8/3\nx = 8/3"} {"input": "Find x in x^3 - 41/6x^2 - 185/6x + 425/3 = 0", "output": "x^3 - 41/6x^2 - 185/6x + 425/3 = 0\n(x - -5)(x - 10/3)(x - 17/2) = 0\nx - -5 = 0\nx - 10/3 = 0\nx - 17/2 = 0\nx = -5\nx = 10/3\nx = 17/2"} {"input": "Solve quickly: 8x + 36 = 0", "output": "8x + 36 = 0\n8x = -36\nx = -36 / 8\nx = -9/2"} {"input": "Find the solution to x^3 - 23/10x^2 - 1/2x = 0", "output": "x^3 - 23/10x^2 - 1/2x = 0\n(x - 0)(x - 5/2)(x - -1/5) = 0\nx - 0 = 0\nx - 5/2 = 0\nx - -1/5 = 0\nx = 0\nx = 5/2\nx = -1/5"} {"input": "Determine x in 1x + 19/7 = 0", "output": "1x + 19/7 = 0\n1x = -19/7\nx = -19/7 / 1\nx = -19/7"} {"input": "Solve x^2 - 2x + 1 = 0", "output": "x^2 - 2x + 1 = 0\n(x - 1)(x - 1) = 0\nx - 1 = 0 or x - 1 = 0\nx = 1\nx = 1"} {"input": "Find x in x^2 - 157/40x + 63/20 = 0", "output": "x^2 - 157/40x + 63/20 = 0\n(x - 9/8)(x - 14/5) = 0\nx - 9/8 = 0 or x - 14/5 = 0\nx = 9/8\nx = 14/5"} {"input": "What value of x satisfies 1x + 7/4 = 0", "output": "1x + 7/4 = 0\n1x = -7/4\nx = -7/4 / 1\nx = -7/4"} {"input": "Determine x in 6x - 18/5 = 0", "output": "6x - 18/5 = 0\n6x = 18/5\nx = 18/5 / 6\nx = 3/5"} {"input": "Solve the equation x^3 + 7/10x^2 - 173/80x - 91/160 = 0", "output": "x^3 + 7/10x^2 - 173/80x - 91/160 = 0\n(x - -7/4)(x - -1/4)(x - 13/10) = 0\nx - -7/4 = 0\nx - -1/4 = 0\nx - 13/10 = 0\nx = -7/4\nx = -1/4\nx = 13/10"} {"input": "Compute the solution of 1x - 2 = 0", "output": "1x - 2 = 0\n1x = 2\nx = 2 / 1\nx = 2"} {"input": "Find x and y such that\n6x + 5y = 87/5\n10x + 7y = 137/5", "output": "6x + 5y = 87/5\n10x + 7y = 137/5\n\nUsing elimination\n10*(6x + 5y = 87/5)\n6*(10x + 7y = 137/5)\n60x + 50y = 174\n60x + 42y = 822/5\nSubtract equations\n8y = 48/5\ny = 48/5/8\ny = 6/5\n\nSubstitute y\n6x + 5(6/5) = 87/5\n6x = 57/5\nx = 57/5/6\nx = 19/10"} {"input": "Solve the equation 4x + 8/7 = 0", "output": "4x + 8/7 = 0\n4x = -8/7\nx = -8/7 / 4\nx = -2/7"} {"input": "Find x for x^3 - 59/56x^2 - 211/98x + 195/98 = 0", "output": "x^3 - 59/56x^2 - 211/98x + 195/98 = 0\n(x - 6/7)(x - 13/8)(x - -10/7) = 0\nx - 6/7 = 0\nx - 13/8 = 0\nx - -10/7 = 0\nx = 6/7\nx = 13/8\nx = -10/7"} {"input": "Solve simultaneously:\n1x + 7y = 31/28\n7x + 8y = 18", "output": "1x + 7y = 31/28\n7x + 8y = 18\n\nUsing elimination\n7*(1x + 7y = 31/28)\n1*(7x + 8y = 18)\n7x + 49y = 31/4\n7x + 8y = 18\nSubtract equations\n41y = -41/4\ny = -41/4/41\ny = -1/4\n\nSubstitute y\n1x + 7(-1/4) = 31/28\n1x = 20/7\nx = 20/7/1\nx = 20/7"} {"input": "Find x for 1x - 19/5 = 0", "output": "1x - 19/5 = 0\n1x = 19/5\nx = 19/5 / 1\nx = 19/5"} {"input": "Solve the equation x^3 - 18/5x^2 + 253/180x - 19/180 = 0", "output": "x^3 - 18/5x^2 + 253/180x - 19/180 = 0\n(x - 1/3)(x - 19/6)(x - 1/10) = 0\nx - 1/3 = 0\nx - 19/6 = 0\nx - 1/10 = 0\nx = 1/3\nx = 19/6\nx = 1/10"} {"input": "Solve 9x + 42 = 0", "output": "9x + 42 = 0\n9x = -42\nx = -42 / 9\nx = -14/3"} {"input": "Find the solution to 3x - 54/7 = 0", "output": "3x - 54/7 = 0\n3x = 54/7\nx = 54/7 / 3\nx = 18/7"} {"input": "Solve the system:\n7x + 8y = -115/3\n5x + 3y = -91/6", "output": "7x + 8y = -115/3\n5x + 3y = -91/6\n\nUsing elimination\n5*(7x + 8y = -115/3)\n7*(5x + 3y = -91/6)\n35x + 40y = -575/3\n35x + 21y = -637/6\nSubtract equations\n19y = -171/2\ny = -171/2/19\ny = -9/2\n\nSubstitute y\n7x + 8(-9/2) = -115/3\n7x = -7/3\nx = -7/3/7\nx = -1/3"} {"input": "Find x and y such that\n3x + 10y = 17\n9x + 1y = -7", "output": "3x + 10y = 17\n9x + 1y = -7\n\nUsing elimination\n9*(3x + 10y = 17)\n3*(9x + 1y = -7)\n27x + 90y = 153\n27x + 3y = -21\nSubtract equations\n87y = 174\ny = 174/87\ny = 2\n\nSubstitute y\n3x + 10(2) = 17\n3x = -3\nx = -3/3\nx = -1"} {"input": "Determine x in x^2 - 2/3x - 16/3 = 0", "output": "x^2 - 2/3x - 16/3 = 0\n(x - 8/3)(x - -2) = 0\nx - 8/3 = 0 or x - -2 = 0\nx = 8/3\nx = -2"} {"input": "Find the solution to x^3 - 67/9x^2 + 428/27x - 224/27 = 0", "output": "x^3 - 67/9x^2 + 428/27x - 224/27 = 0\n(x - 4)(x - 7/9)(x - 8/3) = 0\nx - 4 = 0\nx - 7/9 = 0\nx - 8/3 = 0\nx = 4\nx = 7/9\nx = 8/3"} {"input": "Determine x in x^2 - 1/4x - 5/4 = 0", "output": "x^2 - 1/4x - 5/4 = 0\n(x - -1)(x - 5/4) = 0\nx - -1 = 0 or x - 5/4 = 0\nx = -1\nx = 5/4"} {"input": "Solve the system:\n7x + 7y = -763/12\n2x + 6y = -79/2", "output": "7x + 7y = -763/12\n2x + 6y = -79/2\n\nUsing elimination\n2*(7x + 7y = -763/12)\n7*(2x + 6y = -79/2)\n14x + 14y = -763/6\n14x + 42y = -553/2\nSubtract equations\n-28y = 448/3\ny = 448/3/-28\ny = -16/3\n\nSubstitute y\n7x + 7(-16/3) = -763/12\n7x = -105/4\nx = -105/4/7\nx = -15/4"} {"input": "Solve the equations:\n5x + 3y = 191/28\n8x + 5y = 293/28", "output": "5x + 3y = 191/28\n8x + 5y = 293/28\n\nUsing elimination\n8*(5x + 3y = 191/28)\n5*(8x + 5y = 293/28)\n40x + 24y = 382/7\n40x + 25y = 1465/28\nSubtract equations\n-1y = 9/4\ny = 9/4/-1\ny = -9/4\n\nSubstitute y\n5x + 3(-9/4) = 191/28\n5x = 95/7\nx = 95/7/5\nx = 19/7"} {"input": "Solve the equations:\n5x + 5y = -650/21\n3x + 4y = -481/21", "output": "5x + 5y = -650/21\n3x + 4y = -481/21\n\nUsing elimination\n3*(5x + 5y = -650/21)\n5*(3x + 4y = -481/21)\n15x + 15y = -650/7\n15x + 20y = -2405/21\nSubtract equations\n-5y = 65/3\ny = 65/3/-5\ny = -13/3\n\nSubstitute y\n5x + 5(-13/3) = -650/21\n5x = -65/7\nx = -65/7/5\nx = -13/7"} {"input": "Solve the equation 9x + 126 = 0", "output": "9x + 126 = 0\n9x = -126\nx = -126 / 9\nx = -14"} {"input": "Solve simultaneously:\n9x + 2y = 15/8\n9x + 3y = -9/8", "output": "9x + 2y = 15/8\n9x + 3y = -9/8\n\nUsing elimination\n9*(9x + 2y = 15/8)\n9*(9x + 3y = -9/8)\n81x + 18y = 135/8\n81x + 27y = -81/8\nSubtract equations\n-9y = 27\ny = 27/-9\ny = -3\n\nSubstitute y\n9x + 2(-3) = 15/8\n9x = 63/8\nx = 63/8/9\nx = 7/8"} {"input": "Solve 4x + 56/5 = 0", "output": "4x + 56/5 = 0\n4x = -56/5\nx = -56/5 / 4\nx = -14/5"} {"input": "Solve the system:\n6x + 4y = 23/2\n9x + 1y = 19/4", "output": "6x + 4y = 23/2\n9x + 1y = 19/4\n\nUsing elimination\n9*(6x + 4y = 23/2)\n6*(9x + 1y = 19/4)\n54x + 36y = 207/2\n54x + 6y = 57/2\nSubtract equations\n30y = 75\ny = 75/30\ny = 5/2\n\nSubstitute y\n6x + 4(5/2) = 23/2\n6x = 3/2\nx = 3/2/6\nx = 1/4"} {"input": "Solve the system:\n4x + 3y = -3/2\n1x + 10y = -5", "output": "4x + 3y = -3/2\n1x + 10y = -5\n\nUsing elimination\n1*(4x + 3y = -3/2)\n4*(1x + 10y = -5)\n4x + 3y = -3/2\n4x + 40y = -20\nSubtract equations\n-37y = 37/2\ny = 37/2/-37\ny = -1/2\n\nSubstitute y\n4x + 3(-1/2) = -3/2\n4x = 0\nx = 0/4\nx = 0"} {"input": "Solve 5x - 100/3 = 0", "output": "5x - 100/3 = 0\n5x = 100/3\nx = 100/3 / 5\nx = 20/3"} {"input": "Solve the system:\n6x + 4y = 16/3\n3x + 9y = 22/3", "output": "6x + 4y = 16/3\n3x + 9y = 22/3\n\nUsing elimination\n3*(6x + 4y = 16/3)\n6*(3x + 9y = 22/3)\n18x + 12y = 16\n18x + 54y = 44\nSubtract equations\n-42y = -28\ny = -28/-42\ny = 2/3\n\nSubstitute y\n6x + 4(2/3) = 16/3\n6x = 8/3\nx = 8/3/6\nx = 4/9"} {"input": "What value of x satisfies x^2 + 4x + 3 = 0", "output": "x^2 + 4x + 3 = 0\n(x - -3)(x - -1) = 0\nx - -3 = 0 or x - -1 = 0\nx = -3\nx = -1"} {"input": "Solve quickly: x^2 + 42/5x + 49/5 = 0", "output": "x^2 + 42/5x + 49/5 = 0\n(x - -7/5)(x - -7) = 0\nx - -7/5 = 0 or x - -7 = 0\nx = -7/5\nx = -7"} {"input": "Solve the equation x^3 - 95/18x^2 + 37/54x + 38/3 = 0", "output": "x^3 - 95/18x^2 + 37/54x + 38/3 = 0\n(x - -4/3)(x - 9/2)(x - 19/9) = 0\nx - -4/3 = 0\nx - 9/2 = 0\nx - 19/9 = 0\nx = -4/3\nx = 9/2\nx = 19/9"} {"input": "Solve the equation 9x - 21 = 0", "output": "9x - 21 = 0\n9x = 21\nx = 21 / 9\nx = 7/3"} {"input": "Solve the equations:\n8x + 5y = -263/12\n6x + 3y = -59/4", "output": "8x + 5y = -263/12\n6x + 3y = -59/4\n\nUsing elimination\n6*(8x + 5y = -263/12)\n8*(6x + 3y = -59/4)\n48x + 30y = -263/2\n48x + 24y = -118\nSubtract equations\n6y = -27/2\ny = -27/2/6\ny = -9/4\n\nSubstitute y\n8x + 5(-9/4) = -263/12\n8x = -32/3\nx = -32/3/8\nx = -4/3"} {"input": "Find x for x^3 - 202/15x^2 - 341/15x - 4 = 0", "output": "x^3 - 202/15x^2 - 341/15x - 4 = 0\n(x - -4/3)(x - 15)(x - -1/5) = 0\nx - -4/3 = 0\nx - 15 = 0\nx - -1/5 = 0\nx = -4/3\nx = 15\nx = -1/5"} {"input": "Solve quickly: x^3 - 16/5x^2 - 5x + 36/5 = 0", "output": "x^3 - 16/5x^2 - 5x + 36/5 = 0\n(x - 4)(x - -9/5)(x - 1) = 0\nx - 4 = 0\nx - -9/5 = 0\nx - 1 = 0\nx = 4\nx = -9/5\nx = 1"} {"input": "Solve x^2 - 36 = 0", "output": "x^2 - 36 = 0\n(x - -6)(x - 6) = 0\nx - -6 = 0 or x - 6 = 0\nx = -6\nx = 6"} {"input": "Find x in x^3 - 96/5x^2 + 907/20x + 468/5 = 0", "output": "x^3 - 96/5x^2 + 907/20x + 468/5 = 0\n(x - 16)(x - 9/2)(x - -13/10) = 0\nx - 16 = 0\nx - 9/2 = 0\nx - -13/10 = 0\nx = 16\nx = 9/2\nx = -13/10"} {"input": "Find the solution to 3x - 27/7 = 0", "output": "3x - 27/7 = 0\n3x = 27/7\nx = 27/7 / 3\nx = 9/7"} {"input": "What value of x satisfies x^2 + 7/9x + 4/27 = 0", "output": "x^2 + 7/9x + 4/27 = 0\n(x - -4/9)(x - -1/3) = 0\nx - -4/9 = 0 or x - -1/3 = 0\nx = -4/9\nx = -1/3"} {"input": "Solve quickly: 6x - 18/5 = 0", "output": "6x - 18/5 = 0\n6x = 18/5\nx = 18/5 / 6\nx = 3/5"} {"input": "Solve quickly: 10x - 10/3 = 0", "output": "10x - 10/3 = 0\n10x = 10/3\nx = 10/3 / 10\nx = 1/3"} {"input": "Determine x in x^2 + 59/10x + 17/2 = 0", "output": "x^2 + 59/10x + 17/2 = 0\n(x - -17/5)(x - -5/2) = 0\nx - -17/5 = 0 or x - -5/2 = 0\nx = -17/5\nx = -5/2"} {"input": "Solve the equation x^3 - 7/6x^2 - 28/3x + 19/2 = 0", "output": "x^3 - 7/6x^2 - 28/3x + 19/2 = 0\n(x - 19/6)(x - 1)(x - -3) = 0\nx - 19/6 = 0\nx - 1 = 0\nx - -3 = 0\nx = 19/6\nx = 1\nx = -3"} {"input": "Determine x in 8x + 8/3 = 0", "output": "8x + 8/3 = 0\n8x = -8/3\nx = -8/3 / 8\nx = -1/3"} {"input": "Solve the equation x^2 - 36/5x - 28 = 0", "output": "x^2 - 36/5x - 28 = 0\n(x - 10)(x - -14/5) = 0\nx - 10 = 0 or x - -14/5 = 0\nx = 10\nx = -14/5"} {"input": "Find x in x^3 - 65/14x^2 + 39/14x + 45/7 = 0", "output": "x^3 - 65/14x^2 + 39/14x + 45/7 = 0\n(x - 3)(x - 5/2)(x - -6/7) = 0\nx - 3 = 0\nx - 5/2 = 0\nx - -6/7 = 0\nx = 3\nx = 5/2\nx = -6/7"} {"input": "Determine x in x^3 - 41/9x^2 + 523/81x - 665/243 = 0", "output": "x^3 - 41/9x^2 + 523/81x - 665/243 = 0\n(x - 7/9)(x - 5/3)(x - 19/9) = 0\nx - 7/9 = 0\nx - 5/3 = 0\nx - 19/9 = 0\nx = 7/9\nx = 5/3\nx = 19/9"} {"input": "Solve the equations:\n7x + 2y = 34/3\n6x + 5y = 16/3", "output": "7x + 2y = 34/3\n6x + 5y = 16/3\n\nUsing elimination\n6*(7x + 2y = 34/3)\n7*(6x + 5y = 16/3)\n42x + 12y = 68\n42x + 35y = 112/3\nSubtract equations\n-23y = 92/3\ny = 92/3/-23\ny = -4/3\n\nSubstitute y\n7x + 2(-4/3) = 34/3\n7x = 14\nx = 14/7\nx = 2"} {"input": "Find x for 1x + 17/5 = 0", "output": "1x + 17/5 = 0\n1x = -17/5\nx = -17/5 / 1\nx = -17/5"} {"input": "Solve simultaneously:\n4x + 8y = -140\n6x + 8y = -130", "output": "4x + 8y = -140\n6x + 8y = -130\n\nUsing elimination\n6*(4x + 8y = -140)\n4*(6x + 8y = -130)\n24x + 48y = -840\n24x + 32y = -520\nSubtract equations\n16y = -320\ny = -320/16\ny = -20\n\nSubstitute y\n4x + 8(-20) = -140\n4x = 20\nx = 20/4\nx = 5"} {"input": "Find x and y such that\n3x + 10y = -20\n8x + 5y = -85/2", "output": "3x + 10y = -20\n8x + 5y = -85/2\n\nUsing elimination\n8*(3x + 10y = -20)\n3*(8x + 5y = -85/2)\n24x + 80y = -160\n24x + 15y = -255/2\nSubtract equations\n65y = -65/2\ny = -65/2/65\ny = -1/2\n\nSubstitute y\n3x + 10(-1/2) = -20\n3x = -15\nx = -15/3\nx = -5"} {"input": "Solve the equations:\n5x + 6y = -1\n3x + 4y = -1/5", "output": "5x + 6y = -1\n3x + 4y = -1/5\n\nUsing elimination\n3*(5x + 6y = -1)\n5*(3x + 4y = -1/5)\n15x + 18y = -3\n15x + 20y = -1\nSubtract equations\n-2y = -2\ny = -2/-2\ny = 1\n\nSubstitute y\n5x + 6(1) = -1\n5x = -7\nx = -7/5\nx = -7/5"} {"input": "Solve the equations:\n9x + 8y = 547/20\n5x + 5y = 59/4", "output": "9x + 8y = 547/20\n5x + 5y = 59/4\n\nUsing elimination\n5*(9x + 8y = 547/20)\n9*(5x + 5y = 59/4)\n45x + 40y = 547/4\n45x + 45y = 531/4\nSubtract equations\n-5y = 4\ny = 4/-5\ny = -4/5\n\nSubstitute y\n9x + 8(-4/5) = 547/20\n9x = 135/4\nx = 135/4/9\nx = 15/4"} {"input": "Find x in x^3 - 43/14x^2 - 45/7x = 0", "output": "x^3 - 43/14x^2 - 45/7x = 0\n(x - 9/2)(x - 0)(x - -10/7) = 0\nx - 9/2 = 0\nx - 0 = 0\nx - -10/7 = 0\nx = 9/2\nx = 0\nx = -10/7"} {"input": "Find x and y such that\n2x + 7y = -50/3\n3x + 1y = 13", "output": "2x + 7y = -50/3\n3x + 1y = 13\n\nUsing elimination\n3*(2x + 7y = -50/3)\n2*(3x + 1y = 13)\n6x + 21y = -50\n6x + 2y = 26\nSubtract equations\n19y = -76\ny = -76/19\ny = -4\n\nSubstitute y\n2x + 7(-4) = -50/3\n2x = 34/3\nx = 34/3/2\nx = 17/3"} {"input": "Find x for x^3 - 115/14x^2 - 159/14x + 270/7 = 0", "output": "x^3 - 115/14x^2 - 159/14x + 270/7 = 0\n(x - 9)(x - 12/7)(x - -5/2) = 0\nx - 9 = 0\nx - 12/7 = 0\nx - -5/2 = 0\nx = 9\nx = 12/7\nx = -5/2"} {"input": "Solve the system:\n9x + 8y = 40\n5x + 10y = 100/3", "output": "9x + 8y = 40\n5x + 10y = 100/3\n\nUsing elimination\n5*(9x + 8y = 40)\n9*(5x + 10y = 100/3)\n45x + 40y = 200\n45x + 90y = 300\nSubtract equations\n-50y = -100\ny = -100/-50\ny = 2\n\nSubstitute y\n9x + 8(2) = 40\n9x = 24\nx = 24/9\nx = 8/3"} {"input": "Find x in x^2 + 16/5x - 16/5 = 0", "output": "x^2 + 16/5x - 16/5 = 0\n(x - 4/5)(x - -4) = 0\nx - 4/5 = 0 or x - -4 = 0\nx = 4/5\nx = -4"} {"input": "Find the solution to x^2 + 11/30x - 34/15 = 0", "output": "x^2 + 11/30x - 34/15 = 0\n(x - -17/10)(x - 4/3) = 0\nx - -17/10 = 0 or x - 4/3 = 0\nx = -17/10\nx = 4/3"} {"input": "Solve simultaneously:\n2x + 2y = -43/14\n7x + 9y = -77/4", "output": "2x + 2y = -43/14\n7x + 9y = -77/4\n\nUsing elimination\n7*(2x + 2y = -43/14)\n2*(7x + 9y = -77/4)\n14x + 14y = -43/2\n14x + 18y = -77/2\nSubtract equations\n-4y = 17\ny = 17/-4\ny = -17/4\n\nSubstitute y\n2x + 2(-17/4) = -43/14\n2x = 38/7\nx = 38/7/2\nx = 19/7"} {"input": "Solve simultaneously:\n3x + 9y = 43/2\n6x + 1y = 35/2", "output": "3x + 9y = 43/2\n6x + 1y = 35/2\n\nUsing elimination\n6*(3x + 9y = 43/2)\n3*(6x + 1y = 35/2)\n18x + 54y = 129\n18x + 3y = 105/2\nSubtract equations\n51y = 153/2\ny = 153/2/51\ny = 3/2\n\nSubstitute y\n3x + 9(3/2) = 43/2\n3x = 8\nx = 8/3\nx = 8/3"} {"input": "Solve the equation x^3 + 27/2x^2 - 537/50x - 1309/25 = 0", "output": "x^3 + 27/2x^2 - 537/50x - 1309/25 = 0\n(x - -17/10)(x - 11/5)(x - -14) = 0\nx - -17/10 = 0\nx - 11/5 = 0\nx - -14 = 0\nx = -17/10\nx = 11/5\nx = -14"} {"input": "Solve the equation 9x - 117/4 = 0", "output": "9x - 117/4 = 0\n9x = 117/4\nx = 117/4 / 9\nx = 13/4"} {"input": "Find x in x^2 + 5/6x - 1 = 0", "output": "x^2 + 5/6x - 1 = 0\n(x - 2/3)(x - -3/2) = 0\nx - 2/3 = 0 or x - -3/2 = 0\nx = 2/3\nx = -3/2"} {"input": "Find the solution to 10x - 35 = 0", "output": "10x - 35 = 0\n10x = 35\nx = 35 / 10\nx = 7/2"} {"input": "What value of x satisfies x^3 - 83/30x^2 + 11/5x - 8/15 = 0", "output": "x^3 - 83/30x^2 + 11/5x - 8/15 = 0\n(x - 1/2)(x - 8/5)(x - 2/3) = 0\nx - 1/2 = 0\nx - 8/5 = 0\nx - 2/3 = 0\nx = 1/2\nx = 8/5\nx = 2/3"} {"input": "Solve quickly: 5x + 5 = 0", "output": "5x + 5 = 0\n5x = -5\nx = -5 / 5\nx = -1"} {"input": "Solve the system:\n5x + 10y = -1\n2x + 6y = -6/5", "output": "5x + 10y = -1\n2x + 6y = -6/5\n\nUsing elimination\n2*(5x + 10y = -1)\n5*(2x + 6y = -6/5)\n10x + 20y = -2\n10x + 30y = -6\nSubtract equations\n-10y = 4\ny = 4/-10\ny = -2/5\n\nSubstitute y\n5x + 10(-2/5) = -1\n5x = 3\nx = 3/5\nx = 3/5"} {"input": "Determine x in 5x - 30 = 0", "output": "5x - 30 = 0\n5x = 30\nx = 30 / 5\nx = 6"} {"input": "Find x in x^3 - 28/5x^2 - 1076/45x + 112 = 0", "output": "x^3 - 28/5x^2 - 1076/45x + 112 = 0\n(x - 20/3)(x - 18/5)(x - -14/3) = 0\nx - 20/3 = 0\nx - 18/5 = 0\nx - -14/3 = 0\nx = 20/3\nx = 18/5\nx = -14/3"} {"input": "Find x in x^3 - 4/3x^2 + 1/3x = 0", "output": "x^3 - 4/3x^2 + 1/3x = 0\n(x - 1)(x - 1/3)(x - 0) = 0\nx - 1 = 0\nx - 1/3 = 0\nx - 0 = 0\nx = 1\nx = 1/3\nx = 0"} {"input": "Compute the solution of x^3 + 443/20x^2 + 437/10x + 14 = 0", "output": "x^3 + 443/20x^2 + 437/10x + 14 = 0\n(x - -7/4)(x - -2/5)(x - -20) = 0\nx - -7/4 = 0\nx - -2/5 = 0\nx - -20 = 0\nx = -7/4\nx = -2/5\nx = -20"} {"input": "Solve the equations:\n10x + 7y = -89/10\n7x + 6y = -24/5", "output": "10x + 7y = -89/10\n7x + 6y = -24/5\n\nUsing elimination\n7*(10x + 7y = -89/10)\n10*(7x + 6y = -24/5)\n70x + 49y = -623/10\n70x + 60y = -48\nSubtract equations\n-11y = -143/10\ny = -143/10/-11\ny = 13/10\n\nSubstitute y\n10x + 7(13/10) = -89/10\n10x = -18\nx = -18/10\nx = -9/5"} {"input": "Solve the system:\n8x + 7y = -48/5\n6x + 1y = -104/5", "output": "8x + 7y = -48/5\n6x + 1y = -104/5\n\nUsing elimination\n6*(8x + 7y = -48/5)\n8*(6x + 1y = -104/5)\n48x + 42y = -288/5\n48x + 8y = -832/5\nSubtract equations\n34y = 544/5\ny = 544/5/34\ny = 16/5\n\nSubstitute y\n8x + 7(16/5) = -48/5\n8x = -32\nx = -32/8\nx = -4"} {"input": "Find x for x^2 + 19/12x + 5/12 = 0", "output": "x^2 + 19/12x + 5/12 = 0\n(x - -5/4)(x - -1/3) = 0\nx - -5/4 = 0 or x - -1/3 = 0\nx = -5/4\nx = -1/3"} {"input": "Solve the system:\n5x + 9y = -35\n8x + 10y = -45", "output": "5x + 9y = -35\n8x + 10y = -45\n\nUsing elimination\n8*(5x + 9y = -35)\n5*(8x + 10y = -45)\n40x + 72y = -280\n40x + 50y = -225\nSubtract equations\n22y = -55\ny = -55/22\ny = -5/2\n\nSubstitute y\n5x + 9(-5/2) = -35\n5x = -25/2\nx = -25/2/5\nx = -5/2"} {"input": "Solve the system:\n8x + 8y = 32\n2x + 5y = -13", "output": "8x + 8y = 32\n2x + 5y = -13\n\nUsing elimination\n2*(8x + 8y = 32)\n8*(2x + 5y = -13)\n16x + 16y = 64\n16x + 40y = -104\nSubtract equations\n-24y = 168\ny = 168/-24\ny = -7\n\nSubstitute y\n8x + 8(-7) = 32\n8x = 88\nx = 88/8\nx = 11"} {"input": "Solve the equations:\n9x + 8y = -94/5\n2x + 9y = -57/5", "output": "9x + 8y = -94/5\n2x + 9y = -57/5\n\nUsing elimination\n2*(9x + 8y = -94/5)\n9*(2x + 9y = -57/5)\n18x + 16y = -188/5\n18x + 81y = -513/5\nSubtract equations\n-65y = 65\ny = 65/-65\ny = -1\n\nSubstitute y\n9x + 8(-1) = -94/5\n9x = -54/5\nx = -54/5/9\nx = -6/5"} {"input": "Find x in 1x - 1 = 0", "output": "1x - 1 = 0\n1x = 1\nx = 1 / 1\nx = 1"} {"input": "What value of x satisfies x^2 - 23/18x - 1/3 = 0", "output": "x^2 - 23/18x - 1/3 = 0\n(x - -2/9)(x - 3/2) = 0\nx - -2/9 = 0 or x - 3/2 = 0\nx = -2/9\nx = 3/2"} {"input": "Find x in x^2 + 145/24x - 25/6 = 0", "output": "x^2 + 145/24x - 25/6 = 0\n(x - 5/8)(x - -20/3) = 0\nx - 5/8 = 0 or x - -20/3 = 0\nx = 5/8\nx = -20/3"} {"input": "Compute the solution of x^3 - 151/10x^2 - 178/5x + 561/10 = 0", "output": "x^3 - 151/10x^2 - 178/5x + 561/10 = 0\n(x - -3)(x - 11/10)(x - 17) = 0\nx - -3 = 0\nx - 11/10 = 0\nx - 17 = 0\nx = -3\nx = 11/10\nx = 17"} {"input": "Solve the equations:\n5x + 7y = -197/8\n7x + 9y = -263/8", "output": "5x + 7y = -197/8\n7x + 9y = -263/8\n\nUsing elimination\n7*(5x + 7y = -197/8)\n5*(7x + 9y = -263/8)\n35x + 49y = -1379/8\n35x + 45y = -1315/8\nSubtract equations\n4y = -8\ny = -8/4\ny = -2\n\nSubstitute y\n5x + 7(-2) = -197/8\n5x = -85/8\nx = -85/8/5\nx = -17/8"} {"input": "What value of x satisfies x^3 - 175/12x^2 + 127/2x - 260/3 = 0", "output": "x^3 - 175/12x^2 + 127/2x - 260/3 = 0\n(x - 10/3)(x - 13/4)(x - 8) = 0\nx - 10/3 = 0\nx - 13/4 = 0\nx - 8 = 0\nx = 10/3\nx = 13/4\nx = 8"} {"input": "Solve the equations:\n4x + 2y = 32/7\n6x + 1y = 16/7", "output": "4x + 2y = 32/7\n6x + 1y = 16/7\n\nUsing elimination\n6*(4x + 2y = 32/7)\n4*(6x + 1y = 16/7)\n24x + 12y = 192/7\n24x + 4y = 64/7\nSubtract equations\n8y = 128/7\ny = 128/7/8\ny = 16/7\n\nSubstitute y\n4x + 2(16/7) = 32/7\n4x = 0\nx = 0/4\nx = 0"} {"input": "Compute the solution of x^3 - 87/20x^2 - 267/100x + 1463/400 = 0", "output": "x^3 - 87/20x^2 - 267/100x + 1463/400 = 0\n(x - -11/10)(x - 7/10)(x - 19/4) = 0\nx - -11/10 = 0\nx - 7/10 = 0\nx - 19/4 = 0\nx = -11/10\nx = 7/10\nx = 19/4"} {"input": "Find the solution to 5x - 95/8 = 0", "output": "5x - 95/8 = 0\n5x = 95/8\nx = 95/8 / 5\nx = 19/8"} {"input": "Find x and y such that\n4x + 8y = 8/3\n8x + 4y = 16/3", "output": "4x + 8y = 8/3\n8x + 4y = 16/3\n\nUsing elimination\n8*(4x + 8y = 8/3)\n4*(8x + 4y = 16/3)\n32x + 64y = 64/3\n32x + 16y = 64/3\nSubtract equations\n48y = 0\ny = 0/48\ny = 0\n\nSubstitute y\n4x + 8(0) = 8/3\n4x = 8/3\nx = 8/3/4\nx = 2/3"} {"input": "Find x in 4x - 8/3 = 0", "output": "4x - 8/3 = 0\n4x = 8/3\nx = 8/3 / 4\nx = 2/3"} {"input": "Determine x in x^3 + 2/9x^2 - 71/81x - 8/81 = 0", "output": "x^3 + 2/9x^2 - 71/81x - 8/81 = 0\n(x - 8/9)(x - -1)(x - -1/9) = 0\nx - 8/9 = 0\nx - -1 = 0\nx - -1/9 = 0\nx = 8/9\nx = -1\nx = -1/9"} {"input": "Find x for x^3 + 11/6x^2 - 13/2x - 7/3 = 0", "output": "x^3 + 11/6x^2 - 13/2x - 7/3 = 0\n(x - -1/3)(x - -7/2)(x - 2) = 0\nx - -1/3 = 0\nx - -7/2 = 0\nx - 2 = 0\nx = -1/3\nx = -7/2\nx = 2"} {"input": "Solve quickly: 3x - 10/3 = 0", "output": "3x - 10/3 = 0\n3x = 10/3\nx = 10/3 / 3\nx = 10/9"} {"input": "Determine x in x^2 - 1/12x - 65/6 = 0", "output": "x^2 - 1/12x - 65/6 = 0\n(x - -13/4)(x - 10/3) = 0\nx - -13/4 = 0 or x - 10/3 = 0\nx = -13/4\nx = 10/3"} {"input": "Find x and y such that\n1x + 10y = 11/2\n9x + 6y = 99/2", "output": "1x + 10y = 11/2\n9x + 6y = 99/2\n\nUsing elimination\n9*(1x + 10y = 11/2)\n1*(9x + 6y = 99/2)\n9x + 90y = 99/2\n9x + 6y = 99/2\nSubtract equations\n84y = 0\ny = 0/84\ny = 0\n\nSubstitute y\n1x + 10(0) = 11/2\n1x = 11/2\nx = 11/2/1\nx = 11/2"} {"input": "Compute the solution of 2x + 2 = 0", "output": "2x + 2 = 0\n2x = -2\nx = -2 / 2\nx = -1"} {"input": "Find x and y such that\n6x + 7y = -23\n1x + 4y = -37/3", "output": "6x + 7y = -23\n1x + 4y = -37/3\n\nUsing elimination\n1*(6x + 7y = -23)\n6*(1x + 4y = -37/3)\n6x + 7y = -23\n6x + 24y = -74\nSubtract equations\n-17y = 51\ny = 51/-17\ny = -3\n\nSubstitute y\n6x + 7(-3) = -23\n6x = -2\nx = -2/6\nx = -1/3"} {"input": "What value of x satisfies 3x - 21/4 = 0", "output": "3x - 21/4 = 0\n3x = 21/4\nx = 21/4 / 3\nx = 7/4"} {"input": "Solve quickly: x^3 - 149/6x^2 + 445/3x - 1547/6 = 0", "output": "x^3 - 149/6x^2 + 445/3x - 1547/6 = 0\n(x - 7/2)(x - 17)(x - 13/3) = 0\nx - 7/2 = 0\nx - 17 = 0\nx - 13/3 = 0\nx = 7/2\nx = 17\nx = 13/3"} {"input": "Find x and y such that\n3x + 4y = -46\n7x + 8y = -94", "output": "3x + 4y = -46\n7x + 8y = -94\n\nUsing elimination\n7*(3x + 4y = -46)\n3*(7x + 8y = -94)\n21x + 28y = -322\n21x + 24y = -282\nSubtract equations\n4y = -40\ny = -40/4\ny = -10\n\nSubstitute y\n3x + 4(-10) = -46\n3x = -6\nx = -6/3\nx = -2"} {"input": "Find x in 5x - 55/4 = 0", "output": "5x - 55/4 = 0\n5x = 55/4\nx = 55/4 / 5\nx = 11/4"} {"input": "Find x in x^3 + 19/5x^2 + 127/45x - 7/5 = 0", "output": "x^3 + 19/5x^2 + 127/45x - 7/5 = 0\n(x - -9/5)(x - 1/3)(x - -7/3) = 0\nx - -9/5 = 0\nx - 1/3 = 0\nx - -7/3 = 0\nx = -9/5\nx = 1/3\nx = -7/3"} {"input": "Determine x in x^3 - 9/35x^2 - 36/7x = 0", "output": "x^3 - 9/35x^2 - 36/7x = 0\n(x - -15/7)(x - 0)(x - 12/5) = 0\nx - -15/7 = 0\nx - 0 = 0\nx - 12/5 = 0\nx = -15/7\nx = 0\nx = 12/5"} {"input": "Find x and y such that\n8x + 7y = 148/5\n9x + 3y = 147/5", "output": "8x + 7y = 148/5\n9x + 3y = 147/5\n\nUsing elimination\n9*(8x + 7y = 148/5)\n8*(9x + 3y = 147/5)\n72x + 63y = 1332/5\n72x + 24y = 1176/5\nSubtract equations\n39y = 156/5\ny = 156/5/39\ny = 4/5\n\nSubstitute y\n8x + 7(4/5) = 148/5\n8x = 24\nx = 24/8\nx = 3"} {"input": "Find x in x^2 + 51/40x - 19/16 = 0", "output": "x^2 + 51/40x - 19/16 = 0\n(x - -19/10)(x - 5/8) = 0\nx - -19/10 = 0 or x - 5/8 = 0\nx = -19/10\nx = 5/8"} {"input": "Solve the system:\n2x + 4y = 14\n3x + 3y = 12", "output": "2x + 4y = 14\n3x + 3y = 12\n\nUsing elimination\n3*(2x + 4y = 14)\n2*(3x + 3y = 12)\n6x + 12y = 42\n6x + 6y = 24\nSubtract equations\n6y = 18\ny = 18/6\ny = 3\n\nSubstitute y\n2x + 4(3) = 14\n2x = 2\nx = 2/2\nx = 1"} {"input": "Find x in 4x - 4/9 = 0", "output": "4x - 4/9 = 0\n4x = 4/9\nx = 4/9 / 4\nx = 1/9"} {"input": "Determine x in 6x + 18 = 0", "output": "6x + 18 = 0\n6x = -18\nx = -18 / 6\nx = -3"} {"input": "Compute the solution of x^2 + 33/7x + 20/7 = 0", "output": "x^2 + 33/7x + 20/7 = 0\n(x - -5/7)(x - -4) = 0\nx - -5/7 = 0 or x - -4 = 0\nx = -5/7\nx = -4"} {"input": "Find x and y such that\n3x + 3y = 27/2\n5x + 3y = 17/2", "output": "3x + 3y = 27/2\n5x + 3y = 17/2\n\nUsing elimination\n5*(3x + 3y = 27/2)\n3*(5x + 3y = 17/2)\n15x + 15y = 135/2\n15x + 9y = 51/2\nSubtract equations\n6y = 42\ny = 42/6\ny = 7\n\nSubstitute y\n3x + 3(7) = 27/2\n3x = -15/2\nx = -15/2/3\nx = -5/2"} {"input": "Solve the equation 10x + 110/3 = 0", "output": "10x + 110/3 = 0\n10x = -110/3\nx = -110/3 / 10\nx = -11/3"} {"input": "Solve the system:\n3x + 7y = 134\n6x + 7y = 142", "output": "3x + 7y = 134\n6x + 7y = 142\n\nUsing elimination\n6*(3x + 7y = 134)\n3*(6x + 7y = 142)\n18x + 42y = 804\n18x + 21y = 426\nSubtract equations\n21y = 378\ny = 378/21\ny = 18\n\nSubstitute y\n3x + 7(18) = 134\n3x = 8\nx = 8/3\nx = 8/3"} {"input": "Find x in x^3 + 43/2x^2 + 108x + 315/2 = 0", "output": "x^3 + 43/2x^2 + 108x + 315/2 = 0\n(x - -7/2)(x - -3)(x - -15) = 0\nx - -7/2 = 0\nx - -3 = 0\nx - -15 = 0\nx = -7/2\nx = -3\nx = -15"} {"input": "Find the solution to x^2 - 15/4x - 1 = 0", "output": "x^2 - 15/4x - 1 = 0\n(x - -1/4)(x - 4) = 0\nx - -1/4 = 0 or x - 4 = 0\nx = -1/4\nx = 4"} {"input": "Find x in x^3 - 57/14x^2 + 55/14x = 0", "output": "x^3 - 57/14x^2 + 55/14x = 0\n(x - 11/7)(x - 0)(x - 5/2) = 0\nx - 11/7 = 0\nx - 0 = 0\nx - 5/2 = 0\nx = 11/7\nx = 0\nx = 5/2"} {"input": "Compute the solution of x^3 - 131/180x^2 - 203/30x + 392/45 = 0", "output": "x^3 - 131/180x^2 - 203/30x + 392/45 = 0\n(x - 7/4)(x - -14/5)(x - 16/9) = 0\nx - 7/4 = 0\nx - -14/5 = 0\nx - 16/9 = 0\nx = 7/4\nx = -14/5\nx = 16/9"} {"input": "Determine x in x^3 - 13/6x^2 - 107/192x + 19/128 = 0", "output": "x^3 - 13/6x^2 - 107/192x + 19/128 = 0\n(x - -3/8)(x - 1/6)(x - 19/8) = 0\nx - -3/8 = 0\nx - 1/6 = 0\nx - 19/8 = 0\nx = -3/8\nx = 1/6\nx = 19/8"} {"input": "Solve x^3 + 77/8x^2 + 29x + 26 = 0", "output": "x^3 + 77/8x^2 + 29x + 26 = 0\n(x - -4)(x - -4)(x - -13/8) = 0\nx - -4 = 0\nx - -4 = 0\nx - -13/8 = 0\nx = -4\nx = -4\nx = -13/8"} {"input": "Find the solution to x^2 + 1/8x - 39/16 = 0", "output": "x^2 + 1/8x - 39/16 = 0\n(x - 3/2)(x - -13/8) = 0\nx - 3/2 = 0 or x - -13/8 = 0\nx = 3/2\nx = -13/8"} {"input": "Compute the solution of x^2 - 54/35x - 72/35 = 0", "output": "x^2 - 54/35x - 72/35 = 0\n(x - 12/5)(x - -6/7) = 0\nx - 12/5 = 0 or x - -6/7 = 0\nx = 12/5\nx = -6/7"} {"input": "Solve the system:\n9x + 1y = 71/8\n9x + 6y = -249/8", "output": "9x + 1y = 71/8\n9x + 6y = -249/8\n\nUsing elimination\n9*(9x + 1y = 71/8)\n9*(9x + 6y = -249/8)\n81x + 9y = 639/8\n81x + 54y = -2241/8\nSubtract equations\n-45y = 360\ny = 360/-45\ny = -8\n\nSubstitute y\n9x + 1(-8) = 71/8\n9x = 135/8\nx = 135/8/9\nx = 15/8"} {"input": "Find x and y such that\n9x + 5y = 19/2\n3x + 4y = -5", "output": "9x + 5y = 19/2\n3x + 4y = -5\n\nUsing elimination\n3*(9x + 5y = 19/2)\n9*(3x + 4y = -5)\n27x + 15y = 57/2\n27x + 36y = -45\nSubtract equations\n-21y = 147/2\ny = 147/2/-21\ny = -7/2\n\nSubstitute y\n9x + 5(-7/2) = 19/2\n9x = 27\nx = 27/9\nx = 3"} {"input": "What value of x satisfies x^3 - 293/63x^2 + 170/63x - 8/21 = 0", "output": "x^3 - 293/63x^2 + 170/63x - 8/21 = 0\n(x - 3/7)(x - 2/9)(x - 4) = 0\nx - 3/7 = 0\nx - 2/9 = 0\nx - 4 = 0\nx = 3/7\nx = 2/9\nx = 4"} {"input": "Determine x in 8x + 16 = 0", "output": "8x + 16 = 0\n8x = -16\nx = -16 / 8\nx = -2"} {"input": "What value of x satisfies x^2 + 5/4x + 1/4 = 0", "output": "x^2 + 5/4x + 1/4 = 0\n(x - -1/4)(x - -1) = 0\nx - -1/4 = 0 or x - -1 = 0\nx = -1/4\nx = -1"} {"input": "Solve quickly: x^3 - 28/15x^2 - 7x + 22/15 = 0", "output": "x^3 - 28/15x^2 - 7x + 22/15 = 0\n(x - 11/3)(x - 1/5)(x - -2) = 0\nx - 11/3 = 0\nx - 1/5 = 0\nx - -2 = 0\nx = 11/3\nx = 1/5\nx = -2"} {"input": "Solve the equations:\n7x + 3y = 127/2\n6x + 6y = 123", "output": "7x + 3y = 127/2\n6x + 6y = 123\n\nUsing elimination\n6*(7x + 3y = 127/2)\n7*(6x + 6y = 123)\n42x + 18y = 381\n42x + 42y = 861\nSubtract equations\n-24y = -480\ny = -480/-24\ny = 20\n\nSubstitute y\n7x + 3(20) = 127/2\n7x = 7/2\nx = 7/2/7\nx = 1/2"} {"input": "Solve the equation x^3 - 9/70x^2 - 1632/175x + 3179/350 = 0", "output": "x^3 - 9/70x^2 - 1632/175x + 3179/350 = 0\n(x - 17/7)(x - -17/5)(x - 11/10) = 0\nx - 17/7 = 0\nx - -17/5 = 0\nx - 11/10 = 0\nx = 17/7\nx = -17/5\nx = 11/10"} {"input": "Compute the solution of x^3 - 113/18x^2 + 187/48x + 2299/144 = 0", "output": "x^3 - 113/18x^2 + 187/48x + 2299/144 = 0\n(x - 11/4)(x - 19/4)(x - -11/9) = 0\nx - 11/4 = 0\nx - 19/4 = 0\nx - -11/9 = 0\nx = 11/4\nx = 19/4\nx = -11/9"} {"input": "Solve quickly: x^2 - 34/3x + 21 = 0", "output": "x^2 - 34/3x + 21 = 0\n(x - 9)(x - 7/3) = 0\nx - 9 = 0 or x - 7/3 = 0\nx = 9\nx = 7/3"} {"input": "Solve simultaneously:\n1x + 6y = -97/20\n5x + 7y = -439/20", "output": "1x + 6y = -97/20\n5x + 7y = -439/20\n\nUsing elimination\n5*(1x + 6y = -97/20)\n1*(5x + 7y = -439/20)\n5x + 30y = -97/4\n5x + 7y = -439/20\nSubtract equations\n23y = -23/10\ny = -23/10/23\ny = -1/10\n\nSubstitute y\n1x + 6(-1/10) = -97/20\n1x = -17/4\nx = -17/4/1\nx = -17/4"} {"input": "Compute the solution of 9x + 9/2 = 0", "output": "9x + 9/2 = 0\n9x = -9/2\nx = -9/2 / 9\nx = -1/2"} {"input": "What value of x satisfies x^2 - 64/21x + 19/21 = 0", "output": "x^2 - 64/21x + 19/21 = 0\n(x - 19/7)(x - 1/3) = 0\nx - 19/7 = 0 or x - 1/3 = 0\nx = 19/7\nx = 1/3"} {"input": "What value of x satisfies x^2 - 15/7x = 0", "output": "x^2 - 15/7x = 0\n(x - 0)(x - 15/7) = 0\nx - 0 = 0 or x - 15/7 = 0\nx = 0\nx = 15/7"} {"input": "Find x in x^3 - 55/6x^2 + 3/2x = 0", "output": "x^3 - 55/6x^2 + 3/2x = 0\n(x - 1/6)(x - 9)(x - 0) = 0\nx - 1/6 = 0\nx - 9 = 0\nx - 0 = 0\nx = 1/6\nx = 9\nx = 0"} {"input": "Determine x in x^3 - 182/15x^2 - 637/15x - 8 = 0", "output": "x^3 - 182/15x^2 - 637/15x - 8 = 0\n(x - -8/3)(x - 15)(x - -1/5) = 0\nx - -8/3 = 0\nx - 15 = 0\nx - -1/5 = 0\nx = -8/3\nx = 15\nx = -1/5"} {"input": "Compute the solution of x^3 - 1037/140x^2 + 2249/140x - 627/70 = 0", "output": "x^3 - 1037/140x^2 + 2249/140x - 627/70 = 0\n(x - 11/4)(x - 6/7)(x - 19/5) = 0\nx - 11/4 = 0\nx - 6/7 = 0\nx - 19/5 = 0\nx = 11/4\nx = 6/7\nx = 19/5"} {"input": "Solve 9x + 57/2 = 0", "output": "9x + 57/2 = 0\n9x = -57/2\nx = -57/2 / 9\nx = -19/6"} {"input": "Solve 10x + 55/3 = 0", "output": "10x + 55/3 = 0\n10x = -55/3\nx = -55/3 / 10\nx = -11/6"} {"input": "What value of x satisfies x^2 - 67/35x - 76/35 = 0", "output": "x^2 - 67/35x - 76/35 = 0\n(x - -4/5)(x - 19/7) = 0\nx - -4/5 = 0 or x - 19/7 = 0\nx = -4/5\nx = 19/7"} {"input": "What value of x satisfies x^2 + 5/2x - 44 = 0", "output": "x^2 + 5/2x - 44 = 0\n(x - -8)(x - 11/2) = 0\nx - -8 = 0 or x - 11/2 = 0\nx = -8\nx = 11/2"} {"input": "Find x in x^3 - 47/10x^2 + 128/25x + 14/25 = 0", "output": "x^3 - 47/10x^2 + 128/25x + 14/25 = 0\n(x - -1/10)(x - 14/5)(x - 2) = 0\nx - -1/10 = 0\nx - 14/5 = 0\nx - 2 = 0\nx = -1/10\nx = 14/5\nx = 2"} {"input": "Find x in x^3 - 127/6x^2 + 1043/18x - 17 = 0", "output": "x^3 - 127/6x^2 + 1043/18x - 17 = 0\n(x - 18)(x - 1/3)(x - 17/6) = 0\nx - 18 = 0\nx - 1/3 = 0\nx - 17/6 = 0\nx = 18\nx = 1/3\nx = 17/6"} {"input": "Solve the equations:\n3x + 6y = 25/3\n10x + 2y = 160/9", "output": "3x + 6y = 25/3\n10x + 2y = 160/9\n\nUsing elimination\n10*(3x + 6y = 25/3)\n3*(10x + 2y = 160/9)\n30x + 60y = 250/3\n30x + 6y = 160/3\nSubtract equations\n54y = 30\ny = 30/54\ny = 5/9\n\nSubstitute y\n3x + 6(5/9) = 25/3\n3x = 5\nx = 5/3\nx = 5/3"} {"input": "Solve x^2 - 8x - 9 = 0", "output": "x^2 - 8x - 9 = 0\n(x - -1)(x - 9) = 0\nx - -1 = 0 or x - 9 = 0\nx = -1\nx = 9"} {"input": "Solve quickly: 3x + 27/10 = 0", "output": "3x + 27/10 = 0\n3x = -27/10\nx = -27/10 / 3\nx = -9/10"} {"input": "Compute the solution of x^2 - 20/3x = 0", "output": "x^2 - 20/3x = 0\n(x - 0)(x - 20/3) = 0\nx - 0 = 0 or x - 20/3 = 0\nx = 0\nx = 20/3"} {"input": "Solve simultaneously:\n6x + 10y = -80/3\n10x + 10y = -100/3", "output": "6x + 10y = -80/3\n10x + 10y = -100/3\n\nUsing elimination\n10*(6x + 10y = -80/3)\n6*(10x + 10y = -100/3)\n60x + 100y = -800/3\n60x + 60y = -200\nSubtract equations\n40y = -200/3\ny = -200/3/40\ny = -5/3\n\nSubstitute y\n6x + 10(-5/3) = -80/3\n6x = -10\nx = -10/6\nx = -5/3"} {"input": "Compute the solution of x^3 + 116/15x^2 - 65/3x + 10 = 0", "output": "x^3 + 116/15x^2 - 65/3x + 10 = 0\n(x - 5/3)(x - 3/5)(x - -10) = 0\nx - 5/3 = 0\nx - 3/5 = 0\nx - -10 = 0\nx = 5/3\nx = 3/5\nx = -10"} {"input": "What value of x satisfies x^2 - 31/9x + 26/9 = 0", "output": "x^2 - 31/9x + 26/9 = 0\n(x - 2)(x - 13/9) = 0\nx - 2 = 0 or x - 13/9 = 0\nx = 2\nx = 13/9"} {"input": "Determine x in 3x = 0", "output": "3x = 0\n3x = 0\nx = 0 / 3\nx = 0"} {"input": "Solve simultaneously:\n4x + 10y = 83\n6x + 4y = 73/2", "output": "4x + 10y = 83\n6x + 4y = 73/2\n\nUsing elimination\n6*(4x + 10y = 83)\n4*(6x + 4y = 73/2)\n24x + 60y = 498\n24x + 16y = 146\nSubtract equations\n44y = 352\ny = 352/44\ny = 8\n\nSubstitute y\n4x + 10(8) = 83\n4x = 3\nx = 3/4\nx = 3/4"} {"input": "Find the solution to 10x + 11 = 0", "output": "10x + 11 = 0\n10x = -11\nx = -11 / 10\nx = -11/10"} {"input": "Solve x^3 + 9/4x^2 + 127/200x - 21/50 = 0", "output": "x^3 + 9/4x^2 + 127/200x - 21/50 = 0\n(x - -4/5)(x - 3/10)(x - -7/4) = 0\nx - -4/5 = 0\nx - 3/10 = 0\nx - -7/4 = 0\nx = -4/5\nx = 3/10\nx = -7/4"} {"input": "Find x for x^3 - 757/120x^2 + 1361/120x - 19/4 = 0", "output": "x^3 - 757/120x^2 + 1361/120x - 19/4 = 0\n(x - 19/8)(x - 10/3)(x - 3/5) = 0\nx - 19/8 = 0\nx - 10/3 = 0\nx - 3/5 = 0\nx = 19/8\nx = 10/3\nx = 3/5"} {"input": "Find x for x^3 - 5x^2 + 21/4x = 0", "output": "x^3 - 5x^2 + 21/4x = 0\n(x - 0)(x - 7/2)(x - 3/2) = 0\nx - 0 = 0\nx - 7/2 = 0\nx - 3/2 = 0\nx = 0\nx = 7/2\nx = 3/2"} {"input": "Solve simultaneously:\n2x + 5y = -58/3\n2x + 4y = -103/6", "output": "2x + 5y = -58/3\n2x + 4y = -103/6\n\nUsing elimination\n2*(2x + 5y = -58/3)\n2*(2x + 4y = -103/6)\n4x + 10y = -116/3\n4x + 8y = -103/3\nSubtract equations\n2y = -13/3\ny = -13/3/2\ny = -13/6\n\nSubstitute y\n2x + 5(-13/6) = -58/3\n2x = -17/2\nx = -17/2/2\nx = -17/4"} {"input": "Solve simultaneously:\n9x + 1y = 37/70\n4x + 5y = 236/35", "output": "9x + 1y = 37/70\n4x + 5y = 236/35\n\nUsing elimination\n4*(9x + 1y = 37/70)\n9*(4x + 5y = 236/35)\n36x + 4y = 74/35\n36x + 45y = 2124/35\nSubtract equations\n-41y = -410/7\ny = -410/7/-41\ny = 10/7\n\nSubstitute y\n9x + 1(10/7) = 37/70\n9x = -9/10\nx = -9/10/9\nx = -1/10"} {"input": "Solve 1x - 6/5 = 0", "output": "1x - 6/5 = 0\n1x = 6/5\nx = 6/5 / 1\nx = 6/5"} {"input": "Solve 9x + 117/2 = 0", "output": "9x + 117/2 = 0\n9x = -117/2\nx = -117/2 / 9\nx = -13/2"} {"input": "Compute the solution of x^3 + 35/3x^2 + 38/3x - 40 = 0", "output": "x^3 + 35/3x^2 + 38/3x - 40 = 0\n(x - 4/3)(x - -10)(x - -3) = 0\nx - 4/3 = 0\nx - -10 = 0\nx - -3 = 0\nx = 4/3\nx = -10\nx = -3"} {"input": "Determine x in 2x + 12 = 0", "output": "2x + 12 = 0\n2x = -12\nx = -12 / 2\nx = -6"} {"input": "Compute the solution of x^2 + 29/10x + 19/10 = 0", "output": "x^2 + 29/10x + 19/10 = 0\n(x - -19/10)(x - -1) = 0\nx - -19/10 = 0 or x - -1 = 0\nx = -19/10\nx = -1"} {"input": "Find the solution to 9x - 27 = 0", "output": "9x - 27 = 0\n9x = 27\nx = 27 / 9\nx = 3"} {"input": "Solve x^3 - 26/7x^2 + 29/7x - 10/7 = 0", "output": "x^3 - 26/7x^2 + 29/7x - 10/7 = 0\n(x - 1)(x - 2)(x - 5/7) = 0\nx - 1 = 0\nx - 2 = 0\nx - 5/7 = 0\nx = 1\nx = 2\nx = 5/7"} {"input": "Solve the equations:\n8x + 4y = 124/3\n5x + 8y = 358/3", "output": "8x + 4y = 124/3\n5x + 8y = 358/3\n\nUsing elimination\n5*(8x + 4y = 124/3)\n8*(5x + 8y = 358/3)\n40x + 20y = 620/3\n40x + 64y = 2864/3\nSubtract equations\n-44y = -748\ny = -748/-44\ny = 17\n\nSubstitute y\n8x + 4(17) = 124/3\n8x = -80/3\nx = -80/3/8\nx = -10/3"} {"input": "Compute the solution of x^2 - 59/12x + 6 = 0", "output": "x^2 - 59/12x + 6 = 0\n(x - 8/3)(x - 9/4) = 0\nx - 8/3 = 0 or x - 9/4 = 0\nx = 8/3\nx = 9/4"} {"input": "Solve 1x + 8/3 = 0", "output": "1x + 8/3 = 0\n1x = -8/3\nx = -8/3 / 1\nx = -8/3"} {"input": "Determine x in x^3 - 141/14x^2 + 51/14x + 578/7 = 0", "output": "x^3 - 141/14x^2 + 51/14x + 578/7 = 0\n(x - -17/7)(x - 4)(x - 17/2) = 0\nx - -17/7 = 0\nx - 4 = 0\nx - 17/2 = 0\nx = -17/7\nx = 4\nx = 17/2"} {"input": "Determine x in x^3 - 91/18x^2 - 37/18x + 35/3 = 0", "output": "x^3 - 91/18x^2 - 37/18x + 35/3 = 0\n(x - 14/9)(x - 5)(x - -3/2) = 0\nx - 14/9 = 0\nx - 5 = 0\nx - -3/2 = 0\nx = 14/9\nx = 5\nx = -3/2"} {"input": "Find x for x^2 - 173/36x + 91/18 = 0", "output": "x^2 - 173/36x + 91/18 = 0\n(x - 13/4)(x - 14/9) = 0\nx - 13/4 = 0 or x - 14/9 = 0\nx = 13/4\nx = 14/9"} {"input": "Solve the equations:\n8x + 1y = 23/2\n9x + 1y = 107/8", "output": "8x + 1y = 23/2\n9x + 1y = 107/8\n\nUsing elimination\n9*(8x + 1y = 23/2)\n8*(9x + 1y = 107/8)\n72x + 9y = 207/2\n72x + 8y = 107\nSubtract equations\n1y = -7/2\ny = -7/2/1\ny = -7/2\n\nSubstitute y\n8x + 1(-7/2) = 23/2\n8x = 15\nx = 15/8\nx = 15/8"} {"input": "Find x for x^3 + 179/42x^2 - 5/147x - 1700/147 = 0", "output": "x^3 + 179/42x^2 - 5/147x - 1700/147 = 0\n(x - -17/6)(x - -20/7)(x - 10/7) = 0\nx - -17/6 = 0\nx - -20/7 = 0\nx - 10/7 = 0\nx = -17/6\nx = -20/7\nx = 10/7"} {"input": "Find the solution to 8x + 72/7 = 0", "output": "8x + 72/7 = 0\n8x = -72/7\nx = -72/7 / 8\nx = -9/7"} {"input": "Find x in 4x - 56/9 = 0", "output": "4x - 56/9 = 0\n4x = 56/9\nx = 56/9 / 4\nx = 14/9"} {"input": "Find x in x^2 - 99/5x + 238/5 = 0", "output": "x^2 - 99/5x + 238/5 = 0\n(x - 17)(x - 14/5) = 0\nx - 17 = 0 or x - 14/5 = 0\nx = 17\nx = 14/5"} {"input": "Find x for x^3 + 1x^2 - 173/100x - 819/500 = 0", "output": "x^3 + 1x^2 - 173/100x - 819/500 = 0\n(x - -9/10)(x - 13/10)(x - -7/5) = 0\nx - -9/10 = 0\nx - 13/10 = 0\nx - -7/5 = 0\nx = -9/10\nx = 13/10\nx = -7/5"} {"input": "Determine x in x^3 + 79/120x^2 - 63/20x - 3 = 0", "output": "x^3 + 79/120x^2 - 63/20x - 3 = 0\n(x - -6/5)(x - 15/8)(x - -4/3) = 0\nx - -6/5 = 0\nx - 15/8 = 0\nx - -4/3 = 0\nx = -6/5\nx = 15/8\nx = -4/3"} {"input": "Compute the solution of x^2 + 32/15x - 4 = 0", "output": "x^2 + 32/15x - 4 = 0\n(x - -10/3)(x - 6/5) = 0\nx - -10/3 = 0 or x - 6/5 = 0\nx = -10/3\nx = 6/5"} {"input": "Solve 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Solve the system:\n9x + 7y = -7/2\n7x + 7y = -7/2", "output": "9x + 7y = -7/2\n7x + 7y = -7/2\n\nUsing elimination\n7*(9x + 7y = -7/2)\n9*(7x + 7y = -7/2)\n63x + 49y = -49/2\n63x + 63y = -63/2\nSubtract equations\n-14y = 7\ny = 7/-14\ny = -1/2\n\nSubstitute y\n9x + 7(-1/2) = -7/2\n9x = 0\nx = 0/9\nx = 0"} {"input": "Find the solution to x^3 - 73/40x^2 - 323/40x + 273/20 = 0", "output": "x^3 - 73/40x^2 - 323/40x + 273/20 = 0\n(x - 13/8)(x - 3)(x - -14/5) = 0\nx - 13/8 = 0\nx - 3 = 0\nx - -14/5 = 0\nx = 13/8\nx = 3\nx = -14/5"} {"input": "Solve the equation x^2 + 23/4x - 39/8 = 0", "output": "x^2 + 23/4x - 39/8 = 0\n(x - 3/4)(x - -13/2) = 0\nx - 3/4 = 0 or x - -13/2 = 0\nx = 3/4\nx = -13/2"} {"input": "Compute the solution of x^2 + 37/10x + 33/10 = 0", "output": "x^2 + 37/10x + 33/10 = 0\n(x - -11/5)(x - -3/2) = 0\nx - -11/5 = 0 or x - -3/2 = 0\nx = -11/5\nx = -3/2"} {"input": "Solve quickly: 3x + 30/7 = 0", "output": "3x + 30/7 = 0\n3x = -30/7\nx = -30/7 / 3\nx = -10/7"} {"input": "Find x for 3x + 24/5 = 0", "output": "3x + 24/5 = 0\n3x = -24/5\nx = -24/5 / 3\nx = -8/5"} {"input": "Find the solution to x^3 - 35/24x^2 - 47/144x + 13/144 = 0", "output": "x^3 - 35/24x^2 - 47/144x + 13/144 = 0\n(x - 13/8)(x - -1/3)(x - 1/6) = 0\nx - 13/8 = 0\nx - -1/3 = 0\nx - 1/6 = 0\nx = 13/8\nx = -1/3\nx = 1/6"} {"input": "Find x in x^2 + 43/18x - 5/18 = 0", "output": "x^2 + 43/18x - 5/18 = 0\n(x - -5/2)(x - 1/9) = 0\nx - -5/2 = 0 or x - 1/9 = 0\nx = -5/2\nx = 1/9"} {"input": "Solve the equation x^3 - 3/5x^2 - 22/25x + 24/125 = 0", "output": "x^3 - 3/5x^2 - 22/25x + 24/125 = 0\n(x - 6/5)(x - 1/5)(x - -4/5) = 0\nx - 6/5 = 0\nx - 1/5 = 0\nx - -4/5 = 0\nx = 6/5\nx = 1/5\nx = -4/5"} {"input": "Determine x in 5x + 35/6 = 0", "output": "5x + 35/6 = 0\n5x = -35/6\nx = -35/6 / 5\nx = -7/6"} {"input": "Determine x in x^3 + 4x^2 + 13/4x + 3/4 = 0", "output": "x^3 + 4x^2 + 13/4x + 3/4 = 0\n(x - -1/2)(x - -1/2)(x - -3) = 0\nx - -1/2 = 0\nx - -1/2 = 0\nx - -3 = 0\nx = -1/2\nx = -1/2\nx = -3"} {"input": "Find the solution to x^3 - 35/6x^2 - 1127/6x - 561 = 0", "output": "x^3 - 35/6x^2 - 1127/6x - 561 = 0\n(x - -11/3)(x - 18)(x - -17/2) = 0\nx - -11/3 = 0\nx - 18 = 0\nx - -17/2 = 0\nx = -11/3\nx = 18\nx = -17/2"} {"input": "Determine x in x^2 + 8x - 20 = 0", "output": "x^2 + 8x - 20 = 0\n(x - -10)(x - 2) = 0\nx - -10 = 0 or x - 2 = 0\nx = -10\nx = 2"} {"input": "Solve the equation x^3 + 9/2x^2 - 61/16x - 819/32 = 0", "output": "x^3 + 9/2x^2 - 61/16x - 819/32 = 0\n(x - -13/4)(x - -7/2)(x - 9/4) = 0\nx - -13/4 = 0\nx - -7/2 = 0\nx - 9/4 = 0\nx = -13/4\nx = -7/2\nx = 9/4"} {"input": "What value of x satisfies x^2 + 9x = 0", "output": "x^2 + 9x = 0\n(x - -9)(x - 0) = 0\nx - -9 = 0 or x - 0 = 0\nx = -9\nx = 0"} {"input": "Solve x^3 - 32/5x^2 + 52/25x + 48/25 = 0", "output": "x^3 - 32/5x^2 + 52/25x + 48/25 = 0\n(x - 4/5)(x - 6)(x - -2/5) = 0\nx - 4/5 = 0\nx - 6 = 0\nx - -2/5 = 0\nx = 4/5\nx = 6\nx = -2/5"} {"input": "Find x and y such that\n1x + 7y = -139/8\n6x + 2y = -317/4", "output": "1x + 7y = -139/8\n6x + 2y = -317/4\n\nUsing elimination\n6*(1x + 7y = -139/8)\n1*(6x + 2y = -317/4)\n6x + 42y = -417/4\n6x + 2y = -317/4\nSubtract equations\n40y = -25\ny = -25/40\ny = -5/8\n\nSubstitute y\n1x + 7(-5/8) = -139/8\n1x = -13\nx = -13/1\nx = -13"} {"input": "Solve the equation x^3 - 23/10x^2 - 116/45x + 136/45 = 0", "output": "x^3 - 23/10x^2 - 116/45x + 136/45 = 0\n(x - 4/5)(x - -4/3)(x - 17/6) = 0\nx - 4/5 = 0\nx - -4/3 = 0\nx - 17/6 = 0\nx = 4/5\nx = -4/3\nx = 17/6"} {"input": "Find x for 2x - 32/5 = 0", "output": "2x - 32/5 = 0\n2x = 32/5\nx = 32/5 / 2\nx = 16/5"} {"input": "Find x in x^2 + 38/5x - 16/5 = 0", "output": "x^2 + 38/5x - 16/5 = 0\n(x - 2/5)(x - -8) = 0\nx - 2/5 = 0 or x - -8 = 0\nx = 2/5\nx = -8"} {"input": "Solve the equation x^2 - 16/3x - 19/3 = 0", "output": "x^2 - 16/3x - 19/3 = 0\n(x - -1)(x - 19/3) = 0\nx - -1 = 0 or x - 19/3 = 0\nx = -1\nx = 19/3"} {"input": "Determine x in 8x - 56 = 0", "output": "8x - 56 = 0\n8x = 56\nx = 56 / 8\nx = 7"} {"input": "Determine x in x^2 + 5/3x - 22/3 = 0", "output": "x^2 + 5/3x - 22/3 = 0\n(x - -11/3)(x - 2) = 0\nx - -11/3 = 0 or x - 2 = 0\nx = -11/3\nx = 2"} {"input": "Solve the system:\n8x + 10y = -428/21\n8x + 7y = -38/3", "output": "8x + 10y = -428/21\n8x + 7y = -38/3\n\nUsing elimination\n8*(8x + 10y = -428/21)\n8*(8x + 7y = -38/3)\n64x + 80y = -3424/21\n64x + 56y = -304/3\nSubtract equations\n24y = -432/7\ny = -432/7/24\ny = -18/7\n\nSubstitute y\n8x + 10(-18/7) = -428/21\n8x = 16/3\nx = 16/3/8\nx = 2/3"} {"input": "Solve x^2 + 19/10x + 3/5 = 0", "output": "x^2 + 19/10x + 3/5 = 0\n(x - -2/5)(x - -3/2) = 0\nx - -2/5 = 0 or x - -3/2 = 0\nx = -2/5\nx = -3/2"} {"input": "Find x for 9x + 39/2 = 0", "output": "9x + 39/2 = 0\n9x = -39/2\nx = -39/2 / 9\nx = -13/6"} {"input": "Solve x^3 - 257/63x^2 + 26/7x - 40/63 = 0", "output": "x^3 - 257/63x^2 + 26/7x - 40/63 = 0\n(x - 2/9)(x - 20/7)(x - 1) = 0\nx - 2/9 = 0\nx - 20/7 = 0\nx - 1 = 0\nx = 2/9\nx = 20/7\nx = 1"} {"input": "Determine x in 3x - 6/5 = 0", "output": "3x - 6/5 = 0\n3x = 6/5\nx = 6/5 / 3\nx = 2/5"} {"input": "Solve the equation x^3 + 41/30x^2 - 889/30x + 38 = 0", "output": "x^3 + 41/30x^2 - 889/30x + 38 = 0\n(x - 3/2)(x - 19/5)(x - -20/3) = 0\nx - 3/2 = 0\nx - 19/5 = 0\nx - -20/3 = 0\nx = 3/2\nx = 19/5\nx = -20/3"} {"input": "Find x for x^2 - 104/21x + 128/21 = 0", "output": "x^2 - 104/21x + 128/21 = 0\n(x - 8/3)(x - 16/7) = 0\nx - 8/3 = 0 or x - 16/7 = 0\nx = 8/3\nx = 16/7"} {"input": "Solve quickly: x^2 + 10x + 25 = 0", "output": "x^2 + 10x + 25 = 0\n(x - -5)(x - -5) = 0\nx - -5 = 0 or x - -5 = 0\nx = -5\nx = -5"} {"input": "What value of x satisfies 3x + 48/5 = 0", "output": "3x + 48/5 = 0\n3x = -48/5\nx = -48/5 / 3\nx = -16/5"} {"input": "What value of x satisfies x^3 - 103/15x^2 + 12x - 32/15 = 0", "output": "x^3 - 103/15x^2 + 12x - 32/15 = 0\n(x - 8/3)(x - 1/5)(x - 4) = 0\nx - 8/3 = 0\nx - 1/5 = 0\nx - 4 = 0\nx = 8/3\nx = 1/5\nx = 4"} {"input": "Determine x in x^3 - 25/18x^2 + 41/150x + 11/225 = 0", "output": "x^3 - 25/18x^2 + 41/150x + 11/225 = 0\n(x - 2/5)(x - 11/10)(x - -1/9) = 0\nx - 2/5 = 0\nx - 11/10 = 0\nx - -1/9 = 0\nx = 2/5\nx = 11/10\nx = -1/9"} {"input": "What value of x satisfies 4x - 18 = 0", "output": "4x - 18 = 0\n4x = 18\nx = 18 / 4\nx = 9/2"} {"input": "Compute the solution of x^2 - 37/9x + 38/9 = 0", "output": "x^2 - 37/9x + 38/9 = 0\n(x - 19/9)(x - 2) = 0\nx - 19/9 = 0 or x - 2 = 0\nx = 19/9\nx = 2"} {"input": "Solve quickly: x^3 + 5/6x^2 - 263/192x - 15/16 = 0", "output": "x^3 + 5/6x^2 - 263/192x - 15/16 = 0\n(x - -5/8)(x - -4/3)(x - 9/8) = 0\nx - -5/8 = 0\nx - -4/3 = 0\nx - 9/8 = 0\nx = -5/8\nx = -4/3\nx = 9/8"} {"input": "Find x for 5x - 8 = 0", "output": "5x - 8 = 0\n5x = 8\nx = 8 / 5\nx = 8/5"} {"input": "Compute the solution of 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Compute the solution of 9x + 90 = 0", "output": "9x + 90 = 0\n9x = -90\nx = -90 / 9\nx = -10"} {"input": "Determine x in 6x + 6 = 0", "output": "6x + 6 = 0\n6x = -6\nx = -6 / 6\nx = -1"} {"input": "Solve the system:\n6x + 6y = -720/7\n10x + 3y = -1242/7", "output": "6x + 6y = -720/7\n10x + 3y = -1242/7\n\nUsing elimination\n10*(6x + 6y = -720/7)\n6*(10x + 3y = -1242/7)\n60x + 60y = -7200/7\n60x + 18y = -7452/7\nSubtract equations\n42y = 36\ny = 36/42\ny = 6/7\n\nSubstitute y\n6x + 6(6/7) = -720/7\n6x = -108\nx = -108/6\nx = -18"} {"input": "Find x in x^2 - 10x + 19/4 = 0", "output": "x^2 - 10x + 19/4 = 0\n(x - 19/2)(x - 1/2) = 0\nx - 19/2 = 0 or x - 1/2 = 0\nx = 19/2\nx = 1/2"} {"input": "Find x in 1x + 15 = 0", "output": "1x + 15 = 0\n1x = -15\nx = -15 / 1\nx = -15"} {"input": "Solve quickly: 4x - 32/3 = 0", "output": "4x - 32/3 = 0\n4x = 32/3\nx = 32/3 / 4\nx = 8/3"} {"input": "Solve the equation x^2 + 114/7x - 361/7 = 0", "output": "x^2 + 114/7x - 361/7 = 0\n(x - -19)(x - 19/7) = 0\nx - -19 = 0 or x - 19/7 = 0\nx = -19\nx = 19/7"} {"input": "Solve the equation 5x + 30/7 = 0", "output": "5x + 30/7 = 0\n5x = -30/7\nx = -30/7 / 5\nx = -6/7"} {"input": "Solve simultaneously:\n3x + 8y = 110/3\n9x + 7y = 58/3", "output": "3x + 8y = 110/3\n9x + 7y = 58/3\n\nUsing elimination\n9*(3x + 8y = 110/3)\n3*(9x + 7y = 58/3)\n27x + 72y = 330\n27x + 21y = 58\nSubtract equations\n51y = 272\ny = 272/51\ny = 16/3\n\nSubstitute y\n3x + 8(16/3) = 110/3\n3x = -6\nx = -6/3\nx = -2"} {"input": "Solve the equations:\n5x + 4y = -1\n7x + 5y = -3/2", "output": "5x + 4y = -1\n7x + 5y = -3/2\n\nUsing elimination\n7*(5x + 4y = -1)\n5*(7x + 5y = -3/2)\n35x + 28y = -7\n35x + 25y = -15/2\nSubtract equations\n3y = 1/2\ny = 1/2/3\ny = 1/6\n\nSubstitute y\n5x + 4(1/6) = -1\n5x = -5/3\nx = -5/3/5\nx = -1/3"} {"input": "Solve quickly: 4x - 28 = 0", "output": "4x - 28 = 0\n4x = 28\nx = 28 / 4\nx = 7"} {"input": "Determine x in x^3 - 3/35x^2 - 108/35x = 0", "output": "x^3 - 3/35x^2 - 108/35x = 0\n(x - 9/5)(x - -12/7)(x - 0) = 0\nx - 9/5 = 0\nx - -12/7 = 0\nx - 0 = 0\nx = 9/5\nx = -12/7\nx = 0"} {"input": "Find x in 5x + 5/2 = 0", "output": "5x + 5/2 = 0\n5x = -5/2\nx = -5/2 / 5\nx = -1/2"} {"input": "Solve quickly: x^2 + 11/6x - 17/6 = 0", "output": "x^2 + 11/6x - 17/6 = 0\n(x - 1)(x - -17/6) = 0\nx - 1 = 0 or x - -17/6 = 0\nx = 1\nx = -17/6"} {"input": "Compute the solution of 3x + 11/3 = 0", "output": "3x + 11/3 = 0\n3x = -11/3\nx = -11/3 / 3\nx = -11/9"} {"input": "Compute the solution of 8x + 16 = 0", "output": "8x + 16 = 0\n8x = -16\nx = -16 / 8\nx = -2"} {"input": "Solve the equations:\n7x + 10y = 155/6\n7x + 9y = 265/12", "output": "7x + 10y = 155/6\n7x + 9y = 265/12\n\nUsing elimination\n7*(7x + 10y = 155/6)\n7*(7x + 9y = 265/12)\n49x + 70y = 1085/6\n49x + 63y = 1855/12\nSubtract equations\n7y = 105/4\ny = 105/4/7\ny = 15/4\n\nSubstitute y\n7x + 10(15/4) = 155/6\n7x = -35/3\nx = -35/3/7\nx = -5/3"} {"input": "Solve 10x - 25/4 = 0", "output": "10x - 25/4 = 0\n10x = 25/4\nx = 25/4 / 10\nx = 5/8"} {"input": "Compute the solution of x^2 - 21x + 54 = 0", "output": "x^2 - 21x + 54 = 0\n(x - 18)(x - 3) = 0\nx - 18 = 0 or x - 3 = 0\nx = 18\nx = 3"} {"input": "Solve simultaneously:\n6x + 8y = -86/15\n4x + 7y = -232/45", "output": "6x + 8y = -86/15\n4x + 7y = -232/45\n\nUsing elimination\n4*(6x + 8y = -86/15)\n6*(4x + 7y = -232/45)\n24x + 32y = -344/15\n24x + 42y = -464/15\nSubtract equations\n-10y = 8\ny = 8/-10\ny = -4/5\n\nSubstitute y\n6x + 8(-4/5) = -86/15\n6x = 2/3\nx = 2/3/6\nx = 1/9"} {"input": "Find x and y such that\n2x + 1y = 1/5\n7x + 2y = 19/10", "output": "2x + 1y = 1/5\n7x + 2y = 19/10\n\nUsing elimination\n7*(2x + 1y = 1/5)\n2*(7x + 2y = 19/10)\n14x + 7y = 7/5\n14x + 4y = 19/5\nSubtract equations\n3y = -12/5\ny = -12/5/3\ny = -4/5\n\nSubstitute y\n2x + 1(-4/5) = 1/5\n2x = 1\nx = 1/2\nx = 1/2"} {"input": "Find x in x^3 + 94/9x^2 + 835/36x + 25/3 = 0", "output": "x^3 + 94/9x^2 + 835/36x + 25/3 = 0\n(x - -5/2)(x - -15/2)(x - -4/9) = 0\nx - -5/2 = 0\nx - -15/2 = 0\nx - -4/9 = 0\nx = -5/2\nx = -15/2\nx = -4/9"} {"input": "Solve the equation 7x + 7/2 = 0", "output": "7x + 7/2 = 0\n7x = -7/2\nx = -7/2 / 7\nx = -1/2"} {"input": "Determine x in x^2 + 5/2x + 9/16 = 0", "output": "x^2 + 5/2x + 9/16 = 0\n(x - -9/4)(x - -1/4) = 0\nx - -9/4 = 0 or x - -1/4 = 0\nx = -9/4\nx = -1/4"} {"input": "Solve quickly: x^3 + 34/7x^2 + 33/28x - 27/14 = 0", "output": "x^3 + 34/7x^2 + 33/28x - 27/14 = 0\n(x - 1/2)(x - -9/2)(x - -6/7) = 0\nx - 1/2 = 0\nx - -9/2 = 0\nx - -6/7 = 0\nx = 1/2\nx = -9/2\nx = -6/7"} {"input": "Find x in x^3 + 27x^2 + 194x + 408 = 0", "output": "x^3 + 27x^2 + 194x + 408 = 0\n(x - -4)(x - -6)(x - -17) = 0\nx - -4 = 0\nx - -6 = 0\nx - -17 = 0\nx = -4\nx = -6\nx = -17"} {"input": "Solve the system:\n4x + 8y = -80/7\n8x + 10y = -55/7", "output": "4x + 8y = -80/7\n8x + 10y = -55/7\n\nUsing elimination\n8*(4x + 8y = -80/7)\n4*(8x + 10y = -55/7)\n32x + 64y = -640/7\n32x + 40y = -220/7\nSubtract equations\n24y = -60\ny = -60/24\ny = -5/2\n\nSubstitute y\n4x + 8(-5/2) = -80/7\n4x = 60/7\nx = 60/7/4\nx = 15/7"} {"input": "Find x for x^2 - 95/63x - 16/9 = 0", "output": "x^2 - 95/63x - 16/9 = 0\n(x - -7/9)(x - 16/7) = 0\nx - -7/9 = 0 or x - 16/7 = 0\nx = -7/9\nx = 16/7"} {"input": "Solve quickly: x^3 - 7x^2 - 69/4x - 27/4 = 0", "output": "x^3 - 7x^2 - 69/4x - 27/4 = 0\n(x - -3/2)(x - -1/2)(x - 9) = 0\nx - -3/2 = 0\nx - -1/2 = 0\nx - 9 = 0\nx = -3/2\nx = -1/2\nx = 9"} {"input": "Solve the equations:\n5x + 8y = 20\n10x + 1y = -65/4", "output": "5x + 8y = 20\n10x + 1y = -65/4\n\nUsing elimination\n10*(5x + 8y = 20)\n5*(10x + 1y = -65/4)\n50x + 80y = 200\n50x + 5y = -325/4\nSubtract equations\n75y = 1125/4\ny = 1125/4/75\ny = 15/4\n\nSubstitute y\n5x + 8(15/4) = 20\n5x = -10\nx = -10/5\nx = -2"} {"input": "Find the solution to x^3 + 14x^2 + 105/4x - 297/4 = 0", "output": "x^3 + 14x^2 + 105/4x - 297/4 = 0\n(x - -9/2)(x - -11)(x - 3/2) = 0\nx - -9/2 = 0\nx - -11 = 0\nx - 3/2 = 0\nx = -9/2\nx = -11\nx = 3/2"} {"input": "Find x for x^2 - 26x + 168 = 0", "output": "x^2 - 26x + 168 = 0\n(x - 12)(x - 14) = 0\nx - 12 = 0 or x - 14 = 0\nx = 12\nx = 14"} {"input": "What value of x satisfies x^3 + 14/15x^2 - 8/15x = 0", "output": "x^3 + 14/15x^2 - 8/15x = 0\n(x - -4/3)(x - 2/5)(x - 0) = 0\nx - -4/3 = 0\nx - 2/5 = 0\nx - 0 = 0\nx = -4/3\nx = 2/5\nx = 0"} {"input": "Find x for 5x + 35/9 = 0", "output": "5x + 35/9 = 0\n5x = -35/9\nx = -35/9 / 5\nx = -7/9"} {"input": "Compute the solution of 7x - 77/8 = 0", "output": "7x - 77/8 = 0\n7x = 77/8\nx = 77/8 / 7\nx = 11/8"} {"input": "Find x and y such that\n4x + 3y = 19\n9x + 4y = 469/12", "output": "4x + 3y = 19\n9x + 4y = 469/12\n\nUsing elimination\n9*(4x + 3y = 19)\n4*(9x + 4y = 469/12)\n36x + 27y = 171\n36x + 16y = 469/3\nSubtract equations\n11y = 44/3\ny = 44/3/11\ny = 4/3\n\nSubstitute y\n4x + 3(4/3) = 19\n4x = 15\nx = 15/4\nx = 15/4"} {"input": "Find x in x^3 - 73/10x^2 - 793/10x + 338/5 = 0", "output": "x^3 - 73/10x^2 - 793/10x + 338/5 = 0\n(x - 4/5)(x - 13)(x - -13/2) = 0\nx - 4/5 = 0\nx - 13 = 0\nx - -13/2 = 0\nx = 4/5\nx = 13\nx = -13/2"} {"input": "Solve 5x - 2 = 0", "output": "5x - 2 = 0\n5x = 2\nx = 2 / 5\nx = 2/5"} {"input": "Solve x^3 + 73/4x^2 + 107/8x - 1071/8 = 0", "output": "x^3 + 73/4x^2 + 107/8x - 1071/8 = 0\n(x - -7/2)(x - -17)(x - 9/4) = 0\nx - -7/2 = 0\nx - -17 = 0\nx - 9/4 = 0\nx = -7/2\nx = -17\nx = 9/4"} {"input": "Compute the solution of x^3 + 35/6x^2 + 1681/150x + 532/75 = 0", "output": "x^3 + 35/6x^2 + 1681/150x + 532/75 = 0\n(x - -19/10)(x - -7/3)(x - -8/5) = 0\nx - -19/10 = 0\nx - -7/3 = 0\nx - -8/5 = 0\nx = -19/10\nx = -7/3\nx = -8/5"} {"input": "Solve quickly: x^2 - 91/6x + 38 = 0", "output": "x^2 - 91/6x + 38 = 0\n(x - 12)(x - 19/6) = 0\nx - 12 = 0 or x - 19/6 = 0\nx = 12\nx = 19/6"} {"input": "Solve quickly: x^2 - 29/4x - 63/4 = 0", "output": "x^2 - 29/4x - 63/4 = 0\n(x - -7/4)(x - 9) = 0\nx - -7/4 = 0 or x - 9 = 0\nx = -7/4\nx = 9"} {"input": "Solve simultaneously:\n8x + 10y = 81/7\n10x + 9y = 841/70", "output": "8x + 10y = 81/7\n10x + 9y = 841/70\n\nUsing elimination\n10*(8x + 10y = 81/7)\n8*(10x + 9y = 841/70)\n80x + 100y = 810/7\n80x + 72y = 3364/35\nSubtract equations\n28y = 98/5\ny = 98/5/28\ny = 7/10\n\nSubstitute y\n8x + 10(7/10) = 81/7\n8x = 32/7\nx = 32/7/8\nx = 4/7"} {"input": "Find x and y such that\n1x + 8y = 317/9\n4x + 8y = 350/9", "output": "1x + 8y = 317/9\n4x + 8y = 350/9\n\nUsing elimination\n4*(1x + 8y = 317/9)\n1*(4x + 8y = 350/9)\n4x + 32y = 1268/9\n4x + 8y = 350/9\nSubtract equations\n24y = 102\ny = 102/24\ny = 17/4\n\nSubstitute y\n1x + 8(17/4) = 317/9\n1x = 11/9\nx = 11/9/1\nx = 11/9"} {"input": "Solve the equation 5x + 95/6 = 0", "output": "5x + 95/6 = 0\n5x = -95/6\nx = -95/6 / 5\nx = -19/6"} {"input": "Find the solution to 7x - 49 = 0", "output": "7x - 49 = 0\n7x = 49\nx = 49 / 7\nx = 7"} {"input": "What value of x satisfies x^3 - 71/21x^2 + 320/147x - 12/49 = 0", "output": "x^3 - 71/21x^2 + 320/147x - 12/49 = 0\n(x - 2/3)(x - 1/7)(x - 18/7) = 0\nx - 2/3 = 0\nx - 1/7 = 0\nx - 18/7 = 0\nx = 2/3\nx = 1/7\nx = 18/7"} {"input": "Find the solution to x^2 + 31/36x - 14/9 = 0", "output": "x^2 + 31/36x - 14/9 = 0\n(x - -7/4)(x - 8/9) = 0\nx - -7/4 = 0 or x - 8/9 = 0\nx = -7/4\nx = 8/9"} {"input": "Solve simultaneously:\n4x + 7y = 221/5\n5x + 7y = 43", "output": "4x + 7y = 221/5\n5x + 7y = 43\n\nUsing elimination\n5*(4x + 7y = 221/5)\n4*(5x + 7y = 43)\n20x + 35y = 221\n20x + 28y = 172\nSubtract equations\n7y = 49\ny = 49/7\ny = 7\n\nSubstitute y\n4x + 7(7) = 221/5\n4x = -24/5\nx = -24/5/4\nx = -6/5"} {"input": "Solve the equations:\n1x + 4y = 43/7\n2x + 10y = 235/14", "output": "1x + 4y = 43/7\n2x + 10y = 235/14\n\nUsing elimination\n2*(1x + 4y = 43/7)\n1*(2x + 10y = 235/14)\n2x + 8y = 86/7\n2x + 10y = 235/14\nSubtract equations\n-2y = -9/2\ny = -9/2/-2\ny = 9/4\n\nSubstitute y\n1x + 4(9/4) = 43/7\n1x = -20/7\nx = -20/7/1\nx = -20/7"} {"input": "Solve x^2 + 62/5x + 77/5 = 0", "output": "x^2 + 62/5x + 77/5 = 0\n(x - -7/5)(x - -11) = 0\nx - -7/5 = 0 or x - -11 = 0\nx = -7/5\nx = -11"} {"input": "Solve simultaneously:\n7x + 1y = -11/24\n10x + 10y = 185/12", "output": "7x + 1y = -11/24\n10x + 10y = 185/12\n\nUsing elimination\n10*(7x + 1y = -11/24)\n7*(10x + 10y = 185/12)\n70x + 10y = -55/12\n70x + 70y = 1295/12\nSubtract equations\n-60y = -225/2\ny = -225/2/-60\ny = 15/8\n\nSubstitute y\n7x + 1(15/8) = -11/24\n7x = -7/3\nx = -7/3/7\nx = -1/3"} {"input": "Solve the equation 3x - 14 = 0", "output": "3x - 14 = 0\n3x = 14\nx = 14 / 3\nx = 14/3"} {"input": "Find the solution to x^3 - 669/40x^2 + 639/16x - 1001/40 = 0", "output": "x^3 - 669/40x^2 + 639/16x - 1001/40 = 0\n(x - 14)(x - 13/8)(x - 11/10) = 0\nx - 14 = 0\nx - 13/8 = 0\nx - 11/10 = 0\nx = 14\nx = 13/8\nx = 11/10"} {"input": "Solve the equation 7x + 56 = 0", "output": "7x + 56 = 0\n7x = -56\nx = -56 / 7\nx = -8"} {"input": "Solve quickly: 6x - 30 = 0", "output": "6x - 30 = 0\n6x = 30\nx = 30 / 6\nx = 5"} {"input": "Solve the equations:\n2x + 3y = -26\n4x + 1y = -72", "output": "2x + 3y = -26\n4x + 1y = -72\n\nUsing elimination\n4*(2x + 3y = -26)\n2*(4x + 1y = -72)\n8x + 12y = -104\n8x + 2y = -144\nSubtract equations\n10y = 40\ny = 40/10\ny = 4\n\nSubstitute y\n2x + 3(4) = -26\n2x = -38\nx = -38/2\nx = -19"} {"input": "Solve the system:\n3x + 3y = -1/2\n3x + 6y = -5", "output": "3x + 3y = -1/2\n3x + 6y = -5\n\nUsing elimination\n3*(3x + 3y = -1/2)\n3*(3x + 6y = -5)\n9x + 9y = -3/2\n9x + 18y = -15\nSubtract equations\n-9y = 27/2\ny = 27/2/-9\ny = -3/2\n\nSubstitute y\n3x + 3(-3/2) = -1/2\n3x = 4\nx = 4/3\nx = 4/3"} {"input": "Solve x^2 + 5/4x = 0", "output": "x^2 + 5/4x = 0\n(x - 0)(x - -5/4) = 0\nx - 0 = 0 or x - -5/4 = 0\nx = 0\nx = -5/4"} {"input": "Solve simultaneously:\n9x + 6y = 3/5\n1x + 3y = -81/10", "output": "9x + 6y = 3/5\n1x + 3y = -81/10\n\nUsing elimination\n1*(9x + 6y = 3/5)\n9*(1x + 3y = -81/10)\n9x + 6y = 3/5\n9x + 27y = -729/10\nSubtract equations\n-21y = 147/2\ny = 147/2/-21\ny = -7/2\n\nSubstitute y\n9x + 6(-7/2) = 3/5\n9x = 108/5\nx = 108/5/9\nx = 12/5"} {"input": "Find x in x^2 + 7/3x + 10/9 = 0", "output": "x^2 + 7/3x + 10/9 = 0\n(x - -5/3)(x - -2/3) = 0\nx - -5/3 = 0 or x - -2/3 = 0\nx = -5/3\nx = -2/3"} {"input": "Find x in 3x - 1 = 0", "output": "3x - 1 = 0\n3x = 1\nx = 1 / 3\nx = 1/3"} {"input": "Find x in 1x + 19/9 = 0", "output": "1x + 19/9 = 0\n1x = -19/9\nx = -19/9 / 1\nx = -19/9"} {"input": "Compute the solution of 4x - 16 = 0", "output": "4x - 16 = 0\n4x = 16\nx = 16 / 4\nx = 4"} {"input": "What value of x satisfies 2x - 1/2 = 0", "output": "2x - 1/2 = 0\n2x = 1/2\nx = 1/2 / 2\nx = 1/4"} {"input": "Solve the system:\n3x + 6y = 15/4\n9x + 7y = -9/8", "output": "3x + 6y = 15/4\n9x + 7y = -9/8\n\nUsing elimination\n9*(3x + 6y = 15/4)\n3*(9x + 7y = -9/8)\n27x + 54y = 135/4\n27x + 21y = -27/8\nSubtract equations\n33y = 297/8\ny = 297/8/33\ny = 9/8\n\nSubstitute y\n3x + 6(9/8) = 15/4\n3x = -3\nx = -3/3\nx = -1"} {"input": "Solve x^3 + 113/9x^2 + 20/3x = 0", "output": "x^3 + 113/9x^2 + 20/3x = 0\n(x - 0)(x - -12)(x - -5/9) = 0\nx - 0 = 0\nx - -12 = 0\nx - -5/9 = 0\nx = 0\nx = -12\nx = -5/9"} {"input": "What value of x satisfies 9x - 45/4 = 0", "output": "9x - 45/4 = 0\n9x = 45/4\nx = 45/4 / 9\nx = 5/4"} {"input": "Solve the equation x^2 - 104/5x + 171/5 = 0", "output": "x^2 - 104/5x + 171/5 = 0\n(x - 9/5)(x - 19) = 0\nx - 9/5 = 0 or x - 19 = 0\nx = 9/5\nx = 19"} {"input": "Find x in 9x - 14 = 0", "output": "9x - 14 = 0\n9x = 14\nx = 14 / 9\nx = 14/9"} {"input": "What value of x satisfies x^2 + 97/12x + 44/3 = 0", "output": "x^2 + 97/12x + 44/3 = 0\n(x - -11/4)(x - -16/3) = 0\nx - -11/4 = 0 or x - -16/3 = 0\nx = -11/4\nx = -16/3"} {"input": "Find x in x^2 + 49/18x + 5/9 = 0", "output": "x^2 + 49/18x + 5/9 = 0\n(x - -5/2)(x - -2/9) = 0\nx - -5/2 = 0 or x - -2/9 = 0\nx = -5/2\nx = -2/9"} {"input": "Determine x in x^2 - 23/24x - 119/48 = 0", "output": "x^2 - 23/24x - 119/48 = 0\n(x - 17/8)(x - -7/6) = 0\nx - 17/8 = 0 or x - -7/6 = 0\nx = 17/8\nx = -7/6"} {"input": "Find x and y such that\n8x + 3y = 154/5\n3x + 2y = 147/10", "output": "8x + 3y = 154/5\n3x + 2y = 147/10\n\nUsing elimination\n3*(8x + 3y = 154/5)\n8*(3x + 2y = 147/10)\n24x + 9y = 462/5\n24x + 16y = 588/5\nSubtract equations\n-7y = -126/5\ny = -126/5/-7\ny = 18/5\n\nSubstitute y\n8x + 3(18/5) = 154/5\n8x = 20\nx = 20/8\nx = 5/2"} {"input": "Compute the solution of x^3 + 159/10x^2 + 27/2x = 0", "output": "x^3 + 159/10x^2 + 27/2x = 0\n(x - 0)(x - -9/10)(x - -15) = 0\nx - 0 = 0\nx - -9/10 = 0\nx - -15 = 0\nx = 0\nx = -9/10\nx = -15"} {"input": "Solve quickly: x^3 - 2/7x^2 - 19/7x - 10/7 = 0", "output": "x^3 - 2/7x^2 - 19/7x - 10/7 = 0\n(x - -1)(x - 2)(x - -5/7) = 0\nx - -1 = 0\nx - 2 = 0\nx - -5/7 = 0\nx = -1\nx = 2\nx = -5/7"} {"input": "Solve simultaneously:\n1x + 6y = -79/7\n9x + 6y = -39/7", "output": "1x + 6y = -79/7\n9x + 6y = -39/7\n\nUsing elimination\n9*(1x + 6y = -79/7)\n1*(9x + 6y = -39/7)\n9x + 54y = -711/7\n9x + 6y = -39/7\nSubtract equations\n48y = -96\ny = -96/48\ny = -2\n\nSubstitute y\n1x + 6(-2) = -79/7\n1x = 5/7\nx = 5/7/1\nx = 5/7"} {"input": "Solve the equations:\n1x + 8y = -43/2\n10x + 4y = -44", "output": "1x + 8y = -43/2\n10x + 4y = -44\n\nUsing elimination\n10*(1x + 8y = -43/2)\n1*(10x + 4y = -44)\n10x + 80y = -215\n10x + 4y = -44\nSubtract equations\n76y = -171\ny = -171/76\ny = -9/4\n\nSubstitute y\n1x + 8(-9/4) = -43/2\n1x = -7/2\nx = -7/2/1\nx = -7/2"} {"input": "Find x in x^2 + 25/6x + 19/6 = 0", "output": "x^2 + 25/6x + 19/6 = 0\n(x - -1)(x - -19/6) = 0\nx - -1 = 0 or x - -19/6 = 0\nx = -1\nx = -19/6"} {"input": "Solve the system:\n8x + 4y = -384/35\n5x + 7y = -3", "output": "8x + 4y = -384/35\n5x + 7y = -3\n\nUsing elimination\n5*(8x + 4y = -384/35)\n8*(5x + 7y = -3)\n40x + 20y = -384/7\n40x + 56y = -24\nSubtract equations\n-36y = -216/7\ny = -216/7/-36\ny = 6/7\n\nSubstitute y\n8x + 4(6/7) = -384/35\n8x = -72/5\nx = -72/5/8\nx = -9/5"} {"input": "What value of x satisfies 7x - 98/9 = 0", "output": "7x - 98/9 = 0\n7x = 98/9\nx = 98/9 / 7\nx = 14/9"} {"input": "Find x and y such that\n5x + 3y = 11/2\n9x + 9y = 33/2", "output": "5x + 3y = 11/2\n9x + 9y = 33/2\n\nUsing elimination\n9*(5x + 3y = 11/2)\n5*(9x + 9y = 33/2)\n45x + 27y = 99/2\n45x + 45y = 165/2\nSubtract equations\n-18y = -33\ny = -33/-18\ny = 11/6\n\nSubstitute y\n5x + 3(11/6) = 11/2\n5x = 0\nx = 0/5\nx = 0"} {"input": "What value of x satisfies x^3 + 115/12x^2 + 27x + 221/12 = 0", "output": "x^3 + 115/12x^2 + 27x + 221/12 = 0\n(x - -13/3)(x - -1)(x - -17/4) = 0\nx - -13/3 = 0\nx - -1 = 0\nx - -17/4 = 0\nx = -13/3\nx = -1\nx = -17/4"} {"input": "Solve 3x + 9 = 0", "output": "3x + 9 = 0\n3x = -9\nx = -9 / 3\nx = -3"} {"input": "Find the solution to x^2 + 11/24x + 1/24 = 0", "output": "x^2 + 11/24x + 1/24 = 0\n(x - -1/3)(x - -1/8) = 0\nx - -1/3 = 0 or x - -1/8 = 0\nx = -1/3\nx = -1/8"} {"input": "Solve the equation x^3 - 107/20x^2 + 281/40x - 13/20 = 0", "output": "x^3 - 107/20x^2 + 281/40x - 13/20 = 0\n(x - 2)(x - 1/10)(x - 13/4) = 0\nx - 2 = 0\nx - 1/10 = 0\nx - 13/4 = 0\nx = 2\nx = 1/10\nx = 13/4"} {"input": "Find x for x^3 + 13/5x^2 - 96/25x - 108/125 = 0", "output": "x^3 + 13/5x^2 - 96/25x - 108/125 = 0\n(x - -18/5)(x - -1/5)(x - 6/5) = 0\nx - -18/5 = 0\nx - -1/5 = 0\nx - 6/5 = 0\nx = -18/5\nx = -1/5\nx = 6/5"} {"input": "Solve 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Solve the system:\n10x + 4y = -54\n4x + 6y = -26", "output": "10x + 4y = -54\n4x + 6y = -26\n\nUsing elimination\n4*(10x + 4y = -54)\n10*(4x + 6y = -26)\n40x + 16y = -216\n40x + 60y = -260\nSubtract equations\n-44y = 44\ny = 44/-44\ny = -1\n\nSubstitute y\n10x + 4(-1) = -54\n10x = -50\nx = -50/10\nx = -5"} {"input": "Determine x in x^2 + 1/6x - 13/3 = 0", "output": "x^2 + 1/6x - 13/3 = 0\n(x - 2)(x - -13/6) = 0\nx - 2 = 0 or x - -13/6 = 0\nx = 2\nx = -13/6"} {"input": "Solve simultaneously:\n6x + 10y = 364/15\n8x + 3y = 24/5", "output": "6x + 10y = 364/15\n8x + 3y = 24/5\n\nUsing elimination\n8*(6x + 10y = 364/15)\n6*(8x + 3y = 24/5)\n48x + 80y = 2912/15\n48x + 18y = 144/5\nSubtract equations\n62y = 496/3\ny = 496/3/62\ny = 8/3\n\nSubstitute y\n6x + 10(8/3) = 364/15\n6x = -12/5\nx = -12/5/6\nx = -2/5"} {"input": "Find x and y such that\n7x + 6y = 42\n10x + 7y = 158/3", "output": "7x + 6y = 42\n10x + 7y = 158/3\n\nUsing elimination\n10*(7x + 6y = 42)\n7*(10x + 7y = 158/3)\n70x + 60y = 420\n70x + 49y = 1106/3\nSubtract equations\n11y = 154/3\ny = 154/3/11\ny = 14/3\n\nSubstitute y\n7x + 6(14/3) = 42\n7x = 14\nx = 14/7\nx = 2"} {"input": "Solve the equations:\n9x + 3y = -41\n7x + 2y = -266/9", "output": "9x + 3y = -41\n7x + 2y = -266/9\n\nUsing elimination\n7*(9x + 3y = -41)\n9*(7x + 2y = -266/9)\n63x + 21y = -287\n63x + 18y = -266\nSubtract equations\n3y = -21\ny = -21/3\ny = -7\n\nSubstitute y\n9x + 3(-7) = -41\n9x = -20\nx = -20/9\nx = -20/9"} {"input": "Compute the solution of x^2 - 39/20x + 9/10 = 0", "output": "x^2 - 39/20x + 9/10 = 0\n(x - 6/5)(x - 3/4) = 0\nx - 6/5 = 0 or x - 3/4 = 0\nx = 6/5\nx = 3/4"} {"input": "Solve the equation 2x - 4/5 = 0", "output": "2x - 4/5 = 0\n2x = 4/5\nx = 4/5 / 2\nx = 2/5"} {"input": "Solve the equations:\n7x + 6y = -121/2\n1x + 5y = -47/4", "output": "7x + 6y = -121/2\n1x + 5y = -47/4\n\nUsing elimination\n1*(7x + 6y = -121/2)\n7*(1x + 5y = -47/4)\n7x + 6y = -121/2\n7x + 35y = -329/4\nSubtract equations\n-29y = 87/4\ny = 87/4/-29\ny = -3/4\n\nSubstitute y\n7x + 6(-3/4) = -121/2\n7x = -56\nx = -56/7\nx = -8"} {"input": "Solve x^2 - 45/14x + 25/14 = 0", "output": "x^2 - 45/14x + 25/14 = 0\n(x - 5/2)(x - 5/7) = 0\nx - 5/2 = 0 or x - 5/7 = 0\nx = 5/2\nx = 5/7"} {"input": "Solve the equation 6x - 15 = 0", "output": "6x - 15 = 0\n6x = 15\nx = 15 / 6\nx = 5/2"} {"input": "Solve simultaneously:\n8x + 10y = 64/5\n8x + 6y = 64/5", "output": "8x + 10y = 64/5\n8x + 6y = 64/5\n\nUsing elimination\n8*(8x + 10y = 64/5)\n8*(8x + 6y = 64/5)\n64x + 80y = 512/5\n64x + 48y = 512/5\nSubtract equations\n32y = 0\ny = 0/32\ny = 0\n\nSubstitute y\n8x + 10(0) = 64/5\n8x = 64/5\nx = 64/5/8\nx = 8/5"} {"input": "Solve the system:\n1x + 3y = 236/45\n1x + 6y = 452/45", "output": "1x + 3y = 236/45\n1x + 6y = 452/45\n\nUsing elimination\n1*(1x + 3y = 236/45)\n1*(1x + 6y = 452/45)\n1x + 3y = 236/45\n1x + 6y = 452/45\nSubtract equations\n-3y = -24/5\ny = -24/5/-3\ny = 8/5\n\nSubstitute y\n1x + 3(8/5) = 236/45\n1x = 4/9\nx = 4/9/1\nx = 4/9"} {"input": "Determine x in 7x - 35/3 = 0", "output": "7x - 35/3 = 0\n7x = 35/3\nx = 35/3 / 7\nx = 5/3"} {"input": "Solve x^2 - 101/45x + 4/5 = 0", "output": "x^2 - 101/45x + 4/5 = 0\n(x - 4/9)(x - 9/5) = 0\nx - 4/9 = 0 or x - 9/5 = 0\nx = 4/9\nx = 9/5"} {"input": "What value of x satisfies x^2 - 37/10x - 6/5 = 0", "output": "x^2 - 37/10x - 6/5 = 0\n(x - -3/10)(x - 4) = 0\nx - -3/10 = 0 or x - 4 = 0\nx = -3/10\nx = 4"} {"input": "What value of x satisfies x^2 - 125/72x + 13/72 = 0", "output": "x^2 - 125/72x + 13/72 = 0\n(x - 13/8)(x - 1/9) = 0\nx - 13/8 = 0 or x - 1/9 = 0\nx = 13/8\nx = 1/9"} {"input": "What value of x satisfies 5x + 20 = 0", "output": "5x + 20 = 0\n5x = -20\nx = -20 / 5\nx = -4"} {"input": "Determine x in x^3 - 13/2x^2 - 77/2x + 95 = 0", "output": "x^3 - 13/2x^2 - 77/2x + 95 = 0\n(x - 2)(x - 19/2)(x - -5) = 0\nx - 2 = 0\nx - 19/2 = 0\nx - -5 = 0\nx = 2\nx = 19/2\nx = -5"} {"input": "Find x and y such that\n7x + 9y = 75/4\n10x + 3y = 117/4", "output": "7x + 9y = 75/4\n10x + 3y = 117/4\n\nUsing elimination\n10*(7x + 9y = 75/4)\n7*(10x + 3y = 117/4)\n70x + 90y = 375/2\n70x + 21y = 819/4\nSubtract equations\n69y = -69/4\ny = -69/4/69\ny = -1/4\n\nSubstitute y\n7x + 9(-1/4) = 75/4\n7x = 21\nx = 21/7\nx = 3"} {"input": "Solve quickly: x^2 + 137/10x - 21/5 = 0", "output": "x^2 + 137/10x - 21/5 = 0\n(x - 3/10)(x - -14) = 0\nx - 3/10 = 0 or x - -14 = 0\nx = 3/10\nx = -14"} {"input": "Solve quickly: x^2 + 31/10x + 3/10 = 0", "output": "x^2 + 31/10x + 3/10 = 0\n(x - -3)(x - -1/10) = 0\nx - -3 = 0 or x - -1/10 = 0\nx = -3\nx = -1/10"} {"input": "Solve simultaneously:\n3x + 10y = -117/7\n1x + 9y = -141/7", "output": "3x + 10y = -117/7\n1x + 9y = -141/7\n\nUsing elimination\n1*(3x + 10y = -117/7)\n3*(1x + 9y = -141/7)\n3x + 10y = -117/7\n3x + 27y = -423/7\nSubtract equations\n-17y = 306/7\ny = 306/7/-17\ny = -18/7\n\nSubstitute y\n3x + 10(-18/7) = -117/7\n3x = 9\nx = 9/3\nx = 3"} {"input": "Compute the solution of x^2 + 15/2x - 54 = 0", "output": "x^2 + 15/2x - 54 = 0\n(x - 9/2)(x - -12) = 0\nx - 9/2 = 0 or x - -12 = 0\nx = 9/2\nx = -12"} {"input": "Find x in x^3 - 215/9x^2 + 883/9x + 323 = 0", "output": "x^3 - 215/9x^2 + 883/9x + 323 = 0\n(x - 17)(x - -19/9)(x - 9) = 0\nx - 17 = 0\nx - -19/9 = 0\nx - 9 = 0\nx = 17\nx = -19/9\nx = 9"} {"input": "Compute the solution of 6x + 30/7 = 0", "output": "6x + 30/7 = 0\n6x = -30/7\nx = -30/7 / 6\nx = -5/7"} {"input": "Find x and y such that\n1x + 5y = 45/4\n6x + 10y = 65/2", "output": "1x + 5y = 45/4\n6x + 10y = 65/2\n\nUsing elimination\n6*(1x + 5y = 45/4)\n1*(6x + 10y = 65/2)\n6x + 30y = 135/2\n6x + 10y = 65/2\nSubtract equations\n20y = 35\ny = 35/20\ny = 7/4\n\nSubstitute y\n1x + 5(7/4) = 45/4\n1x = 5/2\nx = 5/2/1\nx = 5/2"} {"input": "Solve the equations:\n9x + 7y = 55/2\n1x + 4y = 19/2", "output": "9x + 7y = 55/2\n1x + 4y = 19/2\n\nUsing elimination\n1*(9x + 7y = 55/2)\n9*(1x + 4y = 19/2)\n9x + 7y = 55/2\n9x + 36y = 171/2\nSubtract equations\n-29y = -58\ny = -58/-29\ny = 2\n\nSubstitute y\n9x + 7(2) = 55/2\n9x = 27/2\nx = 27/2/9\nx = 3/2"} {"input": "Solve simultaneously:\n9x + 7y = -84\n7x + 4y = -445/9", "output": "9x + 7y = -84\n7x + 4y = -445/9\n\nUsing elimination\n7*(9x + 7y = -84)\n9*(7x + 4y = -445/9)\n63x + 49y = -588\n63x + 36y = -445\nSubtract equations\n13y = -143\ny = -143/13\ny = -11\n\nSubstitute y\n9x + 7(-11) = -84\n9x = -7\nx = -7/9\nx = -7/9"} {"input": "Solve simultaneously:\n8x + 5y = 545/8\n10x + 9y = 629/8", "output": "8x + 5y = 545/8\n10x + 9y = 629/8\n\nUsing elimination\n10*(8x + 5y = 545/8)\n8*(10x + 9y = 629/8)\n80x + 50y = 2725/4\n80x + 72y = 629\nSubtract equations\n-22y = 209/4\ny = 209/4/-22\ny = -19/8\n\nSubstitute y\n8x + 5(-19/8) = 545/8\n8x = 80\nx = 80/8\nx = 10"} {"input": "Solve the equation 6x + 54/5 = 0", "output": "6x + 54/5 = 0\n6x = -54/5\nx = -54/5 / 6\nx = -9/5"} {"input": "What value of x satisfies x^3 + 17/2x^2 - 10x - 112 = 0", "output": "x^3 + 17/2x^2 - 10x - 112 = 0\n(x - 7/2)(x - -8)(x - -4) = 0\nx - 7/2 = 0\nx - -8 = 0\nx - -4 = 0\nx = 7/2\nx = -8\nx = -4"} {"input": "Find the solution to x^3 - 59/14x^2 + 1023/175x - 468/175 = 0", "output": "x^3 - 59/14x^2 + 1023/175x - 468/175 = 0\n(x - 12/7)(x - 6/5)(x - 13/10) = 0\nx - 12/7 = 0\nx - 6/5 = 0\nx - 13/10 = 0\nx = 12/7\nx = 6/5\nx = 13/10"} {"input": "Solve the system:\n5x + 3y = 119/6\n10x + 10y = 215/3", "output": "5x + 3y = 119/6\n10x + 10y = 215/3\n\nUsing elimination\n10*(5x + 3y = 119/6)\n5*(10x + 10y = 215/3)\n50x + 30y = 595/3\n50x + 50y = 1075/3\nSubtract equations\n-20y = -160\ny = -160/-20\ny = 8\n\nSubstitute y\n5x + 3(8) = 119/6\n5x = -25/6\nx = -25/6/5\nx = -5/6"} {"input": "Find x in x^2 - 3/2x - 1 = 0", "output": "x^2 - 3/2x - 1 = 0\n(x - -1/2)(x - 2) = 0\nx - -1/2 = 0 or x - 2 = 0\nx = -1/2\nx = 2"} {"input": "Compute the solution of x^3 + 13/5x^2 - 57/20x - 99/20 = 0", "output": "x^3 + 13/5x^2 - 57/20x - 99/20 = 0\n(x - -3)(x - -11/10)(x - 3/2) = 0\nx - -3 = 0\nx - -11/10 = 0\nx - 3/2 = 0\nx = -3\nx = -11/10\nx = 3/2"} {"input": "Find x for x^2 + 79/20x + 3/4 = 0", "output": "x^2 + 79/20x + 3/4 = 0\n(x - -1/5)(x - -15/4) = 0\nx - -1/5 = 0 or x - -15/4 = 0\nx = -1/5\nx = -15/4"} {"input": "Find x in x^2 - 35/2x + 153/2 = 0", "output": "x^2 - 35/2x + 153/2 = 0\n(x - 17/2)(x - 9) = 0\nx - 17/2 = 0 or x - 9 = 0\nx = 17/2\nx = 9"} {"input": "Determine x in x^2 + 21/4x + 19/8 = 0", "output": "x^2 + 21/4x + 19/8 = 0\n(x - -19/4)(x - -1/2) = 0\nx - -19/4 = 0 or x - -1/2 = 0\nx = -19/4\nx = -1/2"} {"input": "Compute the solution of 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Compute the solution of 8x + 14 = 0", "output": "8x + 14 = 0\n8x = -14\nx = -14 / 8\nx = -7/4"} {"input": "Solve quickly: 7x + 105/4 = 0", "output": "7x + 105/4 = 0\n7x = -105/4\nx = -105/4 / 7\nx = -15/4"} {"input": "Solve x^2 - 144/7x + 80/7 = 0", "output": "x^2 - 144/7x + 80/7 = 0\n(x - 4/7)(x - 20) = 0\nx - 4/7 = 0 or x - 20 = 0\nx = 4/7\nx = 20"} {"input": "Solve simultaneously:\n10x + 6y = 74/3\n4x + 2y = 20/3", "output": "10x + 6y = 74/3\n4x + 2y = 20/3\n\nUsing elimination\n4*(10x + 6y = 74/3)\n10*(4x + 2y = 20/3)\n40x + 24y = 296/3\n40x + 20y = 200/3\nSubtract equations\n4y = 32\ny = 32/4\ny = 8\n\nSubstitute y\n10x + 6(8) = 74/3\n10x = -70/3\nx = -70/3/10\nx = -7/3"} {"input": "Find the solution to 5x - 2 = 0", "output": "5x - 2 = 0\n5x = 2\nx = 2 / 5\nx = 2/5"} {"input": "Compute the solution of x^3 + 11/2x^2 - 15x - 63/2 = 0", "output": "x^3 + 11/2x^2 - 15x - 63/2 = 0\n(x - 3)(x - -3/2)(x - -7) = 0\nx - 3 = 0\nx - -3/2 = 0\nx - -7 = 0\nx = 3\nx = -3/2\nx = -7"} {"input": "Solve the equation 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "What value of x satisfies x^2 + 9/10x - 18/5 = 0", "output": "x^2 + 9/10x - 18/5 = 0\n(x - 3/2)(x - -12/5) = 0\nx - 3/2 = 0 or x - -12/5 = 0\nx = 3/2\nx = -12/5"} {"input": "Find the solution to x^2 + 10/3x - 19 = 0", "output": "x^2 + 10/3x - 19 = 0\n(x - 3)(x - -19/3) = 0\nx - 3 = 0 or x - -19/3 = 0\nx = 3\nx = -19/3"} {"input": "Find x in x^2 + 64/15x - 119/15 = 0", "output": "x^2 + 64/15x - 119/15 = 0\n(x - -17/3)(x - 7/5) = 0\nx - -17/3 = 0 or x - 7/5 = 0\nx = -17/3\nx = 7/5"} {"input": "Find x in x^3 - 191/12x^2 + 407/6x - 260/3 = 0", "output": "x^3 - 191/12x^2 + 407/6x - 260/3 = 0\n(x - 13/4)(x - 8/3)(x - 10) = 0\nx - 13/4 = 0\nx - 8/3 = 0\nx - 10 = 0\nx = 13/4\nx = 8/3\nx = 10"} {"input": "Solve 3x = 0", "output": "3x = 0\n3x = 0\nx = 0 / 3\nx = 0"} {"input": "Solve the equations:\n6x + 7y = 79\n4x + 8y = 332/7", "output": "6x + 7y = 79\n4x + 8y = 332/7\n\nUsing elimination\n4*(6x + 7y = 79)\n6*(4x + 8y = 332/7)\n24x + 28y = 316\n24x + 48y = 1992/7\nSubtract equations\n-20y = 220/7\ny = 220/7/-20\ny = -11/7\n\nSubstitute y\n6x + 7(-11/7) = 79\n6x = 90\nx = 90/6\nx = 15"} {"input": "Solve simultaneously:\n2x + 3y = -33/2\n9x + 1y = -47/4", "output": "2x + 3y = -33/2\n9x + 1y = -47/4\n\nUsing elimination\n9*(2x + 3y = -33/2)\n2*(9x + 1y = -47/4)\n18x + 27y = -297/2\n18x + 2y = -47/2\nSubtract equations\n25y = -125\ny = -125/25\ny = -5\n\nSubstitute y\n2x + 3(-5) = -33/2\n2x = -3/2\nx = -3/2/2\nx = -3/4"} {"input": "Find x in x^2 + 67/15x + 24/5 = 0", "output": "x^2 + 67/15x + 24/5 = 0\n(x - -8/3)(x - -9/5) = 0\nx - -8/3 = 0 or x - -9/5 = 0\nx = -8/3\nx = -9/5"} {"input": "Compute the solution of 8x - 40/7 = 0", "output": "8x - 40/7 = 0\n8x = 40/7\nx = 40/7 / 8\nx = 5/7"} {"input": "Find x in 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Solve the system:\n6x + 10y = -70\n2x + 4y = -22", "output": "6x + 10y = -70\n2x + 4y = -22\n\nUsing elimination\n2*(6x + 10y = -70)\n6*(2x + 4y = -22)\n12x + 20y = -140\n12x + 24y = -132\nSubtract equations\n-4y = -8\ny = -8/-4\ny = 2\n\nSubstitute y\n6x + 10(2) = -70\n6x = -90\nx = -90/6\nx = -15"} {"input": "Find x in x^2 + 41/40x - 9/80 = 0", "output": "x^2 + 41/40x - 9/80 = 0\n(x - 1/10)(x - -9/8) = 0\nx - 1/10 = 0 or x - -9/8 = 0\nx = 1/10\nx = -9/8"} {"input": "Solve quickly: 8x - 3 = 0", "output": "8x - 3 = 0\n8x = 3\nx = 3 / 8\nx = 3/8"} {"input": "What value of x satisfies 1x + 19/4 = 0", "output": "1x + 19/4 = 0\n1x = -19/4\nx = -19/4 / 1\nx = -19/4"} {"input": "Find x in 3x + 51/7 = 0", "output": "3x + 51/7 = 0\n3x = -51/7\nx = -51/7 / 3\nx = -17/7"} {"input": "Determine x in 1x + 5/2 = 0", "output": "1x + 5/2 = 0\n1x = -5/2\nx = -5/2 / 1\nx = -5/2"} {"input": "Solve quickly: 6x + 3 = 0", "output": "6x + 3 = 0\n6x = -3\nx = -3 / 6\nx = -1/2"} {"input": "Find x for x^3 + 237/40x^2 + 4619/400x + 741/100 = 0", "output": "x^3 + 237/40x^2 + 4619/400x + 741/100 = 0\n(x - -13/8)(x - -12/5)(x - -19/10) = 0\nx - -13/8 = 0\nx - -12/5 = 0\nx - -19/10 = 0\nx = -13/8\nx = -12/5\nx = -19/10"} {"input": "Solve the system:\n7x + 8y = -59/9\n3x + 8y = -71/9", "output": "7x + 8y = -59/9\n3x + 8y = -71/9\n\nUsing elimination\n3*(7x + 8y = -59/9)\n7*(3x + 8y = -71/9)\n21x + 24y = -59/3\n21x + 56y = -497/9\nSubtract equations\n-32y = 320/9\ny = 320/9/-32\ny = -10/9\n\nSubstitute y\n7x + 8(-10/9) = -59/9\n7x = 7/3\nx = 7/3/7\nx = 1/3"} {"input": "Solve the equation x^2 + 99/14x - 45/14 = 0", "output": "x^2 + 99/14x - 45/14 = 0\n(x - 3/7)(x - -15/2) = 0\nx - 3/7 = 0 or x - -15/2 = 0\nx = 3/7\nx = -15/2"} {"input": "Compute the solution of x^3 + 361/42x^2 + 479/42x + 5/3 = 0", "output": "x^3 + 361/42x^2 + 479/42x + 5/3 = 0\n(x - -7)(x - -1/6)(x - -10/7) = 0\nx - -7 = 0\nx - -1/6 = 0\nx - -10/7 = 0\nx = -7\nx = -1/6\nx = -10/7"} {"input": "Solve the equation x^3 + 73/72x^2 - 15/8x + 7/36 = 0", "output": "x^3 + 73/72x^2 - 15/8x + 7/36 = 0\n(x - -2)(x - 7/8)(x - 1/9) = 0\nx - -2 = 0\nx - 7/8 = 0\nx - 1/9 = 0\nx = -2\nx = 7/8\nx = 1/9"} {"input": "Find x for 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Solve the equations:\n3x + 5y = -19\n5x + 1y = -217/5", "output": "3x + 5y = -19\n5x + 1y = -217/5\n\nUsing elimination\n5*(3x + 5y = -19)\n3*(5x + 1y = -217/5)\n15x + 25y = -95\n15x + 3y = -651/5\nSubtract equations\n22y = 176/5\ny = 176/5/22\ny = 8/5\n\nSubstitute y\n3x + 5(8/5) = -19\n3x = -27\nx = -27/3\nx = -9"} {"input": "Solve x^2 - 7/2x + 5/2 = 0", "output": "x^2 - 7/2x + 5/2 = 0\n(x - 1)(x - 5/2) = 0\nx - 1 = 0 or x - 5/2 = 0\nx = 1\nx = 5/2"} {"input": "Solve quickly: x^3 + 8/3x^2 - 25/12x - 25/4 = 0", "output": "x^3 + 8/3x^2 - 25/12x - 25/4 = 0\n(x - -5/3)(x - 3/2)(x - -5/2) = 0\nx - -5/3 = 0\nx - 3/2 = 0\nx - -5/2 = 0\nx = -5/3\nx = 3/2\nx = -5/2"} {"input": "Find x and y such that\n10x + 3y = -107/21\n6x + 7y = 499/63", "output": "10x + 3y = -107/21\n6x + 7y = 499/63\n\nUsing elimination\n6*(10x + 3y = -107/21)\n10*(6x + 7y = 499/63)\n60x + 18y = -214/7\n60x + 70y = 4990/63\nSubtract equations\n-52y = -988/9\ny = -988/9/-52\ny = 19/9\n\nSubstitute y\n10x + 3(19/9) = -107/21\n10x = -80/7\nx = -80/7/10\nx = -8/7"} {"input": "Solve the system:\n1x + 6y = -4/7\n8x + 6y = 94/7", "output": "1x + 6y = -4/7\n8x + 6y = 94/7\n\nUsing elimination\n8*(1x + 6y = -4/7)\n1*(8x + 6y = 94/7)\n8x + 48y = -32/7\n8x + 6y = 94/7\nSubtract equations\n42y = -18\ny = -18/42\ny = -3/7\n\nSubstitute y\n1x + 6(-3/7) = -4/7\n1x = 2\nx = 2/1\nx = 2"} {"input": "Solve quickly: x^3 - 67/6x^2 + 27x - 40/3 = 0", "output": "x^3 - 67/6x^2 + 27x - 40/3 = 0\n(x - 2/3)(x - 8)(x - 5/2) = 0\nx - 2/3 = 0\nx - 8 = 0\nx - 5/2 = 0\nx = 2/3\nx = 8\nx = 5/2"} {"input": "Solve quickly: x^3 + 3/40x^2 - 109/160x - 21/160 = 0", "output": "x^3 + 3/40x^2 - 109/160x - 21/160 = 0\n(x - -1/5)(x - 7/8)(x - -3/4) = 0\nx - -1/5 = 0\nx - 7/8 = 0\nx - -3/4 = 0\nx = -1/5\nx = 7/8\nx = -3/4"} {"input": "Solve simultaneously:\n1x + 2y = 7/2\n5x + 1y = -101/4", "output": "1x + 2y = 7/2\n5x + 1y = -101/4\n\nUsing elimination\n5*(1x + 2y = 7/2)\n1*(5x + 1y = -101/4)\n5x + 10y = 35/2\n5x + 1y = -101/4\nSubtract equations\n9y = 171/4\ny = 171/4/9\ny = 19/4\n\nSubstitute y\n1x + 2(19/4) = 7/2\n1x = -6\nx = -6/1\nx = -6"} {"input": "Solve quickly: x^3 + 81/35x^2 - 264/7x + 2176/35 = 0", "output": "x^3 + 81/35x^2 - 264/7x + 2176/35 = 0\n(x - 16/7)(x - -8)(x - 17/5) = 0\nx - 16/7 = 0\nx - -8 = 0\nx - 17/5 = 0\nx = 16/7\nx = -8\nx = 17/5"} {"input": "Find the solution to 8x - 52/3 = 0", "output": "8x - 52/3 = 0\n8x = 52/3\nx = 52/3 / 8\nx = 13/6"} {"input": "Solve the equations:\n7x + 8y = 19/2\n10x + 1y = -123/4", "output": "7x + 8y = 19/2\n10x + 1y = -123/4\n\nUsing elimination\n10*(7x + 8y = 19/2)\n7*(10x + 1y = -123/4)\n70x + 80y = 95\n70x + 7y = -861/4\nSubtract equations\n73y = 1241/4\ny = 1241/4/73\ny = 17/4\n\nSubstitute y\n7x + 8(17/4) = 19/2\n7x = -49/2\nx = -49/2/7\nx = -7/2"} {"input": "Solve the equation x^2 + 93/10x - 19/10 = 0", "output": "x^2 + 93/10x - 19/10 = 0\n(x - 1/5)(x - -19/2) = 0\nx - 1/5 = 0 or x - -19/2 = 0\nx = 1/5\nx = -19/2"} {"input": "Solve simultaneously:\n3x + 4y = 30/7\n9x + 8y = 27/7", "output": "3x + 4y = 30/7\n9x + 8y = 27/7\n\nUsing elimination\n9*(3x + 4y = 30/7)\n3*(9x + 8y = 27/7)\n27x + 36y = 270/7\n27x + 24y = 81/7\nSubtract equations\n12y = 27\ny = 27/12\ny = 9/4\n\nSubstitute y\n3x + 4(9/4) = 30/7\n3x = -33/7\nx = -33/7/3\nx = -11/7"} {"input": "Find x in x^2 + 21/8x - 9/8 = 0", "output": "x^2 + 21/8x - 9/8 = 0\n(x - -3)(x - 3/8) = 0\nx - -3 = 0 or x - 3/8 = 0\nx = -3\nx = 3/8"} {"input": "Solve x^3 - 35/72x^2 - 247/72x = 0", "output": "x^3 - 35/72x^2 - 247/72x = 0\n(x - 19/9)(x - -13/8)(x - 0) = 0\nx - 19/9 = 0\nx - -13/8 = 0\nx - 0 = 0\nx = 19/9\nx = -13/8\nx = 0"} {"input": "Solve quickly: 6x - 12 = 0", "output": "6x - 12 = 0\n6x = 12\nx = 12 / 6\nx = 2"} {"input": "Determine x in x^2 + 1/5x - 22/5 = 0", "output": "x^2 + 1/5x - 22/5 = 0\n(x - -11/5)(x - 2) = 0\nx - -11/5 = 0 or x - 2 = 0\nx = -11/5\nx = 2"} {"input": "Find x in x^2 - 8/15x - 4/5 = 0", "output": "x^2 - 8/15x - 4/5 = 0\n(x - -2/3)(x - 6/5) = 0\nx - -2/3 = 0 or x - 6/5 = 0\nx = -2/3\nx = 6/5"} {"input": "Solve the equations:\n10x + 2y = 47/3\n5x + 2y = 59/6", "output": "10x + 2y = 47/3\n5x + 2y = 59/6\n\nUsing elimination\n5*(10x + 2y = 47/3)\n10*(5x + 2y = 59/6)\n50x + 10y = 235/3\n50x + 20y = 295/3\nSubtract equations\n-10y = -20\ny = -20/-10\ny = 2\n\nSubstitute y\n10x + 2(2) = 47/3\n10x = 35/3\nx = 35/3/10\nx = 7/6"} {"input": "Solve quickly: x^3 + 2x^2 - 39/4x - 2261/108 = 0", "output": "x^3 + 2x^2 - 39/4x - 2261/108 = 0\n(x - 19/6)(x - -7/3)(x - -17/6) = 0\nx - 19/6 = 0\nx - -7/3 = 0\nx - -17/6 = 0\nx = 19/6\nx = -7/3\nx = -17/6"} {"input": "Find the solution to x^2 - 5/9x - 28/27 = 0", "output": "x^2 - 5/9x - 28/27 = 0\n(x - 4/3)(x - -7/9) = 0\nx - 4/3 = 0 or x - -7/9 = 0\nx = 4/3\nx = -7/9"} {"input": "Find the solution to 9x - 27/2 = 0", "output": "9x - 27/2 = 0\n9x = 27/2\nx = 27/2 / 9\nx = 3/2"} {"input": "Determine x in x^2 - 23/5x + 18/5 = 0", "output": "x^2 - 23/5x + 18/5 = 0\n(x - 18/5)(x - 1) = 0\nx - 18/5 = 0 or x - 1 = 0\nx = 18/5\nx = 1"} {"input": "Find the solution to x^2 + 13/4x + 5/2 = 0", "output": "x^2 + 13/4x + 5/2 = 0\n(x - -2)(x - -5/4) = 0\nx - -2 = 0 or x - -5/4 = 0\nx = -2\nx = -5/4"} {"input": "Solve the equation x^2 + 89/7x + 60/7 = 0", "output": "x^2 + 89/7x + 60/7 = 0\n(x - -5/7)(x - -12) = 0\nx - -5/7 = 0 or x - -12 = 0\nx = -5/7\nx = -12"} {"input": "What value of x satisfies 7x = 0", "output": "7x = 0\n7x = 0\nx = 0 / 7\nx = 0"} {"input": "What value of x satisfies x^3 + 127/70x^2 - 717/490x - 216/245 = 0", "output": "x^3 + 127/70x^2 - 717/490x - 216/245 = 0\n(x - 9/10)(x - -3/7)(x - -16/7) = 0\nx - 9/10 = 0\nx - -3/7 = 0\nx - -16/7 = 0\nx = 9/10\nx = -3/7\nx = -16/7"} {"input": "Solve the equation x^2 - 23/18x - 55/54 = 0", "output": "x^2 - 23/18x - 55/54 = 0\n(x - -5/9)(x - 11/6) = 0\nx - -5/9 = 0 or x - 11/6 = 0\nx = -5/9\nx = 11/6"} {"input": "Find the solution to 5x + 50/9 = 0", "output": "5x + 50/9 = 0\n5x = -50/9\nx = -50/9 / 5\nx = -10/9"} {"input": "Solve simultaneously:\n3x + 9y = 4\n3x + 4y = 7/3", "output": "3x + 9y = 4\n3x + 4y = 7/3\n\nUsing elimination\n3*(3x + 9y = 4)\n3*(3x + 4y = 7/3)\n9x + 27y = 12\n9x + 12y = 7\nSubtract equations\n15y = 5\ny = 5/15\ny = 1/3\n\nSubstitute y\n3x + 9(1/3) = 4\n3x = 1\nx = 1/3\nx = 1/3"} {"input": "Solve quickly: x^2 + 41/9x + 14/3 = 0", "output": "x^2 + 41/9x + 14/3 = 0\n(x - -14/9)(x - -3) = 0\nx - -14/9 = 0 or x - -3 = 0\nx = -14/9\nx = -3"} {"input": "Find x in x^3 + 3/2x^2 - 3/2x - 1 = 0", "output": "x^3 + 3/2x^2 - 3/2x - 1 = 0\n(x - -1/2)(x - -2)(x - 1) = 0\nx - -1/2 = 0\nx - -2 = 0\nx - 1 = 0\nx = -1/2\nx = -2\nx = 1"} {"input": "Find x and y such that\n8x + 10y = 548/3\n5x + 8y = 895/6", "output": "8x + 10y = 548/3\n5x + 8y = 895/6\n\nUsing elimination\n5*(8x + 10y = 548/3)\n8*(5x + 8y = 895/6)\n40x + 50y = 2740/3\n40x + 64y = 3580/3\nSubtract equations\n-14y = -280\ny = -280/-14\ny = 20\n\nSubstitute y\n8x + 10(20) = 548/3\n8x = -52/3\nx = -52/3/8\nx = -13/6"} {"input": "Compute the solution of x^2 - 3/2x = 0", "output": "x^2 - 3/2x = 0\n(x - 0)(x - 3/2) = 0\nx - 0 = 0 or x - 3/2 = 0\nx = 0\nx = 3/2"} {"input": "Find the solution to x^3 + 343/30x^2 + 115/6x + 38/5 = 0", "output": "x^3 + 343/30x^2 + 115/6x + 38/5 = 0\n(x - -19/2)(x - -3/5)(x - -4/3) = 0\nx - -19/2 = 0\nx - -3/5 = 0\nx - -4/3 = 0\nx = -19/2\nx = -3/5\nx = -4/3"} {"input": "Solve quickly: 7x + 14 = 0", "output": "7x + 14 = 0\n7x = -14\nx = -14 / 7\nx = -2"} {"input": "Solve x^3 + 22/9x^2 + 4/27x - 40/27 = 0", "output": "x^3 + 22/9x^2 + 4/27x - 40/27 = 0\n(x - -10/9)(x - 2/3)(x - -2) = 0\nx - -10/9 = 0\nx - 2/3 = 0\nx - -2 = 0\nx = -10/9\nx = 2/3\nx = -2"} {"input": "Solve the equations:\n9x + 9y = 315/4\n7x + 5y = 185/4", "output": "9x + 9y = 315/4\n7x + 5y = 185/4\n\nUsing elimination\n7*(9x + 9y = 315/4)\n9*(7x + 5y = 185/4)\n63x + 63y = 2205/4\n63x + 45y = 1665/4\nSubtract equations\n18y = 135\ny = 135/18\ny = 15/2\n\nSubstitute y\n9x + 9(15/2) = 315/4\n9x = 45/4\nx = 45/4/9\nx = 5/4"} {"input": "What value of x satisfies x^3 - 299/126x^2 - 75/7x + 36/7 = 0", "output": "x^3 - 299/126x^2 - 75/7x + 36/7 = 0\n(x - 4/9)(x - 9/2)(x - -18/7) = 0\nx - 4/9 = 0\nx - 9/2 = 0\nx - -18/7 = 0\nx = 4/9\nx = 9/2\nx = -18/7"} {"input": "Determine x in x^3 + 9/10x^2 - 4x = 0", "output": "x^3 + 9/10x^2 - 4x = 0\n(x - 8/5)(x - 0)(x - -5/2) = 0\nx - 8/5 = 0\nx - 0 = 0\nx - -5/2 = 0\nx = 8/5\nx = 0\nx = -5/2"} {"input": "Solve simultaneously:\n4x + 3y = 16/3\n4x + 1y = 56/3", "output": "4x + 3y = 16/3\n4x + 1y = 56/3\n\nUsing elimination\n4*(4x + 3y = 16/3)\n4*(4x + 1y = 56/3)\n16x + 12y = 64/3\n16x + 4y = 224/3\nSubtract equations\n8y = -160/3\ny = -160/3/8\ny = -20/3\n\nSubstitute y\n4x + 3(-20/3) = 16/3\n4x = 76/3\nx = 76/3/4\nx = 19/3"} {"input": "Solve the equation x^3 + 31/18x^2 - 143/18x + 14/3 = 0", "output": "x^3 + 31/18x^2 - 143/18x + 14/3 = 0\n(x - 3/2)(x - -4)(x - 7/9) = 0\nx - 3/2 = 0\nx - -4 = 0\nx - 7/9 = 0\nx = 3/2\nx = -4\nx = 7/9"} {"input": "Solve the equation x^2 - 7x + 12 = 0", "output": "x^2 - 7x + 12 = 0\n(x - 4)(x - 3) = 0\nx - 4 = 0 or x - 3 = 0\nx = 4\nx = 3"} {"input": "What value of x satisfies x^3 + 83/8x^2 + 423/16x + 315/16 = 0", "output": "x^3 + 83/8x^2 + 423/16x + 315/16 = 0\n(x - -15/8)(x - -7)(x - -3/2) = 0\nx - -15/8 = 0\nx - -7 = 0\nx - -3/2 = 0\nx = -15/8\nx = -7\nx = -3/2"} {"input": "Solve the system:\n7x + 4y = -163/5\n10x + 7y = -256/5", "output": "7x + 4y = -163/5\n10x + 7y = -256/5\n\nUsing elimination\n10*(7x + 4y = -163/5)\n7*(10x + 7y = -256/5)\n70x + 40y = -326\n70x + 49y = -1792/5\nSubtract equations\n-9y = 162/5\ny = 162/5/-9\ny = -18/5\n\nSubstitute y\n7x + 4(-18/5) = -163/5\n7x = -91/5\nx = -91/5/7\nx = -13/5"} {"input": "Solve quickly: 5x - 10/9 = 0", "output": "5x - 10/9 = 0\n5x = 10/9\nx = 10/9 / 5\nx = 2/9"} {"input": "Find x in x^2 + 13/2x + 15/2 = 0", "output": "x^2 + 13/2x + 15/2 = 0\n(x - -5)(x - -3/2) = 0\nx - -5 = 0 or x - -3/2 = 0\nx = -5\nx = -3/2"} {"input": "Determine x in 5x - 95/3 = 0", "output": "5x - 95/3 = 0\n5x = 95/3\nx = 95/3 / 5\nx = 19/3"} {"input": "Solve quickly: 5x + 15 = 0", "output": "5x + 15 = 0\n5x = -15\nx = -15 / 5\nx = -3"} {"input": "Find the solution to x^2 - 2x - 8 = 0", "output": "x^2 - 2x - 8 = 0\n(x - 4)(x - -2) = 0\nx - 4 = 0 or x - -2 = 0\nx = 4\nx = -2"} {"input": "Solve quickly: x^2 - 50/3x - 17/3 = 0", "output": "x^2 - 50/3x - 17/3 = 0\n(x - 17)(x - -1/3) = 0\nx - 17 = 0 or x - -1/3 = 0\nx = 17\nx = -1/3"} {"input": "Find x and y such that\n10x + 8y = -247/12\n10x + 9y = -87/4", "output": "10x + 8y = -247/12\n10x + 9y = -87/4\n\nUsing elimination\n10*(10x + 8y = -247/12)\n10*(10x + 9y = -87/4)\n100x + 80y = -1235/6\n100x + 90y = -435/2\nSubtract equations\n-10y = 35/3\ny = 35/3/-10\ny = -7/6\n\nSubstitute y\n10x + 8(-7/6) = -247/12\n10x = -45/4\nx = -45/4/10\nx = -9/8"} {"input": "Solve the system:\n9x + 1y = -149/4\n5x + 6y = -67/6", "output": "9x + 1y = -149/4\n5x + 6y = -67/6\n\nUsing elimination\n5*(9x + 1y = -149/4)\n9*(5x + 6y = -67/6)\n45x + 5y = -745/4\n45x + 54y = -201/2\nSubtract equations\n-49y = -343/4\ny = -343/4/-49\ny = 7/4\n\nSubstitute y\n9x + 1(7/4) = -149/4\n9x = -39\nx = -39/9\nx = -13/3"} {"input": "Find x and y such that\n4x + 4y = 388/15\n6x + 8y = 722/15", "output": "4x + 4y = 388/15\n6x + 8y = 722/15\n\nUsing elimination\n6*(4x + 4y = 388/15)\n4*(6x + 8y = 722/15)\n24x + 24y = 776/5\n24x + 32y = 2888/15\nSubtract equations\n-8y = -112/3\ny = -112/3/-8\ny = 14/3\n\nSubstitute y\n4x + 4(14/3) = 388/15\n4x = 36/5\nx = 36/5/4\nx = 9/5"} {"input": "Compute the solution of x^3 + 37/15x^2 - 236/15x + 68/5 = 0", "output": "x^3 + 37/15x^2 - 236/15x + 68/5 = 0\n(x - 2)(x - -17/3)(x - 6/5) = 0\nx - 2 = 0\nx - -17/3 = 0\nx - 6/5 = 0\nx = 2\nx = -17/3\nx = 6/5"} {"input": "Solve 4x + 26/3 = 0", "output": "4x + 26/3 = 0\n4x = -26/3\nx = -26/3 / 4\nx = -13/6"} {"input": "Solve the system:\n8x + 8y = 32/5\n8x + 2y = -22/5", "output": "8x + 8y = 32/5\n8x + 2y = -22/5\n\nUsing elimination\n8*(8x + 8y = 32/5)\n8*(8x + 2y = -22/5)\n64x + 64y = 256/5\n64x + 16y = -176/5\nSubtract equations\n48y = 432/5\ny = 432/5/48\ny = 9/5\n\nSubstitute y\n8x + 8(9/5) = 32/5\n8x = -8\nx = -8/8\nx = -1"} {"input": "Find the solution to x^2 + 89/5x - 18/5 = 0", "output": "x^2 + 89/5x - 18/5 = 0\n(x - -18)(x - 1/5) = 0\nx - -18 = 0 or x - 1/5 = 0\nx = -18\nx = 1/5"} {"input": "Solve simultaneously:\n1x + 4y = -56/9\n9x + 1y = 91/9", "output": "1x + 4y = -56/9\n9x + 1y = 91/9\n\nUsing elimination\n9*(1x + 4y = -56/9)\n1*(9x + 1y = 91/9)\n9x + 36y = -56\n9x + 1y = 91/9\nSubtract equations\n35y = -595/9\ny = -595/9/35\ny = -17/9\n\nSubstitute y\n1x + 4(-17/9) = -56/9\n1x = 4/3\nx = 4/3/1\nx = 4/3"} {"input": "Find the solution to x^2 - 44/3x + 140/3 = 0", "output": "x^2 - 44/3x + 140/3 = 0\n(x - 14/3)(x - 10) = 0\nx - 14/3 = 0 or x - 10 = 0\nx = 14/3\nx = 10"} {"input": "Solve the equation 6x + 6 = 0", "output": "6x + 6 = 0\n6x = -6\nx = -6 / 6\nx = -1"} {"input": "What value of x satisfies x^2 - 81/14x + 8 = 0", "output": "x^2 - 81/14x + 8 = 0\n(x - 7/2)(x - 16/7) = 0\nx - 7/2 = 0 or x - 16/7 = 0\nx = 7/2\nx = 16/7"} {"input": "Solve quickly: x^2 + 13/3x - 3/4 = 0", "output": "x^2 + 13/3x - 3/4 = 0\n(x - 1/6)(x - -9/2) = 0\nx - 1/6 = 0 or x - -9/2 = 0\nx = 1/6\nx = -9/2"} {"input": "Solve the system:\n6x + 3y = -166/5\n8x + 8y = -688/15", "output": "6x + 3y = -166/5\n8x + 8y = -688/15\n\nUsing elimination\n8*(6x + 3y = -166/5)\n6*(8x + 8y = -688/15)\n48x + 24y = -1328/5\n48x + 48y = -1376/5\nSubtract equations\n-24y = 48/5\ny = 48/5/-24\ny = -2/5\n\nSubstitute y\n6x + 3(-2/5) = -166/5\n6x = -32\nx = -32/6\nx = -16/3"} {"input": "Compute the solution of 2x - 15/2 = 0", "output": "2x - 15/2 = 0\n2x = 15/2\nx = 15/2 / 2\nx = 15/4"} {"input": "What value of x satisfies 3x + 27/2 = 0", "output": "3x + 27/2 = 0\n3x = -27/2\nx = -27/2 / 3\nx = -9/2"} {"input": "Compute the solution of x^2 + 14/15x - 16/15 = 0", "output": "x^2 + 14/15x - 16/15 = 0\n(x - -8/5)(x - 2/3) = 0\nx - -8/5 = 0 or x - 2/3 = 0\nx = -8/5\nx = 2/3"} {"input": "Find x for x^3 + 37/2x^2 + 1643/64x + 187/64 = 0", "output": "x^3 + 37/2x^2 + 1643/64x + 187/64 = 0\n(x - -11/8)(x - -1/8)(x - -17) = 0\nx - -11/8 = 0\nx - -1/8 = 0\nx - -17 = 0\nx = -11/8\nx = -1/8\nx = -17"} {"input": "Find x in x^3 - 187/72x^2 + 265/144x - 7/24 = 0", "output": "x^3 - 187/72x^2 + 265/144x - 7/24 = 0\n(x - 3/2)(x - 7/8)(x - 2/9) = 0\nx - 3/2 = 0\nx - 7/8 = 0\nx - 2/9 = 0\nx = 3/2\nx = 7/8\nx = 2/9"} {"input": "Find x in x^3 + 47/15x^2 - 157/60x - 13/2 = 0", "output": "x^3 + 47/15x^2 - 157/60x - 13/2 = 0\n(x - 3/2)(x - -13/10)(x - -10/3) = 0\nx - 3/2 = 0\nx - -13/10 = 0\nx - -10/3 = 0\nx = 3/2\nx = -13/10\nx = -10/3"} {"input": "Compute the solution of x^2 - 46/9x - 16/3 = 0", "output": "x^2 - 46/9x - 16/3 = 0\n(x - 6)(x - -8/9) = 0\nx - 6 = 0 or x - -8/9 = 0\nx = 6\nx = -8/9"} {"input": "Solve x^3 - 71/15x^2 + 446/75x - 112/75 = 0", "output": "x^3 - 71/15x^2 + 446/75x - 112/75 = 0\n(x - 1/3)(x - 14/5)(x - 8/5) = 0\nx - 1/3 = 0\nx - 14/5 = 0\nx - 8/5 = 0\nx = 1/3\nx = 14/5\nx = 8/5"} {"input": "Compute the solution of x^2 - 31/45x - 34/15 = 0", "output": "x^2 - 31/45x - 34/15 = 0\n(x - -6/5)(x - 17/9) = 0\nx - -6/5 = 0 or x - 17/9 = 0\nx = -6/5\nx = 17/9"} {"input": "What value of x satisfies 1x + 2 = 0", "output": "1x + 2 = 0\n1x = -2\nx = -2 / 1\nx = -2"} {"input": "Solve the system:\n10x + 3y = 191/7\n10x + 7y = 219/7", "output": "10x + 3y = 191/7\n10x + 7y = 219/7\n\nUsing elimination\n10*(10x + 3y = 191/7)\n10*(10x + 7y = 219/7)\n100x + 30y = 1910/7\n100x + 70y = 2190/7\nSubtract equations\n-40y = -40\ny = -40/-40\ny = 1\n\nSubstitute y\n10x + 3(1) = 191/7\n10x = 170/7\nx = 170/7/10\nx = 17/7"} {"input": "Find the solution to 2x - 2/3 = 0", "output": "2x - 2/3 = 0\n2x = 2/3\nx = 2/3 / 2\nx = 1/3"} {"input": "Find x for 3x - 54/7 = 0", "output": "3x - 54/7 = 0\n3x = 54/7\nx = 54/7 / 3\nx = 18/7"} {"input": "Solve simultaneously:\n7x + 10y = 654/35\n10x + 10y = 114/7", "output": "7x + 10y = 654/35\n10x + 10y = 114/7\n\nUsing elimination\n10*(7x + 10y = 654/35)\n7*(10x + 10y = 114/7)\n70x + 100y = 1308/7\n70x + 70y = 114\nSubtract equations\n30y = 510/7\ny = 510/7/30\ny = 17/7\n\nSubstitute y\n7x + 10(17/7) = 654/35\n7x = -28/5\nx = -28/5/7\nx = -4/5"} {"input": "Solve the equations:\n3x + 6y = 30\n1x + 6y = 34", "output": "3x + 6y = 30\n1x + 6y = 34\n\nUsing elimination\n1*(3x + 6y = 30)\n3*(1x + 6y = 34)\n3x + 6y = 30\n3x + 18y = 102\nSubtract equations\n-12y = -72\ny = -72/-12\ny = 6\n\nSubstitute y\n3x + 6(6) = 30\n3x = -6\nx = -6/3\nx = -2"} {"input": "Determine x in x^3 - 93/5x^2 - 551/20x - 9 = 0", "output": "x^3 - 93/5x^2 - 551/20x - 9 = 0\n(x - 20)(x - -9/10)(x - -1/2) = 0\nx - 20 = 0\nx - -9/10 = 0\nx - -1/2 = 0\nx = 20\nx = -9/10\nx = -1/2"} {"input": "Find the solution to 9x + 12 = 0", "output": "9x + 12 = 0\n9x = -12\nx = -12 / 9\nx = -4/3"} {"input": "Compute the solution of x^2 + 21x + 80 = 0", "output": "x^2 + 21x + 80 = 0\n(x - -16)(x - -5) = 0\nx - -16 = 0 or x - -5 = 0\nx = -16\nx = -5"} {"input": "Find x in 6x + 10/3 = 0", "output": "6x + 10/3 = 0\n6x = -10/3\nx = -10/3 / 6\nx = -5/9"} {"input": "Solve 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Solve the system:\n4x + 2y = 44/15\n9x + 1y = -187/30", "output": "4x + 2y = 44/15\n9x + 1y = -187/30\n\nUsing elimination\n9*(4x + 2y = 44/15)\n4*(9x + 1y = -187/30)\n36x + 18y = 132/5\n36x + 4y = -374/15\nSubtract equations\n14y = 154/3\ny = 154/3/14\ny = 11/3\n\nSubstitute y\n4x + 2(11/3) = 44/15\n4x = -22/5\nx = -22/5/4\nx = -11/10"} {"input": "Find x in x^2 - 49/12x + 49/12 = 0", "output": "x^2 - 49/12x + 49/12 = 0\n(x - 7/3)(x - 7/4) = 0\nx - 7/3 = 0 or x - 7/4 = 0\nx = 7/3\nx = 7/4"} {"input": "Solve quickly: x^3 - 11/21x^2 - 10x + 200/21 = 0", "output": "x^3 - 11/21x^2 - 10x + 200/21 = 0\n(x - 20/7)(x - -10/3)(x - 1) = 0\nx - 20/7 = 0\nx - -10/3 = 0\nx - 1 = 0\nx = 20/7\nx = -10/3\nx = 1"} {"input": "Find x and y such that\n3x + 1y = 29/3\n2x + 5y = 67/3", "output": "3x + 1y = 29/3\n2x + 5y = 67/3\n\nUsing elimination\n2*(3x + 1y = 29/3)\n3*(2x + 5y = 67/3)\n6x + 2y = 58/3\n6x + 15y = 67\nSubtract equations\n-13y = -143/3\ny = -143/3/-13\ny = 11/3\n\nSubstitute y\n3x + 1(11/3) = 29/3\n3x = 6\nx = 6/3\nx = 2"} {"input": "Compute the solution of 8x - 18 = 0", "output": "8x - 18 = 0\n8x = 18\nx = 18 / 8\nx = 9/4"} {"input": "Solve simultaneously:\n5x + 1y = 31/21\n8x + 6y = -122/21", "output": "5x + 1y = 31/21\n8x + 6y = -122/21\n\nUsing elimination\n8*(5x + 1y = 31/21)\n5*(8x + 6y = -122/21)\n40x + 8y = 248/21\n40x + 30y = -610/21\nSubtract equations\n-22y = 286/7\ny = 286/7/-22\ny = -13/7\n\nSubstitute y\n5x + 1(-13/7) = 31/21\n5x = 10/3\nx = 10/3/5\nx = 2/3"} {"input": "Determine x in x^3 + 13/18x^2 - 53/18x - 8/3 = 0", "output": "x^3 + 13/18x^2 - 53/18x - 8/3 = 0\n(x - 16/9)(x - -1)(x - -3/2) = 0\nx - 16/9 = 0\nx - -1 = 0\nx - -3/2 = 0\nx = 16/9\nx = -1\nx = -3/2"} {"input": "Solve the system:\n3x + 2y = -31\n6x + 7y = -263/4", "output": "3x + 2y = -31\n6x + 7y = -263/4\n\nUsing elimination\n6*(3x + 2y = -31)\n3*(6x + 7y = -263/4)\n18x + 12y = -186\n18x + 21y = -789/4\nSubtract equations\n-9y = 45/4\ny = 45/4/-9\ny = -5/4\n\nSubstitute y\n3x + 2(-5/4) = -31\n3x = -57/2\nx = -57/2/3\nx = -19/2"} {"input": "What value of x satisfies x^2 - 7/3x + 2/3 = 0", "output": "x^2 - 7/3x + 2/3 = 0\n(x - 2)(x - 1/3) = 0\nx - 2 = 0 or x - 1/3 = 0\nx = 2\nx = 1/3"} {"input": "Compute the solution of 9x + 45/8 = 0", "output": "9x + 45/8 = 0\n9x = -45/8\nx = -45/8 / 9\nx = -5/8"} {"input": "Determine x in x^3 + 233/28x^2 + 1283/56x + 585/28 = 0", "output": "x^3 + 233/28x^2 + 1283/56x + 585/28 = 0\n(x - -18/7)(x - -5/2)(x - -13/4) = 0\nx - -18/7 = 0\nx - -5/2 = 0\nx - -13/4 = 0\nx = -18/7\nx = -5/2\nx = -13/4"} {"input": "Solve quickly: 6x + 60 = 0", "output": "6x + 60 = 0\n6x = -60\nx = -60 / 6\nx = -10"} {"input": "Solve simultaneously:\n8x + 7y = -10\n5x + 1y = -23/8", "output": "8x + 7y = -10\n5x + 1y = -23/8\n\nUsing elimination\n5*(8x + 7y = -10)\n8*(5x + 1y = -23/8)\n40x + 35y = -50\n40x + 8y = -23\nSubtract equations\n27y = -27\ny = -27/27\ny = -1\n\nSubstitute y\n8x + 7(-1) = -10\n8x = -3\nx = -3/8\nx = -3/8"} {"input": "Solve quickly: x^2 + 157/36x + 19/4 = 0", "output": "x^2 + 157/36x + 19/4 = 0\n(x - -9/4)(x - -19/9) = 0\nx - -9/4 = 0 or x - -19/9 = 0\nx = -9/4\nx = -19/9"} {"input": "Solve the system:\n5x + 8y = 293/8\n9x + 7y = 335/8", "output": "5x + 8y = 293/8\n9x + 7y = 335/8\n\nUsing elimination\n9*(5x + 8y = 293/8)\n5*(9x + 7y = 335/8)\n45x + 72y = 2637/8\n45x + 35y = 1675/8\nSubtract equations\n37y = 481/4\ny = 481/4/37\ny = 13/4\n\nSubstitute y\n5x + 8(13/4) = 293/8\n5x = 85/8\nx = 85/8/5\nx = 17/8"} {"input": "Solve quickly: 1x - 3/2 = 0", "output": "1x - 3/2 = 0\n1x = 3/2\nx = 3/2 / 1\nx = 3/2"} {"input": "Find the solution to x^3 - 29/6x^2 - 55/2x + 325/3 = 0", "output": "x^3 - 29/6x^2 - 55/2x + 325/3 = 0\n(x - -5)(x - 10/3)(x - 13/2) = 0\nx - -5 = 0\nx - 10/3 = 0\nx - 13/2 = 0\nx = -5\nx = 10/3\nx = 13/2"} {"input": "Solve the equation 3x + 48/7 = 0", "output": "3x + 48/7 = 0\n3x = -48/7\nx = -48/7 / 3\nx = -16/7"} {"input": "Solve x^3 + 269/105x^2 + 142/105x - 8/21 = 0", "output": "x^3 + 269/105x^2 + 142/105x - 8/21 = 0\n(x - 1/5)(x - -4/3)(x - -10/7) = 0\nx - 1/5 = 0\nx - -4/3 = 0\nx - -10/7 = 0\nx = 1/5\nx = -4/3\nx = -10/7"} {"input": "Solve the equation x^3 + 16/5x^2 - 28/5x - 48/5 = 0", "output": "x^3 + 16/5x^2 - 28/5x - 48/5 = 0\n(x - -6/5)(x - 2)(x - -4) = 0\nx - -6/5 = 0\nx - 2 = 0\nx - -4 = 0\nx = -6/5\nx = 2\nx = -4"} {"input": "Solve x^2 + 21/5x - 54/5 = 0", "output": "x^2 + 21/5x - 54/5 = 0\n(x - 9/5)(x - -6) = 0\nx - 9/5 = 0 or x - -6 = 0\nx = 9/5\nx = -6"} {"input": "Solve the equations:\n4x + 5y = -655/8\n6x + 4y = -243/2", "output": "4x + 5y = -655/8\n6x + 4y = -243/2\n\nUsing elimination\n6*(4x + 5y = -655/8)\n4*(6x + 4y = -243/2)\n24x + 30y = -1965/4\n24x + 16y = -486\nSubtract equations\n14y = -21/4\ny = -21/4/14\ny = -3/8\n\nSubstitute y\n4x + 5(-3/8) = -655/8\n4x = -80\nx = -80/4\nx = -20"} {"input": "Find x for x^3 + 221/10x^2 + 95x - 208/5 = 0", "output": "x^3 + 221/10x^2 + 95x - 208/5 = 0\n(x - -16)(x - 2/5)(x - -13/2) = 0\nx - -16 = 0\nx - 2/5 = 0\nx - -13/2 = 0\nx = -16\nx = 2/5\nx = -13/2"} {"input": "Solve the system:\n2x + 8y = -292/15\n8x + 1y = -424/15", "output": "2x + 8y = -292/15\n8x + 1y = -424/15\n\nUsing elimination\n8*(2x + 8y = -292/15)\n2*(8x + 1y = -424/15)\n16x + 64y = -2336/15\n16x + 2y = -848/15\nSubtract equations\n62y = -496/5\ny = -496/5/62\ny = -8/5\n\nSubstitute y\n2x + 8(-8/5) = -292/15\n2x = -20/3\nx = -20/3/2\nx = -10/3"} {"input": "What value of x satisfies 8x - 104/3 = 0", "output": "8x - 104/3 = 0\n8x = 104/3\nx = 104/3 / 8\nx = 13/3"} {"input": "What value of x satisfies 1x + 11 = 0", "output": "1x + 11 = 0\n1x = -11\nx = -11 / 1\nx = -11"} {"input": "Find x for x^2 - 34/5x + 24/5 = 0", "output": "x^2 - 34/5x + 24/5 = 0\n(x - 6)(x - 4/5) = 0\nx - 6 = 0 or x - 4/5 = 0\nx = 6\nx = 4/5"} {"input": "Determine x in x^3 + 293/24x^2 + 691/16x + 2261/48 = 0", "output": "x^3 + 293/24x^2 + 691/16x + 2261/48 = 0\n(x - -19/8)(x - -17/6)(x - -7) = 0\nx - -19/8 = 0\nx - -17/6 = 0\nx - -7 = 0\nx = -19/8\nx = -17/6\nx = -7"} {"input": "Determine x in 10x - 6 = 0", "output": "10x - 6 = 0\n10x = 6\nx = 6 / 10\nx = 3/5"} {"input": "Find x and y such that\n3x + 9y = 177/14\n2x + 4y = 38/7", "output": "3x + 9y = 177/14\n2x + 4y = 38/7\n\nUsing elimination\n2*(3x + 9y = 177/14)\n3*(2x + 4y = 38/7)\n6x + 18y = 177/7\n6x + 12y = 114/7\nSubtract equations\n6y = 9\ny = 9/6\ny = 3/2\n\nSubstitute y\n3x + 9(3/2) = 177/14\n3x = -6/7\nx = -6/7/3\nx = -2/7"} {"input": "Find x and y such that\n10x + 1y = -26\n6x + 1y = -16", "output": "10x + 1y = -26\n6x + 1y = -16\n\nUsing elimination\n6*(10x + 1y = -26)\n10*(6x + 1y = -16)\n60x + 6y = -156\n60x + 10y = -160\nSubtract equations\n-4y = 4\ny = 4/-4\ny = -1\n\nSubstitute y\n10x + 1(-1) = -26\n10x = -25\nx = -25/10\nx = -5/2"} {"input": "Solve the equations:\n8x + 2y = 892/9\n6x + 5y = 718/9", "output": "8x + 2y = 892/9\n6x + 5y = 718/9\n\nUsing elimination\n6*(8x + 2y = 892/9)\n8*(6x + 5y = 718/9)\n48x + 12y = 1784/3\n48x + 40y = 5744/9\nSubtract equations\n-28y = -392/9\ny = -392/9/-28\ny = 14/9\n\nSubstitute y\n8x + 2(14/9) = 892/9\n8x = 96\nx = 96/8\nx = 12"} {"input": "Solve x^3 - 233/72x^2 + 1379/648x + 5/18 = 0", "output": "x^3 - 233/72x^2 + 1379/648x + 5/18 = 0\n(x - 9/8)(x - 20/9)(x - -1/9) = 0\nx - 9/8 = 0\nx - 20/9 = 0\nx - -1/9 = 0\nx = 9/8\nx = 20/9\nx = -1/9"} {"input": "Solve x^3 - 775/36x^2 + 1777/36x - 76/3 = 0", "output": "x^3 - 775/36x^2 + 1777/36x - 76/3 = 0\n(x - 19)(x - 3/4)(x - 16/9) = 0\nx - 19 = 0\nx - 3/4 = 0\nx - 16/9 = 0\nx = 19\nx = 3/4\nx = 16/9"} {"input": "Solve the equation x^3 + 18/5x^2 - 1x - 18/5 = 0", "output": "x^3 + 18/5x^2 - 1x - 18/5 = 0\n(x - -1)(x - 1)(x - -18/5) = 0\nx - -1 = 0\nx - 1 = 0\nx - -18/5 = 0\nx = -1\nx = 1\nx = -18/5"} {"input": "Find x for 7x - 63/4 = 0", "output": "7x - 63/4 = 0\n7x = 63/4\nx = 63/4 / 7\nx = 9/4"} {"input": "Solve the equations:\n9x + 3y = -21\n1x + 1y = -7", "output": "9x + 3y = -21\n1x + 1y = -7\n\nUsing elimination\n1*(9x + 3y = -21)\n9*(1x + 1y = -7)\n9x + 3y = -21\n9x + 9y = -63\nSubtract equations\n-6y = 42\ny = 42/-6\ny = -7\n\nSubstitute y\n9x + 3(-7) = -21\n9x = 0\nx = 0/9\nx = 0"} {"input": "Solve the system:\n5x + 2y = 53/63\n8x + 1y = -23/63", "output": "5x + 2y = 53/63\n8x + 1y = -23/63\n\nUsing elimination\n8*(5x + 2y = 53/63)\n5*(8x + 1y = -23/63)\n40x + 16y = 424/63\n40x + 5y = -115/63\nSubtract equations\n11y = 77/9\ny = 77/9/11\ny = 7/9\n\nSubstitute y\n5x + 2(7/9) = 53/63\n5x = -5/7\nx = -5/7/5\nx = -1/7"} {"input": "Solve the equations:\n10x + 5y = 130/3\n10x + 6y = 137/3", "output": "10x + 5y = 130/3\n10x + 6y = 137/3\n\nUsing elimination\n10*(10x + 5y = 130/3)\n10*(10x + 6y = 137/3)\n100x + 50y = 1300/3\n100x + 60y = 1370/3\nSubtract equations\n-10y = -70/3\ny = -70/3/-10\ny = 7/3\n\nSubstitute y\n10x + 5(7/3) = 130/3\n10x = 95/3\nx = 95/3/10\nx = 19/6"} {"input": "Solve 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "Find x for 6x - 6 = 0", "output": "6x - 6 = 0\n6x = 6\nx = 6 / 6\nx = 1"} {"input": "Compute the solution of x^2 + 35/6x + 13/2 = 0", "output": "x^2 + 35/6x + 13/2 = 0\n(x - -13/3)(x - -3/2) = 0\nx - -13/3 = 0 or x - -3/2 = 0\nx = -13/3\nx = -3/2"} {"input": "Solve the equation 1x + 1 = 0", "output": "1x + 1 = 0\n1x = -1\nx = -1 / 1\nx = -1"} {"input": "Find x for x^2 - 17/8x - 21/8 = 0", "output": "x^2 - 17/8x - 21/8 = 0\n(x - 3)(x - -7/8) = 0\nx - 3 = 0 or x - -7/8 = 0\nx = 3\nx = -7/8"} {"input": "Find x for x^2 + 21/2x + 19/2 = 0", "output": "x^2 + 21/2x + 19/2 = 0\n(x - -19/2)(x - -1) = 0\nx - -19/2 = 0 or x - -1 = 0\nx = -19/2\nx = -1"} {"input": "Find x for 9x - 9/10 = 0", "output": "9x - 9/10 = 0\n9x = 9/10\nx = 9/10 / 9\nx = 1/10"} {"input": "Determine x in x^3 + 221/28x^2 - 16/7x - 80/7 = 0", "output": "x^3 + 221/28x^2 - 16/7x - 80/7 = 0\n(x - 5/4)(x - -8)(x - -8/7) = 0\nx - 5/4 = 0\nx - -8 = 0\nx - -8/7 = 0\nx = 5/4\nx = -8\nx = -8/7"} {"input": "What value of x satisfies x^2 - 9x + 45/4 = 0", "output": "x^2 - 9x + 45/4 = 0\n(x - 3/2)(x - 15/2) = 0\nx - 3/2 = 0 or x - 15/2 = 0\nx = 3/2\nx = 15/2"} {"input": "Determine x in 5x + 90/7 = 0", "output": "5x + 90/7 = 0\n5x = -90/7\nx = -90/7 / 5\nx = -18/7"} {"input": "Solve 1x = 0", "output": "1x = 0\n1x = 0\nx = 0 / 1\nx = 0"} {"input": "What value of x satisfies x^2 + 53/30x - 133/30 = 0", "output": "x^2 + 53/30x - 133/30 = 0\n(x - 7/5)(x - -19/6) = 0\nx - 7/5 = 0 or x - -19/6 = 0\nx = 7/5\nx = -19/6"} {"input": "Find the solution to x^3 + 136/15x^2 - 5x - 252/5 = 0", "output": "x^3 + 136/15x^2 - 5x - 252/5 = 0\n(x - -12/5)(x - -9)(x - 7/3) = 0\nx - -12/5 = 0\nx - -9 = 0\nx - 7/3 = 0\nx = -12/5\nx = -9\nx = 7/3"} {"input": "Solve simultaneously:\n8x + 5y = -83/4\n4x + 4y = -7", "output": "8x + 5y = -83/4\n4x + 4y = -7\n\nUsing elimination\n4*(8x + 5y = -83/4)\n8*(4x + 4y = -7)\n32x + 20y = -83\n32x + 32y = -56\nSubtract equations\n-12y = -27\ny = -27/-12\ny = 9/4\n\nSubstitute y\n8x + 5(9/4) = -83/4\n8x = -32\nx = -32/8\nx = -4"} {"input": "Solve the system:\n3x + 10y = 188/3\n1x + 7y = 125/3", "output": "3x + 10y = 188/3\n1x + 7y = 125/3\n\nUsing elimination\n1*(3x + 10y = 188/3)\n3*(1x + 7y = 125/3)\n3x + 10y = 188/3\n3x + 21y = 125\nSubtract equations\n-11y = -187/3\ny = -187/3/-11\ny = 17/3\n\nSubstitute y\n3x + 10(17/3) = 188/3\n3x = 6\nx = 6/3\nx = 2"} {"input": "Find x and y such that\n3x + 2y = -16/3\n2x + 2y = -44/9", "output": "3x + 2y = -16/3\n2x + 2y = -44/9\n\nUsing elimination\n2*(3x + 2y = -16/3)\n3*(2x + 2y = -44/9)\n6x + 4y = -32/3\n6x + 6y = -44/3\nSubtract equations\n-2y = 4\ny = 4/-2\ny = -2\n\nSubstitute y\n3x + 2(-2) = -16/3\n3x = -4/3\nx = -4/3/3\nx = -4/9"} {"input": "Find x for x^3 + 35/3x^2 - 316/3x + 156 = 0", "output": "x^3 + 35/3x^2 - 316/3x + 156 = 0\n(x - 13/3)(x - -18)(x - 2) = 0\nx - 13/3 = 0\nx - -18 = 0\nx - 2 = 0\nx = 13/3\nx = -18\nx = 2"} {"input": "Find x in x^2 - 20/9x - 32/27 = 0", "output": "x^2 - 20/9x - 32/27 = 0\n(x - 8/3)(x - -4/9) = 0\nx - 8/3 = 0 or x - -4/9 = 0\nx = 8/3\nx = -4/9"} {"input": "What value of x satisfies x^2 - 13/4x = 0", "output": "x^2 - 13/4x = 0\n(x - 0)(x - 13/4) = 0\nx - 0 = 0 or x - 13/4 = 0\nx = 0\nx = 13/4"} {"input": "Find x for x^3 - 6x^2 + 11/4x = 0", "output": "x^3 - 6x^2 + 11/4x = 0\n(x - 11/2)(x - 1/2)(x - 0) = 0\nx - 11/2 = 0\nx - 1/2 = 0\nx - 0 = 0\nx = 11/2\nx = 1/2\nx = 0"} {"input": "Solve the equation x^2 - 61/36x + 5/9 = 0", "output": "x^2 - 61/36x + 5/9 = 0\n(x - 5/4)(x - 4/9) = 0\nx - 5/4 = 0 or x - 4/9 = 0\nx = 5/4\nx = 4/9"} {"input": "What value of x satisfies x^2 - 9/16 = 0", "output": "x^2 - 9/16 = 0\n(x - -3/4)(x - 3/4) = 0\nx - -3/4 = 0 or x - 3/4 = 0\nx = -3/4\nx = 3/4"} {"input": "Solve quickly: 6x - 33/5 = 0", "output": "6x - 33/5 = 0\n6x = 33/5\nx = 33/5 / 6\nx = 11/10"} {"input": "Solve the equations:\n6x + 3y = -347/15\n3x + 7y = -1043/45", "output": "6x + 3y = -347/15\n3x + 7y = -1043/45\n\nUsing elimination\n3*(6x + 3y = -347/15)\n6*(3x + 7y = -1043/45)\n18x + 9y = -347/5\n18x + 42y = -2086/15\nSubtract equations\n-33y = 209/3\ny = 209/3/-33\ny = -19/9\n\nSubstitute y\n6x + 3(-19/9) = -347/15\n6x = -84/5\nx = -84/5/6\nx = -14/5"} {"input": "Determine x in x^3 - 77/12x^2 - 229/2x - 855/4 = 0", "output": "x^3 - 77/12x^2 - 229/2x - 855/4 = 0\n(x - 15)(x - -19/3)(x - -9/4) = 0\nx - 15 = 0\nx - -19/3 = 0\nx - -9/4 = 0\nx = 15\nx = -19/3\nx = -9/4"} {"input": "Find the solution to x^3 + 31/3x^2 + 101/3x + 35 = 0", "output": "x^3 + 31/3x^2 + 101/3x + 35 = 0\n(x - -3)(x - -7/3)(x - -5) = 0\nx - -3 = 0\nx - -7/3 = 0\nx - -5 = 0\nx = -3\nx = -7/3\nx = -5"} {"input": "Find x in x^3 + 1/2x^2 - 4x - 2 = 0", "output": "x^3 + 1/2x^2 - 4x - 2 = 0\n(x - -2)(x - -1/2)(x - 2) = 0\nx - -2 = 0\nx - -1/2 = 0\nx - 2 = 0\nx = -2\nx = -1/2\nx = 2"} {"input": "Solve the equation x^3 + 11/9x^2 - 292/81x - 2240/729 = 0", "output": "x^3 + 11/9x^2 - 292/81x - 2240/729 = 0\n(x - -7/9)(x - -20/9)(x - 16/9) = 0\nx - -7/9 = 0\nx - -20/9 = 0\nx - 16/9 = 0\nx = -7/9\nx = -20/9\nx = 16/9"} {"input": "What value of x satisfies x^3 + 11/6x^2 - 1/2x - 1/3 = 0", "output": "x^3 + 11/6x^2 - 1/2x - 1/3 = 0\n(x - -2)(x - 1/2)(x - -1/3) = 0\nx - -2 = 0\nx - 1/2 = 0\nx - -1/3 = 0\nx = -2\nx = 1/2\nx = -1/3"} {"input": "Find x in 3x - 21/4 = 0", "output": "3x - 21/4 = 0\n3x = 21/4\nx = 21/4 / 3\nx = 7/4"} {"input": "Find the solution to 10x + 4 = 0", "output": "10x + 4 = 0\n10x = -4\nx = -4 / 10\nx = -2/5"} {"input": "Solve the system:\n4x + 2y = -59/3\n1x + 2y = -65/12", "output": "4x + 2y = -59/3\n1x + 2y = -65/12\n\nUsing elimination\n1*(4x + 2y = -59/3)\n4*(1x + 2y = -65/12)\n4x + 2y = -59/3\n4x + 8y = -65/3\nSubtract equations\n-6y = 2\ny = 2/-6\ny = -1/3\n\nSubstitute y\n4x + 2(-1/3) = -59/3\n4x = -19\nx = -19/4\nx = -19/4"} {"input": "Find x and y such that\n9x + 1y = 39/4\n1x + 1y = 15/4", "output": "9x + 1y = 39/4\n1x + 1y = 15/4\n\nUsing elimination\n1*(9x + 1y = 39/4)\n9*(1x + 1y = 15/4)\n9x + 1y = 39/4\n9x + 9y = 135/4\nSubtract equations\n-8y = -24\ny = -24/-8\ny = 3\n\nSubstitute y\n9x + 1(3) = 39/4\n9x = 27/4\nx = 27/4/9\nx = 3/4"} {"input": "What value of x satisfies 1x + 3 = 0", "output": "1x + 3 = 0\n1x = -3\nx = -3 / 1\nx = -3"} {"input": "Determine x in x^2 - 61/5x + 144/5 = 0", "output": "x^2 - 61/5x + 144/5 = 0\n(x - 9)(x - 16/5) = 0\nx - 9 = 0 or x - 16/5 = 0\nx = 9\nx = 16/5"} {"input": "Solve the equation x^3 + 28/15x^2 - 113/5x - 176/3 = 0", "output": "x^3 + 28/15x^2 - 113/5x - 176/3 = 0\n(x - 5)(x - -16/5)(x - -11/3) = 0\nx - 5 = 0\nx - -16/5 = 0\nx - -11/3 = 0\nx = 5\nx = -16/5\nx = -11/3"} {"input": "Solve the equation 9x - 9/2 = 0", "output": "9x - 9/2 = 0\n9x = 9/2\nx = 9/2 / 9\nx = 1/2"} {"input": "Solve the system:\n7x + 1y = 365/21\n4x + 6y = 62/21", "output": "7x + 1y = 365/21\n4x + 6y = 62/21\n\nUsing elimination\n4*(7x + 1y = 365/21)\n7*(4x + 6y = 62/21)\n28x + 4y = 1460/21\n28x + 42y = 62/3\nSubtract equations\n-38y = 342/7\ny = 342/7/-38\ny = -9/7\n\nSubstitute y\n7x + 1(-9/7) = 365/21\n7x = 56/3\nx = 56/3/7\nx = 8/3"} {"input": "Solve the equation x^2 + 19x = 0", "output": "x^2 + 19x = 0\n(x - 0)(x - -19) = 0\nx - 0 = 0 or x - -19 = 0\nx = 0\nx = -19"} {"input": "Solve 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "Solve the system:\n5x + 3y = -563/9\n2x + 8y = -1388/9", "output": "5x + 3y = -563/9\n2x + 8y = -1388/9\n\nUsing elimination\n2*(5x + 3y = -563/9)\n5*(2x + 8y = -1388/9)\n10x + 6y = -1126/9\n10x + 40y = -6940/9\nSubtract equations\n-34y = 646\ny = 646/-34\ny = -19\n\nSubstitute y\n5x + 3(-19) = -563/9\n5x = -50/9\nx = -50/9/5\nx = -10/9"} {"input": "Find x in x^3 - 3/2x^2 - 49x - 24 = 0", "output": "x^3 - 3/2x^2 - 49x - 24 = 0\n(x - 8)(x - -1/2)(x - -6) = 0\nx - 8 = 0\nx - -1/2 = 0\nx - -6 = 0\nx = 8\nx = -1/2\nx = -6"} {"input": "Solve simultaneously:\n1x + 8y = 277/20\n2x + 3y = -9/10", "output": "1x + 8y = 277/20\n2x + 3y = -9/10\n\nUsing elimination\n2*(1x + 8y = 277/20)\n1*(2x + 3y = -9/10)\n2x + 16y = 277/10\n2x + 3y = -9/10\nSubtract equations\n13y = 143/5\ny = 143/5/13\ny = 11/5\n\nSubstitute y\n1x + 8(11/5) = 277/20\n1x = -15/4\nx = -15/4/1\nx = -15/4"} {"input": "Find the solution to x^3 - 9/2x^2 - 89/18x + 110/9 = 0", "output": "x^3 - 9/2x^2 - 89/18x + 110/9 = 0\n(x - 5)(x - -11/6)(x - 4/3) = 0\nx - 5 = 0\nx - -11/6 = 0\nx - 4/3 = 0\nx = 5\nx = -11/6\nx = 4/3"} {"input": "Find x and y such that\n2x + 2y = -11/6\n10x + 9y = -113/12", "output": "2x + 2y = -11/6\n10x + 9y = -113/12\n\nUsing elimination\n10*(2x + 2y = -11/6)\n2*(10x + 9y = -113/12)\n20x + 20y = -55/3\n20x + 18y = -113/6\nSubtract equations\n2y = 1/2\ny = 1/2/2\ny = 1/4\n\nSubstitute y\n2x + 2(1/4) = -11/6\n2x = -7/3\nx = -7/3/2\nx = -7/6"} {"input": "Determine x in 3x + 39/10 = 0", "output": "3x + 39/10 = 0\n3x = -39/10\nx = -39/10 / 3\nx = -13/10"} {"input": "Solve simultaneously:\n5x + 5y = -35/6\n10x + 5y = -35/3", "output": "5x + 5y = -35/6\n10x + 5y = -35/3\n\nUsing elimination\n10*(5x + 5y = -35/6)\n5*(10x + 5y = -35/3)\n50x + 50y = -175/3\n50x + 25y = -175/3\nSubtract equations\n25y = 0\ny = 0/25\ny = 0\n\nSubstitute y\n5x + 5(0) = -35/6\n5x = -35/6\nx = -35/6/5\nx = -7/6"} {"input": "Find x for x^2 + 47/9x + 104/27 = 0", "output": "x^2 + 47/9x + 104/27 = 0\n(x - -8/9)(x - -13/3) = 0\nx - -8/9 = 0 or x - -13/3 = 0\nx = -8/9\nx = -13/3"} {"input": "Determine x in x^2 - 63/20x - 187/40 = 0", "output": "x^2 - 63/20x - 187/40 = 0\n(x - 17/4)(x - -11/10) = 0\nx - 17/4 = 0 or x - -11/10 = 0\nx = 17/4\nx = -11/10"} {"input": "Find the solution to x^3 + 11/14x^2 - 51/14x - 27/7 = 0", "output": "x^3 + 11/14x^2 - 51/14x - 27/7 = 0\n(x - 2)(x - -3/2)(x - -9/7) = 0\nx - 2 = 0\nx - -3/2 = 0\nx - -9/7 = 0\nx = 2\nx = -3/2\nx = -9/7"} {"input": "Compute the solution of x^2 + 10/3x + 1 = 0", "output": "x^2 + 10/3x + 1 = 0\n(x - -3)(x - -1/3) = 0\nx - -3 = 0 or x - -1/3 = 0\nx = -3\nx = -1/3"} {"input": "Find x and y such that\n4x + 9y = -325/21\n4x + 5y = -193/21", "output": "4x + 9y = -325/21\n4x + 5y = -193/21\n\nUsing elimination\n4*(4x + 9y = -325/21)\n4*(4x + 5y = -193/21)\n16x + 36y = -1300/21\n16x + 20y = -772/21\nSubtract equations\n16y = -176/7\ny = -176/7/16\ny = -11/7\n\nSubstitute y\n4x + 9(-11/7) = -325/21\n4x = -4/3\nx = -4/3/4\nx = -1/3"} {"input": "Solve x^3 + 947/56x^2 - 13/8x - 51/28 = 0", "output": "x^3 + 947/56x^2 - 13/8x - 51/28 = 0\n(x - -2/7)(x - -17)(x - 3/8) = 0\nx - -2/7 = 0\nx - -17 = 0\nx - 3/8 = 0\nx = -2/7\nx = -17\nx = 3/8"} {"input": "Find x for 7x + 14 = 0", "output": "7x + 14 = 0\n7x = -14\nx = -14 / 7\nx = -2"} {"input": "Solve simultaneously:\n9x + 8y = 1101/35\n2x + 3y = 296/35", "output": "9x + 8y = 1101/35\n2x + 3y = 296/35\n\nUsing elimination\n2*(9x + 8y = 1101/35)\n9*(2x + 3y = 296/35)\n18x + 16y = 2202/35\n18x + 27y = 2664/35\nSubtract equations\n-11y = -66/5\ny = -66/5/-11\ny = 6/5\n\nSubstitute y\n9x + 8(6/5) = 1101/35\n9x = 153/7\nx = 153/7/9\nx = 17/7"} {"input": "Solve simultaneously:\n9x + 5y = 61/7\n8x + 4y = 484/63", "output": "9x + 5y = 61/7\n8x + 4y = 484/63\n\nUsing elimination\n8*(9x + 5y = 61/7)\n9*(8x + 4y = 484/63)\n72x + 40y = 488/7\n72x + 36y = 484/7\nSubtract equations\n4y = 4/7\ny = 4/7/4\ny = 1/7\n\nSubstitute y\n9x + 5(1/7) = 61/7\n9x = 8\nx = 8/9\nx = 8/9"} {"input": "Find x for 7x + 56/5 = 0", "output": "7x + 56/5 = 0\n7x = -56/5\nx = -56/5 / 7\nx = -8/5"} {"input": "Solve the equations:\n9x + 8y = 43/14\n5x + 2y = 13/42", "output": "9x + 8y = 43/14\n5x + 2y = 13/42\n\nUsing elimination\n5*(9x + 8y = 43/14)\n9*(5x + 2y = 13/42)\n45x + 40y = 215/14\n45x + 18y = 39/14\nSubtract equations\n22y = 88/7\ny = 88/7/22\ny = 4/7\n\nSubstitute y\n9x + 8(4/7) = 43/14\n9x = -3/2\nx = -3/2/9\nx = -1/6"} {"input": "Find x in 3x + 9/8 = 0", "output": "3x + 9/8 = 0\n3x = -9/8\nx = -9/8 / 3\nx = -3/8"} {"input": "Solve the equation 9x - 45/2 = 0", "output": "9x - 45/2 = 0\n9x = 45/2\nx = 45/2 / 9\nx = 5/2"} {"input": "What value of x satisfies 9x - 12 = 0", "output": "9x - 12 = 0\n9x = 12\nx = 12 / 9\nx = 4/3"} {"input": "Find x for x^3 + 10/9x^2 - 23/81x - 44/243 = 0", "output": "x^3 + 10/9x^2 - 23/81x - 44/243 = 0\n(x - -1/3)(x - 4/9)(x - -11/9) = 0\nx - -1/3 = 0\nx - 4/9 = 0\nx - -11/9 = 0\nx = -1/3\nx = 4/9\nx = -11/9"} {"input": "Find x for 7x + 56/5 = 0", "output": "7x + 56/5 = 0\n7x = -56/5\nx = -56/5 / 7\nx = -8/5"} {"input": "Find x for x^3 + 11/6x^2 + 1/2x = 0", "output": "x^3 + 11/6x^2 + 1/2x = 0\n(x - -3/2)(x - 0)(x - -1/3) = 0\nx - -3/2 = 0\nx - 0 = 0\nx - -1/3 = 0\nx = -3/2\nx = 0\nx = -1/3"} {"input": "What value of x satisfies x^2 - 137/14x + 19/7 = 0", "output": "x^2 - 137/14x + 19/7 = 0\n(x - 2/7)(x - 19/2) = 0\nx - 2/7 = 0 or x - 19/2 = 0\nx = 2/7\nx = 19/2"} {"input": "Solve the system:\n7x + 10y = -44\n7x + 6y = -46", "output": "7x + 10y = -44\n7x + 6y = -46\n\nUsing elimination\n7*(7x + 10y = -44)\n7*(7x + 6y = -46)\n49x + 70y = -308\n49x + 42y = -322\nSubtract equations\n28y = 14\ny = 14/28\ny = 1/2\n\nSubstitute y\n7x + 10(1/2) = -44\n7x = -49\nx = -49/7\nx = -7"} {"input": "Solve x^3 - 2x^2 - 20x - 24 = 0", "output": "x^3 - 2x^2 - 20x - 24 = 0\n(x - -2)(x - -2)(x - 6) = 0\nx - -2 = 0\nx - -2 = 0\nx - 6 = 0\nx = -2\nx = -2\nx = 6"} {"input": "Determine x in x^2 - 4x + 32/9 = 0", "output": "x^2 - 4x + 32/9 = 0\n(x - 8/3)(x - 4/3) = 0\nx - 8/3 = 0 or x - 4/3 = 0\nx = 8/3\nx = 4/3"} {"input": "Find the solution to 5x - 9/2 = 0", "output": "5x - 9/2 = 0\n5x = 9/2\nx = 9/2 / 5\nx = 9/10"} {"input": "Compute the solution of 1x + 10 = 0", "output": "1x + 10 = 0\n1x = -10\nx = -10 / 1\nx = -10"} {"input": "Find x for 6x + 30 = 0", "output": "6x + 30 = 0\n6x = -30\nx = -30 / 6\nx = -5"} {"input": "Find x for x^2 - 67/63x - 80/63 = 0", "output": "x^2 - 67/63x - 80/63 = 0\n(x - 16/9)(x - -5/7) = 0\nx - 16/9 = 0 or x - -5/7 = 0\nx = 16/9\nx = -5/7"} {"input": "Solve the equations:\n9x + 1y = -142\n3x + 3y = -18", "output": "9x + 1y = -142\n3x + 3y = -18\n\nUsing elimination\n3*(9x + 1y = -142)\n9*(3x + 3y = -18)\n27x + 3y = -426\n27x + 27y = -162\nSubtract equations\n-24y = -264\ny = -264/-24\ny = 11\n\nSubstitute y\n9x + 1(11) = -142\n9x = -153\nx = -153/9\nx = -17"} {"input": "Solve the equations:\n9x + 10y = 119/5\n9x + 8y = 203/10", "output": "9x + 10y = 119/5\n9x + 8y = 203/10\n\nUsing elimination\n9*(9x + 10y = 119/5)\n9*(9x + 8y = 203/10)\n81x + 90y = 1071/5\n81x + 72y = 1827/10\nSubtract equations\n18y = 63/2\ny = 63/2/18\ny = 7/4\n\nSubstitute y\n9x + 10(7/4) = 119/5\n9x = 63/10\nx = 63/10/9\nx = 7/10"} {"input": "What value of x satisfies x^2 + 6x - 160 = 0", "output": "x^2 + 6x - 160 = 0\n(x - 10)(x - -16) = 0\nx - 10 = 0 or x - -16 = 0\nx = 10\nx = -16"} {"input": "Solve the equation 2x - 14 = 0", "output": "2x - 14 = 0\n2x = 14\nx = 14 / 2\nx = 7"} {"input": "Solve the system:\n9x + 1y = 35/4\n10x + 8y = -77/2", "output": "9x + 1y = 35/4\n10x + 8y = -77/2\n\nUsing elimination\n10*(9x + 1y = 35/4)\n9*(10x + 8y = -77/2)\n90x + 10y = 175/2\n90x + 72y = -693/2\nSubtract equations\n-62y = 434\ny = 434/-62\ny = -7\n\nSubstitute y\n9x + 1(-7) = 35/4\n9x = 63/4\nx = 63/4/9\nx = 7/4"} {"input": "Find the solution to x^3 - 37/7x^2 - 50/49x + 600/49 = 0", "output": "x^3 - 37/7x^2 - 50/49x + 600/49 = 0\n(x - 12/7)(x - 5)(x - -10/7) = 0\nx - 12/7 = 0\nx - 5 = 0\nx - -10/7 = 0\nx = 12/7\nx = 5\nx = -10/7"} {"input": "Solve the system:\n9x + 9y = -195/4\n2x + 8y = -118/3", "output": "9x + 9y = -195/4\n2x + 8y = -118/3\n\nUsing elimination\n2*(9x + 9y = -195/4)\n9*(2x + 8y = -118/3)\n18x + 18y = -195/2\n18x + 72y = -354\nSubtract equations\n-54y = 513/2\ny = 513/2/-54\ny = -19/4\n\nSubstitute y\n9x + 9(-19/4) = -195/4\n9x = -6\nx = -6/9\nx = -2/3"} {"input": "Solve the equation x^2 - 38/15x - 32/15 = 0", "output": "x^2 - 38/15x - 32/15 = 0\n(x - 16/5)(x - -2/3) = 0\nx - 16/5 = 0 or x - -2/3 = 0\nx = 16/5\nx = -2/3"} {"input": "Solve x^3 - 33/8x^2 - 159/16x + 209/16 = 0", "output": "x^3 - 33/8x^2 - 159/16x + 209/16 = 0\n(x - -19/8)(x - 11/2)(x - 1) = 0\nx - -19/8 = 0\nx - 11/2 = 0\nx - 1 = 0\nx = -19/8\nx = 11/2\nx = 1"} {"input": "What value of x satisfies x^2 - 15x - 16 = 0", "output": "x^2 - 15x - 16 = 0\n(x - 16)(x - -1) = 0\nx - 16 = 0 or x - -1 = 0\nx = 16\nx = -1"} {"input": "Solve quickly: 1x + 4/3 = 0", "output": "1x + 4/3 = 0\n1x = -4/3\nx = -4/3 / 1\nx = -4/3"} {"input": "Find x and y such that\n6x + 1y = 97/10\n8x + 6y = 53/5", "output": "6x + 1y = 97/10\n8x + 6y = 53/5\n\nUsing elimination\n8*(6x + 1y = 97/10)\n6*(8x + 6y = 53/5)\n48x + 8y = 388/5\n48x + 36y = 318/5\nSubtract equations\n-28y = 14\ny = 14/-28\ny = -1/2\n\nSubstitute y\n6x + 1(-1/2) = 97/10\n6x = 51/5\nx = 51/5/6\nx = 17/10"} {"input": "Find x and y such that\n4x + 9y = 194/9\n7x + 8y = 200/9", "output": "4x + 9y = 194/9\n7x + 8y = 200/9\n\nUsing elimination\n7*(4x + 9y = 194/9)\n4*(7x + 8y = 200/9)\n28x + 63y = 1358/9\n28x + 32y = 800/9\nSubtract equations\n31y = 62\ny = 62/31\ny = 2\n\nSubstitute y\n4x + 9(2) = 194/9\n4x = 32/9\nx = 32/9/4\nx = 8/9"} {"input": "Solve quickly: x^2 + 9/10x + 1/5 = 0", "output": "x^2 + 9/10x + 1/5 = 0\n(x - -2/5)(x - -1/2) = 0\nx - -2/5 = 0 or x - -1/2 = 0\nx = -2/5\nx = -1/2"} {"input": "Solve quickly: 10x - 5/3 = 0", "output": "10x - 5/3 = 0\n10x = 5/3\nx = 5/3 / 10\nx = 1/6"} {"input": "Find the solution to x^3 + 16/9x^2 - 220/9x + 16/3 = 0", "output": "x^3 + 16/9x^2 - 220/9x + 16/3 = 0\n(x - -6)(x - 2/9)(x - 4) = 0\nx - -6 = 0\nx - 2/9 = 0\nx - 4 = 0\nx = -6\nx = 2/9\nx = 4"} {"input": "Solve simultaneously:\n1x + 7y = 148/5\n7x + 3y = 116/5", "output": "1x + 7y = 148/5\n7x + 3y = 116/5\n\nUsing elimination\n7*(1x + 7y = 148/5)\n1*(7x + 3y = 116/5)\n7x + 49y = 1036/5\n7x + 3y = 116/5\nSubtract equations\n46y = 184\ny = 184/46\ny = 4\n\nSubstitute y\n1x + 7(4) = 148/5\n1x = 8/5\nx = 8/5/1\nx = 8/5"} {"input": "Find x and y such that\n8x + 3y = 35/3\n7x + 8y = 79/3", "output": "8x + 3y = 35/3\n7x + 8y = 79/3\n\nUsing elimination\n7*(8x + 3y = 35/3)\n8*(7x + 8y = 79/3)\n56x + 21y = 245/3\n56x + 64y = 632/3\nSubtract equations\n-43y = -129\ny = -129/-43\ny = 3\n\nSubstitute y\n8x + 3(3) = 35/3\n8x = 8/3\nx = 8/3/8\nx = 1/3"} {"input": "Solve simultaneously:\n6x + 10y = -45\n1x + 5y = -45/2", "output": "6x + 10y = -45\n1x + 5y = -45/2\n\nUsing elimination\n1*(6x + 10y = -45)\n6*(1x + 5y = -45/2)\n6x + 10y = -45\n6x + 30y = -135\nSubtract equations\n-20y = 90\ny = 90/-20\ny = -9/2\n\nSubstitute y\n6x + 10(-9/2) = -45\n6x = 0\nx = 0/6\nx = 0"} {"input": "Solve the equations:\n8x + 4y = 178/15\n4x + 7y = 353/30", "output": "8x + 4y = 178/15\n4x + 7y = 353/30\n\nUsing elimination\n4*(8x + 4y = 178/15)\n8*(4x + 7y = 353/30)\n32x + 16y = 712/15\n32x + 56y = 1412/15\nSubtract equations\n-40y = -140/3\ny = -140/3/-40\ny = 7/6\n\nSubstitute y\n8x + 4(7/6) = 178/15\n8x = 36/5\nx = 36/5/8\nx = 9/10"} {"input": "Solve x^2 + 17/15x - 14/5 = 0", "output": "x^2 + 17/15x - 14/5 = 0\n(x - -7/3)(x - 6/5) = 0\nx - -7/3 = 0 or x - 6/5 = 0\nx = -7/3\nx = 6/5"} {"input": "Find the solution to x^3 + 49/9x^2 + 133/27x + 13/27 = 0", "output": "x^3 + 49/9x^2 + 133/27x + 13/27 = 0\n(x - -1)(x - -13/3)(x - -1/9) = 0\nx - -1 = 0\nx - -13/3 = 0\nx - -1/9 = 0\nx = -1\nx = -13/3\nx = -1/9"} {"input": "Find the solution to x^3 + 123/56x^2 + 47/112x - 99/112 = 0", "output": "x^3 + 123/56x^2 + 47/112x - 99/112 = 0\n(x - -11/7)(x - 1/2)(x - -9/8) = 0\nx - -11/7 = 0\nx - 1/2 = 0\nx - -9/8 = 0\nx = -11/7\nx = 1/2\nx = -9/8"} {"input": "Solve the equation x^3 + 7/24x^2 - 55/24x = 0", "output": "x^3 + 7/24x^2 - 55/24x = 0\n(x - -5/3)(x - 0)(x - 11/8) = 0\nx - -5/3 = 0\nx - 0 = 0\nx - 11/8 = 0\nx = -5/3\nx = 0\nx = 11/8"} {"input": "What value of x satisfies x^2 + 139/10x + 114/5 = 0", "output": "x^2 + 139/10x + 114/5 = 0\n(x - -19/10)(x - -12) = 0\nx - -19/10 = 0 or x - -12 = 0\nx = -19/10\nx = -12"} {"input": "Find x and y such that\n8x + 3y = 285/7\n10x + 4y = 352/7", "output": "8x + 3y = 285/7\n10x + 4y = 352/7\n\nUsing elimination\n10*(8x + 3y = 285/7)\n8*(10x + 4y = 352/7)\n80x + 30y = 2850/7\n80x + 32y = 2816/7\nSubtract equations\n-2y = 34/7\ny = 34/7/-2\ny = -17/7\n\nSubstitute y\n8x + 3(-17/7) = 285/7\n8x = 48\nx = 48/8\nx = 6"} {"input": "Compute the solution of x^3 - 29/9x^2 + 56/27x = 0", "output": "x^3 - 29/9x^2 + 56/27x = 0\n(x - 8/9)(x - 7/3)(x - 0) = 0\nx - 8/9 = 0\nx - 7/3 = 0\nx - 0 = 0\nx = 8/9\nx = 7/3\nx = 0"} {"input": "What value of x satisfies x^3 + 55/14x^2 - 214/7x + 16 = 0", "output": "x^3 + 55/14x^2 - 214/7x + 16 = 0\n(x - -8)(x - 4/7)(x - 7/2) = 0\nx - -8 = 0\nx - 4/7 = 0\nx - 7/2 = 0\nx = -8\nx = 4/7\nx = 7/2"} {"input": "Solve simultaneously:\n9x + 1y = 253/8\n9x + 10y = 1477/8", "output": "9x + 1y = 253/8\n9x + 10y = 1477/8\n\nUsing elimination\n9*(9x + 1y = 253/8)\n9*(9x + 10y = 1477/8)\n81x + 9y = 2277/8\n81x + 90y = 13293/8\nSubtract equations\n-81y = -1377\ny = -1377/-81\ny = 17\n\nSubstitute y\n9x + 1(17) = 253/8\n9x = 117/8\nx = 117/8/9\nx = 13/8"} {"input": "Solve simultaneously:\n3x + 7y = -3/2\n6x + 7y = -69/2", "output": "3x + 7y = -3/2\n6x + 7y = -69/2\n\nUsing elimination\n6*(3x + 7y = -3/2)\n3*(6x + 7y = -69/2)\n18x + 42y = -9\n18x + 21y = -207/2\nSubtract equations\n21y = 189/2\ny = 189/2/21\ny = 9/2\n\nSubstitute y\n3x + 7(9/2) = -3/2\n3x = -33\nx = -33/3\nx = -11"} {"input": "Solve x^3 + 85/18x^2 + 6x + 10/9 = 0", "output": "x^3 + 85/18x^2 + 6x + 10/9 = 0\n(x - -2)(x - -2/9)(x - -5/2) = 0\nx - -2 = 0\nx - -2/9 = 0\nx - -5/2 = 0\nx = -2\nx = -2/9\nx = -5/2"} {"input": "Solve 8x + 96/5 = 0", "output": "8x + 96/5 = 0\n8x = -96/5\nx = -96/5 / 8\nx = -12/5"} {"input": "Determine x in 4x - 24 = 0", "output": "4x - 24 = 0\n4x = 24\nx = 24 / 4\nx = 6"} {"input": "What value of x satisfies x^3 - 607/60x^2 + 391/15x - 289/60 = 0", "output": "x^3 - 607/60x^2 + 391/15x - 289/60 = 0\n(x - 17/4)(x - 1/5)(x - 17/3) = 0\nx - 17/4 = 0\nx - 1/5 = 0\nx - 17/3 = 0\nx = 17/4\nx = 1/5\nx = 17/3"} {"input": "Compute the solution of x^2 - 18/5x = 0", "output": "x^2 - 18/5x = 0\n(x - 0)(x - 18/5) = 0\nx - 0 = 0 or x - 18/5 = 0\nx = 0\nx = 18/5"} {"input": "Find x and y such that\n5x + 4y = -641/35\n7x + 5y = -49/2", "output": "5x + 4y = -641/35\n7x + 5y = -49/2\n\nUsing elimination\n7*(5x + 4y = -641/35)\n5*(7x + 5y = -49/2)\n35x + 28y = -641/5\n35x + 25y = -245/2\nSubtract equations\n3y = -57/10\ny = -57/10/3\ny = -19/10\n\nSubstitute y\n5x + 4(-19/10) = -641/35\n5x = -75/7\nx = -75/7/5\nx = -15/7"} {"input": "Solve 5x + 50/9 = 0", "output": "5x + 50/9 = 0\n5x = -50/9\nx = -50/9 / 5\nx = -10/9"} {"input": "Solve quickly: 7x - 28 = 0", "output": "7x - 28 = 0\n7x = 28\nx = 28 / 7\nx = 4"} {"input": "Find x in x^3 + 597/40x^2 + 903/40x - 637/20 = 0", "output": "x^3 + 597/40x^2 + 903/40x - 637/20 = 0\n(x - 7/8)(x - -14/5)(x - -13) = 0\nx - 7/8 = 0\nx - -14/5 = 0\nx - -13 = 0\nx = 7/8\nx = -14/5\nx = -13"} {"input": "Determine x in 6x + 22/3 = 0", "output": "6x + 22/3 = 0\n6x = -22/3\nx = -22/3 / 6\nx = -11/9"} {"input": "Solve the equation x^2 - 36/49 = 0", "output": "x^2 - 36/49 = 0\n(x - 6/7)(x - -6/7) = 0\nx - 6/7 = 0 or x - -6/7 = 0\nx = 6/7\nx = -6/7"} {"input": "Solve quickly: x^3 - 113/20x^2 + 209/20x - 63/10 = 0", "output": "x^3 - 113/20x^2 + 209/20x - 63/10 = 0\n(x - 7/5)(x - 2)(x - 9/4) = 0\nx - 7/5 = 0\nx - 2 = 0\nx - 9/4 = 0\nx = 7/5\nx = 2\nx = 9/4"} {"input": "Compute the solution of 7x + 35 = 0", "output": "7x + 35 = 0\n7x = -35\nx = -35 / 7\nx = -5"} {"input": "Find the solution to x^3 - 13/15x^2 - 62/5x + 304/15 = 0", "output": "x^3 - 13/15x^2 - 62/5x + 304/15 = 0\n(x - 2)(x - -19/5)(x - 8/3) = 0\nx - 2 = 0\nx - -19/5 = 0\nx - 8/3 = 0\nx = 2\nx = -19/5\nx = 8/3"} {"input": "Solve the equation x^2 + 2/3x - 1/3 = 0", "output": "x^2 + 2/3x - 1/3 = 0\n(x - -1)(x - 1/3) = 0\nx - -1 = 0 or x - 1/3 = 0\nx = -1\nx = 1/3"} {"input": "Determine x in x^2 + 7/4x = 0", "output": "x^2 + 7/4x = 0\n(x - -7/4)(x - 0) = 0\nx - -7/4 = 0 or x - 0 = 0\nx = -7/4\nx = 0"} {"input": "Solve the equation 3x + 30 = 0", "output": "3x + 30 = 0\n3x = -30\nx = -30 / 3\nx = -10"} {"input": "Find the solution to x^3 - 1x^2 - 4x + 4 = 0", "output": "x^3 - 1x^2 - 4x + 4 = 0\n(x - 1)(x - 2)(x - -2) = 0\nx - 1 = 0\nx - 2 = 0\nx - -2 = 0\nx = 1\nx = 2\nx = -2"} {"input": "Solve the system:\n8x + 10y = -200/3\n4x + 7y = -68/3", "output": "8x + 10y = -200/3\n4x + 7y = -68/3\n\nUsing elimination\n4*(8x + 10y = -200/3)\n8*(4x + 7y = -68/3)\n32x + 40y = -800/3\n32x + 56y = -544/3\nSubtract equations\n-16y = -256/3\ny = -256/3/-16\ny = 16/3\n\nSubstitute y\n8x + 10(16/3) = -200/3\n8x = -120\nx = -120/8\nx = -15"} {"input": "Solve the equation x^3 + 35/12x^2 - 23/12x - 5 = 0", "output": "x^3 + 35/12x^2 - 23/12x - 5 = 0\n(x - 4/3)(x - -3)(x - -5/4) = 0\nx - 4/3 = 0\nx - -3 = 0\nx - -5/4 = 0\nx = 4/3\nx = -3\nx = -5/4"} {"input": "Find x in x^3 + 23/180x^2 - 65/72x + 11/60 = 0", "output": "x^3 + 23/180x^2 - 65/72x + 11/60 = 0\n(x - 3/4)(x - 2/9)(x - -11/10) = 0\nx - 3/4 = 0\nx - 2/9 = 0\nx - -11/10 = 0\nx = 3/4\nx = 2/9\nx = -11/10"} {"input": "Solve the equation x^3 - 229/42x^2 + 1157/126x - 40/9 = 0", "output": "x^3 - 229/42x^2 + 1157/126x - 40/9 = 0\n(x - 16/7)(x - 5/6)(x - 7/3) = 0\nx - 16/7 = 0\nx - 5/6 = 0\nx - 7/3 = 0\nx = 16/7\nx = 5/6\nx = 7/3"} {"input": "Compute the solution of x^2 + 10x + 75/4 = 0", "output": "x^2 + 10x + 75/4 = 0\n(x - -15/2)(x - -5/2) = 0\nx - -15/2 = 0 or x - -5/2 = 0\nx = -15/2\nx = -5/2"} {"input": "Solve 1x - 2 = 0", "output": "1x - 2 = 0\n1x = 2\nx = 2 / 1\nx = 2"} {"input": "Solve the equations:\n7x + 8y = 415/21\n8x + 10y = 482/21", "output": "7x + 8y = 415/21\n8x + 10y = 482/21\n\nUsing elimination\n8*(7x + 8y = 415/21)\n7*(8x + 10y = 482/21)\n56x + 64y = 3320/21\n56x + 70y = 482/3\nSubtract equations\n-6y = -18/7\ny = -18/7/-6\ny = 3/7\n\nSubstitute y\n7x + 8(3/7) = 415/21\n7x = 49/3\nx = 49/3/7\nx = 7/3"} {"input": "Find x and y such that\n10x + 9y = -709/15\n4x + 9y = -559/15", "output": "10x + 9y = -709/15\n4x + 9y = -559/15\n\nUsing elimination\n4*(10x + 9y = -709/15)\n10*(4x + 9y = -559/15)\n40x + 36y = -2836/15\n40x + 90y = -1118/3\nSubtract equations\n-54y = 918/5\ny = 918/5/-54\ny = -17/5\n\nSubstitute y\n10x + 9(-17/5) = -709/15\n10x = -50/3\nx = -50/3/10\nx = -5/3"} {"input": "Find the solution to x^3 + 35/6x^2 + 25/3x = 0", "output": "x^3 + 35/6x^2 + 25/3x = 0\n(x - -10/3)(x - -5/2)(x - 0) = 0\nx - -10/3 = 0\nx - -5/2 = 0\nx - 0 = 0\nx = -10/3\nx = -5/2\nx = 0"} {"input": "Find x in x^2 + 27/10x - 81/10 = 0", "output": "x^2 + 27/10x - 81/10 = 0\n(x - 9/5)(x - -9/2) = 0\nx - 9/5 = 0 or x - -9/2 = 0\nx = 9/5\nx = -9/2"} {"input": "Find the solution to x^2 + 17/3x = 0", "output": "x^2 + 17/3x = 0\n(x - -17/3)(x - 0) = 0\nx - -17/3 = 0 or x - 0 = 0\nx = -17/3\nx = 0"} {"input": "Find x and y such that\n8x + 1y = -121/7\n7x + 8y = -170/7", "output": "8x + 1y = -121/7\n7x + 8y = -170/7\n\nUsing elimination\n7*(8x + 1y = -121/7)\n8*(7x + 8y = -170/7)\n56x + 7y = -121\n56x + 64y = -1360/7\nSubtract equations\n-57y = 513/7\ny = 513/7/-57\ny = -9/7\n\nSubstitute y\n8x + 1(-9/7) = -121/7\n8x = -16\nx = -16/8\nx = -2"} {"input": "Find x for x^3 - 313/180x^2 - 341/60x + 51/5 = 0", "output": "x^3 - 313/180x^2 - 341/60x + 51/5 = 0\n(x - 17/9)(x - 9/4)(x - -12/5) = 0\nx - 17/9 = 0\nx - 9/4 = 0\nx - -12/5 = 0\nx = 17/9\nx = 9/4\nx = -12/5"} {"input": "Solve the equation 1x + 3/8 = 0", "output": "1x + 3/8 = 0\n1x = -3/8\nx = -3/8 / 1\nx = -3/8"} {"input": "What value of x satisfies x^2 + 7/3x - 16 = 0", "output": "x^2 + 7/3x - 16 = 0\n(x - 3)(x - -16/3) = 0\nx - 3 = 0 or x - -16/3 = 0\nx = 3\nx = -16/3"} {"input": "Solve x^3 + 92/35x^2 + 47/35x + 6/35 = 0", "output": "x^3 + 92/35x^2 + 47/35x + 6/35 = 0\n(x - -3/7)(x - -2)(x - -1/5) = 0\nx - -3/7 = 0\nx - -2 = 0\nx - -1/5 = 0\nx = -3/7\nx = -2\nx = -1/5"} {"input": "Solve quickly: x^2 - 2/5x = 0", "output": "x^2 - 2/5x = 0\n(x - 2/5)(x - 0) = 0\nx - 2/5 = 0 or x - 0 = 0\nx = 2/5\nx = 0"} {"input": "Solve the system:\n9x + 1y = 1555/9\n2x + 8y = 470/9", "output": "9x + 1y = 1555/9\n2x + 8y = 470/9\n\nUsing elimination\n2*(9x + 1y = 1555/9)\n9*(2x + 8y = 470/9)\n18x + 2y = 3110/9\n18x + 72y = 470\nSubtract equations\n-70y = -1120/9\ny = -1120/9/-70\ny = 16/9\n\nSubstitute y\n9x + 1(16/9) = 1555/9\n9x = 171\nx = 171/9\nx = 19"} {"input": "What value of x satisfies x^2 + 35/36x - 25/9 = 0", "output": "x^2 + 35/36x - 25/9 = 0\n(x - 5/4)(x - -20/9) = 0\nx - 5/4 = 0 or x - -20/9 = 0\nx = 5/4\nx = -20/9"} {"input": "What value of x satisfies x^3 - 116/9x^2 - 827/27x - 140/9 = 0", "output": "x^3 - 116/9x^2 - 827/27x - 140/9 = 0\n(x - -4/3)(x - 15)(x - -7/9) = 0\nx - -4/3 = 0\nx - 15 = 0\nx - -7/9 = 0\nx = -4/3\nx = 15\nx = -7/9"} {"input": "What value of x satisfies x^2 + 13x + 40 = 0", "output": "x^2 + 13x + 40 = 0\n(x - -8)(x - -5) = 0\nx - -8 = 0 or x - -5 = 0\nx = -8\nx = -5"} {"input": "Solve the system:\n2x + 9y = 10/3\n4x + 8y = 40/9", "output": "2x + 9y = 10/3\n4x + 8y = 40/9\n\nUsing elimination\n4*(2x + 9y = 10/3)\n2*(4x + 8y = 40/9)\n8x + 36y = 40/3\n8x + 16y = 80/9\nSubtract equations\n20y = 40/9\ny = 40/9/20\ny = 2/9\n\nSubstitute y\n2x + 9(2/9) = 10/3\n2x = 4/3\nx = 4/3/2\nx = 2/3"} {"input": "Find the solution to x^3 - 37/6x^2 + 23/3x + 11/2 = 0", "output": "x^3 - 37/6x^2 + 23/3x + 11/2 = 0\n(x - 3)(x - 11/3)(x - -1/2) = 0\nx - 3 = 0\nx - 11/3 = 0\nx - -1/2 = 0\nx = 3\nx = 11/3\nx = -1/2"} {"input": "What value of x satisfies x^3 + 35/4x^2 + 63/8x - 45/4 = 0", "output": "x^3 + 35/4x^2 + 63/8x - 45/4 = 0\n(x - 3/4)(x - -15/2)(x - -2) = 0\nx - 3/4 = 0\nx - -15/2 = 0\nx - -2 = 0\nx = 3/4\nx = -15/2\nx = -2"} {"input": "Find the solution to 10x + 55/4 = 0", "output": "10x + 55/4 = 0\n10x = -55/4\nx = -55/4 / 10\nx = -11/8"} {"input": "Find x and y such that\n3x + 10y = 70\n5x + 9y = 195/2", "output": "3x + 10y = 70\n5x + 9y = 195/2\n\nUsing elimination\n5*(3x + 10y = 70)\n3*(5x + 9y = 195/2)\n15x + 50y = 350\n15x + 27y = 585/2\nSubtract equations\n23y = 115/2\ny = 115/2/23\ny = 5/2\n\nSubstitute y\n3x + 10(5/2) = 70\n3x = 45\nx = 45/3\nx = 15"} {"input": "Solve the equation 3x - 10/3 = 0", "output": "3x - 10/3 = 0\n3x = 10/3\nx = 10/3 / 3\nx = 10/9"} {"input": "Compute the solution of x^2 + 28/3x + 65/3 = 0", "output": "x^2 + 28/3x + 65/3 = 0\n(x - -13/3)(x - -5) = 0\nx - -13/3 = 0 or x - -5 = 0\nx = -13/3\nx = -5"} {"input": "Solve x^2 + 1/3x - 2/9 = 0", "output": "x^2 + 1/3x - 2/9 = 0\n(x - 1/3)(x - -2/3) = 0\nx - 1/3 = 0 or x - -2/3 = 0\nx = 1/3\nx = -2/3"} {"input": "What value of x satisfies 1x + 5/6 = 0", "output": "1x + 5/6 = 0\n1x = -5/6\nx = -5/6 / 1\nx = -5/6"} {"input": "Determine x in x^2 - 15x - 54 = 0", "output": "x^2 - 15x - 54 = 0\n(x - 18)(x - -3) = 0\nx - 18 = 0 or x - -3 = 0\nx = 18\nx = -3"} {"input": "Find x for 9x + 45 = 0", "output": "9x + 45 = 0\n9x = -45\nx = -45 / 9\nx = -5"} {"input": "Solve 5x - 15/2 = 0", "output": "5x - 15/2 = 0\n5x = 15/2\nx = 15/2 / 5\nx = 3/2"} {"input": "Compute the solution of x^3 + 5/3x^2 - 157/300x - 13/10 = 0", "output": "x^3 + 5/3x^2 - 157/300x - 13/10 = 0\n(x - -6/5)(x - -13/10)(x - 5/6) = 0\nx - -6/5 = 0\nx - -13/10 = 0\nx - 5/6 = 0\nx = -6/5\nx = -13/10\nx = 5/6"} {"input": "Find the solution to x^3 - 197/21x^2 - 710/21x + 200/7 = 0", "output": "x^3 - 197/21x^2 - 710/21x + 200/7 = 0\n(x - -10/3)(x - 12)(x - 5/7) = 0\nx - -10/3 = 0\nx - 12 = 0\nx - 5/7 = 0\nx = -10/3\nx = 12\nx = 5/7"} {"input": "Find the solution to x^3 + 223/42x^2 + 277/42x + 44/21 = 0", "output": "x^3 + 223/42x^2 + 277/42x + 44/21 = 0\n(x - -11/3)(x - -1/2)(x - -8/7) = 0\nx - -11/3 = 0\nx - -1/2 = 0\nx - -8/7 = 0\nx = -11/3\nx = -1/2\nx = -8/7"} {"input": "Compute the solution of x^3 + 113/7x^2 + 428/7x + 352/7 = 0", "output": "x^3 + 113/7x^2 + 428/7x + 352/7 = 0\n(x - -4)(x - -11)(x - -8/7) = 0\nx - -4 = 0\nx - -11 = 0\nx - -8/7 = 0\nx = -4\nx = -11\nx = -8/7"} {"input": "Solve the equation 7x + 21 = 0", "output": "7x + 21 = 0\n7x = -21\nx = -21 / 7\nx = -3"} {"input": "Solve the system:\n3x + 7y = 6\n10x + 3y = -1/3", "output": "3x + 7y = 6\n10x + 3y = -1/3\n\nUsing elimination\n10*(3x + 7y = 6)\n3*(10x + 3y = -1/3)\n30x + 70y = 60\n30x + 9y = -1\nSubtract equations\n61y = 61\ny = 61/61\ny = 1\n\nSubstitute y\n3x + 7(1) = 6\n3x = -1\nx = -1/3\nx = -1/3"} {"input": "Find x for x^3 - 23/70x^2 - 203/50x - 442/175 = 0", "output": "x^3 - 23/70x^2 - 203/50x - 442/175 = 0\n(x - -4/5)(x - 17/7)(x - -13/10) = 0\nx - -4/5 = 0\nx - 17/7 = 0\nx - -13/10 = 0\nx = -4/5\nx = 17/7\nx = -13/10"} {"input": "Compute the solution of x^2 - 15/2x + 25/2 = 0", "output": "x^2 - 15/2x + 25/2 = 0\n(x - 5)(x - 5/2) = 0\nx - 5 = 0 or x - 5/2 = 0\nx = 5\nx = 5/2"} {"input": "Solve quickly: 3x - 21/5 = 0", "output": "3x - 21/5 = 0\n3x = 21/5\nx = 21/5 / 3\nx = 7/5"} {"input": "Find x for x^2 + 33/2x + 135/2 = 0", "output": "x^2 + 33/2x + 135/2 = 0\n(x - -15/2)(x - -9) = 0\nx - -15/2 = 0 or x - -9 = 0\nx = -15/2\nx = -9"} {"input": "Compute the solution of x^3 + 11/5x^2 - 46/5x - 96/5 = 0", "output": "x^3 + 11/5x^2 - 46/5x - 96/5 = 0\n(x - -16/5)(x - -2)(x - 3) = 0\nx - -16/5 = 0\nx - -2 = 0\nx - 3 = 0\nx = -16/5\nx = -2\nx = 3"} {"input": "Solve the equation 3x - 57/7 = 0", "output": "3x - 57/7 = 0\n3x = 57/7\nx = 57/7 / 3\nx = 19/7"} {"input": "Find x and y such that\n3x + 5y = 389/10\n6x + 3y = 144/5", "output": "3x + 5y = 389/10\n6x + 3y = 144/5\n\nUsing elimination\n6*(3x + 5y = 389/10)\n3*(6x + 3y = 144/5)\n18x + 30y = 1167/5\n18x + 9y = 432/5\nSubtract equations\n21y = 147\ny = 147/21\ny = 7\n\nSubstitute y\n3x + 5(7) = 389/10\n3x = 39/10\nx = 39/10/3\nx = 13/10"} {"input": "Determine x in x^3 - 11/30x^2 - 607/60x - 119/40 = 0", "output": "x^3 - 11/30x^2 - 607/60x - 119/40 = 0\n(x - -3/10)(x - -17/6)(x - 7/2) = 0\nx - -3/10 = 0\nx - -17/6 = 0\nx - 7/2 = 0\nx = -3/10\nx = -17/6\nx = 7/2"} {"input": "Find x in x^2 - 55/6x + 119/6 = 0", "output": "x^2 - 55/6x + 119/6 = 0\n(x - 7/2)(x - 17/3) = 0\nx - 7/2 = 0 or x - 17/3 = 0\nx = 7/2\nx = 17/3"} {"input": "Solve the equation x^2 - 71/12x + 35/6 = 0", "output": "x^2 - 71/12x + 35/6 = 0\n(x - 14/3)(x - 5/4) = 0\nx - 14/3 = 0 or x - 5/4 = 0\nx = 14/3\nx = 5/4"} {"input": "Solve the equation 2x + 9/4 = 0", "output": "2x + 9/4 = 0\n2x = -9/4\nx = -9/4 / 2\nx = -9/8"} {"input": "Solve 7x + 21/2 = 0", "output": "7x + 21/2 = 0\n7x = -21/2\nx = -21/2 / 7\nx = -3/2"} {"input": "Solve quickly: 4x + 3 = 0", "output": "4x + 3 = 0\n4x = -3\nx = -3 / 4\nx = -3/4"} {"input": "Solve simultaneously:\n9x + 9y = 63/10\n6x + 2y = 51/5", "output": "9x + 9y = 63/10\n6x + 2y = 51/5\n\nUsing elimination\n6*(9x + 9y = 63/10)\n9*(6x + 2y = 51/5)\n54x + 54y = 189/5\n54x + 18y = 459/5\nSubtract equations\n36y = -54\ny = -54/36\ny = -3/2\n\nSubstitute y\n9x + 9(-3/2) = 63/10\n9x = 99/5\nx = 99/5/9\nx = 11/5"} {"input": "Find x and y such that\n3x + 3y = 19/12\n10x + 4y = 119/18", "output": "3x + 3y = 19/12\n10x + 4y = 119/18\n\nUsing elimination\n10*(3x + 3y = 19/12)\n3*(10x + 4y = 119/18)\n30x + 30y = 95/6\n30x + 12y = 119/6\nSubtract equations\n18y = -4\ny = -4/18\ny = -2/9\n\nSubstitute y\n3x + 3(-2/9) = 19/12\n3x = 9/4\nx = 9/4/3\nx = 3/4"} {"input": "What value of x satisfies x^3 - 27/10x^2 - 47/5x + 84/5 = 0", "output": "x^3 - 27/10x^2 - 47/5x + 84/5 = 0\n(x - 4)(x - -14/5)(x - 3/2) = 0\nx - 4 = 0\nx - -14/5 = 0\nx - 3/2 = 0\nx = 4\nx = -14/5\nx = 3/2"} {"input": "Solve quickly: 8x - 136 = 0", "output": "8x - 136 = 0\n8x = 136\nx = 136 / 8\nx = 17"} {"input": "Find x in 4x + 72/7 = 0", "output": "4x + 72/7 = 0\n4x = -72/7\nx = -72/7 / 4\nx = -18/7"} {"input": "Compute the solution of 2x + 1 = 0", "output": "2x + 1 = 0\n2x = -1\nx = -1 / 2\nx = -1/2"} {"input": "Solve the equation x^3 - 57/8x^2 - 627/16x - 605/16 = 0", "output": "x^3 - 57/8x^2 - 627/16x - 605/16 = 0\n(x - -11/8)(x - 11)(x - -5/2) = 0\nx - -11/8 = 0\nx - 11 = 0\nx - -5/2 = 0\nx = -11/8\nx = 11\nx = -5/2"} {"input": "Solve simultaneously:\n10x + 3y = -50/3\n3x + 3y = -5", "output": "10x + 3y = -50/3\n3x + 3y = -5\n\nUsing elimination\n3*(10x + 3y = -50/3)\n10*(3x + 3y = -5)\n30x + 9y = -50\n30x + 30y = -50\nSubtract equations\n-21y = 0\ny = 0/-21\ny = 0\n\nSubstitute y\n10x + 3(0) = -50/3\n10x = -50/3\nx = -50/3/10\nx = -5/3"} {"input": "Find the solution to x^3 - 9/4x^2 - 4x + 39/16 = 0", "output": "x^3 - 9/4x^2 - 4x + 39/16 = 0\n(x - 1/2)(x - -3/2)(x - 13/4) = 0\nx - 1/2 = 0\nx - -3/2 = 0\nx - 13/4 = 0\nx = 1/2\nx = -3/2\nx = 13/4"} {"input": "Solve simultaneously:\n7x + 6y = 74\n9x + 9y = 96", "output": "7x + 6y = 74\n9x + 9y = 96\n\nUsing elimination\n9*(7x + 6y = 74)\n7*(9x + 9y = 96)\n63x + 54y = 666\n63x + 63y = 672\nSubtract equations\n-9y = -6\ny = -6/-9\ny = 2/3\n\nSubstitute y\n7x + 6(2/3) = 74\n7x = 70\nx = 70/7\nx = 10"} {"input": "Find x in 10x + 70/3 = 0", "output": "10x + 70/3 = 0\n10x = -70/3\nx = -70/3 / 10\nx = -7/3"} {"input": "Find the solution to 5x + 9 = 0", "output": "5x + 9 = 0\n5x = -9\nx = -9 / 5\nx = -9/5"} {"input": "Find x and y such that\n2x + 2y = -94/7\n2x + 9y = -178/7", "output": "2x + 2y = -94/7\n2x + 9y = -178/7\n\nUsing elimination\n2*(2x + 2y = -94/7)\n2*(2x + 9y = -178/7)\n4x + 4y = -188/7\n4x + 18y = -356/7\nSubtract equations\n-14y = 24\ny = 24/-14\ny = -12/7\n\nSubstitute y\n2x + 2(-12/7) = -94/7\n2x = -10\nx = -10/2\nx = -5"} {"input": "Solve the system:\n4x + 7y = -92/9\n2x + 2y = -25/9", "output": "4x + 7y = -92/9\n2x + 2y = -25/9\n\nUsing elimination\n2*(4x + 7y = -92/9)\n4*(2x + 2y = -25/9)\n8x + 14y = -184/9\n8x + 8y = -100/9\nSubtract equations\n6y = -28/3\ny = -28/3/6\ny = -14/9\n\nSubstitute y\n4x + 7(-14/9) = -92/9\n4x = 2/3\nx = 2/3/4\nx = 1/6"} {"input": "Solve simultaneously:\n9x + 6y = -63/10\n3x + 8y = 69/10", "output": "9x + 6y = -63/10\n3x + 8y = 69/10\n\nUsing elimination\n3*(9x + 6y = -63/10)\n9*(3x + 8y = 69/10)\n27x + 18y = -189/10\n27x + 72y = 621/10\nSubtract equations\n-54y = -81\ny = -81/-54\ny = 3/2\n\nSubstitute y\n9x + 6(3/2) = -63/10\n9x = -153/10\nx = -153/10/9\nx = -17/10"} {"input": "Solve simultaneously:\n6x + 3y = -147/10\n4x + 10y = -269/5", "output": "6x + 3y = -147/10\n4x + 10y = -269/5\n\nUsing elimination\n4*(6x + 3y = -147/10)\n6*(4x + 10y = -269/5)\n24x + 12y = -294/5\n24x + 60y = -1614/5\nSubtract equations\n-48y = 264\ny = 264/-48\ny = -11/2\n\nSubstitute y\n6x + 3(-11/2) = -147/10\n6x = 9/5\nx = 9/5/6\nx = 3/10"} {"input": "Solve the equation x^2 - 27/35x - 22/7 = 0", "output": "x^2 - 27/35x - 22/7 = 0\n(x - -10/7)(x - 11/5) = 0\nx - -10/7 = 0 or x - 11/5 = 0\nx = -10/7\nx = 11/5"} {"input": "Solve x^3 - 233/30x^2 - 109/5x + 152/3 = 0", "output": "x^3 - 233/30x^2 - 109/5x + 152/3 = 0\n(x - 19/2)(x - 8/5)(x - -10/3) = 0\nx - 19/2 = 0\nx - 8/5 = 0\nx - -10/3 = 0\nx = 19/2\nx = 8/5\nx = -10/3"} {"input": "Solve the system:\n4x + 3y = -257/10\n9x + 4y = -186/5", "output": "4x + 3y = -257/10\n9x + 4y = -186/5\n\nUsing elimination\n9*(4x + 3y = -257/10)\n4*(9x + 4y = -186/5)\n36x + 27y = -2313/10\n36x + 16y = -744/5\nSubtract equations\n11y = -165/2\ny = -165/2/11\ny = -15/2\n\nSubstitute y\n4x + 3(-15/2) = -257/10\n4x = -16/5\nx = -16/5/4\nx = -4/5"} {"input": "Find x in 10x - 150 = 0", "output": "10x - 150 = 0\n10x = 150\nx = 150 / 10\nx = 15"} {"input": "Find x in 5x - 50/7 = 0", "output": "5x - 50/7 = 0\n5x = 50/7\nx = 50/7 / 5\nx = 10/7"} {"input": "Compute the solution of 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Solve the system:\n10x + 3y = -89/6\n2x + 9y = 461/6", "output": "10x + 3y = -89/6\n2x + 9y = 461/6\n\nUsing elimination\n2*(10x + 3y = -89/6)\n10*(2x + 9y = 461/6)\n20x + 6y = -89/3\n20x + 90y = 2305/3\nSubtract equations\n-84y = -798\ny = -798/-84\ny = 19/2\n\nSubstitute y\n10x + 3(19/2) = -89/6\n10x = -130/3\nx = -130/3/10\nx = -13/3"} {"input": "Compute the solution of 1x + 16/5 = 0", "output": "1x + 16/5 = 0\n1x = -16/5\nx = -16/5 / 1\nx = -16/5"} {"input": "Compute the solution of 5x - 5/3 = 0", "output": "5x - 5/3 = 0\n5x = 5/3\nx = 5/3 / 5\nx = 1/3"} {"input": "Solve the equations:\n5x + 6y = 77/4\n6x + 8y = 161/6", "output": "5x + 6y = 77/4\n6x + 8y = 161/6\n\nUsing elimination\n6*(5x + 6y = 77/4)\n5*(6x + 8y = 161/6)\n30x + 36y = 231/2\n30x + 40y = 805/6\nSubtract equations\n-4y = -56/3\ny = -56/3/-4\ny = 14/3\n\nSubstitute y\n5x + 6(14/3) = 77/4\n5x = -35/4\nx = -35/4/5\nx = -7/4"} {"input": "Solve quickly: 2x + 32/7 = 0", "output": "2x + 32/7 = 0\n2x = -32/7\nx = -32/7 / 2\nx = -16/7"} {"input": "Solve quickly: x^2 - 22/5x + 117/25 = 0", "output": "x^2 - 22/5x + 117/25 = 0\n(x - 13/5)(x - 9/5) = 0\nx - 13/5 = 0 or x - 9/5 = 0\nx = 13/5\nx = 9/5"} {"input": "What value of x satisfies x^3 + 214/45x^2 + 151/180x - 7/5 = 0", "output": "x^3 + 214/45x^2 + 151/180x - 7/5 = 0\n(x - -7/10)(x - 4/9)(x - -9/2) = 0\nx - -7/10 = 0\nx - 4/9 = 0\nx - -9/2 = 0\nx = -7/10\nx = 4/9\nx = -9/2"} {"input": "Solve simultaneously:\n8x + 2y = -66/7\n8x + 3y = -85/7", "output": "8x + 2y = -66/7\n8x + 3y = -85/7\n\nUsing elimination\n8*(8x + 2y = -66/7)\n8*(8x + 3y = -85/7)\n64x + 16y = -528/7\n64x + 24y = -680/7\nSubtract equations\n-8y = 152/7\ny = 152/7/-8\ny = -19/7\n\nSubstitute y\n8x + 2(-19/7) = -66/7\n8x = -4\nx = -4/8\nx = -1/2"} {"input": "Compute the solution of x^3 + 19x^2 - 251/4x - 2907/2 = 0", "output": "x^3 + 19x^2 - 251/4x - 2907/2 = 0\n(x - 17/2)(x - -18)(x - -19/2) = 0\nx - 17/2 = 0\nx - -18 = 0\nx - -19/2 = 0\nx = 17/2\nx = -18\nx = -19/2"} {"input": "Compute the solution of x^2 + 17/2x + 4 = 0", "output": "x^2 + 17/2x + 4 = 0\n(x - -8)(x - -1/2) = 0\nx - -8 = 0 or x - -1/2 = 0\nx = -8\nx = -1/2"} {"input": "Solve the system:\n8x + 7y = 72\n10x + 2y = 36", "output": "8x + 7y = 72\n10x + 2y = 36\n\nUsing elimination\n10*(8x + 7y = 72)\n8*(10x + 2y = 36)\n80x + 70y = 720\n80x + 16y = 288\nSubtract equations\n54y = 432\ny = 432/54\ny = 8\n\nSubstitute y\n8x + 7(8) = 72\n8x = 16\nx = 16/8\nx = 2"} {"input": "Solve the equation x^3 - 123/10x^2 - 591/25x - 56/25 = 0", "output": "x^3 - 123/10x^2 - 591/25x - 56/25 = 0\n(x - 14)(x - -8/5)(x - -1/10) = 0\nx - 14 = 0\nx - -8/5 = 0\nx - -1/10 = 0\nx = 14\nx = -8/5\nx = -1/10"} {"input": "Compute the solution of x^3 + 49/20x^2 + 3/2x = 0", "output": "x^3 + 49/20x^2 + 3/2x = 0\n(x - -6/5)(x - 0)(x - -5/4) = 0\nx - -6/5 = 0\nx - 0 = 0\nx - -5/4 = 0\nx = -6/5\nx = 0\nx = -5/4"} {"input": "Solve the equation x^2 + 27/5x - 18/5 = 0", "output": "x^2 + 27/5x - 18/5 = 0\n(x - -6)(x - 3/5) = 0\nx - -6 = 0 or x - 3/5 = 0\nx = -6\nx = 3/5"} {"input": "Find x in 2x + 4 = 0", "output": "2x + 4 = 0\n2x = -4\nx = -4 / 2\nx = -2"} {"input": "Solve 3x + 13/3 = 0", "output": "3x + 13/3 = 0\n3x = -13/3\nx = -13/3 / 3\nx = -13/9"} {"input": "Find x and y such that\n10x + 5y = 63/2\n7x + 4y = 479/20", "output": "10x + 5y = 63/2\n7x + 4y = 479/20\n\nUsing elimination\n7*(10x + 5y = 63/2)\n10*(7x + 4y = 479/20)\n70x + 35y = 441/2\n70x + 40y = 479/2\nSubtract equations\n-5y = -19\ny = -19/-5\ny = 19/5\n\nSubstitute y\n10x + 5(19/5) = 63/2\n10x = 25/2\nx = 25/2/10\nx = 5/4"} {"input": "Find x and y such that\n6x + 1y = -105\n9x + 1y = -156", "output": "6x + 1y = -105\n9x + 1y = -156\n\nUsing elimination\n9*(6x + 1y = -105)\n6*(9x + 1y = -156)\n54x + 9y = -945\n54x + 6y = -936\nSubtract equations\n3y = -9\ny = -9/3\ny = -3\n\nSubstitute y\n6x + 1(-3) = -105\n6x = -102\nx = -102/6\nx = -17"} {"input": "Solve the system:\n7x + 7y = -77\n7x + 3y = -25", "output": "7x + 7y = -77\n7x + 3y = -25\n\nUsing elimination\n7*(7x + 7y = -77)\n7*(7x + 3y = -25)\n49x + 49y = -539\n49x + 21y = -175\nSubtract equations\n28y = -364\ny = -364/28\ny = -13\n\nSubstitute y\n7x + 7(-13) = -77\n7x = 14\nx = 14/7\nx = 2"} {"input": "Determine x in x^3 + 701/72x^2 + 149/24x - 15/4 = 0", "output": "x^3 + 701/72x^2 + 149/24x - 15/4 = 0\n(x - -9)(x - -10/9)(x - 3/8) = 0\nx - -9 = 0\nx - -10/9 = 0\nx - 3/8 = 0\nx = -9\nx = -10/9\nx = 3/8"} {"input": "Compute the solution of x^2 + 2x = 0", "output": "x^2 + 2x = 0\n(x - -2)(x - 0) = 0\nx - -2 = 0 or x - 0 = 0\nx = -2\nx = 0"} {"input": "Solve the equations:\n4x + 2y = 20/3\n6x + 1y = 34/3", "output": "4x + 2y = 20/3\n6x + 1y = 34/3\n\nUsing elimination\n6*(4x + 2y = 20/3)\n4*(6x + 1y = 34/3)\n24x + 12y = 40\n24x + 4y = 136/3\nSubtract equations\n8y = -16/3\ny = -16/3/8\ny = -2/3\n\nSubstitute y\n4x + 2(-2/3) = 20/3\n4x = 8\nx = 8/4\nx = 2"} {"input": "Find x for x^2 - 69/40x - 17/20 = 0", "output": "x^2 - 69/40x - 17/20 = 0\n(x - -2/5)(x - 17/8) = 0\nx - -2/5 = 0 or x - 17/8 = 0\nx = -2/5\nx = 17/8"} {"input": "Find x in x^2 - 23/20x + 3/10 = 0", "output": "x^2 - 23/20x + 3/10 = 0\n(x - 2/5)(x - 3/4) = 0\nx - 2/5 = 0 or x - 3/4 = 0\nx = 2/5\nx = 3/4"} {"input": "Find x for x^3 + 79/15x^2 + 86/15x - 16/5 = 0", "output": "x^3 + 79/15x^2 + 86/15x - 16/5 = 0\n(x - -3)(x - -8/3)(x - 2/5) = 0\nx - -3 = 0\nx - -8/3 = 0\nx - 2/5 = 0\nx = -3\nx = -8/3\nx = 2/5"} {"input": "Find x for 5x + 85/3 = 0", "output": "5x + 85/3 = 0\n5x = -85/3\nx = -85/3 / 5\nx = -17/3"} {"input": "Solve simultaneously:\n4x + 5y = 107/2\n6x + 9y = 159/2", "output": "4x + 5y = 107/2\n6x + 9y = 159/2\n\nUsing elimination\n6*(4x + 5y = 107/2)\n4*(6x + 9y = 159/2)\n24x + 30y = 321\n24x + 36y = 318\nSubtract equations\n-6y = 3\ny = 3/-6\ny = -1/2\n\nSubstitute y\n4x + 5(-1/2) = 107/2\n4x = 56\nx = 56/4\nx = 14"} {"input": "Find x in x^2 - 113/18x + 8 = 0", "output": "x^2 - 113/18x + 8 = 0\n(x - 9/2)(x - 16/9) = 0\nx - 9/2 = 0 or x - 16/9 = 0\nx = 9/2\nx = 16/9"} {"input": "Solve the equations:\n6x + 10y = -244/5\n1x + 7y = -126/5", "output": "6x + 10y = -244/5\n1x + 7y = -126/5\n\nUsing elimination\n1*(6x + 10y = -244/5)\n6*(1x + 7y = -126/5)\n6x + 10y = -244/5\n6x + 42y = -756/5\nSubtract equations\n-32y = 512/5\ny = 512/5/-32\ny = -16/5\n\nSubstitute y\n6x + 10(-16/5) = -244/5\n6x = -84/5\nx = -84/5/6\nx = -14/5"} {"input": "What value of x satisfies x^3 + 17/5x^2 + 32/25x - 28/25 = 0", "output": "x^3 + 17/5x^2 + 32/25x - 28/25 = 0\n(x - -14/5)(x - 2/5)(x - -1) = 0\nx - -14/5 = 0\nx - 2/5 = 0\nx - -1 = 0\nx = -14/5\nx = 2/5\nx = -1"} {"input": "Solve x^3 + 11/40x^2 - 51/5x - 27/2 = 0", "output": "x^3 + 11/40x^2 - 51/5x - 27/2 = 0\n(x - -15/8)(x - 18/5)(x - -2) = 0\nx - -15/8 = 0\nx - 18/5 = 0\nx - -2 = 0\nx = -15/8\nx = 18/5\nx = -2"} {"input": "Solve quickly: x^3 - 67/36x^2 - 497/108x - 55/54 = 0", "output": "x^3 - 67/36x^2 - 497/108x - 55/54 = 0\n(x - 10/3)(x - -1/4)(x - -11/9) = 0\nx - 10/3 = 0\nx - -1/4 = 0\nx - -11/9 = 0\nx = 10/3\nx = -1/4\nx = -11/9"} {"input": "Solve quickly: x^3 - 27/4x^2 - 485/8x - 57/2 = 0", "output": "x^3 - 27/4x^2 - 485/8x - 57/2 = 0\n(x - 12)(x - -1/2)(x - -19/4) = 0\nx - 12 = 0\nx - -1/2 = 0\nx - -19/4 = 0\nx = 12\nx = -1/2\nx = -19/4"} {"input": "Find the solution to x^3 - 835/126x^2 + 241/18x - 77/9 = 0", "output": "x^3 - 835/126x^2 + 241/18x - 77/9 = 0\n(x - 14/9)(x - 11/7)(x - 7/2) = 0\nx - 14/9 = 0\nx - 11/7 = 0\nx - 7/2 = 0\nx = 14/9\nx = 11/7\nx = 7/2"} {"input": "Solve the equations:\n4x + 2y = -33/5\n9x + 8y = -76/5", "output": "4x + 2y = -33/5\n9x + 8y = -76/5\n\nUsing elimination\n9*(4x + 2y = -33/5)\n4*(9x + 8y = -76/5)\n36x + 18y = -297/5\n36x + 32y = -304/5\nSubtract equations\n-14y = 7/5\ny = 7/5/-14\ny = -1/10\n\nSubstitute y\n4x + 2(-1/10) = -33/5\n4x = -32/5\nx = -32/5/4\nx = -8/5"} {"input": "Find x and y such that\n7x + 7y = -28/3\n6x + 9y = -6", "output": "7x + 7y = -28/3\n6x + 9y = -6\n\nUsing elimination\n6*(7x + 7y = -28/3)\n7*(6x + 9y = -6)\n42x + 42y = -56\n42x + 63y = -42\nSubtract equations\n-21y = -14\ny = -14/-21\ny = 2/3\n\nSubstitute y\n7x + 7(2/3) = -28/3\n7x = -14\nx = -14/7\nx = -2"} {"input": "Solve x^2 - 13/21x - 190/21 = 0", "output": "x^2 - 13/21x - 190/21 = 0\n(x - 10/3)(x - -19/7) = 0\nx - 10/3 = 0 or x - -19/7 = 0\nx = 10/3\nx = -19/7"} {"input": "Find x for 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Determine x in 4x - 52 = 0", "output": "4x - 52 = 0\n4x = 52\nx = 52 / 4\nx = 13"} {"input": "Solve simultaneously:\n1x + 6y = 267/35\n7x + 9y = 69/5", "output": "1x + 6y = 267/35\n7x + 9y = 69/5\n\nUsing elimination\n7*(1x + 6y = 267/35)\n1*(7x + 9y = 69/5)\n7x + 42y = 267/5\n7x + 9y = 69/5\nSubtract equations\n33y = 198/5\ny = 198/5/33\ny = 6/5\n\nSubstitute y\n1x + 6(6/5) = 267/35\n1x = 3/7\nx = 3/7/1\nx = 3/7"} {"input": "Find x and y such that\n2x + 5y = 0\n1x + 8y = 22", "output": "2x + 5y = 0\n1x + 8y = 22\n\nUsing elimination\n1*(2x + 5y = 0)\n2*(1x + 8y = 22)\n2x + 5y = 0\n2x + 16y = 44\nSubtract equations\n-11y = -44\ny = -44/-11\ny = 4\n\nSubstitute y\n2x + 5(4) = 0\n2x = -20\nx = -20/2\nx = -10"} {"input": "Find the solution to 8x - 11 = 0", "output": "8x - 11 = 0\n8x = 11\nx = 11 / 8\nx = 11/8"} {"input": "Solve 7x - 7/2 = 0", "output": "7x - 7/2 = 0\n7x = 7/2\nx = 7/2 / 7\nx = 1/2"} {"input": "Solve the system:\n9x + 10y = -213/8\n5x + 5y = -105/8", "output": "9x + 10y = -213/8\n5x + 5y = -105/8\n\nUsing elimination\n5*(9x + 10y = -213/8)\n9*(5x + 5y = -105/8)\n45x + 50y = -1065/8\n45x + 45y = -945/8\nSubtract equations\n5y = -15\ny = -15/5\ny = -3\n\nSubstitute y\n9x + 10(-3) = -213/8\n9x = 27/8\nx = 27/8/9\nx = 3/8"} {"input": "Find x in x^2 + 88/15x + 17/15 = 0", "output": "x^2 + 88/15x + 17/15 = 0\n(x - -17/3)(x - -1/5) = 0\nx - -17/3 = 0 or x - -1/5 = 0\nx = -17/3\nx = -1/5"} {"input": "What value of x satisfies x^3 - 2/5x^2 - 225x + 90 = 0", "output": "x^3 - 2/5x^2 - 225x + 90 = 0\n(x - 15)(x - 2/5)(x - -15) = 0\nx - 15 = 0\nx - 2/5 = 0\nx - -15 = 0\nx = 15\nx = 2/5\nx = -15"} {"input": "Solve the equations:\n1x + 9y = 1/3\n2x + 7y = 28/9", "output": "1x + 9y = 1/3\n2x + 7y = 28/9\n\nUsing elimination\n2*(1x + 9y = 1/3)\n1*(2x + 7y = 28/9)\n2x + 18y = 2/3\n2x + 7y = 28/9\nSubtract equations\n11y = -22/9\ny = -22/9/11\ny = -2/9\n\nSubstitute y\n1x + 9(-2/9) = 1/3\n1x = 7/3\nx = 7/3/1\nx = 7/3"} {"input": "Solve the system:\n7x + 3y = 103\n6x + 10y = 14", "output": "7x + 3y = 103\n6x + 10y = 14\n\nUsing elimination\n6*(7x + 3y = 103)\n7*(6x + 10y = 14)\n42x + 18y = 618\n42x + 70y = 98\nSubtract equations\n-52y = 520\ny = 520/-52\ny = -10\n\nSubstitute y\n7x + 3(-10) = 103\n7x = 133\nx = 133/7\nx = 19"} {"input": "Find x and y such that\n4x + 6y = 10/7\n1x + 9y = -50/7", "output": "4x + 6y = 10/7\n1x + 9y = -50/7\n\nUsing elimination\n1*(4x + 6y = 10/7)\n4*(1x + 9y = -50/7)\n4x + 6y = 10/7\n4x + 36y = -200/7\nSubtract equations\n-30y = 30\ny = 30/-30\ny = -1\n\nSubstitute y\n4x + 6(-1) = 10/7\n4x = 52/7\nx = 52/7/4\nx = 13/7"} {"input": "Find x in x^3 - 77/18x^2 - 100/27x + 25/54 = 0", "output": "x^3 - 77/18x^2 - 100/27x + 25/54 = 0\n(x - 5)(x - -5/6)(x - 1/9) = 0\nx - 5 = 0\nx - -5/6 = 0\nx - 1/9 = 0\nx = 5\nx = -5/6\nx = 1/9"} {"input": "Solve the equations:\n9x + 4y = 189/5\n6x + 2y = 132/5", "output": "9x + 4y = 189/5\n6x + 2y = 132/5\n\nUsing elimination\n6*(9x + 4y = 189/5)\n9*(6x + 2y = 132/5)\n54x + 24y = 1134/5\n54x + 18y = 1188/5\nSubtract equations\n6y = -54/5\ny = -54/5/6\ny = -9/5\n\nSubstitute y\n9x + 4(-9/5) = 189/5\n9x = 45\nx = 45/9\nx = 5"} {"input": "Find x for x^2 + 9x + 18 = 0", "output": "x^2 + 9x + 18 = 0\n(x - -3)(x - -6) = 0\nx - -3 = 0 or x - -6 = 0\nx = -3\nx = -6"} {"input": "Solve the equation 9x + 45/2 = 0", "output": "9x + 45/2 = 0\n9x = -45/2\nx = -45/2 / 9\nx = -5/2"} {"input": "Compute the solution of 10x - 25/4 = 0", "output": "10x - 25/4 = 0\n10x = 25/4\nx = 25/4 / 10\nx = 5/8"} {"input": "Find x for 10x + 20 = 0", "output": "10x + 20 = 0\n10x = -20\nx = -20 / 10\nx = -2"} {"input": "Solve the system:\n4x + 6y = 309/14\n9x + 1y = 1081/56", "output": "4x + 6y = 309/14\n9x + 1y = 1081/56\n\nUsing elimination\n9*(4x + 6y = 309/14)\n4*(9x + 1y = 1081/56)\n36x + 54y = 2781/14\n36x + 4y = 1081/14\nSubtract equations\n50y = 850/7\ny = 850/7/50\ny = 17/7\n\nSubstitute y\n4x + 6(17/7) = 309/14\n4x = 15/2\nx = 15/2/4\nx = 15/8"} {"input": "Determine x in x^2 - 11/8x - 19/8 = 0", "output": "x^2 - 11/8x - 19/8 = 0\n(x - -1)(x - 19/8) = 0\nx - -1 = 0 or x - 19/8 = 0\nx = -1\nx = 19/8"} {"input": "Find x for 4x + 12/5 = 0", "output": "4x + 12/5 = 0\n4x = -12/5\nx = -12/5 / 4\nx = -3/5"} {"input": "Find x in x^2 - 1/3x - 154/81 = 0", "output": "x^2 - 1/3x - 154/81 = 0\n(x - -11/9)(x - 14/9) = 0\nx - -11/9 = 0 or x - 14/9 = 0\nx = -11/9\nx = 14/9"} {"input": "What value of x satisfies 1x - 5 = 0", "output": "1x - 5 = 0\n1x = 5\nx = 5 / 1\nx = 5"} {"input": "Solve simultaneously:\n9x + 2y = 77/5\n8x + 10y = 212/9", "output": "9x + 2y = 77/5\n8x + 10y = 212/9\n\nUsing elimination\n8*(9x + 2y = 77/5)\n9*(8x + 10y = 212/9)\n72x + 16y = 616/5\n72x + 90y = 212\nSubtract equations\n-74y = -444/5\ny = -444/5/-74\ny = 6/5\n\nSubstitute y\n9x + 2(6/5) = 77/5\n9x = 13\nx = 13/9\nx = 13/9"} {"input": "Solve simultaneously:\n4x + 7y = -449/5\n8x + 9y = -523/5", "output": "4x + 7y = -449/5\n8x + 9y = -523/5\n\nUsing elimination\n8*(4x + 7y = -449/5)\n4*(8x + 9y = -523/5)\n32x + 56y = -3592/5\n32x + 36y = -2092/5\nSubtract equations\n20y = -300\ny = -300/20\ny = -15\n\nSubstitute y\n4x + 7(-15) = -449/5\n4x = 76/5\nx = 76/5/4\nx = 19/5"} {"input": "Solve the equations:\n1x + 6y = -37/3\n6x + 8y = -190/9", "output": "1x + 6y = -37/3\n6x + 8y = -190/9\n\nUsing elimination\n6*(1x + 6y = -37/3)\n1*(6x + 8y = -190/9)\n6x + 36y = -74\n6x + 8y = -190/9\nSubtract equations\n28y = -476/9\ny = -476/9/28\ny = -17/9\n\nSubstitute y\n1x + 6(-17/9) = -37/3\n1x = -1\nx = -1/1\nx = -1"} {"input": "Find the solution to 3x + 1/3 = 0", "output": "3x + 1/3 = 0\n3x = -1/3\nx = -1/3 / 3\nx = -1/9"} {"input": "Solve quickly: x^2 - 2/45x - 91/45 = 0", "output": "x^2 - 2/45x - 91/45 = 0\n(x - -7/5)(x - 13/9) = 0\nx - -7/5 = 0 or x - 13/9 = 0\nx = -7/5\nx = 13/9"} {"input": "Compute the solution of x^2 + 5x - 6 = 0", "output": "x^2 + 5x - 6 = 0\n(x - 1)(x - -6) = 0\nx - 1 = 0 or x - -6 = 0\nx = 1\nx = -6"} {"input": "Find the solution to x^3 + 11/15x^2 - 12/5x - 32/15 = 0", "output": "x^3 + 11/15x^2 - 12/5x - 32/15 = 0\n(x - 8/5)(x - -4/3)(x - -1) = 0\nx - 8/5 = 0\nx - -4/3 = 0\nx - -1 = 0\nx = 8/5\nx = -4/3\nx = -1"} {"input": "What value of x satisfies x^2 - 7/2x + 17/9 = 0", "output": "x^2 - 7/2x + 17/9 = 0\n(x - 17/6)(x - 2/3) = 0\nx - 17/6 = 0 or x - 2/3 = 0\nx = 17/6\nx = 2/3"} {"input": "Solve x^3 - 148/15x^2 - 89/20x + 187/6 = 0", "output": "x^3 - 148/15x^2 - 89/20x + 187/6 = 0\n(x - -11/6)(x - 17/10)(x - 10) = 0\nx - -11/6 = 0\nx - 17/10 = 0\nx - 10 = 0\nx = -11/6\nx = 17/10\nx = 10"} {"input": "Solve the equation x^2 - 8/3x - 11/3 = 0", "output": "x^2 - 8/3x - 11/3 = 0\n(x - -1)(x - 11/3) = 0\nx - -1 = 0 or x - 11/3 = 0\nx = -1\nx = 11/3"} {"input": "Solve quickly: x^2 - 76/45x - 1/5 = 0", "output": "x^2 - 76/45x - 1/5 = 0\n(x - -1/9)(x - 9/5) = 0\nx - -1/9 = 0 or x - 9/5 = 0\nx = -1/9\nx = 9/5"} {"input": "Find the solution to 8x - 16 = 0", "output": "8x - 16 = 0\n8x = 16\nx = 16 / 8\nx = 2"} {"input": "Solve x^2 + 33/4x + 133/8 = 0", "output": "x^2 + 33/4x + 133/8 = 0\n(x - -19/4)(x - -7/2) = 0\nx - -19/4 = 0 or x - -7/2 = 0\nx = -19/4\nx = -7/2"} {"input": "Solve simultaneously:\n2x + 3y = 194/7\n5x + 7y = 457/7", "output": "2x + 3y = 194/7\n5x + 7y = 457/7\n\nUsing elimination\n5*(2x + 3y = 194/7)\n2*(5x + 7y = 457/7)\n10x + 15y = 970/7\n10x + 14y = 914/7\nSubtract equations\n1y = 8\ny = 8/1\ny = 8\n\nSubstitute y\n2x + 3(8) = 194/7\n2x = 26/7\nx = 26/7/2\nx = 13/7"} {"input": "Solve x^3 - 191/10x^2 + 57x + 135/2 = 0", "output": "x^3 - 191/10x^2 + 57x + 135/2 = 0\n(x - 15)(x - -9/10)(x - 5) = 0\nx - 15 = 0\nx - -9/10 = 0\nx - 5 = 0\nx = 15\nx = -9/10\nx = 5"} {"input": "Find the solution to x^2 - 52/9x + 35/9 = 0", "output": "x^2 - 52/9x + 35/9 = 0\n(x - 5)(x - 7/9) = 0\nx - 5 = 0 or x - 7/9 = 0\nx = 5\nx = 7/9"} {"input": "Determine x in 1x - 11/10 = 0", "output": "1x - 11/10 = 0\n1x = 11/10\nx = 11/10 / 1\nx = 11/10"} {"input": "Find x for x^3 + 35/9x^2 + 34/9x = 0", "output": "x^3 + 35/9x^2 + 34/9x = 0\n(x - -2)(x - -17/9)(x - 0) = 0\nx - -2 = 0\nx - -17/9 = 0\nx - 0 = 0\nx = -2\nx = -17/9\nx = 0"} {"input": "Find the solution to x^3 - 37/6x^2 - 34/3x + 10 = 0", "output": "x^3 - 37/6x^2 - 34/3x + 10 = 0\n(x - 2/3)(x - 15/2)(x - -2) = 0\nx - 2/3 = 0\nx - 15/2 = 0\nx - -2 = 0\nx = 2/3\nx = 15/2\nx = -2"} {"input": "Find the solution to 8x - 2 = 0", "output": "8x - 2 = 0\n8x = 2\nx = 2 / 8\nx = 1/4"} {"input": "What value of x satisfies 4x - 52/3 = 0", "output": "4x - 52/3 = 0\n4x = 52/3\nx = 52/3 / 4\nx = 13/3"} {"input": "Solve quickly: x^3 + 79/24x^2 - 46/3x - 85/8 = 0", "output": "x^3 + 79/24x^2 - 46/3x - 85/8 = 0\n(x - -5/8)(x - -17/3)(x - 3) = 0\nx - -5/8 = 0\nx - -17/3 = 0\nx - 3 = 0\nx = -5/8\nx = -17/3\nx = 3"} {"input": "Solve simultaneously:\n10x + 1y = 454/63\n2x + 5y = -82/63", "output": "10x + 1y = 454/63\n2x + 5y = -82/63\n\nUsing elimination\n2*(10x + 1y = 454/63)\n10*(2x + 5y = -82/63)\n20x + 2y = 908/63\n20x + 50y = -820/63\nSubtract equations\n-48y = 192/7\ny = 192/7/-48\ny = -4/7\n\nSubstitute y\n10x + 1(-4/7) = 454/63\n10x = 70/9\nx = 70/9/10\nx = 7/9"} {"input": "What value of x satisfies 7x + 21/10 = 0", "output": "7x + 21/10 = 0\n7x = -21/10\nx = -21/10 / 7\nx = -3/10"} {"input": "Find x for x^2 - 92/45x - 28/5 = 0", "output": "x^2 - 92/45x - 28/5 = 0\n(x - 18/5)(x - -14/9) = 0\nx - 18/5 = 0 or x - -14/9 = 0\nx = 18/5\nx = -14/9"} {"input": "Solve the equation x^3 + 41/20x^2 - 257/40x - 99/8 = 0", "output": "x^3 + 41/20x^2 - 257/40x - 99/8 = 0\n(x - -9/5)(x - -11/4)(x - 5/2) = 0\nx - -9/5 = 0\nx - -11/4 = 0\nx - 5/2 = 0\nx = -9/5\nx = -11/4\nx = 5/2"} {"input": "Find x in x^2 + 28/3x + 64/3 = 0", "output": "x^2 + 28/3x + 64/3 = 0\n(x - -4)(x - -16/3) = 0\nx - -4 = 0 or x - -16/3 = 0\nx = -4\nx = -16/3"} {"input": "Determine x in x^2 - 25x + 100 = 0", "output": "x^2 - 25x + 100 = 0\n(x - 20)(x - 5) = 0\nx - 20 = 0 or x - 5 = 0\nx = 20\nx = 5"} {"input": "Solve quickly: 4x - 18/5 = 0", "output": "4x - 18/5 = 0\n4x = 18/5\nx = 18/5 / 4\nx = 9/10"} {"input": "Solve the equation x^3 + 119/10x^2 + 154/5x - 16/5 = 0", "output": "x^3 + 119/10x^2 + 154/5x - 16/5 = 0\n(x - -4)(x - -8)(x - 1/10) = 0\nx - -4 = 0\nx - -8 = 0\nx - 1/10 = 0\nx = -4\nx = -8\nx = 1/10"} {"input": "Find x and y such that\n1x + 4y = 119/18\n1x + 8y = 247/18", "output": "1x + 4y = 119/18\n1x + 8y = 247/18\n\nUsing elimination\n1*(1x + 4y = 119/18)\n1*(1x + 8y = 247/18)\n1x + 4y = 119/18\n1x + 8y = 247/18\nSubtract equations\n-4y = -64/9\ny = -64/9/-4\ny = 16/9\n\nSubstitute y\n1x + 4(16/9) = 119/18\n1x = -1/2\nx = -1/2/1\nx = -1/2"} {"input": "Solve the system:\n2x + 6y = -18\n6x + 10y = -98/3", "output": "2x + 6y = -18\n6x + 10y = -98/3\n\nUsing elimination\n6*(2x + 6y = -18)\n2*(6x + 10y = -98/3)\n12x + 36y = -108\n12x + 20y = -196/3\nSubtract equations\n16y = -128/3\ny = -128/3/16\ny = -8/3\n\nSubstitute y\n2x + 6(-8/3) = -18\n2x = -2\nx = -2/2\nx = -1"} {"input": "Compute the solution of 10x + 10/3 = 0", "output": "10x + 10/3 = 0\n10x = -10/3\nx = -10/3 / 10\nx = -1/3"} {"input": "Find x in 5x - 13 = 0", "output": "5x - 13 = 0\n5x = 13\nx = 13 / 5\nx = 13/5"} {"input": "Solve quickly: x^2 - 40/9x + 13/3 = 0", "output": "x^2 - 40/9x + 13/3 = 0\n(x - 13/9)(x - 3) = 0\nx - 13/9 = 0 or x - 3 = 0\nx = 13/9\nx = 3"} {"input": "Solve the equation x^3 - 844/105x^2 + 1481/105x + 38/5 = 0", "output": "x^3 - 844/105x^2 + 1481/105x + 38/5 = 0\n(x - 19/5)(x - 14/3)(x - -3/7) = 0\nx - 19/5 = 0\nx - 14/3 = 0\nx - -3/7 = 0\nx = 19/5\nx = 14/3\nx = -3/7"} {"input": "Find x for 2x + 14/3 = 0", "output": "2x + 14/3 = 0\n2x = -14/3\nx = -14/3 / 2\nx = -7/3"} {"input": "Find x for x^3 + 109/56x^2 - 123/112x - 297/112 = 0", "output": "x^3 + 109/56x^2 - 123/112x - 297/112 = 0\n(x - -3/2)(x - -11/7)(x - 9/8) = 0\nx - -3/2 = 0\nx - -11/7 = 0\nx - 9/8 = 0\nx = -3/2\nx = -11/7\nx = 9/8"} {"input": "Determine x in 7x + 7/8 = 0", "output": "7x + 7/8 = 0\n7x = -7/8\nx = -7/8 / 7\nx = -1/8"} {"input": "Find the solution to 1x + 7/8 = 0", "output": "1x + 7/8 = 0\n1x = -7/8\nx = -7/8 / 1\nx = -7/8"} {"input": "Find the solution to x^2 - 11/2x - 63/2 = 0", "output": "x^2 - 11/2x - 63/2 = 0\n(x - 9)(x - -7/2) = 0\nx - 9 = 0 or x - -7/2 = 0\nx = 9\nx = -7/2"} {"input": "Compute the solution of 1x + 5/4 = 0", "output": "1x + 5/4 = 0\n1x = -5/4\nx = -5/4 / 1\nx = -5/4"} {"input": "Solve the equation 1x - 1/6 = 0", "output": "1x - 1/6 = 0\n1x = 1/6\nx = 1/6 / 1\nx = 1/6"} {"input": "Find x for x^2 + 115/18x - 25/3 = 0", "output": "x^2 + 115/18x - 25/3 = 0\n(x - 10/9)(x - -15/2) = 0\nx - 10/9 = 0 or x - -15/2 = 0\nx = 10/9\nx = -15/2"} {"input": "Solve x^2 + 1/4x - 7/2 = 0", "output": "x^2 + 1/4x - 7/2 = 0\n(x - -2)(x - 7/4) = 0\nx - -2 = 0 or x - 7/4 = 0\nx = -2\nx = 7/4"} {"input": "Find x and y such that\n4x + 5y = 33\n9x + 10y = 279/4", "output": "4x + 5y = 33\n9x + 10y = 279/4\n\nUsing elimination\n9*(4x + 5y = 33)\n4*(9x + 10y = 279/4)\n36x + 45y = 297\n36x + 40y = 279\nSubtract equations\n5y = 18\ny = 18/5\ny = 18/5\n\nSubstitute y\n4x + 5(18/5) = 33\n4x = 15\nx = 15/4\nx = 15/4"} {"input": "Find the solution to x^2 - 59/30x + 1/2 = 0", "output": "x^2 - 59/30x + 1/2 = 0\n(x - 3/10)(x - 5/3) = 0\nx - 3/10 = 0 or x - 5/3 = 0\nx = 3/10\nx = 5/3"} {"input": "Compute the solution of x^3 - 101/180x^2 - 188/45x + 17/20 = 0", "output": "x^3 - 101/180x^2 - 188/45x + 17/20 = 0\n(x - -17/9)(x - 1/5)(x - 9/4) = 0\nx - -17/9 = 0\nx - 1/5 = 0\nx - 9/4 = 0\nx = -17/9\nx = 1/5\nx = 9/4"} {"input": "Solve 3x - 6 = 0", "output": "3x - 6 = 0\n3x = 6\nx = 6 / 3\nx = 2"} {"input": "Find x in x^3 - 21/8x^2 - 49/16x = 0", "output": "x^3 - 21/8x^2 - 49/16x = 0\n(x - 7/2)(x - -7/8)(x - 0) = 0\nx - 7/2 = 0\nx - -7/8 = 0\nx - 0 = 0\nx = 7/2\nx = -7/8\nx = 0"} {"input": "Solve quickly: 1x - 19/9 = 0", "output": "1x - 19/9 = 0\n1x = 19/9\nx = 19/9 / 1\nx = 19/9"} {"input": "Solve the equations:\n7x + 10y = 347/15\n7x + 4y = 227/15", "output": "7x + 10y = 347/15\n7x + 4y = 227/15\n\nUsing elimination\n7*(7x + 10y = 347/15)\n7*(7x + 4y = 227/15)\n49x + 70y = 2429/15\n49x + 28y = 1589/15\nSubtract equations\n42y = 56\ny = 56/42\ny = 4/3\n\nSubstitute y\n7x + 10(4/3) = 347/15\n7x = 49/5\nx = 49/5/7\nx = 7/5"} {"input": "Solve x^3 - 313/14x^2 + 579/7x - 540/7 = 0", "output": "x^3 - 313/14x^2 + 579/7x - 540/7 = 0\n(x - 18)(x - 20/7)(x - 3/2) = 0\nx - 18 = 0\nx - 20/7 = 0\nx - 3/2 = 0\nx = 18\nx = 20/7\nx = 3/2"} {"input": "Solve simultaneously:\n5x + 7y = 23/5\n7x + 10y = 33/5", "output": "5x + 7y = 23/5\n7x + 10y = 33/5\n\nUsing elimination\n7*(5x + 7y = 23/5)\n5*(7x + 10y = 33/5)\n35x + 49y = 161/5\n35x + 50y = 33\nSubtract equations\n-1y = -4/5\ny = -4/5/-1\ny = 4/5\n\nSubstitute y\n5x + 7(4/5) = 23/5\n5x = -1\nx = -1/5\nx = -1/5"} {"input": "Determine x in x^3 - 289/30x^2 + 114/5x - 6 = 0", "output": "x^3 - 289/30x^2 + 114/5x - 6 = 0\n(x - 3/10)(x - 10/3)(x - 6) = 0\nx - 3/10 = 0\nx - 10/3 = 0\nx - 6 = 0\nx = 3/10\nx = 10/3\nx = 6"} {"input": "Find the solution to 1x - 3/2 = 0", "output": "1x - 3/2 = 0\n1x = 3/2\nx = 3/2 / 1\nx = 3/2"} {"input": "Find x for x^2 + 43/15x - 42/5 = 0", "output": "x^2 + 43/15x - 42/5 = 0\n(x - 9/5)(x - -14/3) = 0\nx - 9/5 = 0 or x - -14/3 = 0\nx = 9/5\nx = -14/3"} {"input": "Compute the solution of x^3 - 55/18x^2 + 26/9x - 5/6 = 0", "output": "x^3 - 55/18x^2 + 26/9x - 5/6 = 0\n(x - 5/9)(x - 3/2)(x - 1) = 0\nx - 5/9 = 0\nx - 3/2 = 0\nx - 1 = 0\nx = 5/9\nx = 3/2\nx = 1"} {"input": "Solve the system:\n2x + 10y = 73/2\n6x + 3y = 303/4", "output": "2x + 10y = 73/2\n6x + 3y = 303/4\n\nUsing elimination\n6*(2x + 10y = 73/2)\n2*(6x + 3y = 303/4)\n12x + 60y = 219\n12x + 6y = 303/2\nSubtract equations\n54y = 135/2\ny = 135/2/54\ny = 5/4\n\nSubstitute y\n2x + 10(5/4) = 73/2\n2x = 24\nx = 24/2\nx = 12"} {"input": "Find x in x^3 + 103/10x^2 - 4x - 70 = 0", "output": "x^3 + 103/10x^2 - 4x - 70 = 0\n(x - -14/5)(x - 5/2)(x - -10) = 0\nx - -14/5 = 0\nx - 5/2 = 0\nx - -10 = 0\nx = -14/5\nx = 5/2\nx = -10"} {"input": "Find x for 4x - 8/7 = 0", "output": "4x - 8/7 = 0\n4x = 8/7\nx = 8/7 / 4\nx = 2/7"} {"input": "Solve x^3 + 71/14x^2 - 45/7x - 36/7 = 0", "output": "x^3 + 71/14x^2 - 45/7x - 36/7 = 0\n(x - 3/2)(x - -4/7)(x - -6) = 0\nx - 3/2 = 0\nx - -4/7 = 0\nx - -6 = 0\nx = 3/2\nx = -4/7\nx = -6"} {"input": "Find the solution to x^3 - 41/6x^2 + 25/6x + 25 = 0", "output": "x^3 - 41/6x^2 + 25/6x + 25 = 0\n(x - 5)(x - 10/3)(x - -3/2) = 0\nx - 5 = 0\nx - 10/3 = 0\nx - -3/2 = 0\nx = 5\nx = 10/3\nx = -3/2"} {"input": "Solve the system:\n2x + 9y = 13\n1x + 4y = 17/3", "output": "2x + 9y = 13\n1x + 4y = 17/3\n\nUsing elimination\n1*(2x + 9y = 13)\n2*(1x + 4y = 17/3)\n2x + 9y = 13\n2x + 8y = 34/3\nSubtract equations\n1y = 5/3\ny = 5/3/1\ny = 5/3\n\nSubstitute y\n2x + 9(5/3) = 13\n2x = -2\nx = -2/2\nx = -1"} {"input": "What value of x satisfies x^3 - 29/12x^2 - 91/24x + 49/8 = 0", "output": "x^3 - 29/12x^2 - 91/24x + 49/8 = 0\n(x - -7/4)(x - 3)(x - 7/6) = 0\nx - -7/4 = 0\nx - 3 = 0\nx - 7/6 = 0\nx = -7/4\nx = 3\nx = 7/6"} {"input": "Find the solution to 6x + 24/7 = 0", "output": "6x + 24/7 = 0\n6x = -24/7\nx = -24/7 / 6\nx = -4/7"} {"input": "Determine x in x^3 + 43/28x^2 - 145/196x - 13/49 = 0", "output": "x^3 + 43/28x^2 - 145/196x - 13/49 = 0\n(x - -1/4)(x - 4/7)(x - -13/7) = 0\nx - -1/4 = 0\nx - 4/7 = 0\nx - -13/7 = 0\nx = -1/4\nx = 4/7\nx = -13/7"} {"input": "Find the solution to x^3 - 271/35x^2 + 11/5x + 21 = 0", "output": "x^3 - 271/35x^2 + 11/5x + 21 = 0\n(x - 15/7)(x - -7/5)(x - 7) = 0\nx - 15/7 = 0\nx - -7/5 = 0\nx - 7 = 0\nx = 15/7\nx = -7/5\nx = 7"} {"input": "Find x in x^2 - 3/7x = 0", "output": "x^2 - 3/7x = 0\n(x - 3/7)(x - 0) = 0\nx - 3/7 = 0 or x - 0 = 0\nx = 3/7\nx = 0"} {"input": "Compute the solution of 2x - 17/5 = 0", "output": "2x - 17/5 = 0\n2x = 17/5\nx = 17/5 / 2\nx = 17/10"} {"input": "What value of x satisfies 6x + 15/2 = 0", "output": "6x + 15/2 = 0\n6x = -15/2\nx = -15/2 / 6\nx = -5/4"} {"input": "Solve x^3 + 2/9x^2 - 71/36x - 11/12 = 0", "output": "x^3 + 2/9x^2 - 71/36x - 11/12 = 0\n(x - 3/2)(x - -11/9)(x - -1/2) = 0\nx - 3/2 = 0\nx - -11/9 = 0\nx - -1/2 = 0\nx = 3/2\nx = -11/9\nx = -1/2"} {"input": "Find x for x^2 + 11/6x - 91/3 = 0", "output": "x^2 + 11/6x - 91/3 = 0\n(x - -13/2)(x - 14/3) = 0\nx - -13/2 = 0 or x - 14/3 = 0\nx = -13/2\nx = 14/3"} {"input": "Solve the system:\n8x + 1y = -535/8\n2x + 2y = -59/4", "output": "8x + 1y = -535/8\n2x + 2y = -59/4\n\nUsing elimination\n2*(8x + 1y = -535/8)\n8*(2x + 2y = -59/4)\n16x + 2y = -535/4\n16x + 16y = -118\nSubtract equations\n-14y = -63/4\ny = -63/4/-14\ny = 9/8\n\nSubstitute y\n8x + 1(9/8) = -535/8\n8x = -68\nx = -68/8\nx = -17/2"} {"input": "What value of x satisfies 4x + 4 = 0", "output": "4x + 4 = 0\n4x = -4\nx = -4 / 4\nx = -1"} {"input": "Find x for 8x - 48 = 0", "output": "8x - 48 = 0\n8x = 48\nx = 48 / 8\nx = 6"} {"input": "Find x for x^3 + 9/7x^2 - 202/49x - 240/49 = 0", "output": "x^3 + 9/7x^2 - 202/49x - 240/49 = 0\n(x - -8/7)(x - -15/7)(x - 2) = 0\nx - -8/7 = 0\nx - -15/7 = 0\nx - 2 = 0\nx = -8/7\nx = -15/7\nx = 2"} {"input": "Solve the equation 10x - 8 = 0", "output": "10x - 8 = 0\n10x = 8\nx = 8 / 10\nx = 4/5"} {"input": "Solve the equations:\n4x + 6y = -158/9\n3x + 6y = -53/3", "output": "4x + 6y = -158/9\n3x + 6y = -53/3\n\nUsing elimination\n3*(4x + 6y = -158/9)\n4*(3x + 6y = -53/3)\n12x + 18y = -158/3\n12x + 24y = -212/3\nSubtract equations\n-6y = 18\ny = 18/-6\ny = -3\n\nSubstitute y\n4x + 6(-3) = -158/9\n4x = 4/9\nx = 4/9/4\nx = 1/9"} {"input": "Solve the equation x^3 - 43/3x^2 + 39x - 77/3 = 0", "output": "x^3 - 43/3x^2 + 39x - 77/3 = 0\n(x - 7/3)(x - 1)(x - 11) = 0\nx - 7/3 = 0\nx - 1 = 0\nx - 11 = 0\nx = 7/3\nx = 1\nx = 11"} {"input": "Find x in 7x - 133/10 = 0", "output": "7x - 133/10 = 0\n7x = 133/10\nx = 133/10 / 7\nx = 19/10"} {"input": "Find x in x^3 - 11/18x^2 - 241/54x + 110/27 = 0", "output": "x^3 - 11/18x^2 - 241/54x + 110/27 = 0\n(x - 11/6)(x - 1)(x - -20/9) = 0\nx - 11/6 = 0\nx - 1 = 0\nx - -20/9 = 0\nx = 11/6\nx = 1\nx = -20/9"} {"input": "Compute the solution of x^3 - 55/7x^2 + 568/49x - 132/49 = 0", "output": "x^3 - 55/7x^2 + 568/49x - 132/49 = 0\n(x - 2/7)(x - 6)(x - 11/7) = 0\nx - 2/7 = 0\nx - 6 = 0\nx - 11/7 = 0\nx = 2/7\nx = 6\nx = 11/7"} {"input": "Solve x^3 + 169/180x^2 - 2077/180x + 323/30 = 0", "output": "x^3 + 169/180x^2 - 2077/180x + 323/30 = 0\n(x - 19/9)(x - -17/4)(x - 6/5) = 0\nx - 19/9 = 0\nx - -17/4 = 0\nx - 6/5 = 0\nx = 19/9\nx = -17/4\nx = 6/5"} {"input": "Find x in x^2 - 3x - 304 = 0", "output": "x^2 - 3x - 304 = 0\n(x - -16)(x - 19) = 0\nx - -16 = 0 or x - 19 = 0\nx = -16\nx = 19"} {"input": "Solve quickly: 1x - 17/6 = 0", "output": "1x - 17/6 = 0\n1x = 17/6\nx = 17/6 / 1\nx = 17/6"} {"input": "Find the solution to x^2 + 21/4x + 5/4 = 0", "output": "x^2 + 21/4x + 5/4 = 0\n(x - -1/4)(x - -5) = 0\nx - -1/4 = 0 or x - -5 = 0\nx = -1/4\nx = -5"} {"input": "Solve the equation 5x - 8 = 0", "output": "5x - 8 = 0\n5x = 8\nx = 8 / 5\nx = 8/5"} {"input": "Find x for 2x + 36 = 0", "output": "2x + 36 = 0\n2x = -36\nx = -36 / 2\nx = -18"} {"input": "Solve the system:\n6x + 5y = 37\n2x + 1y = 9", "output": "6x + 5y = 37\n2x + 1y = 9\n\nUsing elimination\n2*(6x + 5y = 37)\n6*(2x + 1y = 9)\n12x + 10y = 74\n12x + 6y = 54\nSubtract equations\n4y = 20\ny = 20/4\ny = 5\n\nSubstitute y\n6x + 5(5) = 37\n6x = 12\nx = 12/6\nx = 2"} {"input": "Find the solution to x^3 + 15/2x^2 + 81/16x - 595/16 = 0", "output": "x^3 + 15/2x^2 + 81/16x - 595/16 = 0\n(x - 7/4)(x - -17/4)(x - -5) = 0\nx - 7/4 = 0\nx - -17/4 = 0\nx - -5 = 0\nx = 7/4\nx = -17/4\nx = -5"} {"input": "Solve the equation x^3 + 59/30x^2 - 29/10x - 17/3 = 0", "output": "x^3 + 59/30x^2 - 29/10x - 17/3 = 0\n(x - 17/10)(x - -2)(x - -5/3) = 0\nx - 17/10 = 0\nx - -2 = 0\nx - -5/3 = 0\nx = 17/10\nx = -2\nx = -5/3"} {"input": "Compute the solution of x^3 + 18/5x^2 + 233/100x - 21/20 = 0", "output": "x^3 + 18/5x^2 + 233/100x - 21/20 = 0\n(x - -5/2)(x - -7/5)(x - 3/10) = 0\nx - -5/2 = 0\nx - -7/5 = 0\nx - 3/10 = 0\nx = -5/2\nx = -7/5\nx = 3/10"} {"input": "Solve quickly: 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Solve the equation x^2 - 196/45x + 196/45 = 0", "output": "x^2 - 196/45x + 196/45 = 0\n(x - 14/5)(x - 14/9) = 0\nx - 14/5 = 0 or x - 14/9 = 0\nx = 14/5\nx = 14/9"} {"input": "Solve the equations:\n10x + 3y = 8\n5x + 3y = 8", "output": "10x + 3y = 8\n5x + 3y = 8\n\nUsing elimination\n5*(10x + 3y = 8)\n10*(5x + 3y = 8)\n50x + 15y = 40\n50x + 30y = 80\nSubtract equations\n-15y = -40\ny = -40/-15\ny = 8/3\n\nSubstitute y\n10x + 3(8/3) = 8\n10x = 0\nx = 0/10\nx = 0"} {"input": "Solve quickly: x^3 + 19/2x^2 + 27x + 45/2 = 0", "output": "x^3 + 19/2x^2 + 27x + 45/2 = 0\n(x - -5)(x - -3/2)(x - -3) = 0\nx - -5 = 0\nx - -3/2 = 0\nx - -3 = 0\nx = -5\nx = -3/2\nx = -3"} {"input": "What value of x satisfies x^2 - 37/45x + 2/15 = 0", "output": "x^2 - 37/45x + 2/15 = 0\n(x - 2/9)(x - 3/5) = 0\nx - 2/9 = 0 or x - 3/5 = 0\nx = 2/9\nx = 3/5"} {"input": "Solve the equation x^2 - 7/6x - 10/3 = 0", "output": "x^2 - 7/6x - 10/3 = 0\n(x - -4/3)(x - 5/2) = 0\nx - -4/3 = 0 or x - 5/2 = 0\nx = -4/3\nx = 5/2"} {"input": "Find x and y such that\n1x + 9y = -58/7\n7x + 6y = 50/7", "output": "1x + 9y = -58/7\n7x + 6y = 50/7\n\nUsing elimination\n7*(1x + 9y = -58/7)\n1*(7x + 6y = 50/7)\n7x + 63y = -58\n7x + 6y = 50/7\nSubtract equations\n57y = -456/7\ny = -456/7/57\ny = -8/7\n\nSubstitute y\n1x + 9(-8/7) = -58/7\n1x = 2\nx = 2/1\nx = 2"} {"input": "Solve the equation x^2 - 25/16 = 0", "output": "x^2 - 25/16 = 0\n(x - -5/4)(x - 5/4) = 0\nx - -5/4 = 0 or x - 5/4 = 0\nx = -5/4\nx = 5/4"} {"input": "Solve quickly: x^3 - 59/10x^2 + 242/25x - 112/25 = 0", "output": "x^3 - 59/10x^2 + 242/25x - 112/25 = 0\n(x - 8/5)(x - 7/2)(x - 4/5) = 0\nx - 8/5 = 0\nx - 7/2 = 0\nx - 4/5 = 0\nx = 8/5\nx = 7/2\nx = 4/5"} {"input": "Find the solution to 9x + 6 = 0", "output": "9x + 6 = 0\n9x = -6\nx = -6 / 9\nx = -2/3"} {"input": "Find x and y such that\n3x + 5y = 444/7\n3x + 3y = 426/7", "output": "3x + 5y = 444/7\n3x + 3y = 426/7\n\nUsing elimination\n3*(3x + 5y = 444/7)\n3*(3x + 3y = 426/7)\n9x + 15y = 1332/7\n9x + 9y = 1278/7\nSubtract equations\n6y = 54/7\ny = 54/7/6\ny = 9/7\n\nSubstitute y\n3x + 5(9/7) = 444/7\n3x = 57\nx = 57/3\nx = 19"} {"input": "Solve the system:\n3x + 8y = 171/28\n10x + 3y = 1/14", "output": "3x + 8y = 171/28\n10x + 3y = 1/14\n\nUsing elimination\n10*(3x + 8y = 171/28)\n3*(10x + 3y = 1/14)\n30x + 80y = 855/14\n30x + 9y = 3/14\nSubtract equations\n71y = 426/7\ny = 426/7/71\ny = 6/7\n\nSubstitute y\n3x + 8(6/7) = 171/28\n3x = -3/4\nx = -3/4/3\nx = -1/4"} {"input": "Solve quickly: x^3 - 412/21x^2 - 96/7x + 2560/21 = 0", "output": "x^3 - 412/21x^2 - 96/7x + 2560/21 = 0\n(x - 16/7)(x - -8/3)(x - 20) = 0\nx - 16/7 = 0\nx - -8/3 = 0\nx - 20 = 0\nx = 16/7\nx = -8/3\nx = 20"} {"input": "What value of x satisfies x^2 - 145/56x + 3/2 = 0", "output": "x^2 - 145/56x + 3/2 = 0\n(x - 7/8)(x - 12/7) = 0\nx - 7/8 = 0 or x - 12/7 = 0\nx = 7/8\nx = 12/7"} {"input": "Find x for x^3 - 7/9x^2 - 34/9x + 32/9 = 0", "output": "x^3 - 7/9x^2 - 34/9x + 32/9 = 0\n(x - 1)(x - 16/9)(x - -2) = 0\nx - 1 = 0\nx - 16/9 = 0\nx - -2 = 0\nx = 1\nx = 16/9\nx = -2"} {"input": "Find x in 5x - 10 = 0", "output": "5x - 10 = 0\n5x = 10\nx = 10 / 5\nx = 2"} {"input": "Find x in x^3 + 509/252x^2 - 505/252x - 13/3 = 0", "output": "x^3 + 509/252x^2 - 505/252x - 13/3 = 0\n(x - -12/7)(x - 13/9)(x - -7/4) = 0\nx - -12/7 = 0\nx - 13/9 = 0\nx - -7/4 = 0\nx = -12/7\nx = 13/9\nx = -7/4"} {"input": "Solve x^3 + 311/18x^2 + 287/6x + 245/9 = 0", "output": "x^3 + 311/18x^2 + 287/6x + 245/9 = 0\n(x - -14)(x - -7/9)(x - -5/2) = 0\nx - -14 = 0\nx - -7/9 = 0\nx - -5/2 = 0\nx = -14\nx = -7/9\nx = -5/2"} {"input": "Compute the solution of x^3 - 9/7x^2 - 10/49x + 24/49 = 0", "output": "x^3 - 9/7x^2 - 10/49x + 24/49 = 0\n(x - -4/7)(x - 6/7)(x - 1) = 0\nx - -4/7 = 0\nx - 6/7 = 0\nx - 1 = 0\nx = -4/7\nx = 6/7\nx = 1"} {"input": "Find x in 7x + 91/10 = 0", "output": "7x + 91/10 = 0\n7x = -91/10\nx = -91/10 / 7\nx = -13/10"} {"input": "Find x in x^3 - 35/18x^2 - 2407/450x - 11/5 = 0", "output": "x^3 - 35/18x^2 - 2407/450x - 11/5 = 0\n(x - -5/9)(x - 18/5)(x - -11/10) = 0\nx - -5/9 = 0\nx - 18/5 = 0\nx - -11/10 = 0\nx = -5/9\nx = 18/5\nx = -11/10"} {"input": "Solve x^2 + 37/10x + 7/10 = 0", "output": "x^2 + 37/10x + 7/10 = 0\n(x - -1/5)(x - -7/2) = 0\nx - -1/5 = 0 or x - -7/2 = 0\nx = -1/5\nx = -7/2"} {"input": "Solve simultaneously:\n4x + 9y = 1\n6x + 3y = -9", "output": "4x + 9y = 1\n6x + 3y = -9\n\nUsing elimination\n6*(4x + 9y = 1)\n4*(6x + 3y = -9)\n24x + 54y = 6\n24x + 12y = -36\nSubtract equations\n42y = 42\ny = 42/42\ny = 1\n\nSubstitute y\n4x + 9(1) = 1\n4x = -8\nx = -8/4\nx = -2"} {"input": "Solve the equations:\n9x + 8y = 83/5\n8x + 3y = 323/40", "output": "9x + 8y = 83/5\n8x + 3y = 323/40\n\nUsing elimination\n8*(9x + 8y = 83/5)\n9*(8x + 3y = 323/40)\n72x + 64y = 664/5\n72x + 27y = 2907/40\nSubtract equations\n37y = 481/8\ny = 481/8/37\ny = 13/8\n\nSubstitute y\n9x + 8(13/8) = 83/5\n9x = 18/5\nx = 18/5/9\nx = 2/5"} {"input": "Solve quickly: x^3 - 17/30x^2 - 71/6x + 57/5 = 0", "output": "x^3 - 17/30x^2 - 71/6x + 57/5 = 0\n(x - -18/5)(x - 19/6)(x - 1) = 0\nx - -18/5 = 0\nx - 19/6 = 0\nx - 1 = 0\nx = -18/5\nx = 19/6\nx = 1"} {"input": "What value of x satisfies 4x - 16 = 0", "output": "4x - 16 = 0\n4x = 16\nx = 16 / 4\nx = 4"} {"input": "Find the solution to x^2 - 4x + 187/49 = 0", "output": "x^2 - 4x + 187/49 = 0\n(x - 11/7)(x - 17/7) = 0\nx - 11/7 = 0 or x - 17/7 = 0\nx = 11/7\nx = 17/7"} {"input": "Solve the equation x^3 - 88/105x^2 - 449/105x - 8/5 = 0", "output": "x^3 - 88/105x^2 - 449/105x - 8/5 = 0\n(x - -3/7)(x - -7/5)(x - 8/3) = 0\nx - -3/7 = 0\nx - -7/5 = 0\nx - 8/3 = 0\nx = -3/7\nx = -7/5\nx = 8/3"} {"input": "Solve the system:\n8x + 7y = 56/5\n4x + 5y = 256/35", "output": "8x + 7y = 56/5\n4x + 5y = 256/35\n\nUsing elimination\n4*(8x + 7y = 56/5)\n8*(4x + 5y = 256/35)\n32x + 28y = 224/5\n32x + 40y = 2048/35\nSubtract equations\n-12y = -96/7\ny = -96/7/-12\ny = 8/7\n\nSubstitute y\n8x + 7(8/7) = 56/5\n8x = 16/5\nx = 16/5/8\nx = 2/5"} {"input": "Find x for x^3 - 67/12x^2 + 23/12x + 5 = 0", "output": "x^3 - 67/12x^2 + 23/12x + 5 = 0\n(x - 5)(x - 4/3)(x - -3/4) = 0\nx - 5 = 0\nx - 4/3 = 0\nx - -3/4 = 0\nx = 5\nx = 4/3\nx = -3/4"} {"input": "Solve quickly: x^2 - 11/40x - 1/20 = 0", "output": "x^2 - 11/40x - 1/20 = 0\n(x - -1/8)(x - 2/5) = 0\nx - -1/8 = 0 or x - 2/5 = 0\nx = -1/8\nx = 2/5"} {"input": "Solve the equations:\n1x + 3y = 67/2\n7x + 4y = 129/2", "output": "1x + 3y = 67/2\n7x + 4y = 129/2\n\nUsing elimination\n7*(1x + 3y = 67/2)\n1*(7x + 4y = 129/2)\n7x + 21y = 469/2\n7x + 4y = 129/2\nSubtract equations\n17y = 170\ny = 170/17\ny = 10\n\nSubstitute y\n1x + 3(10) = 67/2\n1x = 7/2\nx = 7/2/1\nx = 7/2"} {"input": "Find the solution to 1x + 3/2 = 0", "output": "1x + 3/2 = 0\n1x = -3/2\nx = -3/2 / 1\nx = -3/2"} {"input": "Solve quickly: x^2 - 7x + 6 = 0", "output": "x^2 - 7x + 6 = 0\n(x - 1)(x - 6) = 0\nx - 1 = 0 or x - 6 = 0\nx = 1\nx = 6"} {"input": "Find the solution to x^3 + 175/18x^2 + 1279/54x + 380/27 = 0", "output": "x^3 + 175/18x^2 + 1279/54x + 380/27 = 0\n(x - -19/3)(x - -8/9)(x - -5/2) = 0\nx - -19/3 = 0\nx - -8/9 = 0\nx - -5/2 = 0\nx = -19/3\nx = -8/9\nx = -5/2"} {"input": "What value of x satisfies x^3 - 1139/70x^2 + 23/10x + 1144/35 = 0", "output": "x^3 - 1139/70x^2 + 23/10x + 1144/35 = 0\n(x - -13/10)(x - 16)(x - 11/7) = 0\nx - -13/10 = 0\nx - 16 = 0\nx - 11/7 = 0\nx = -13/10\nx = 16\nx = 11/7"} {"input": "Find x in x^3 + 23/56x^2 - 843/392x - 297/196 = 0", "output": "x^3 + 23/56x^2 - 843/392x - 297/196 = 0\n(x - -6/7)(x - -9/8)(x - 11/7) = 0\nx - -6/7 = 0\nx - -9/8 = 0\nx - 11/7 = 0\nx = -6/7\nx = -9/8\nx = 11/7"} {"input": "What value of x satisfies 4x + 24 = 0", "output": "4x + 24 = 0\n4x = -24\nx = -24 / 4\nx = -6"} {"input": "Solve x^2 + 77/10x - 171/10 = 0", "output": "x^2 + 77/10x - 171/10 = 0\n(x - 9/5)(x - -19/2) = 0\nx - 9/5 = 0 or x - -19/2 = 0\nx = 9/5\nx = -19/2"} {"input": "Determine x in x^3 + 12x^2 + 153/4x + 135/4 = 0", "output": "x^3 + 12x^2 + 153/4x + 135/4 = 0\n(x - -3/2)(x - -3)(x - -15/2) = 0\nx - -3/2 = 0\nx - -3 = 0\nx - -15/2 = 0\nx = -3/2\nx = -3\nx = -15/2"} {"input": "Solve the equations:\n10x + 2y = 34/3\n10x + 3y = 31/3", "output": "10x + 2y = 34/3\n10x + 3y = 31/3\n\nUsing elimination\n10*(10x + 2y = 34/3)\n10*(10x + 3y = 31/3)\n100x + 20y = 340/3\n100x + 30y = 310/3\nSubtract equations\n-10y = 10\ny = 10/-10\ny = -1\n\nSubstitute y\n10x + 2(-1) = 34/3\n10x = 40/3\nx = 40/3/10\nx = 4/3"} {"input": "Compute the solution of x^3 + 55/3x^2 + 439/9x - 55/3 = 0", "output": "x^3 + 55/3x^2 + 439/9x - 55/3 = 0\n(x - -15)(x - 1/3)(x - -11/3) = 0\nx - -15 = 0\nx - 1/3 = 0\nx - -11/3 = 0\nx = -15\nx = 1/3\nx = -11/3"} {"input": "Solve the system:\n1x + 9y = -3\n9x + 1y = 133", "output": "1x + 9y = -3\n9x + 1y = 133\n\nUsing elimination\n9*(1x + 9y = -3)\n1*(9x + 1y = 133)\n9x + 81y = -27\n9x + 1y = 133\nSubtract equations\n80y = -160\ny = -160/80\ny = -2\n\nSubstitute y\n1x + 9(-2) = -3\n1x = 15\nx = 15/1\nx = 15"} {"input": "Compute the solution of x^2 - 72/35x - 128/35 = 0", "output": "x^2 - 72/35x - 128/35 = 0\n(x - 16/5)(x - -8/7) = 0\nx - 16/5 = 0 or x - -8/7 = 0\nx = 16/5\nx = -8/7"} {"input": "Find x for x^2 - 46/7x + 72/7 = 0", "output": "x^2 - 46/7x + 72/7 = 0\n(x - 18/7)(x - 4) = 0\nx - 18/7 = 0 or x - 4 = 0\nx = 18/7\nx = 4"} {"input": "Solve simultaneously:\n2x + 4y = 534/35\n7x + 2y = 729/35", "output": "2x + 4y = 534/35\n7x + 2y = 729/35\n\nUsing elimination\n7*(2x + 4y = 534/35)\n2*(7x + 2y = 729/35)\n14x + 28y = 534/5\n14x + 4y = 1458/35\nSubtract equations\n24y = 456/7\ny = 456/7/24\ny = 19/7\n\nSubstitute y\n2x + 4(19/7) = 534/35\n2x = 22/5\nx = 22/5/2\nx = 11/5"} {"input": "Find x in 3x - 45/4 = 0", "output": "3x - 45/4 = 0\n3x = 45/4\nx = 45/4 / 3\nx = 15/4"} {"input": "What value of x satisfies x^3 + 325/84x^2 + 113/28x + 20/21 = 0", "output": "x^3 + 325/84x^2 + 113/28x + 20/21 = 0\n(x - -16/7)(x - -1/3)(x - -5/4) = 0\nx - -16/7 = 0\nx - -1/3 = 0\nx - -5/4 = 0\nx = -16/7\nx = -1/3\nx = -5/4"} {"input": "Find x for x^2 - 9/2x - 5/2 = 0", "output": "x^2 - 9/2x - 5/2 = 0\n(x - -1/2)(x - 5) = 0\nx - -1/2 = 0 or x - 5 = 0\nx = -1/2\nx = 5"} {"input": "Solve quickly: x^2 - 5x + 21/4 = 0", "output": "x^2 - 5x + 21/4 = 0\n(x - 7/2)(x - 3/2) = 0\nx - 7/2 = 0 or x - 3/2 = 0\nx = 7/2\nx = 3/2"} {"input": "Determine x in 3x + 2/3 = 0", "output": "3x + 2/3 = 0\n3x = -2/3\nx = -2/3 / 3\nx = -2/9"} {"input": "Find x in x^2 + 21/5x + 16/5 = 0", "output": "x^2 + 21/5x + 16/5 = 0\n(x - -1)(x - -16/5) = 0\nx - -1 = 0 or x - -16/5 = 0\nx = -1\nx = -16/5"} {"input": "Find x in x^3 + 3x^2 + 2x = 0", "output": "x^3 + 3x^2 + 2x = 0\n(x - -1)(x - 0)(x - -2) = 0\nx - -1 = 0\nx - 0 = 0\nx - -2 = 0\nx = -1\nx = 0\nx = -2"} {"input": "Find x for x^3 - 149/30x^2 + 41/5x - 9/2 = 0", "output": "x^3 - 149/30x^2 + 41/5x - 9/2 = 0\n(x - 3/2)(x - 5/3)(x - 9/5) = 0\nx - 3/2 = 0\nx - 5/3 = 0\nx - 9/5 = 0\nx = 3/2\nx = 5/3\nx = 9/5"} {"input": "Find the solution to x^3 - 7/8x^2 - 77/32x + 5/16 = 0", "output": "x^3 - 7/8x^2 - 77/32x + 5/16 = 0\n(x - 1/8)(x - 2)(x - -5/4) = 0\nx - 1/8 = 0\nx - 2 = 0\nx - -5/4 = 0\nx = 1/8\nx = 2\nx = -5/4"} {"input": "Find the solution to 7x + 14/9 = 0", "output": "7x + 14/9 = 0\n7x = -14/9\nx = -14/9 / 7\nx = -2/9"} {"input": "Compute the solution of x^3 + 70/9x^2 + 121/27x - 182/27 = 0", "output": "x^3 + 70/9x^2 + 121/27x - 182/27 = 0\n(x - 2/3)(x - -13/9)(x - -7) = 0\nx - 2/3 = 0\nx - -13/9 = 0\nx - -7 = 0\nx = 2/3\nx = -13/9\nx = -7"} {"input": "Solve the system:\n4x + 1y = -287/30\n9x + 2y = -311/15", "output": "4x + 1y = -287/30\n9x + 2y = -311/15\n\nUsing elimination\n9*(4x + 1y = -287/30)\n4*(9x + 2y = -311/15)\n36x + 9y = -861/10\n36x + 8y = -1244/15\nSubtract equations\n1y = -19/6\ny = -19/6/1\ny = -19/6\n\nSubstitute y\n4x + 1(-19/6) = -287/30\n4x = -32/5\nx = -32/5/4\nx = -8/5"} {"input": "Solve the system:\n9x + 2y = -31/63\n1x + 8y = -439/63", "output": "9x + 2y = -31/63\n1x + 8y = -439/63\n\nUsing elimination\n1*(9x + 2y = -31/63)\n9*(1x + 8y = -439/63)\n9x + 2y = -31/63\n9x + 72y = -439/7\nSubtract equations\n-70y = 560/9\ny = 560/9/-70\ny = -8/9\n\nSubstitute y\n9x + 2(-8/9) = -31/63\n9x = 9/7\nx = 9/7/9\nx = 1/7"} {"input": "Determine x in 3x - 6/5 = 0", "output": "3x - 6/5 = 0\n3x = 6/5\nx = 6/5 / 3\nx = 2/5"} {"input": "Determine x in x^3 + 123/14x^2 + 73/14x - 60/7 = 0", "output": "x^3 + 123/14x^2 + 73/14x - 60/7 = 0\n(x - -3/2)(x - 5/7)(x - -8) = 0\nx - -3/2 = 0\nx - 5/7 = 0\nx - -8 = 0\nx = -3/2\nx = 5/7\nx = -8"} {"input": "Compute the solution of x^3 + 97/6x^2 - 91/6x - 17 = 0", "output": "x^3 + 97/6x^2 - 91/6x - 17 = 0\n(x - 3/2)(x - -17)(x - -2/3) = 0\nx - 3/2 = 0\nx - -17 = 0\nx - -2/3 = 0\nx = 3/2\nx = -17\nx = -2/3"} {"input": "Solve simultaneously:\n6x + 9y = 5\n9x + 3y = -10", "output": "6x + 9y = 5\n9x + 3y = -10\n\nUsing elimination\n9*(6x + 9y = 5)\n6*(9x + 3y = -10)\n54x + 81y = 45\n54x + 18y = -60\nSubtract equations\n63y = 105\ny = 105/63\ny = 5/3\n\nSubstitute y\n6x + 9(5/3) = 5\n6x = -10\nx = -10/6\nx = -5/3"} {"input": "Compute the solution of x^2 + 8x + 16 = 0", "output": "x^2 + 8x + 16 = 0\n(x - -4)(x - -4) = 0\nx - -4 = 0 or x - -4 = 0\nx = -4\nx = -4"} {"input": "Solve quickly: x^3 - 21/4x^2 + 67/8x - 33/8 = 0", "output": "x^3 - 21/4x^2 + 67/8x - 33/8 = 0\n(x - 1)(x - 11/4)(x - 3/2) = 0\nx - 1 = 0\nx - 11/4 = 0\nx - 3/2 = 0\nx = 1\nx = 11/4\nx = 3/2"} {"input": "Find the solution to x^2 + 83/8x - 39/2 = 0", "output": "x^2 + 83/8x - 39/2 = 0\n(x - 13/8)(x - -12) = 0\nx - 13/8 = 0 or x - -12 = 0\nx = 13/8\nx = -12"} {"input": "Find x in 6x - 21 = 0", "output": "6x - 21 = 0\n6x = 21\nx = 21 / 6\nx = 7/2"} {"input": "Find x for x^3 - 49/6x^2 - 15/2x + 119/3 = 0", "output": "x^3 - 49/6x^2 - 15/2x + 119/3 = 0\n(x - -7/3)(x - 17/2)(x - 2) = 0\nx - -7/3 = 0\nx - 17/2 = 0\nx - 2 = 0\nx = -7/3\nx = 17/2\nx = 2"} {"input": "Solve the system:\n9x + 9y = -18\n8x + 2y = -28", "output": "9x + 9y = -18\n8x + 2y = -28\n\nUsing elimination\n8*(9x + 9y = -18)\n9*(8x + 2y = -28)\n72x + 72y = -144\n72x + 18y = -252\nSubtract equations\n54y = 108\ny = 108/54\ny = 2\n\nSubstitute y\n9x + 9(2) = -18\n9x = -36\nx = -36/9\nx = -4"} {"input": "Find the solution to 5x - 90 = 0", "output": "5x - 90 = 0\n5x = 90\nx = 90 / 5\nx = 18"} {"input": "What value of x satisfies x^3 - 7/2x^2 + 179/64x + 13/32 = 0", "output": "x^3 - 7/2x^2 + 179/64x + 13/32 = 0\n(x - -1/8)(x - 2)(x - 13/8) = 0\nx - -1/8 = 0\nx - 2 = 0\nx - 13/8 = 0\nx = -1/8\nx = 2\nx = 13/8"} {"input": "Find x in x^3 + 89/6x^2 + 149/3x - 40 = 0", "output": "x^3 + 89/6x^2 + 149/3x - 40 = 0\n(x - -15/2)(x - -8)(x - 2/3) = 0\nx - -15/2 = 0\nx - -8 = 0\nx - 2/3 = 0\nx = -15/2\nx = -8\nx = 2/3"} {"input": "Find the solution to x^3 - 151/90x^2 - 641/54x - 1309/135 = 0", "output": "x^3 - 151/90x^2 - 641/54x - 1309/135 = 0\n(x - 14/3)(x - -17/9)(x - -11/10) = 0\nx - 14/3 = 0\nx - -17/9 = 0\nx - -11/10 = 0\nx = 14/3\nx = -17/9\nx = -11/10"} {"input": "Find x in x^3 + 4/3x^2 - 25/9x - 28/27 = 0", "output": "x^3 + 4/3x^2 - 25/9x - 28/27 = 0\n(x - -7/3)(x - 4/3)(x - -1/3) = 0\nx - -7/3 = 0\nx - 4/3 = 0\nx - -1/3 = 0\nx = -7/3\nx = 4/3\nx = -1/3"} {"input": "Compute the solution of x^3 - 23/3x^2 - 200/9x - 100/9 = 0", "output": "x^3 - 23/3x^2 - 200/9x - 100/9 = 0\n(x - -5/3)(x - -2/3)(x - 10) = 0\nx - -5/3 = 0\nx - -2/3 = 0\nx - 10 = 0\nx = -5/3\nx = -2/3\nx = 10"} {"input": "Solve the equation x^2 + 101/45x + 52/45 = 0", "output": "x^2 + 101/45x + 52/45 = 0\n(x - -4/5)(x - -13/9) = 0\nx - -4/5 = 0 or x - -13/9 = 0\nx = -4/5\nx = -13/9"} {"input": "What value of x satisfies x^3 + 91/5x^2 + 462/5x + 432/5 = 0", "output": "x^3 + 91/5x^2 + 462/5x + 432/5 = 0\n(x - -9)(x - -6/5)(x - -8) = 0\nx - -9 = 0\nx - -6/5 = 0\nx - -8 = 0\nx = -9\nx = -6/5\nx = -8"} {"input": "Solve x^2 - 7/10x - 13/5 = 0", "output": "x^2 - 7/10x - 13/5 = 0\n(x - 2)(x - -13/10) = 0\nx - 2 = 0 or x - -13/10 = 0\nx = 2\nx = -13/10"} {"input": "Find x and y such that\n10x + 4y = 16\n4x + 6y = 13", "output": "10x + 4y = 16\n4x + 6y = 13\n\nUsing elimination\n4*(10x + 4y = 16)\n10*(4x + 6y = 13)\n40x + 16y = 64\n40x + 60y = 130\nSubtract equations\n-44y = -66\ny = -66/-44\ny = 3/2\n\nSubstitute y\n10x + 4(3/2) = 16\n10x = 10\nx = 10/10\nx = 1"} {"input": "Compute the solution of x^2 + 7/6x - 1/2 = 0", "output": "x^2 + 7/6x - 1/2 = 0\n(x - -3/2)(x - 1/3) = 0\nx - -3/2 = 0 or x - 1/3 = 0\nx = -3/2\nx = 1/3"} {"input": "What value of x satisfies x^2 - 5/2x - 25/2 = 0", "output": "x^2 - 5/2x - 25/2 = 0\n(x - 5)(x - -5/2) = 0\nx - 5 = 0 or x - -5/2 = 0\nx = 5\nx = -5/2"} {"input": "Compute the solution of x^2 + 62/35x - 32/7 = 0", "output": "x^2 + 62/35x - 32/7 = 0\n(x - 10/7)(x - -16/5) = 0\nx - 10/7 = 0 or x - -16/5 = 0\nx = 10/7\nx = -16/5"} {"input": "What value of x satisfies x^2 - 16 = 0", "output": "x^2 - 16 = 0\n(x - -4)(x - 4) = 0\nx - -4 = 0 or x - 4 = 0\nx = -4\nx = 4"} {"input": "Find x and y such that\n6x + 3y = -111/4\n9x + 8y = -25", "output": "6x + 3y = -111/4\n9x + 8y = -25\n\nUsing elimination\n9*(6x + 3y = -111/4)\n6*(9x + 8y = -25)\n54x + 27y = -999/4\n54x + 48y = -150\nSubtract equations\n-21y = -399/4\ny = -399/4/-21\ny = 19/4\n\nSubstitute y\n6x + 3(19/4) = -111/4\n6x = -42\nx = -42/6\nx = -7"} {"input": "What value of x satisfies x^3 + 47/5x^2 + 2/5x - 144/5 = 0", "output": "x^3 + 47/5x^2 + 2/5x - 144/5 = 0\n(x - -9)(x - 8/5)(x - -2) = 0\nx - -9 = 0\nx - 8/5 = 0\nx - -2 = 0\nx = -9\nx = 8/5\nx = -2"} {"input": "Solve the equation 4x + 5 = 0", "output": "4x + 5 = 0\n4x = -5\nx = -5 / 4\nx = -5/4"} {"input": "Solve x^2 - 7/4x + 5/8 = 0", "output": "x^2 - 7/4x + 5/8 = 0\n(x - 5/4)(x - 1/2) = 0\nx - 5/4 = 0 or x - 1/2 = 0\nx = 5/4\nx = 1/2"} {"input": "Find x for 2x - 10/3 = 0", "output": "2x - 10/3 = 0\n2x = 10/3\nx = 10/3 / 2\nx = 5/3"} {"input": "Find the solution to x^3 - 5/6x^2 - 46x - 30 = 0", "output": "x^3 - 5/6x^2 - 46x - 30 = 0\n(x - -6)(x - 15/2)(x - -2/3) = 0\nx - -6 = 0\nx - 15/2 = 0\nx - -2/3 = 0\nx = -6\nx = 15/2\nx = -2/3"} {"input": "Find the solution to x^2 + 5/3x = 0", "output": "x^2 + 5/3x = 0\n(x - 0)(x - -5/3) = 0\nx - 0 = 0 or x - -5/3 = 0\nx = 0\nx = -5/3"} {"input": "Determine x in x^3 - 61/8x^2 - 67/8x + 255/32 = 0", "output": "x^3 - 61/8x^2 - 67/8x + 255/32 = 0\n(x - -3/2)(x - 5/8)(x - 17/2) = 0\nx - -3/2 = 0\nx - 5/8 = 0\nx - 17/2 = 0\nx = -3/2\nx = 5/8\nx = 17/2"} {"input": "Find x in x^2 - 23x + 90 = 0", "output": "x^2 - 23x + 90 = 0\n(x - 18)(x - 5) = 0\nx - 18 = 0 or x - 5 = 0\nx = 18\nx = 5"} {"input": "Find the solution to x^2 - 99/5x + 238/5 = 0", "output": "x^2 - 99/5x + 238/5 = 0\n(x - 14/5)(x - 17) = 0\nx - 14/5 = 0 or x - 17 = 0\nx = 14/5\nx = 17"} {"input": "Solve x^2 + 97/40x + 13/10 = 0", "output": "x^2 + 97/40x + 13/10 = 0\n(x - -4/5)(x - -13/8) = 0\nx - -4/5 = 0 or x - -13/8 = 0\nx = -4/5\nx = -13/8"} {"input": "Solve simultaneously:\n5x + 3y = 119/12\n6x + 7y = 17/4", "output": "5x + 3y = 119/12\n6x + 7y = 17/4\n\nUsing elimination\n6*(5x + 3y = 119/12)\n5*(6x + 7y = 17/4)\n30x + 18y = 119/2\n30x + 35y = 85/4\nSubtract equations\n-17y = 153/4\ny = 153/4/-17\ny = -9/4\n\nSubstitute y\n5x + 3(-9/4) = 119/12\n5x = 50/3\nx = 50/3/5\nx = 10/3"} {"input": "Compute the solution of x^3 + 131/40x^2 + 69/20x + 189/160 = 0", "output": "x^3 + 131/40x^2 + 69/20x + 189/160 = 0\n(x - -7/8)(x - -9/10)(x - -3/2) = 0\nx - -7/8 = 0\nx - -9/10 = 0\nx - -3/2 = 0\nx = -7/8\nx = -9/10\nx = -3/2"} {"input": "What value of x satisfies x^2 - 25/6x + 25/9 = 0", "output": "x^2 - 25/6x + 25/9 = 0\n(x - 10/3)(x - 5/6) = 0\nx - 10/3 = 0 or x - 5/6 = 0\nx = 10/3\nx = 5/6"} {"input": "What value of x satisfies x^3 - 87/28x^2 + 723/448x + 19/64 = 0", "output": "x^3 - 87/28x^2 + 723/448x + 19/64 = 0\n(x - 7/8)(x - -1/7)(x - 19/8) = 0\nx - 7/8 = 0\nx - -1/7 = 0\nx - 19/8 = 0\nx = 7/8\nx = -1/7\nx = 19/8"} {"input": "Determine x in x^2 + 63/40x + 9/20 = 0", "output": "x^2 + 63/40x + 9/20 = 0\n(x - -6/5)(x - -3/8) = 0\nx - -6/5 = 0 or x - -3/8 = 0\nx = -6/5\nx = -3/8"} {"input": "Find x in 5x + 45 = 0", "output": "5x + 45 = 0\n5x = -45\nx = -45 / 5\nx = -9"} {"input": "Find x for 10x = 0", "output": "10x = 0\n10x = 0\nx = 0 / 10\nx = 0"} {"input": "Find the solution to x^3 - 599/45x^2 + 718/45x - 8/3 = 0", "output": "x^3 - 599/45x^2 + 718/45x - 8/3 = 0\n(x - 12)(x - 10/9)(x - 1/5) = 0\nx - 12 = 0\nx - 10/9 = 0\nx - 1/5 = 0\nx = 12\nx = 10/9\nx = 1/5"} {"input": "Compute the solution of x^2 + 179/90x + 17/90 = 0", "output": "x^2 + 179/90x + 17/90 = 0\n(x - -1/10)(x - -17/9) = 0\nx - -1/10 = 0 or x - -17/9 = 0\nx = -1/10\nx = -17/9"} {"input": "Solve quickly: x^3 + 11/7x^2 - 100/7x + 100/7 = 0", "output": "x^3 + 11/7x^2 - 100/7x + 100/7 = 0\n(x - 2)(x - 10/7)(x - -5) = 0\nx - 2 = 0\nx - 10/7 = 0\nx - -5 = 0\nx = 2\nx = 10/7\nx = -5"} {"input": "Solve x^3 + 203/30x^2 + 107/10x + 21/5 = 0", "output": "x^3 + 203/30x^2 + 107/10x + 21/5 = 0\n(x - -3/2)(x - -3/5)(x - -14/3) = 0\nx - -3/2 = 0\nx - -3/5 = 0\nx - -14/3 = 0\nx = -3/2\nx = -3/5\nx = -14/3"} {"input": "Solve quickly: x^2 + 2/21x - 55/21 = 0", "output": "x^2 + 2/21x - 55/21 = 0\n(x - -5/3)(x - 11/7) = 0\nx - -5/3 = 0 or x - 11/7 = 0\nx = -5/3\nx = 11/7"} {"input": "Find x for x^3 - 109/24x^2 - 313/24x - 15/2 = 0", "output": "x^3 - 109/24x^2 - 313/24x - 15/2 = 0\n(x - 20/3)(x - -1)(x - -9/8) = 0\nx - 20/3 = 0\nx - -1 = 0\nx - -9/8 = 0\nx = 20/3\nx = -1\nx = -9/8"} {"input": "Find x for x^2 - 13/10x - 169/50 = 0", "output": "x^2 - 13/10x - 169/50 = 0\n(x - 13/5)(x - -13/10) = 0\nx - 13/5 = 0 or x - -13/10 = 0\nx = 13/5\nx = -13/10"} {"input": "Find x in x^2 - 43/2x + 30 = 0", "output": "x^2 - 43/2x + 30 = 0\n(x - 3/2)(x - 20) = 0\nx - 3/2 = 0 or x - 20 = 0\nx = 3/2\nx = 20"} {"input": "Find x in x^3 + 55/12x^2 + 13/4x - 9/2 = 0", "output": "x^3 + 55/12x^2 + 13/4x - 9/2 = 0\n(x - -3)(x - 2/3)(x - -9/4) = 0\nx - -3 = 0\nx - 2/3 = 0\nx - -9/4 = 0\nx = -3\nx = 2/3\nx = -9/4"} {"input": "Solve the system:\n7x + 7y = 63/4\n10x + 8y = 41/2", "output": "7x + 7y = 63/4\n10x + 8y = 41/2\n\nUsing elimination\n10*(7x + 7y = 63/4)\n7*(10x + 8y = 41/2)\n70x + 70y = 315/2\n70x + 56y = 287/2\nSubtract equations\n14y = 14\ny = 14/14\ny = 1\n\nSubstitute y\n7x + 7(1) = 63/4\n7x = 35/4\nx = 35/4/7\nx = 5/4"} {"input": "Compute the solution of x^2 - 16/21x + 1/7 = 0", "output": "x^2 - 16/21x + 1/7 = 0\n(x - 3/7)(x - 1/3) = 0\nx - 3/7 = 0 or x - 1/3 = 0\nx = 3/7\nx = 1/3"} {"input": "Find x in x^3 - 7/6x^2 - 493/18x + 578/9 = 0", "output": "x^3 - 7/6x^2 - 493/18x + 578/9 = 0\n(x - -17/3)(x - 17/6)(x - 4) = 0\nx - -17/3 = 0\nx - 17/6 = 0\nx - 4 = 0\nx = -17/3\nx = 17/6\nx = 4"} {"input": "Solve quickly: x^3 + 295/36x^2 - 1/4x - 130/9 = 0", "output": "x^3 + 295/36x^2 - 1/4x - 130/9 = 0\n(x - 5/4)(x - -13/9)(x - -8) = 0\nx - 5/4 = 0\nx - -13/9 = 0\nx - -8 = 0\nx = 5/4\nx = -13/9\nx = -8"} {"input": "Find x in x^3 + 1/2x^2 - 27x + 36 = 0", "output": "x^3 + 1/2x^2 - 27x + 36 = 0\n(x - -6)(x - 3/2)(x - 4) = 0\nx - -6 = 0\nx - 3/2 = 0\nx - 4 = 0\nx = -6\nx = 3/2\nx = 4"} {"input": "Determine x in 6x + 96 = 0", "output": "6x + 96 = 0\n6x = -96\nx = -96 / 6\nx = -16"} {"input": "Solve the equation x^3 + 11/4x^2 + 43/18x + 2/3 = 0", "output": "x^3 + 11/4x^2 + 43/18x + 2/3 = 0\n(x - -2/3)(x - -4/3)(x - -3/4) = 0\nx - -2/3 = 0\nx - -4/3 = 0\nx - -3/4 = 0\nx = -2/3\nx = -4/3\nx = -3/4"} {"input": "Solve the equation 1x - 5/2 = 0", "output": "1x - 5/2 = 0\n1x = 5/2\nx = 5/2 / 1\nx = 5/2"} {"input": "Compute the solution of x^3 - 1252/105x^2 + 1581/35x - 1156/21 = 0", "output": "x^3 - 1252/105x^2 + 1581/35x - 1156/21 = 0\n(x - 17/3)(x - 17/5)(x - 20/7) = 0\nx - 17/3 = 0\nx - 17/5 = 0\nx - 20/7 = 0\nx = 17/3\nx = 17/5\nx = 20/7"} {"input": "Compute the solution of x^2 + 7/4x - 57/4 = 0", "output": "x^2 + 7/4x - 57/4 = 0\n(x - -19/4)(x - 3) = 0\nx - -19/4 = 0 or x - 3 = 0\nx = -19/4\nx = 3"} {"input": "Find x for 6x + 30 = 0", "output": "6x + 30 = 0\n6x = -30\nx = -30 / 6\nx = -5"} {"input": "Solve quickly: 5x + 80/7 = 0", "output": "5x + 80/7 = 0\n5x = -80/7\nx = -80/7 / 5\nx = -16/7"} {"input": "Find the solution to x^3 - 65/6x^2 - 27x - 91/6 = 0", "output": "x^3 - 65/6x^2 - 27x - 91/6 = 0\n(x - 13)(x - -1)(x - -7/6) = 0\nx - 13 = 0\nx - -1 = 0\nx - -7/6 = 0\nx = 13\nx = -1\nx = -7/6"} {"input": "Determine x in x^3 - 167/15x^2 + 122/5x + 16/3 = 0", "output": "x^3 - 167/15x^2 + 122/5x + 16/3 = 0\n(x - 10/3)(x - 8)(x - -1/5) = 0\nx - 10/3 = 0\nx - 8 = 0\nx - -1/5 = 0\nx = 10/3\nx = 8\nx = -1/5"} {"input": "What value of x satisfies 1x + 4/9 = 0", "output": "1x + 4/9 = 0\n1x = -4/9\nx = -4/9 / 1\nx = -4/9"} {"input": "Solve quickly: x^2 - 9/8x + 1/8 = 0", "output": "x^2 - 9/8x + 1/8 = 0\n(x - 1/8)(x - 1) = 0\nx - 1/8 = 0 or x - 1 = 0\nx = 1/8\nx = 1"} {"input": "Solve x^3 + 67/72x^2 + 61/216x + 1/36 = 0", "output": "x^3 + 67/72x^2 + 61/216x + 1/36 = 0\n(x - -3/8)(x - -1/3)(x - -2/9) = 0\nx - -3/8 = 0\nx - -1/3 = 0\nx - -2/9 = 0\nx = -3/8\nx = -1/3\nx = -2/9"} {"input": "Find x for x^3 + 7/2x^2 - 9/2x = 0", "output": "x^3 + 7/2x^2 - 9/2x = 0\n(x - -9/2)(x - 1)(x - 0) = 0\nx - -9/2 = 0\nx - 1 = 0\nx - 0 = 0\nx = -9/2\nx = 1\nx = 0"} {"input": "Solve the equations:\n10x + 4y = -2/7\n8x + 7y = 183/14", "output": "10x + 4y = -2/7\n8x + 7y = 183/14\n\nUsing elimination\n8*(10x + 4y = -2/7)\n10*(8x + 7y = 183/14)\n80x + 32y = -16/7\n80x + 70y = 915/7\nSubtract equations\n-38y = -133\ny = -133/-38\ny = 7/2\n\nSubstitute y\n10x + 4(7/2) = -2/7\n10x = -100/7\nx = -100/7/10\nx = -10/7"} {"input": "Solve the equations:\n9x + 6y = 3\n7x + 1y = -4/3", "output": "9x + 6y = 3\n7x + 1y = -4/3\n\nUsing elimination\n7*(9x + 6y = 3)\n9*(7x + 1y = -4/3)\n63x + 42y = 21\n63x + 9y = -12\nSubtract equations\n33y = 33\ny = 33/33\ny = 1\n\nSubstitute y\n9x + 6(1) = 3\n9x = -3\nx = -3/9\nx = -1/3"} {"input": "Find x in x^2 - 209/30x + 361/30 = 0", "output": "x^2 - 209/30x + 361/30 = 0\n(x - 19/6)(x - 19/5) = 0\nx - 19/6 = 0 or x - 19/5 = 0\nx = 19/6\nx = 19/5"} {"input": "Find x in x^3 - 267/28x^2 - 1177/28x - 39 = 0", "output": "x^3 - 267/28x^2 - 1177/28x - 39 = 0\n(x - -7/4)(x - 13)(x - -12/7) = 0\nx - -7/4 = 0\nx - 13 = 0\nx - -12/7 = 0\nx = -7/4\nx = 13\nx = -12/7"} {"input": "Solve quickly: x^3 + 11/5x^2 - 137/25x + 57/25 = 0", "output": "x^3 + 11/5x^2 - 137/25x + 57/25 = 0\n(x - 3/5)(x - 1)(x - -19/5) = 0\nx - 3/5 = 0\nx - 1 = 0\nx - -19/5 = 0\nx = 3/5\nx = 1\nx = -19/5"} {"input": "Solve the equation x^2 - 17/8x - 77/16 = 0", "output": "x^2 - 17/8x - 77/16 = 0\n(x - -11/8)(x - 7/2) = 0\nx - -11/8 = 0 or x - 7/2 = 0\nx = -11/8\nx = 7/2"} {"input": "Determine x in x^2 + 217/10x + 34 = 0", "output": "x^2 + 217/10x + 34 = 0\n(x - -20)(x - -17/10) = 0\nx - -20 = 0 or x - -17/10 = 0\nx = -20\nx = -17/10"} {"input": "Solve simultaneously:\n2x + 8y = -1058/63\n3x + 5y = -151/21", "output": "2x + 8y = -1058/63\n3x + 5y = -151/21\n\nUsing elimination\n3*(2x + 8y = -1058/63)\n2*(3x + 5y = -151/21)\n6x + 24y = -1058/21\n6x + 10y = -302/21\nSubtract equations\n14y = -36\ny = -36/14\ny = -18/7\n\nSubstitute y\n2x + 8(-18/7) = -1058/63\n2x = 34/9\nx = 34/9/2\nx = 17/9"} {"input": "Find x and y such that\n2x + 2y = -113/7\n2x + 8y = -428/7", "output": "2x + 2y = -113/7\n2x + 8y = -428/7\n\nUsing elimination\n2*(2x + 2y = -113/7)\n2*(2x + 8y = -428/7)\n4x + 4y = -226/7\n4x + 16y = -856/7\nSubtract equations\n-12y = 90\ny = 90/-12\ny = -15/2\n\nSubstitute y\n2x + 2(-15/2) = -113/7\n2x = -8/7\nx = -8/7/2\nx = -4/7"} {"input": "Solve x^2 + 1/20x - 21/40 = 0", "output": "x^2 + 1/20x - 21/40 = 0\n(x - 7/10)(x - -3/4) = 0\nx - 7/10 = 0 or x - -3/4 = 0\nx = 7/10\nx = -3/4"} {"input": "Compute the solution of 10x - 95 = 0", "output": "10x - 95 = 0\n10x = 95\nx = 95 / 10\nx = 19/2"} {"input": "Solve simultaneously:\n3x + 9y = 213/8\n5x + 4y = 119/2", "output": "3x + 9y = 213/8\n5x + 4y = 119/2\n\nUsing elimination\n5*(3x + 9y = 213/8)\n3*(5x + 4y = 119/2)\n15x + 45y = 1065/8\n15x + 12y = 357/2\nSubtract equations\n33y = -363/8\ny = -363/8/33\ny = -11/8\n\nSubstitute y\n3x + 9(-11/8) = 213/8\n3x = 39\nx = 39/3\nx = 13"} {"input": "Find the solution to 3x - 6 = 0", "output": "3x - 6 = 0\n3x = 6\nx = 6 / 3\nx = 2"} {"input": "Solve the system:\n1x + 4y = 31/3\n7x + 2y = 113/3", "output": "1x + 4y = 31/3\n7x + 2y = 113/3\n\nUsing elimination\n7*(1x + 4y = 31/3)\n1*(7x + 2y = 113/3)\n7x + 28y = 217/3\n7x + 2y = 113/3\nSubtract equations\n26y = 104/3\ny = 104/3/26\ny = 4/3\n\nSubstitute y\n1x + 4(4/3) = 31/3\n1x = 5\nx = 5/1\nx = 5"} {"input": "Solve x^3 + 37/40x^2 - 29/5x - 221/32 = 0", "output": "x^3 + 37/40x^2 - 29/5x - 221/32 = 0\n(x - -17/8)(x - 5/2)(x - -13/10) = 0\nx - -17/8 = 0\nx - 5/2 = 0\nx - -13/10 = 0\nx = -17/8\nx = 5/2\nx = -13/10"} {"input": "Find x in 3x - 2 = 0", "output": "3x - 2 = 0\n3x = 2\nx = 2 / 3\nx = 2/3"} {"input": "Determine x in x^2 + 5/2x - 25/2 = 0", "output": "x^2 + 5/2x - 25/2 = 0\n(x - -5)(x - 5/2) = 0\nx - -5 = 0 or x - 5/2 = 0\nx = -5\nx = 5/2"} {"input": "Solve the equations:\n10x + 7y = -205/21\n6x + 8y = 10/21", "output": "10x + 7y = -205/21\n6x + 8y = 10/21\n\nUsing elimination\n6*(10x + 7y = -205/21)\n10*(6x + 8y = 10/21)\n60x + 42y = -410/7\n60x + 80y = 100/21\nSubtract equations\n-38y = -190/3\ny = -190/3/-38\ny = 5/3\n\nSubstitute y\n10x + 7(5/3) = -205/21\n10x = -150/7\nx = -150/7/10\nx = -15/7"} {"input": "Find the solution to x^2 + 21/10x - 1 = 0", "output": "x^2 + 21/10x - 1 = 0\n(x - 2/5)(x - -5/2) = 0\nx - 2/5 = 0 or x - -5/2 = 0\nx = 2/5\nx = -5/2"} {"input": "Compute the solution of x^3 + 87/20x^2 - 67/40x - 63/4 = 0", "output": "x^3 + 87/20x^2 - 67/40x - 63/4 = 0\n(x - -18/5)(x - -5/2)(x - 7/4) = 0\nx - -18/5 = 0\nx - -5/2 = 0\nx - 7/4 = 0\nx = -18/5\nx = -5/2\nx = 7/4"} {"input": "Solve simultaneously:\n2x + 2y = 185/36\n3x + 9y = 491/24", "output": "2x + 2y = 185/36\n3x + 9y = 491/24\n\nUsing elimination\n3*(2x + 2y = 185/36)\n2*(3x + 9y = 491/24)\n6x + 6y = 185/12\n6x + 18y = 491/12\nSubtract equations\n-12y = -51/2\ny = -51/2/-12\ny = 17/8\n\nSubstitute y\n2x + 2(17/8) = 185/36\n2x = 8/9\nx = 8/9/2\nx = 4/9"} {"input": "Compute the solution of x^3 + 527/180x^2 + 211/90x + 8/15 = 0", "output": "x^3 + 527/180x^2 + 211/90x + 8/15 = 0\n(x - -2/5)(x - -16/9)(x - -3/4) = 0\nx - -2/5 = 0\nx - -16/9 = 0\nx - -3/4 = 0\nx = -2/5\nx = -16/9\nx = -3/4"} {"input": "Find the solution to x^3 + 48/5x^2 + 333/20x + 27/4 = 0", "output": "x^3 + 48/5x^2 + 333/20x + 27/4 = 0\n(x - -15/2)(x - -3/5)(x - -3/2) = 0\nx - -15/2 = 0\nx - -3/5 = 0\nx - -3/2 = 0\nx = -15/2\nx = -3/5\nx = -3/2"} {"input": "Find x and y such that\n3x + 3y = -163/24\n3x + 7y = -295/24", "output": "3x + 3y = -163/24\n3x + 7y = -295/24\n\nUsing elimination\n3*(3x + 3y = -163/24)\n3*(3x + 7y = -295/24)\n9x + 9y = -163/8\n9x + 21y = -295/8\nSubtract equations\n-12y = 33/2\ny = 33/2/-12\ny = -11/8\n\nSubstitute y\n3x + 3(-11/8) = -163/24\n3x = -8/3\nx = -8/3/3\nx = -8/9"} {"input": "What value of x satisfies x^2 + 31/4x - 45/4 = 0", "output": "x^2 + 31/4x - 45/4 = 0\n(x - -9)(x - 5/4) = 0\nx - -9 = 0 or x - 5/4 = 0\nx = -9\nx = 5/4"} {"input": "Solve the equations:\n3x + 5y = 13/2\n8x + 10y = 77/3", "output": "3x + 5y = 13/2\n8x + 10y = 77/3\n\nUsing elimination\n8*(3x + 5y = 13/2)\n3*(8x + 10y = 77/3)\n24x + 40y = 52\n24x + 30y = 77\nSubtract equations\n10y = -25\ny = -25/10\ny = -5/2\n\nSubstitute y\n3x + 5(-5/2) = 13/2\n3x = 19\nx = 19/3\nx = 19/3"} {"input": "Compute the solution of x^3 - 167/360x^2 - 419/360x - 11/90 = 0", "output": "x^3 - 167/360x^2 - 419/360x - 11/90 = 0\n(x - -4/5)(x - 11/8)(x - -1/9) = 0\nx - -4/5 = 0\nx - 11/8 = 0\nx - -1/9 = 0\nx = -4/5\nx = 11/8\nx = -1/9"} {"input": "Solve simultaneously:\n10x + 4y = -44/7\n9x + 10y = -174/7", "output": "10x + 4y = -44/7\n9x + 10y = -174/7\n\nUsing elimination\n9*(10x + 4y = -44/7)\n10*(9x + 10y = -174/7)\n90x + 36y = -396/7\n90x + 100y = -1740/7\nSubtract equations\n-64y = 192\ny = 192/-64\ny = -3\n\nSubstitute y\n10x + 4(-3) = -44/7\n10x = 40/7\nx = 40/7/10\nx = 4/7"} {"input": "What value of x satisfies 3x - 9/5 = 0", "output": "3x - 9/5 = 0\n3x = 9/5\nx = 9/5 / 3\nx = 3/5"} {"input": "Find x for x^3 - 193/18x^2 + 35/9x + 100/3 = 0", "output": "x^3 - 193/18x^2 + 35/9x + 100/3 = 0\n(x - -3/2)(x - 20/9)(x - 10) = 0\nx - -3/2 = 0\nx - 20/9 = 0\nx - 10 = 0\nx = -3/2\nx = 20/9\nx = 10"} {"input": "Find x in 10x + 190 = 0", "output": "10x + 190 = 0\n10x = -190\nx = -190 / 10\nx = -19"} {"input": "Compute the solution of x^2 - 19/5x + 18/5 = 0", "output": "x^2 - 19/5x + 18/5 = 0\n(x - 2)(x - 9/5) = 0\nx - 2 = 0 or x - 9/5 = 0\nx = 2\nx = 9/5"} {"input": "Solve quickly: x^2 + 28/3x - 55/3 = 0", "output": "x^2 + 28/3x - 55/3 = 0\n(x - -11)(x - 5/3) = 0\nx - -11 = 0 or x - 5/3 = 0\nx = -11\nx = 5/3"} {"input": "Find x for x^3 + 22/3x^2 + 40/3x = 0", "output": "x^3 + 22/3x^2 + 40/3x = 0\n(x - -10/3)(x - -4)(x - 0) = 0\nx - -10/3 = 0\nx - -4 = 0\nx - 0 = 0\nx = -10/3\nx = -4\nx = 0"} {"input": "Find x for 3x + 27/5 = 0", "output": "3x + 27/5 = 0\n3x = -27/5\nx = -27/5 / 3\nx = -9/5"} {"input": "Find x in x^2 + 5x + 56/9 = 0", "output": "x^2 + 5x + 56/9 = 0\n(x - -8/3)(x - -7/3) = 0\nx - -8/3 = 0 or x - -7/3 = 0\nx = -8/3\nx = -7/3"} {"input": "Determine x in 3x + 6 = 0", "output": "3x + 6 = 0\n3x = -6\nx = -6 / 3\nx = -2"} {"input": "Solve the system:\n10x + 3y = -231/2\n3x + 4y = -30", "output": "10x + 3y = -231/2\n3x + 4y = -30\n\nUsing elimination\n3*(10x + 3y = -231/2)\n10*(3x + 4y = -30)\n30x + 9y = -693/2\n30x + 40y = -300\nSubtract equations\n-31y = -93/2\ny = -93/2/-31\ny = 3/2\n\nSubstitute y\n10x + 3(3/2) = -231/2\n10x = -120\nx = -120/10\nx = -12"} {"input": "Find x in 6x - 20/3 = 0", "output": "6x - 20/3 = 0\n6x = 20/3\nx = 20/3 / 6\nx = 10/9"} {"input": "Find x in x^2 - 53/2x + 130 = 0", "output": "x^2 - 53/2x + 130 = 0\n(x - 20)(x - 13/2) = 0\nx - 20 = 0 or x - 13/2 = 0\nx = 20\nx = 13/2"} {"input": "Find x and y such that\n1x + 9y = 7\n4x + 4y = 52/3", "output": "1x + 9y = 7\n4x + 4y = 52/3\n\nUsing elimination\n4*(1x + 9y = 7)\n1*(4x + 4y = 52/3)\n4x + 36y = 28\n4x + 4y = 52/3\nSubtract equations\n32y = 32/3\ny = 32/3/32\ny = 1/3\n\nSubstitute y\n1x + 9(1/3) = 7\n1x = 4\nx = 4/1\nx = 4"} {"input": "What value of x satisfies 9x - 27/5 = 0", "output": "9x - 27/5 = 0\n9x = 27/5\nx = 27/5 / 9\nx = 3/5"} {"input": "Find the solution to x^2 - 121/36 = 0", "output": "x^2 - 121/36 = 0\n(x - 11/6)(x - -11/6) = 0\nx - 11/6 = 0 or x - -11/6 = 0\nx = 11/6\nx = -11/6"} {"input": "What value of x satisfies 10x - 90 = 0", "output": "10x - 90 = 0\n10x = 90\nx = 90 / 10\nx = 9"} {"input": "Find x in x^2 + 13/3x = 0", "output": "x^2 + 13/3x = 0\n(x - 0)(x - -13/3) = 0\nx - 0 = 0 or x - -13/3 = 0\nx = 0\nx = -13/3"} {"input": "Find x for x^2 + 3/4x - 9/8 = 0", "output": "x^2 + 3/4x - 9/8 = 0\n(x - 3/4)(x - -3/2) = 0\nx - 3/4 = 0 or x - -3/2 = 0\nx = 3/4\nx = -3/2"} {"input": "Solve simultaneously:\n9x + 5y = 73/4\n6x + 1y = 89/10", "output": "9x + 5y = 73/4\n6x + 1y = 89/10\n\nUsing elimination\n6*(9x + 5y = 73/4)\n9*(6x + 1y = 89/10)\n54x + 30y = 219/2\n54x + 9y = 801/10\nSubtract equations\n21y = 147/5\ny = 147/5/21\ny = 7/5\n\nSubstitute y\n9x + 5(7/5) = 73/4\n9x = 45/4\nx = 45/4/9\nx = 5/4"} {"input": "Determine x in x^2 + 11/28x - 6/7 = 0", "output": "x^2 + 11/28x - 6/7 = 0\n(x - 3/4)(x - -8/7) = 0\nx - 3/4 = 0 or x - -8/7 = 0\nx = 3/4\nx = -8/7"} {"input": "Compute the solution of 9x + 27/2 = 0", "output": "9x + 27/2 = 0\n9x = -27/2\nx = -27/2 / 9\nx = -3/2"} {"input": "Compute the solution of 9x - 15 = 0", "output": "9x - 15 = 0\n9x = 15\nx = 15 / 9\nx = 5/3"} {"input": "Solve the equation x^2 + 1/8x - 33/16 = 0", "output": "x^2 + 1/8x - 33/16 = 0\n(x - -3/2)(x - 11/8) = 0\nx - -3/2 = 0 or x - 11/8 = 0\nx = -3/2\nx = 11/8"} {"input": "Find x and y such that\n4x + 4y = 56/3\n5x + 1y = 74/3", "output": "4x + 4y = 56/3\n5x + 1y = 74/3\n\nUsing elimination\n5*(4x + 4y = 56/3)\n4*(5x + 1y = 74/3)\n20x + 20y = 280/3\n20x + 4y = 296/3\nSubtract equations\n16y = -16/3\ny = -16/3/16\ny = -1/3\n\nSubstitute y\n4x + 4(-1/3) = 56/3\n4x = 20\nx = 20/4\nx = 5"} {"input": "Determine x in x^2 + 41/8x - 105/8 = 0", "output": "x^2 + 41/8x - 105/8 = 0\n(x - 15/8)(x - -7) = 0\nx - 15/8 = 0 or x - -7 = 0\nx = 15/8\nx = -7"} {"input": "Solve simultaneously:\n9x + 6y = 387/5\n9x + 9y = 801/10", "output": "9x + 6y = 387/5\n9x + 9y = 801/10\n\nUsing elimination\n9*(9x + 6y = 387/5)\n9*(9x + 9y = 801/10)\n81x + 54y = 3483/5\n81x + 81y = 7209/10\nSubtract equations\n-27y = -243/10\ny = -243/10/-27\ny = 9/10\n\nSubstitute y\n9x + 6(9/10) = 387/5\n9x = 72\nx = 72/9\nx = 8"} {"input": "Solve quickly: 9x + 72/5 = 0", "output": "9x + 72/5 = 0\n9x = -72/5\nx = -72/5 / 9\nx = -8/5"} {"input": "Find x for x^2 + 22/3x + 19/3 = 0", "output": "x^2 + 22/3x + 19/3 = 0\n(x - -1)(x - -19/3) = 0\nx - -1 = 0 or x - -19/3 = 0\nx = -1\nx = -19/3"} {"input": "Find x in x^2 + 76/45x - 1/5 = 0", "output": "x^2 + 76/45x - 1/5 = 0\n(x - -9/5)(x - 1/9) = 0\nx - -9/5 = 0 or x - 1/9 = 0\nx = -9/5\nx = 1/9"} {"input": "What value of x satisfies x^3 - 21/2x^2 + 67/2x - 30 = 0", "output": "x^3 - 21/2x^2 + 67/2x - 30 = 0\n(x - 3/2)(x - 5)(x - 4) = 0\nx - 3/2 = 0\nx - 5 = 0\nx - 4 = 0\nx = 3/2\nx = 5\nx = 4"} {"input": "What value of x satisfies 4x + 38/3 = 0", "output": "4x + 38/3 = 0\n4x = -38/3\nx = -38/3 / 4\nx = -19/6"} {"input": "Solve the equation 10x - 10 = 0", "output": "10x - 10 = 0\n10x = 10\nx = 10 / 10\nx = 1"} {"input": "Determine x in 9x + 6 = 0", "output": "9x + 6 = 0\n9x = -6\nx = -6 / 9\nx = -2/3"} {"input": "Solve quickly: 2x - 19/3 = 0", "output": "2x - 19/3 = 0\n2x = 19/3\nx = 19/3 / 2\nx = 19/6"} {"input": "Solve the system:\n7x + 5y = -313/6\n9x + 9y = -123/2", "output": "7x + 5y = -313/6\n9x + 9y = -123/2\n\nUsing elimination\n9*(7x + 5y = -313/6)\n7*(9x + 9y = -123/2)\n63x + 45y = -939/2\n63x + 63y = -861/2\nSubtract equations\n-18y = -39\ny = -39/-18\ny = 13/6\n\nSubstitute y\n7x + 5(13/6) = -313/6\n7x = -63\nx = -63/7\nx = -9"} {"input": "Solve quickly: 5x + 55/7 = 0", "output": "5x + 55/7 = 0\n5x = -55/7\nx = -55/7 / 5\nx = -11/7"} {"input": "Solve the system:\n10x + 6y = 230/3\n8x + 9y = 247/3", "output": "10x + 6y = 230/3\n8x + 9y = 247/3\n\nUsing elimination\n8*(10x + 6y = 230/3)\n10*(8x + 9y = 247/3)\n80x + 48y = 1840/3\n80x + 90y = 2470/3\nSubtract equations\n-42y = -210\ny = -210/-42\ny = 5\n\nSubstitute y\n10x + 6(5) = 230/3\n10x = 140/3\nx = 140/3/10\nx = 14/3"} {"input": "Compute the solution of 4x + 4/9 = 0", "output": "4x + 4/9 = 0\n4x = -4/9\nx = -4/9 / 4\nx = -1/9"} {"input": "Find the solution to 3x + 57 = 0", "output": "3x + 57 = 0\n3x = -57\nx = -57 / 3\nx = -19"} {"input": "Determine x in x^2 - 1x - 11/100 = 0", "output": "x^2 - 1x - 11/100 = 0\n(x - 11/10)(x - -1/10) = 0\nx - 11/10 = 0 or x - -1/10 = 0\nx = 11/10\nx = -1/10"} {"input": "Find x in x^3 - 77/6x^2 + 35/2x + 325/3 = 0", "output": "x^3 - 77/6x^2 + 35/2x + 325/3 = 0\n(x - 10)(x - 5)(x - -13/6) = 0\nx - 10 = 0\nx - 5 = 0\nx - -13/6 = 0\nx = 10\nx = 5\nx = -13/6"} {"input": "Compute the solution of x^2 - 89/18x + 2 = 0", "output": "x^2 - 89/18x + 2 = 0\n(x - 4/9)(x - 9/2) = 0\nx - 4/9 = 0 or x - 9/2 = 0\nx = 4/9\nx = 9/2"} {"input": "Determine x in x^2 - 16 = 0", "output": "x^2 - 16 = 0\n(x - 4)(x - -4) = 0\nx - 4 = 0 or x - -4 = 0\nx = 4\nx = -4"} {"input": "Compute the solution of x^2 + 3x + 2 = 0", "output": "x^2 + 3x + 2 = 0\n(x - -2)(x - -1) = 0\nx - -2 = 0 or x - -1 = 0\nx = -2\nx = -1"} {"input": "Determine x in x^2 + 11/4x - 39/2 = 0", "output": "x^2 + 11/4x - 39/2 = 0\n(x - 13/4)(x - -6) = 0\nx - 13/4 = 0 or x - -6 = 0\nx = 13/4\nx = -6"} {"input": "Find the solution to 7x + 2 = 0", "output": "7x + 2 = 0\n7x = -2\nx = -2 / 7\nx = -2/7"} {"input": "Find x in x^3 - 11/42x^2 - 5/2x + 25/21 = 0", "output": "x^3 - 11/42x^2 - 5/2x + 25/21 = 0\n(x - 1/2)(x - 10/7)(x - -5/3) = 0\nx - 1/2 = 0\nx - 10/7 = 0\nx - -5/3 = 0\nx = 1/2\nx = 10/7\nx = -5/3"} {"input": "Solve quickly: x^2 - 27/4x + 19/2 = 0", "output": "x^2 - 27/4x + 19/2 = 0\n(x - 19/4)(x - 2) = 0\nx - 19/4 = 0 or x - 2 = 0\nx = 19/4\nx = 2"} {"input": "Find x for x^3 - 47/12x^2 + 19/24x + 11/24 = 0", "output": "x^3 - 47/12x^2 + 19/24x + 11/24 = 0\n(x - 11/3)(x - 1/2)(x - -1/4) = 0\nx - 11/3 = 0\nx - 1/2 = 0\nx - -1/4 = 0\nx = 11/3\nx = 1/2\nx = -1/4"} {"input": "Determine x in x^2 - 67/18x + 10/3 = 0", "output": "x^2 - 67/18x + 10/3 = 0\n(x - 3/2)(x - 20/9) = 0\nx - 3/2 = 0 or x - 20/9 = 0\nx = 3/2\nx = 20/9"} {"input": "Find x and y such that\n5x + 4y = 19\n10x + 10y = 42", "output": "5x + 4y = 19\n10x + 10y = 42\n\nUsing elimination\n10*(5x + 4y = 19)\n5*(10x + 10y = 42)\n50x + 40y = 190\n50x + 50y = 210\nSubtract equations\n-10y = -20\ny = -20/-10\ny = 2\n\nSubstitute y\n5x + 4(2) = 19\n5x = 11\nx = 11/5\nx = 11/5"} {"input": "Find x in x^3 + 13/2x^2 + 1/2x - 35 = 0", "output": "x^3 + 13/2x^2 + 1/2x - 35 = 0\n(x - -5)(x - 2)(x - -7/2) = 0\nx - -5 = 0\nx - 2 = 0\nx - -7/2 = 0\nx = -5\nx = 2\nx = -7/2"} {"input": "Determine x in 10x + 13 = 0", "output": "10x + 13 = 0\n10x = -13\nx = -13 / 10\nx = -13/10"} {"input": "Solve quickly: x^3 + 106/15x^2 + 312/25x + 448/75 = 0", "output": "x^3 + 106/15x^2 + 312/25x + 448/75 = 0\n(x - -8/5)(x - -14/3)(x - -4/5) = 0\nx - -8/5 = 0\nx - -14/3 = 0\nx - -4/5 = 0\nx = -8/5\nx = -14/3\nx = -4/5"} {"input": "Compute the solution of 3x - 17 = 0", "output": "3x - 17 = 0\n3x = 17\nx = 17 / 3\nx = 17/3"} {"input": "Compute the solution of 1x + 13/6 = 0", "output": "1x + 13/6 = 0\n1x = -13/6\nx = -13/6 / 1\nx = -13/6"} {"input": "Find x in x^3 + 33/14x^2 - 731/350x - 66/35 = 0", "output": "x^3 + 33/14x^2 - 731/350x - 66/35 = 0\n(x - -20/7)(x - -3/5)(x - 11/10) = 0\nx - -20/7 = 0\nx - -3/5 = 0\nx - 11/10 = 0\nx = -20/7\nx = -3/5\nx = 11/10"} {"input": "Find x for x^3 - 17/3x^2 - 249x - 247/3 = 0", "output": "x^3 - 17/3x^2 - 249x - 247/3 = 0\n(x - -13)(x - 19)(x - -1/3) = 0\nx - -13 = 0\nx - 19 = 0\nx - -1/3 = 0\nx = -13\nx = 19\nx = -1/3"} {"input": "Solve the equations:\n9x + 6y = 126\n8x + 7y = 112", "output": "9x + 6y = 126\n8x + 7y = 112\n\nUsing elimination\n8*(9x + 6y = 126)\n9*(8x + 7y = 112)\n72x + 48y = 1008\n72x + 63y = 1008\nSubtract equations\n-15y = 0\ny = 0/-15\ny = 0\n\nSubstitute y\n9x + 6(0) = 126\n9x = 126\nx = 126/9\nx = 14"} {"input": "Find the solution to 3x + 24/5 = 0", "output": "3x + 24/5 = 0\n3x = -24/5\nx = -24/5 / 3\nx = -8/5"} {"input": "Find x in 6x - 39 = 0", "output": "6x - 39 = 0\n6x = 39\nx = 39 / 6\nx = 13/2"} {"input": "Find x and y such that\n5x + 1y = -14/9\n10x + 10y = -340/9", "output": "5x + 1y = -14/9\n10x + 10y = -340/9\n\nUsing elimination\n10*(5x + 1y = -14/9)\n5*(10x + 10y = -340/9)\n50x + 10y = -140/9\n50x + 50y = -1700/9\nSubtract equations\n-40y = 520/3\ny = 520/3/-40\ny = -13/3\n\nSubstitute y\n5x + 1(-13/3) = -14/9\n5x = 25/9\nx = 25/9/5\nx = 5/9"} {"input": "Solve the equations:\n1x + 10y = -22\n7x + 9y = -221/5", "output": "1x + 10y = -22\n7x + 9y = -221/5\n\nUsing elimination\n7*(1x + 10y = -22)\n1*(7x + 9y = -221/5)\n7x + 70y = -154\n7x + 9y = -221/5\nSubtract equations\n61y = -549/5\ny = -549/5/61\ny = -9/5\n\nSubstitute y\n1x + 10(-9/5) = -22\n1x = -4\nx = -4/1\nx = -4"} {"input": "Solve the equations:\n3x + 3y = -15/2\n9x + 5y = -69/2", "output": "3x + 3y = -15/2\n9x + 5y = -69/2\n\nUsing elimination\n9*(3x + 3y = -15/2)\n3*(9x + 5y = -69/2)\n27x + 27y = -135/2\n27x + 15y = -207/2\nSubtract equations\n12y = 36\ny = 36/12\ny = 3\n\nSubstitute y\n3x + 3(3) = -15/2\n3x = -33/2\nx = -33/2/3\nx = -11/2"} {"input": "Solve the equation x^3 - 7/3x^2 - 20/3x = 0", "output": "x^3 - 7/3x^2 - 20/3x = 0\n(x - 4)(x - -5/3)(x - 0) = 0\nx - 4 = 0\nx - -5/3 = 0\nx - 0 = 0\nx = 4\nx = -5/3\nx = 0"} {"input": "Solve the equation x^2 + 63/4x - 4 = 0", "output": "x^2 + 63/4x - 4 = 0\n(x - 1/4)(x - -16) = 0\nx - 1/4 = 0 or x - -16 = 0\nx = 1/4\nx = -16"} {"input": "Determine x in x^2 + 19/10x = 0", "output": "x^2 + 19/10x = 0\n(x - 0)(x - -19/10) = 0\nx - 0 = 0 or x - -19/10 = 0\nx = 0\nx = -19/10"} {"input": "Solve x^3 + 147/20x^2 - 128/5x + 9 = 0", "output": "x^3 + 147/20x^2 - 128/5x + 9 = 0\n(x - 2/5)(x - -10)(x - 9/4) = 0\nx - 2/5 = 0\nx - -10 = 0\nx - 9/4 = 0\nx = 2/5\nx = -10\nx = 9/4"} {"input": "Solve the system:\n2x + 9y = 0\n4x + 2y = 0", "output": "2x + 9y = 0\n4x + 2y = 0\n\nUsing elimination\n4*(2x + 9y = 0)\n2*(4x + 2y = 0)\n8x + 36y = 0\n8x + 4y = 0\nSubtract equations\n32y = 0\ny = 0/32\ny = 0\n\nSubstitute y\n2x + 9(0) = 0\n2x = 0\nx = 0/2\nx = 0"} {"input": "Solve the equation x^3 + 8x^2 + 13x + 6 = 0", "output": "x^3 + 8x^2 + 13x + 6 = 0\n(x - -1)(x - -6)(x - -1) = 0\nx - -1 = 0\nx - -6 = 0\nx - -1 = 0\nx = -1\nx = -6\nx = -1"} {"input": "Solve the equation 1x - 1/3 = 0", "output": "1x - 1/3 = 0\n1x = 1/3\nx = 1/3 / 1\nx = 1/3"} {"input": "Solve x^2 - 324/49 = 0", "output": "x^2 - 324/49 = 0\n(x - -18/7)(x - 18/7) = 0\nx - -18/7 = 0 or x - 18/7 = 0\nx = -18/7\nx = 18/7"} {"input": "Compute the solution of 9x + 9/4 = 0", "output": "9x + 9/4 = 0\n9x = -9/4\nx = -9/4 / 9\nx = -1/4"} {"input": "Find the solution to x^2 + 53/36x - 5/3 = 0", "output": "x^2 + 53/36x - 5/3 = 0\n(x - 3/4)(x - -20/9) = 0\nx - 3/4 = 0 or x - -20/9 = 0\nx = 3/4\nx = -20/9"} {"input": "Determine x in x^2 + 13/3x - 42 = 0", "output": "x^2 + 13/3x - 42 = 0\n(x - 14/3)(x - -9) = 0\nx - 14/3 = 0 or x - -9 = 0\nx = 14/3\nx = -9"} {"input": "Solve the equation x^2 + 13/18x - 7/6 = 0", "output": "x^2 + 13/18x - 7/6 = 0\n(x - -3/2)(x - 7/9) = 0\nx - -3/2 = 0 or x - 7/9 = 0\nx = -3/2\nx = 7/9"} {"input": "Compute the solution of x^3 + 1/3x^2 - 110/3x - 200/3 = 0", "output": "x^3 + 1/3x^2 - 110/3x - 200/3 = 0\n(x - -2)(x - 20/3)(x - -5) = 0\nx - -2 = 0\nx - 20/3 = 0\nx - -5 = 0\nx = -2\nx = 20/3\nx = -5"} {"input": "Find x for 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Compute the solution of 2x + 6 = 0", "output": "2x + 6 = 0\n2x = -6\nx = -6 / 2\nx = -3"} {"input": "Solve quickly: x^2 + 1/4x - 95/4 = 0", "output": "x^2 + 1/4x - 95/4 = 0\n(x - -5)(x - 19/4) = 0\nx - -5 = 0 or x - 19/4 = 0\nx = -5\nx = 19/4"} {"input": "Find the solution to x^3 + 53/6x^2 - 71/2x + 30 = 0", "output": "x^3 + 53/6x^2 - 71/2x + 30 = 0\n(x - 3/2)(x - 5/3)(x - -12) = 0\nx - 3/2 = 0\nx - 5/3 = 0\nx - -12 = 0\nx = 3/2\nx = 5/3\nx = -12"} {"input": "Find the solution to x^2 + 29/90x + 1/45 = 0", "output": "x^2 + 29/90x + 1/45 = 0\n(x - -2/9)(x - -1/10) = 0\nx - -2/9 = 0 or x - -1/10 = 0\nx = -2/9\nx = -1/10"} {"input": "Solve quickly: 2x + 16 = 0", "output": "2x + 16 = 0\n2x = -16\nx = -16 / 2\nx = -8"} {"input": "Solve the system:\n1x + 7y = -29/10\n10x + 3y = -11/5", "output": "1x + 7y = -29/10\n10x + 3y = -11/5\n\nUsing elimination\n10*(1x + 7y = -29/10)\n1*(10x + 3y = -11/5)\n10x + 70y = -29\n10x + 3y = -11/5\nSubtract equations\n67y = -134/5\ny = -134/5/67\ny = -2/5\n\nSubstitute y\n1x + 7(-2/5) = -29/10\n1x = -1/10\nx = -1/10/1\nx = -1/10"} {"input": "Solve the equations:\n9x + 2y = -909/14\n10x + 2y = -507/7", "output": "9x + 2y = -909/14\n10x + 2y = -507/7\n\nUsing elimination\n10*(9x + 2y = -909/14)\n9*(10x + 2y = -507/7)\n90x + 20y = -4545/7\n90x + 18y = -4563/7\nSubtract equations\n2y = 18/7\ny = 18/7/2\ny = 9/7\n\nSubstitute y\n9x + 2(9/7) = -909/14\n9x = -135/2\nx = -135/2/9\nx = -15/2"} {"input": "Solve the equation x^2 - 68/45x - 32/15 = 0", "output": "x^2 - 68/45x - 32/15 = 0\n(x - -8/9)(x - 12/5) = 0\nx - -8/9 = 0 or x - 12/5 = 0\nx = -8/9\nx = 12/5"} {"input": "What value of x satisfies x^2 + 30/7x + 27/7 = 0", "output": "x^2 + 30/7x + 27/7 = 0\n(x - -9/7)(x - -3) = 0\nx - -9/7 = 0 or x - -3 = 0\nx = -9/7\nx = -3"} {"input": "Compute the solution of 10x - 100/9 = 0", "output": "10x - 100/9 = 0\n10x = 100/9\nx = 100/9 / 10\nx = 10/9"} {"input": "Solve simultaneously:\n7x + 9y = -841/30\n6x + 7y = -231/10", "output": "7x + 9y = -841/30\n6x + 7y = -231/10\n\nUsing elimination\n6*(7x + 9y = -841/30)\n7*(6x + 7y = -231/10)\n42x + 54y = -841/5\n42x + 49y = -1617/10\nSubtract equations\n5y = -13/2\ny = -13/2/5\ny = -13/10\n\nSubstitute y\n7x + 9(-13/10) = -841/30\n7x = -49/3\nx = -49/3/7\nx = -7/3"} {"input": "Solve the system:\n3x + 5y = -23/4\n2x + 7y = -41/4", "output": "3x + 5y = -23/4\n2x + 7y = -41/4\n\nUsing elimination\n2*(3x + 5y = -23/4)\n3*(2x + 7y = -41/4)\n6x + 10y = -23/2\n6x + 21y = -123/4\nSubtract equations\n-11y = 77/4\ny = 77/4/-11\ny = -7/4\n\nSubstitute y\n3x + 5(-7/4) = -23/4\n3x = 3\nx = 3/3\nx = 1"} {"input": "Solve quickly: x^2 - 25/6x + 34/9 = 0", "output": "x^2 - 25/6x + 34/9 = 0\n(x - 17/6)(x - 4/3) = 0\nx - 17/6 = 0 or x - 4/3 = 0\nx = 17/6\nx = 4/3"} {"input": "Find the solution to 8x - 16/3 = 0", "output": "8x - 16/3 = 0\n8x = 16/3\nx = 16/3 / 8\nx = 2/3"} {"input": "Determine x in x^2 + 7x - 8 = 0", "output": "x^2 + 7x - 8 = 0\n(x - 1)(x - -8) = 0\nx - 1 = 0 or x - -8 = 0\nx = 1\nx = -8"} {"input": "Solve quickly: x^3 - 71/14x^2 + 7x - 33/14 = 0", "output": "x^3 - 71/14x^2 + 7x - 33/14 = 0\n(x - 3)(x - 11/7)(x - 1/2) = 0\nx - 3 = 0\nx - 11/7 = 0\nx - 1/2 = 0\nx = 3\nx = 11/7\nx = 1/2"} {"input": "Solve simultaneously:\n9x + 3y = 68/7\n8x + 3y = 55/7", "output": "9x + 3y = 68/7\n8x + 3y = 55/7\n\nUsing elimination\n8*(9x + 3y = 68/7)\n9*(8x + 3y = 55/7)\n72x + 24y = 544/7\n72x + 27y = 495/7\nSubtract equations\n-3y = 7\ny = 7/-3\ny = -7/3\n\nSubstitute y\n9x + 3(-7/3) = 68/7\n9x = 117/7\nx = 117/7/9\nx = 13/7"} {"input": "Solve the system:\n1x + 5y = -713/56\n4x + 10y = -761/28", "output": "1x + 5y = -713/56\n4x + 10y = -761/28\n\nUsing elimination\n4*(1x + 5y = -713/56)\n1*(4x + 10y = -761/28)\n4x + 20y = -713/14\n4x + 10y = -761/28\nSubtract equations\n10y = -95/4\ny = -95/4/10\ny = -19/8\n\nSubstitute y\n1x + 5(-19/8) = -713/56\n1x = -6/7\nx = -6/7/1\nx = -6/7"} {"input": "What value of x satisfies 10x + 20 = 0", "output": "10x + 20 = 0\n10x = -20\nx = -20 / 10\nx = -2"} {"input": "Find x and y such that\n6x + 1y = 67/3\n4x + 7y = 17", "output": "6x + 1y = 67/3\n4x + 7y = 17\n\nUsing elimination\n4*(6x + 1y = 67/3)\n6*(4x + 7y = 17)\n24x + 4y = 268/3\n24x + 42y = 102\nSubtract equations\n-38y = -38/3\ny = -38/3/-38\ny = 1/3\n\nSubstitute y\n6x + 1(1/3) = 67/3\n6x = 22\nx = 22/6\nx = 11/3"} {"input": "Find the solution to x^3 + 97/35x^2 - 158/35x - 352/35 = 0", "output": "x^3 + 97/35x^2 - 158/35x - 352/35 = 0\n(x - -16/5)(x - -11/7)(x - 2) = 0\nx - -16/5 = 0\nx - -11/7 = 0\nx - 2 = 0\nx = -16/5\nx = -11/7\nx = 2"} {"input": "Solve simultaneously:\n7x + 4y = -8/9\n1x + 4y = 76/9", "output": "7x + 4y = -8/9\n1x + 4y = 76/9\n\nUsing elimination\n1*(7x + 4y = -8/9)\n7*(1x + 4y = 76/9)\n7x + 4y = -8/9\n7x + 28y = 532/9\nSubtract equations\n-24y = -60\ny = -60/-24\ny = 5/2\n\nSubstitute y\n7x + 4(5/2) = -8/9\n7x = -98/9\nx = -98/9/7\nx = -14/9"} {"input": "Solve the equations:\n4x + 6y = 1/3\n6x + 10y = 2", "output": "4x + 6y = 1/3\n6x + 10y = 2\n\nUsing elimination\n6*(4x + 6y = 1/3)\n4*(6x + 10y = 2)\n24x + 36y = 2\n24x + 40y = 8\nSubtract equations\n-4y = -6\ny = -6/-4\ny = 3/2\n\nSubstitute y\n4x + 6(3/2) = 1/3\n4x = -26/3\nx = -26/3/4\nx = -13/6"} {"input": "Solve the equations:\n9x + 10y = -180\n1x + 7y = -325/3", "output": "9x + 10y = -180\n1x + 7y = -325/3\n\nUsing elimination\n1*(9x + 10y = -180)\n9*(1x + 7y = -325/3)\n9x + 10y = -180\n9x + 63y = -975\nSubtract equations\n-53y = 795\ny = 795/-53\ny = -15\n\nSubstitute y\n9x + 10(-15) = -180\n9x = -30\nx = -30/9\nx = -10/3"} {"input": "Solve the equation x^2 + 11/10x - 7/2 = 0", "output": "x^2 + 11/10x - 7/2 = 0\n(x - 7/5)(x - -5/2) = 0\nx - 7/5 = 0 or x - -5/2 = 0\nx = 7/5\nx = -5/2"} {"input": "Solve the equation x^3 - 53/28x^2 + 6/7x = 0", "output": "x^3 - 53/28x^2 + 6/7x = 0\n(x - 3/4)(x - 0)(x - 8/7) = 0\nx - 3/4 = 0\nx - 0 = 0\nx - 8/7 = 0\nx = 3/4\nx = 0\nx = 8/7"} {"input": "Determine x in x^2 - 19x = 0", "output": "x^2 - 19x = 0\n(x - 19)(x - 0) = 0\nx - 19 = 0 or x - 0 = 0\nx = 19\nx = 0"} {"input": "Solve x^2 - 12/5x + 27/20 = 0", "output": "x^2 - 12/5x + 27/20 = 0\n(x - 9/10)(x - 3/2) = 0\nx - 9/10 = 0 or x - 3/2 = 0\nx = 9/10\nx = 3/2"} {"input": "Solve the system:\n1x + 7y = 11/6\n7x + 2y = -32/3", "output": "1x + 7y = 11/6\n7x + 2y = -32/3\n\nUsing elimination\n7*(1x + 7y = 11/6)\n1*(7x + 2y = -32/3)\n7x + 49y = 77/6\n7x + 2y = -32/3\nSubtract equations\n47y = 47/2\ny = 47/2/47\ny = 1/2\n\nSubstitute y\n1x + 7(1/2) = 11/6\n1x = -5/3\nx = -5/3/1\nx = -5/3"} {"input": "Find x and y such that\n3x + 7y = -808/45\n8x + 9y = -132/5", "output": "3x + 7y = -808/45\n8x + 9y = -132/5\n\nUsing elimination\n8*(3x + 7y = -808/45)\n3*(8x + 9y = -132/5)\n24x + 56y = -6464/45\n24x + 27y = -396/5\nSubtract equations\n29y = -580/9\ny = -580/9/29\ny = -20/9\n\nSubstitute y\n3x + 7(-20/9) = -808/45\n3x = -12/5\nx = -12/5/3\nx = -4/5"} {"input": "Find x for 2x - 10 = 0", "output": "2x - 10 = 0\n2x = 10\nx = 10 / 2\nx = 5"} {"input": "Compute the solution of x^2 + 18x - 19 = 0", "output": "x^2 + 18x - 19 = 0\n(x - -19)(x - 1) = 0\nx - -19 = 0 or x - 1 = 0\nx = -19\nx = 1"} {"input": "Solve x^2 - 7/9x - 2/9 = 0", "output": "x^2 - 7/9x - 2/9 = 0\n(x - 1)(x - -2/9) = 0\nx - 1 = 0 or x - -2/9 = 0\nx = 1\nx = -2/9"} {"input": "Find x in 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Solve 1x - 1/2 = 0", "output": "1x - 1/2 = 0\n1x = 1/2\nx = 1/2 / 1\nx = 1/2"} {"input": "Solve the equation 6x - 20 = 0", "output": "6x - 20 = 0\n6x = 20\nx = 20 / 6\nx = 10/3"} {"input": "Compute the solution of 4x + 12 = 0", "output": "4x + 12 = 0\n4x = -12\nx = -12 / 4\nx = -3"} {"input": "Compute the solution of 3x - 60/7 = 0", "output": "3x - 60/7 = 0\n3x = 60/7\nx = 60/7 / 3\nx = 20/7"} {"input": "Compute the solution of x^2 + 145/21x + 76/21 = 0", "output": "x^2 + 145/21x + 76/21 = 0\n(x - -19/3)(x - -4/7) = 0\nx - -19/3 = 0 or x - -4/7 = 0\nx = -19/3\nx = -4/7"} {"input": "Solve the equation 8x + 64/5 = 0", "output": "8x + 64/5 = 0\n8x = -64/5\nx = -64/5 / 8\nx = -8/5"} {"input": "Solve simultaneously:\n7x + 5y = 10\n5x + 3y = 8", "output": "7x + 5y = 10\n5x + 3y = 8\n\nUsing elimination\n5*(7x + 5y = 10)\n7*(5x + 3y = 8)\n35x + 25y = 50\n35x + 21y = 56\nSubtract equations\n4y = -6\ny = -6/4\ny = -3/2\n\nSubstitute y\n7x + 5(-3/2) = 10\n7x = 35/2\nx = 35/2/7\nx = 5/2"} {"input": "Solve x^3 + 107/40x^2 + 173/400x - 133/200 = 0", "output": "x^3 + 107/40x^2 + 173/400x - 133/200 = 0\n(x - 2/5)(x - -19/8)(x - -7/10) = 0\nx - 2/5 = 0\nx - -19/8 = 0\nx - -7/10 = 0\nx = 2/5\nx = -19/8\nx = -7/10"} {"input": "Find the solution to x^3 + 199/21x^2 - 92/3x - 32/7 = 0", "output": "x^3 + 199/21x^2 - 92/3x - 32/7 = 0\n(x - 8/3)(x - -12)(x - -1/7) = 0\nx - 8/3 = 0\nx - -12 = 0\nx - -1/7 = 0\nx = 8/3\nx = -12\nx = -1/7"} {"input": "Solve x^3 + 169/70x^2 - 187/50x - 1482/175 = 0", "output": "x^3 + 169/70x^2 - 187/50x - 1482/175 = 0\n(x - -12/7)(x - 19/10)(x - -13/5) = 0\nx - -12/7 = 0\nx - 19/10 = 0\nx - -13/5 = 0\nx = -12/7\nx = 19/10\nx = -13/5"} {"input": "Solve quickly: x^2 - 1x - 285/16 = 0", "output": "x^2 - 1x - 285/16 = 0\n(x - 19/4)(x - -15/4) = 0\nx - 19/4 = 0 or x - -15/4 = 0\nx = 19/4\nx = -15/4"} {"input": "Solve the equation 3x - 15/4 = 0", "output": "3x - 15/4 = 0\n3x = 15/4\nx = 15/4 / 3\nx = 5/4"} {"input": "Compute the solution of 7x - 70/3 = 0", "output": "7x - 70/3 = 0\n7x = 70/3\nx = 70/3 / 7\nx = 10/3"} {"input": "Solve quickly: x^3 - 10/63x^2 - 43/63x - 10/63 = 0", "output": "x^3 - 10/63x^2 - 43/63x - 10/63 = 0\n(x - -5/9)(x - 1)(x - -2/7) = 0\nx - -5/9 = 0\nx - 1 = 0\nx - -2/7 = 0\nx = -5/9\nx = 1\nx = -2/7"} {"input": "Compute the solution of 1x + 1/2 = 0", "output": "1x + 1/2 = 0\n1x = -1/2\nx = -1/2 / 1\nx = -1/2"} {"input": "Determine x in x^2 + 7x + 20/9 = 0", "output": "x^2 + 7x + 20/9 = 0\n(x - -20/3)(x - -1/3) = 0\nx - -20/3 = 0 or x - -1/3 = 0\nx = -20/3\nx = -1/3"} {"input": "Find x in 8x + 12 = 0", "output": "8x + 12 = 0\n8x = -12\nx = -12 / 8\nx = -3/2"} {"input": "Find x and y such that\n7x + 5y = 6\n3x + 7y = 42/5", "output": "7x + 5y = 6\n3x + 7y = 42/5\n\nUsing elimination\n3*(7x + 5y = 6)\n7*(3x + 7y = 42/5)\n21x + 15y = 18\n21x + 49y = 294/5\nSubtract equations\n-34y = -204/5\ny = -204/5/-34\ny = 6/5\n\nSubstitute y\n7x + 5(6/5) = 6\n7x = 0\nx = 0/7\nx = 0"} {"input": "What value of x satisfies x^3 + 20/3x^2 - 17/3x - 70/3 = 0", "output": "x^3 + 20/3x^2 - 17/3x - 70/3 = 0\n(x - -5/3)(x - -7)(x - 2) = 0\nx - -5/3 = 0\nx - -7 = 0\nx - 2 = 0\nx = -5/3\nx = -7\nx = 2"} {"input": "Determine x in 9x - 81/4 = 0", "output": "9x - 81/4 = 0\n9x = 81/4\nx = 81/4 / 9\nx = 9/4"} {"input": "Compute the solution of x^3 - 71/21x^2 + 87/28x - 3/7 = 0", "output": "x^3 - 71/21x^2 + 87/28x - 3/7 = 0\n(x - 12/7)(x - 3/2)(x - 1/6) = 0\nx - 12/7 = 0\nx - 3/2 = 0\nx - 1/6 = 0\nx = 12/7\nx = 3/2\nx = 1/6"} {"input": "Find the solution to 3x - 2 = 0", "output": "3x - 2 = 0\n3x = 2\nx = 2 / 3\nx = 2/3"} {"input": "Find the solution to x^3 - 68/35x^2 + 47/700x + 19/700 = 0", "output": "x^3 - 68/35x^2 + 47/700x + 19/700 = 0\n(x - 19/10)(x - 1/7)(x - -1/10) = 0\nx - 19/10 = 0\nx - 1/7 = 0\nx - -1/10 = 0\nx = 19/10\nx = 1/7\nx = -1/10"} {"input": "Solve the equation 10x + 65/3 = 0", "output": "10x + 65/3 = 0\n10x = -65/3\nx = -65/3 / 10\nx = -13/6"} {"input": "Find the solution to x^2 + 7/3x - 8/9 = 0", "output": "x^2 + 7/3x - 8/9 = 0\n(x - -8/3)(x - 1/3) = 0\nx - -8/3 = 0 or x - 1/3 = 0\nx = -8/3\nx = 1/3"} {"input": "Solve simultaneously:\n5x + 4y = 7\n1x + 1y = 1", "output": "5x + 4y = 7\n1x + 1y = 1\n\nUsing elimination\n1*(5x + 4y = 7)\n5*(1x + 1y = 1)\n5x + 4y = 7\n5x + 5y = 5\nSubtract equations\n-1y = 2\ny = 2/-1\ny = -2\n\nSubstitute y\n5x + 4(-2) = 7\n5x = 15\nx = 15/5\nx = 3"} {"input": "Compute the solution of x^2 + 31/15x + 14/15 = 0", "output": "x^2 + 31/15x + 14/15 = 0\n(x - -2/3)(x - -7/5) = 0\nx - -2/3 = 0 or x - -7/5 = 0\nx = -2/3\nx = -7/5"} {"input": "Solve simultaneously:\n4x + 8y = -472/5\n8x + 7y = -494/5", "output": "4x + 8y = -472/5\n8x + 7y = -494/5\n\nUsing elimination\n8*(4x + 8y = -472/5)\n4*(8x + 7y = -494/5)\n32x + 64y = -3776/5\n32x + 28y = -1976/5\nSubtract equations\n36y = -360\ny = -360/36\ny = -10\n\nSubstitute y\n4x + 8(-10) = -472/5\n4x = -72/5\nx = -72/5/4\nx = -18/5"} {"input": "What value of x satisfies 6x + 48 = 0", "output": "6x + 48 = 0\n6x = -48\nx = -48 / 6\nx = -8"} {"input": "Solve simultaneously:\n3x + 2y = -4\n7x + 1y = -61/3", "output": "3x + 2y = -4\n7x + 1y = -61/3\n\nUsing elimination\n7*(3x + 2y = -4)\n3*(7x + 1y = -61/3)\n21x + 14y = -28\n21x + 3y = -61\nSubtract equations\n11y = 33\ny = 33/11\ny = 3\n\nSubstitute y\n3x + 2(3) = -4\n3x = -10\nx = -10/3\nx = -10/3"} {"input": "Find x in x^2 + 1/6x - 19/2 = 0", "output": "x^2 + 1/6x - 19/2 = 0\n(x - 3)(x - -19/6) = 0\nx - 3 = 0 or x - -19/6 = 0\nx = 3\nx = -19/6"} {"input": "Solve the equation x^2 - 5x - 126 = 0", "output": "x^2 - 5x - 126 = 0\n(x - -9)(x - 14) = 0\nx - -9 = 0 or x - 14 = 0\nx = -9\nx = 14"} {"input": "Find x in x^2 - 1/18x - 7/3 = 0", "output": "x^2 - 1/18x - 7/3 = 0\n(x - 14/9)(x - -3/2) = 0\nx - 14/9 = 0 or x - -3/2 = 0\nx = 14/9\nx = -3/2"} {"input": "Solve simultaneously:\n4x + 7y = -59/8\n7x + 7y = -35/8", "output": "4x + 7y = -59/8\n7x + 7y = -35/8\n\nUsing elimination\n7*(4x + 7y = -59/8)\n4*(7x + 7y = -35/8)\n28x + 49y = -413/8\n28x + 28y = -35/2\nSubtract equations\n21y = -273/8\ny = -273/8/21\ny = -13/8\n\nSubstitute y\n4x + 7(-13/8) = -59/8\n4x = 4\nx = 4/4\nx = 1"} {"input": "Compute the solution of 6x - 114 = 0", "output": "6x - 114 = 0\n6x = 114\nx = 114 / 6\nx = 19"} {"input": "Solve the equation 9x + 27/5 = 0", "output": "9x + 27/5 = 0\n9x = -27/5\nx = -27/5 / 9\nx = -3/5"} {"input": "Solve the equation 7x - 56 = 0", "output": "7x - 56 = 0\n7x = 56\nx = 56 / 7\nx = 8"} {"input": "Solve quickly: 4x - 20/3 = 0", "output": "4x - 20/3 = 0\n4x = 20/3\nx = 20/3 / 4\nx = 5/3"} {"input": "Find x in x^2 + 119/24x - 2 = 0", "output": "x^2 + 119/24x - 2 = 0\n(x - 3/8)(x - -16/3) = 0\nx - 3/8 = 0 or x - -16/3 = 0\nx = 3/8\nx = -16/3"} {"input": "Compute the solution of x^3 - 17x^2 - 74x + 1440 = 0", "output": "x^3 - 17x^2 - 74x + 1440 = 0\n(x - 16)(x - 10)(x - -9) = 0\nx - 16 = 0\nx - 10 = 0\nx - -9 = 0\nx = 16\nx = 10\nx = -9"} {"input": "Solve quickly: 7x - 49/2 = 0", "output": "7x - 49/2 = 0\n7x = 49/2\nx = 49/2 / 7\nx = 7/2"} {"input": "Compute the solution of x^3 + 562/45x^2 - 33/5x + 26/45 = 0", "output": "x^3 + 562/45x^2 - 33/5x + 26/45 = 0\n(x - -13)(x - 1/9)(x - 2/5) = 0\nx - -13 = 0\nx - 1/9 = 0\nx - 2/5 = 0\nx = -13\nx = 1/9\nx = 2/5"} {"input": "Solve simultaneously:\n3x + 2y = 43/4\n6x + 3y = 45/2", "output": "3x + 2y = 43/4\n6x + 3y = 45/2\n\nUsing elimination\n6*(3x + 2y = 43/4)\n3*(6x + 3y = 45/2)\n18x + 12y = 129/2\n18x + 9y = 135/2\nSubtract equations\n3y = -3\ny = -3/3\ny = -1\n\nSubstitute y\n3x + 2(-1) = 43/4\n3x = 51/4\nx = 51/4/3\nx = 17/4"} {"input": "Compute the solution of 3x + 19/3 = 0", "output": "3x + 19/3 = 0\n3x = -19/3\nx = -19/3 / 3\nx = -19/9"} {"input": "Solve quickly: x^2 - 43/10x + 39/10 = 0", "output": "x^2 - 43/10x + 39/10 = 0\n(x - 3)(x - 13/10) = 0\nx - 3 = 0 or x - 13/10 = 0\nx = 3\nx = 13/10"} {"input": "Find x in x^2 + 47/72x - 55/24 = 0", "output": "x^2 + 47/72x - 55/24 = 0\n(x - -15/8)(x - 11/9) = 0\nx - -15/8 = 0 or x - 11/9 = 0\nx = -15/8\nx = 11/9"} {"input": "Find x for x^3 - 97/12x^2 + 37/2x - 38/3 = 0", "output": "x^3 - 97/12x^2 + 37/2x - 38/3 = 0\n(x - 4/3)(x - 19/4)(x - 2) = 0\nx - 4/3 = 0\nx - 19/4 = 0\nx - 2 = 0\nx = 4/3\nx = 19/4\nx = 2"} {"input": "What value of x satisfies 3x + 6/7 = 0", "output": "3x + 6/7 = 0\n3x = -6/7\nx = -6/7 / 3\nx = -2/7"} {"input": "Solve 1x - 5/4 = 0", "output": "1x - 5/4 = 0\n1x = 5/4\nx = 5/4 / 1\nx = 5/4"} {"input": "What value of x satisfies 4x + 44/3 = 0", "output": "4x + 44/3 = 0\n4x = -44/3\nx = -44/3 / 4\nx = -11/3"} {"input": "Solve the system:\n8x + 10y = 36\n7x + 8y = 57/2", "output": "8x + 10y = 36\n7x + 8y = 57/2\n\nUsing elimination\n7*(8x + 10y = 36)\n8*(7x + 8y = 57/2)\n56x + 70y = 252\n56x + 64y = 228\nSubtract equations\n6y = 24\ny = 24/6\ny = 4\n\nSubstitute y\n8x + 10(4) = 36\n8x = -4\nx = -4/8\nx = -1/2"} {"input": "Solve the equations:\n3x + 7y = -6\n3x + 10y = -6", "output": "3x + 7y = -6\n3x + 10y = -6\n\nUsing elimination\n3*(3x + 7y = -6)\n3*(3x + 10y = -6)\n9x + 21y = -18\n9x + 30y = -18\nSubtract equations\n-9y = 0\ny = 0/-9\ny = 0\n\nSubstitute y\n3x + 7(0) = -6\n3x = -6\nx = -6/3\nx = -2"} {"input": "Find the solution to x^2 + 37/6x - 19/18 = 0", "output": "x^2 + 37/6x - 19/18 = 0\n(x - 1/6)(x - -19/3) = 0\nx - 1/6 = 0 or x - -19/3 = 0\nx = 1/6\nx = -19/3"} {"input": "Solve quickly: x^3 + 55/24x^2 - 107/48x - 5/16 = 0", "output": "x^3 + 55/24x^2 - 107/48x - 5/16 = 0\n(x - -3)(x - -1/8)(x - 5/6) = 0\nx - -3 = 0\nx - -1/8 = 0\nx - 5/6 = 0\nx = -3\nx = -1/8\nx = 5/6"} {"input": "Solve simultaneously:\n10x + 6y = 529/7\n9x + 1y = 367/14", "output": "10x + 6y = 529/7\n9x + 1y = 367/14\n\nUsing elimination\n9*(10x + 6y = 529/7)\n10*(9x + 1y = 367/14)\n90x + 54y = 4761/7\n90x + 10y = 1835/7\nSubtract equations\n44y = 418\ny = 418/44\ny = 19/2\n\nSubstitute y\n10x + 6(19/2) = 529/7\n10x = 130/7\nx = 130/7/10\nx = 13/7"} {"input": "What value of x satisfies 2x - 5 = 0", "output": "2x - 5 = 0\n2x = 5\nx = 5 / 2\nx = 5/2"} {"input": "Find the solution to x^3 + 83/10x^2 - 411/10x + 198/5 = 0", "output": "x^3 + 83/10x^2 - 411/10x + 198/5 = 0\n(x - -12)(x - 3/2)(x - 11/5) = 0\nx - -12 = 0\nx - 3/2 = 0\nx - 11/5 = 0\nx = -12\nx = 3/2\nx = 11/5"} {"input": "Solve 10x - 95/3 = 0", "output": "10x - 95/3 = 0\n10x = 95/3\nx = 95/3 / 10\nx = 19/6"} {"input": "Solve the system:\n10x + 1y = -108\n4x + 8y = -28", "output": "10x + 1y = -108\n4x + 8y = -28\n\nUsing elimination\n4*(10x + 1y = -108)\n10*(4x + 8y = -28)\n40x + 4y = -432\n40x + 80y = -280\nSubtract equations\n-76y = -152\ny = -152/-76\ny = 2\n\nSubstitute y\n10x + 1(2) = -108\n10x = -110\nx = -110/10\nx = -11"} {"input": "Find the solution to 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Find x in x^2 + 141/10x + 7/5 = 0", "output": "x^2 + 141/10x + 7/5 = 0\n(x - -1/10)(x - -14) = 0\nx - -1/10 = 0 or x - -14 = 0\nx = -1/10\nx = -14"} {"input": "Solve x^3 - 344/105x^2 + 368/105x - 128/105 = 0", "output": "x^3 - 344/105x^2 + 368/105x - 128/105 = 0\n(x - 8/7)(x - 4/3)(x - 4/5) = 0\nx - 8/7 = 0\nx - 4/3 = 0\nx - 4/5 = 0\nx = 8/7\nx = 4/3\nx = 4/5"} {"input": "What value of x satisfies 1x + 13/5 = 0", "output": "1x + 13/5 = 0\n1x = -13/5\nx = -13/5 / 1\nx = -13/5"} {"input": "Determine x in x^3 + 61/35x^2 - 1509/140x + 513/70 = 0", "output": "x^3 + 61/35x^2 - 1509/140x + 513/70 = 0\n(x - -9/2)(x - 6/7)(x - 19/10) = 0\nx - -9/2 = 0\nx - 6/7 = 0\nx - 19/10 = 0\nx = -9/2\nx = 6/7\nx = 19/10"} {"input": "Find x in x^2 + 14x - 15 = 0", "output": "x^2 + 14x - 15 = 0\n(x - 1)(x - -15) = 0\nx - 1 = 0 or x - -15 = 0\nx = 1\nx = -15"} {"input": "Compute the solution of x^3 - 305/8x^2 + 793/2x - 680 = 0", "output": "x^3 - 305/8x^2 + 793/2x - 680 = 0\n(x - 20)(x - 16)(x - 17/8) = 0\nx - 20 = 0\nx - 16 = 0\nx - 17/8 = 0\nx = 20\nx = 16\nx = 17/8"} {"input": "Solve simultaneously:\n2x + 5y = -4\n10x + 3y = 2", "output": "2x + 5y = -4\n10x + 3y = 2\n\nUsing elimination\n10*(2x + 5y = -4)\n2*(10x + 3y = 2)\n20x + 50y = -40\n20x + 6y = 4\nSubtract equations\n44y = -44\ny = -44/44\ny = -1\n\nSubstitute y\n2x + 5(-1) = -4\n2x = 1\nx = 1/2\nx = 1/2"} {"input": "Compute the solution of x^3 + 73/20x^2 - 229/10x - 323/4 = 0", "output": "x^3 + 73/20x^2 - 229/10x - 323/4 = 0\n(x - 19/4)(x - -5)(x - -17/5) = 0\nx - 19/4 = 0\nx - -5 = 0\nx - -17/5 = 0\nx = 19/4\nx = -5\nx = -17/5"} {"input": "Solve the system:\n3x + 10y = 73\n2x + 10y = 72", "output": "3x + 10y = 73\n2x + 10y = 72\n\nUsing elimination\n2*(3x + 10y = 73)\n3*(2x + 10y = 72)\n6x + 20y = 146\n6x + 30y = 216\nSubtract equations\n-10y = -70\ny = -70/-10\ny = 7\n\nSubstitute y\n3x + 10(7) = 73\n3x = 3\nx = 3/3\nx = 1"} {"input": "Compute the solution of x^2 + 16x + 63 = 0", "output": "x^2 + 16x + 63 = 0\n(x - -9)(x - -7) = 0\nx - -9 = 0 or x - -7 = 0\nx = -9\nx = -7"} {"input": "Solve quickly: 1x - 1/6 = 0", "output": "1x - 1/6 = 0\n1x = 1/6\nx = 1/6 / 1\nx = 1/6"} {"input": "Compute the solution of 6x - 72/5 = 0", "output": "6x - 72/5 = 0\n6x = 72/5\nx = 72/5 / 6\nx = 12/5"} {"input": "Find the solution to x^2 - 19/45x - 14/15 = 0", "output": "x^2 - 19/45x - 14/15 = 0\n(x - -7/9)(x - 6/5) = 0\nx - -7/9 = 0 or x - 6/5 = 0\nx = -7/9\nx = 6/5"} {"input": "Find x in x^2 + 9/5x + 4/5 = 0", "output": "x^2 + 9/5x + 4/5 = 0\n(x - -4/5)(x - -1) = 0\nx - -4/5 = 0 or x - -1 = 0\nx = -4/5\nx = -1"} {"input": "Find x and y such that\n6x + 10y = -1349/35\n6x + 5y = -874/35", "output": "6x + 10y = -1349/35\n6x + 5y = -874/35\n\nUsing elimination\n6*(6x + 10y = -1349/35)\n6*(6x + 5y = -874/35)\n36x + 60y = -8094/35\n36x + 30y = -5244/35\nSubtract equations\n30y = -570/7\ny = -570/7/30\ny = -19/7\n\nSubstitute y\n6x + 10(-19/7) = -1349/35\n6x = -57/5\nx = -57/5/6\nx = -19/10"} {"input": "Determine x in x^2 - 69/10x + 13/5 = 0", "output": "x^2 - 69/10x + 13/5 = 0\n(x - 2/5)(x - 13/2) = 0\nx - 2/5 = 0 or x - 13/2 = 0\nx = 2/5\nx = 13/2"} {"input": "Find the solution to 2x + 36/7 = 0", "output": "2x + 36/7 = 0\n2x = -36/7\nx = -36/7 / 2\nx = -18/7"} {"input": "Solve the system:\n9x + 4y = 114/5\n6x + 3y = 73/5", "output": "9x + 4y = 114/5\n6x + 3y = 73/5\n\nUsing elimination\n6*(9x + 4y = 114/5)\n9*(6x + 3y = 73/5)\n54x + 24y = 684/5\n54x + 27y = 657/5\nSubtract equations\n-3y = 27/5\ny = 27/5/-3\ny = -9/5\n\nSubstitute y\n9x + 4(-9/5) = 114/5\n9x = 30\nx = 30/9\nx = 10/3"} {"input": "Solve simultaneously:\n3x + 1y = -25/2\n1x + 5y = 1/2", "output": "3x + 1y = -25/2\n1x + 5y = 1/2\n\nUsing elimination\n1*(3x + 1y = -25/2)\n3*(1x + 5y = 1/2)\n3x + 1y = -25/2\n3x + 15y = 3/2\nSubtract equations\n-14y = -14\ny = -14/-14\ny = 1\n\nSubstitute y\n3x + 1(1) = -25/2\n3x = -27/2\nx = -27/2/3\nx = -9/2"} {"input": "Determine x in x^2 + 15x - 54 = 0", "output": "x^2 + 15x - 54 = 0\n(x - 3)(x - -18) = 0\nx - 3 = 0 or x - -18 = 0\nx = 3\nx = -18"} {"input": "Solve the system:\n7x + 6y = -73/9\n4x + 8y = -76/9", "output": "7x + 6y = -73/9\n4x + 8y = -76/9\n\nUsing elimination\n4*(7x + 6y = -73/9)\n7*(4x + 8y = -76/9)\n28x + 24y = -292/9\n28x + 56y = -532/9\nSubtract equations\n-32y = 80/3\ny = 80/3/-32\ny = -5/6\n\nSubstitute y\n7x + 6(-5/6) = -73/9\n7x = -28/9\nx = -28/9/7\nx = -4/9"} {"input": "Solve quickly: x^3 - 31/8x^2 - 59/8x + 35/4 = 0", "output": "x^3 - 31/8x^2 - 59/8x + 35/4 = 0\n(x - -2)(x - 5)(x - 7/8) = 0\nx - -2 = 0\nx - 5 = 0\nx - 7/8 = 0\nx = -2\nx = 5\nx = 7/8"} {"input": "Find x in 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "Find x for x^2 - 27/4x + 9/2 = 0", "output": "x^2 - 27/4x + 9/2 = 0\n(x - 3/4)(x - 6) = 0\nx - 3/4 = 0 or x - 6 = 0\nx = 3/4\nx = 6"} {"input": "Find the solution to x^3 - 26/5x^2 + 63/20x = 0", "output": "x^3 - 26/5x^2 + 63/20x = 0\n(x - 7/10)(x - 0)(x - 9/2) = 0\nx - 7/10 = 0\nx - 0 = 0\nx - 9/2 = 0\nx = 7/10\nx = 0\nx = 9/2"} {"input": "Solve 3x + 57/8 = 0", "output": "3x + 57/8 = 0\n3x = -57/8\nx = -57/8 / 3\nx = -19/8"} {"input": "Compute the solution of x^2 - 13/45x - 14/9 = 0", "output": "x^2 - 13/45x - 14/9 = 0\n(x - -10/9)(x - 7/5) = 0\nx - -10/9 = 0 or x - 7/5 = 0\nx = -10/9\nx = 7/5"} {"input": "Solve the system:\n1x + 4y = 122/5\n5x + 3y = 20", "output": "1x + 4y = 122/5\n5x + 3y = 20\n\nUsing elimination\n5*(1x + 4y = 122/5)\n1*(5x + 3y = 20)\n5x + 20y = 122\n5x + 3y = 20\nSubtract equations\n17y = 102\ny = 102/17\ny = 6\n\nSubstitute y\n1x + 4(6) = 122/5\n1x = 2/5\nx = 2/5/1\nx = 2/5"} {"input": "Solve quickly: 5x - 35/8 = 0", "output": "5x - 35/8 = 0\n5x = 35/8\nx = 35/8 / 5\nx = 7/8"} {"input": "Find the solution to x^3 - 1x^2 - 15/4x + 9/2 = 0", "output": "x^3 - 1x^2 - 15/4x + 9/2 = 0\n(x - -2)(x - 3/2)(x - 3/2) = 0\nx - -2 = 0\nx - 3/2 = 0\nx - 3/2 = 0\nx = -2\nx = 3/2\nx = 3/2"} {"input": "Find x for x^3 - 127/20x^2 + 9/5x + 9/5 = 0", "output": "x^3 - 127/20x^2 + 9/5x + 9/5 = 0\n(x - -2/5)(x - 6)(x - 3/4) = 0\nx - -2/5 = 0\nx - 6 = 0\nx - 3/4 = 0\nx = -2/5\nx = 6\nx = 3/4"} {"input": "Solve x^2 + 11/3x + 10/3 = 0", "output": "x^2 + 11/3x + 10/3 = 0\n(x - -2)(x - -5/3) = 0\nx - -2 = 0 or x - -5/3 = 0\nx = -2\nx = -5/3"} {"input": "Determine x in 3x - 3 = 0", "output": "3x - 3 = 0\n3x = 3\nx = 3 / 3\nx = 1"} {"input": "Solve simultaneously:\n8x + 2y = 328/9\n6x + 2y = 106/3", "output": "8x + 2y = 328/9\n6x + 2y = 106/3\n\nUsing elimination\n6*(8x + 2y = 328/9)\n8*(6x + 2y = 106/3)\n48x + 12y = 656/3\n48x + 16y = 848/3\nSubtract equations\n-4y = -64\ny = -64/-4\ny = 16\n\nSubstitute y\n8x + 2(16) = 328/9\n8x = 40/9\nx = 40/9/8\nx = 5/9"} {"input": "Find the solution to 9x + 153 = 0", "output": "9x + 153 = 0\n9x = -153\nx = -153 / 9\nx = -17"} {"input": "Compute the solution of x^3 - 26/9x^2 - 200/27x + 1600/81 = 0", "output": "x^3 - 26/9x^2 - 200/27x + 1600/81 = 0\n(x - 20/9)(x - 10/3)(x - -8/3) = 0\nx - 20/9 = 0\nx - 10/3 = 0\nx - -8/3 = 0\nx = 20/9\nx = 10/3\nx = -8/3"} {"input": "Solve 5x - 65/3 = 0", "output": "5x - 65/3 = 0\n5x = 65/3\nx = 65/3 / 5\nx = 13/3"} {"input": "Compute the solution of x^2 + 3/4x - 7/4 = 0", "output": "x^2 + 3/4x - 7/4 = 0\n(x - -7/4)(x - 1) = 0\nx - -7/4 = 0 or x - 1 = 0\nx = -7/4\nx = 1"} {"input": "Solve the equation 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "What value of x satisfies 4x - 3 = 0", "output": "4x - 3 = 0\n4x = 3\nx = 3 / 4\nx = 3/4"} {"input": "Find x for 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Solve the equation 3x + 24 = 0", "output": "3x + 24 = 0\n3x = -24\nx = -24 / 3\nx = -8"} {"input": "Solve simultaneously:\n8x + 4y = -184/5\n6x + 8y = -288/5", "output": "8x + 4y = -184/5\n6x + 8y = -288/5\n\nUsing elimination\n6*(8x + 4y = -184/5)\n8*(6x + 8y = -288/5)\n48x + 24y = -1104/5\n48x + 64y = -2304/5\nSubtract equations\n-40y = 240\ny = 240/-40\ny = -6\n\nSubstitute y\n8x + 4(-6) = -184/5\n8x = -64/5\nx = -64/5/8\nx = -8/5"} {"input": "Find x for x^3 - 7/5x^2 - 32/5x + 52/5 = 0", "output": "x^3 - 7/5x^2 - 32/5x + 52/5 = 0\n(x - 2)(x - 2)(x - -13/5) = 0\nx - 2 = 0\nx - 2 = 0\nx - -13/5 = 0\nx = 2\nx = 2\nx = -13/5"} {"input": "Find the solution to x^2 - 12/7x - 27/7 = 0", "output": "x^2 - 12/7x - 27/7 = 0\n(x - 3)(x - -9/7) = 0\nx - 3 = 0 or x - -9/7 = 0\nx = 3\nx = -9/7"} {"input": "What value of x satisfies x^2 - 19/2x + 45/2 = 0", "output": "x^2 - 19/2x + 45/2 = 0\n(x - 9/2)(x - 5) = 0\nx - 9/2 = 0 or x - 5 = 0\nx = 9/2\nx = 5"} {"input": "Solve the system:\n9x + 4y = 349/7\n8x + 4y = 928/21", "output": "9x + 4y = 349/7\n8x + 4y = 928/21\n\nUsing elimination\n8*(9x + 4y = 349/7)\n9*(8x + 4y = 928/21)\n72x + 32y = 2792/7\n72x + 36y = 2784/7\nSubtract equations\n-4y = 8/7\ny = 8/7/-4\ny = -2/7\n\nSubstitute y\n9x + 4(-2/7) = 349/7\n9x = 51\nx = 51/9\nx = 17/3"} {"input": "Find the solution to x^2 + 37/8x + 39/8 = 0", "output": "x^2 + 37/8x + 39/8 = 0\n(x - -13/8)(x - -3) = 0\nx - -13/8 = 0 or x - -3 = 0\nx = -13/8\nx = -3"} {"input": "Solve the equations:\n10x + 1y = -55/3\n9x + 1y = -49/3", "output": "10x + 1y = -55/3\n9x + 1y = -49/3\n\nUsing elimination\n9*(10x + 1y = -55/3)\n10*(9x + 1y = -49/3)\n90x + 9y = -165\n90x + 10y = -490/3\nSubtract equations\n-1y = -5/3\ny = -5/3/-1\ny = 5/3\n\nSubstitute y\n10x + 1(5/3) = -55/3\n10x = -20\nx = -20/10\nx = -2"} {"input": "Find x in 7x - 63/5 = 0", "output": "7x - 63/5 = 0\n7x = 63/5\nx = 63/5 / 7\nx = 9/5"} {"input": "Solve the equations:\n6x + 4y = 145/6\n6x + 10y = 241/6", "output": "6x + 4y = 145/6\n6x + 10y = 241/6\n\nUsing elimination\n6*(6x + 4y = 145/6)\n6*(6x + 10y = 241/6)\n36x + 24y = 145\n36x + 60y = 241\nSubtract equations\n-36y = -96\ny = -96/-36\ny = 8/3\n\nSubstitute y\n6x + 4(8/3) = 145/6\n6x = 27/2\nx = 27/2/6\nx = 9/4"} {"input": "Solve the system:\n7x + 2y = -341/30\n6x + 3y = -83/5", "output": "7x + 2y = -341/30\n6x + 3y = -83/5\n\nUsing elimination\n6*(7x + 2y = -341/30)\n7*(6x + 3y = -83/5)\n42x + 12y = -341/5\n42x + 21y = -581/5\nSubtract equations\n-9y = 48\ny = 48/-9\ny = -16/3\n\nSubstitute y\n7x + 2(-16/3) = -341/30\n7x = -7/10\nx = -7/10/7\nx = -1/10"} {"input": "Solve x^2 - 7/10x - 17/10 = 0", "output": "x^2 - 7/10x - 17/10 = 0\n(x - -1)(x - 17/10) = 0\nx - -1 = 0 or x - 17/10 = 0\nx = -1\nx = 17/10"} {"input": "What value of x satisfies 6x + 24 = 0", "output": "6x + 24 = 0\n6x = -24\nx = -24 / 6\nx = -4"} {"input": "Find x for 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Solve simultaneously:\n3x + 7y = 25\n10x + 6y = 14", "output": "3x + 7y = 25\n10x + 6y = 14\n\nUsing elimination\n10*(3x + 7y = 25)\n3*(10x + 6y = 14)\n30x + 70y = 250\n30x + 18y = 42\nSubtract equations\n52y = 208\ny = 208/52\ny = 4\n\nSubstitute y\n3x + 7(4) = 25\n3x = -3\nx = -3/3\nx = -1"} {"input": "Compute the solution of x^3 - 92/35x^2 + 361/175x - 12/25 = 0", "output": "x^3 - 92/35x^2 + 361/175x - 12/25 = 0\n(x - 3/7)(x - 7/5)(x - 4/5) = 0\nx - 3/7 = 0\nx - 7/5 = 0\nx - 4/5 = 0\nx = 3/7\nx = 7/5\nx = 4/5"} {"input": "Solve the system:\n5x + 10y = -305/12\n10x + 8y = -113/6", "output": "5x + 10y = -305/12\n10x + 8y = -113/6\n\nUsing elimination\n10*(5x + 10y = -305/12)\n5*(10x + 8y = -113/6)\n50x + 100y = -1525/6\n50x + 40y = -565/6\nSubtract equations\n60y = -160\ny = -160/60\ny = -8/3\n\nSubstitute y\n5x + 10(-8/3) = -305/12\n5x = 5/4\nx = 5/4/5\nx = 1/4"} {"input": "Solve the system:\n4x + 4y = -8/3\n7x + 8y = -15/2", "output": "4x + 4y = -8/3\n7x + 8y = -15/2\n\nUsing elimination\n7*(4x + 4y = -8/3)\n4*(7x + 8y = -15/2)\n28x + 28y = -56/3\n28x + 32y = -30\nSubtract equations\n-4y = 34/3\ny = 34/3/-4\ny = -17/6\n\nSubstitute y\n4x + 4(-17/6) = -8/3\n4x = 26/3\nx = 26/3/4\nx = 13/6"} {"input": "What value of x satisfies x^2 + 8/9x - 19/3 = 0", "output": "x^2 + 8/9x - 19/3 = 0\n(x - -3)(x - 19/9) = 0\nx - -3 = 0 or x - 19/9 = 0\nx = -3\nx = 19/9"} {"input": "Solve quickly: 10x - 65/3 = 0", "output": "10x - 65/3 = 0\n10x = 65/3\nx = 65/3 / 10\nx = 13/6"} {"input": "Solve quickly: 9x + 7 = 0", "output": "9x + 7 = 0\n9x = -7\nx = -7 / 9\nx = -7/9"} {"input": "Solve simultaneously:\n1x + 2y = -13/3\n8x + 8y = -76/3", "output": "1x + 2y = -13/3\n8x + 8y = -76/3\n\nUsing elimination\n8*(1x + 2y = -13/3)\n1*(8x + 8y = -76/3)\n8x + 16y = -104/3\n8x + 8y = -76/3\nSubtract equations\n8y = -28/3\ny = -28/3/8\ny = -7/6\n\nSubstitute y\n1x + 2(-7/6) = -13/3\n1x = -2\nx = -2/1\nx = -2"} {"input": "Solve the equations:\n10x + 8y = -137/6\n7x + 1y = -17/12", "output": "10x + 8y = -137/6\n7x + 1y = -17/12\n\nUsing elimination\n7*(10x + 8y = -137/6)\n10*(7x + 1y = -17/12)\n70x + 56y = -959/6\n70x + 10y = -85/6\nSubtract equations\n46y = -437/3\ny = -437/3/46\ny = -19/6\n\nSubstitute y\n10x + 8(-19/6) = -137/6\n10x = 5/2\nx = 5/2/10\nx = 1/4"} {"input": "What value of x satisfies x^3 + 7/3x^2 - 91/3x - 95/3 = 0", "output": "x^3 + 7/3x^2 - 91/3x - 95/3 = 0\n(x - -1)(x - -19/3)(x - 5) = 0\nx - -1 = 0\nx - -19/3 = 0\nx - 5 = 0\nx = -1\nx = -19/3\nx = 5"} {"input": "Compute the solution of 9x - 117/5 = 0", "output": "9x - 117/5 = 0\n9x = 117/5\nx = 117/5 / 9\nx = 13/5"} {"input": "Find the solution to x^2 - 19/2x + 45/2 = 0", "output": "x^2 - 19/2x + 45/2 = 0\n(x - 9/2)(x - 5) = 0\nx - 9/2 = 0 or x - 5 = 0\nx = 9/2\nx = 5"} {"input": "Find x in x^3 + 29/6x^2 - 11/16x - 455/24 = 0", "output": "x^3 + 29/6x^2 - 11/16x - 455/24 = 0\n(x - -13/4)(x - -10/3)(x - 7/4) = 0\nx - -13/4 = 0\nx - -10/3 = 0\nx - 7/4 = 0\nx = -13/4\nx = -10/3\nx = 7/4"} {"input": "Find the solution to x^2 + 9/5x - 2/5 = 0", "output": "x^2 + 9/5x - 2/5 = 0\n(x - 1/5)(x - -2) = 0\nx - 1/5 = 0 or x - -2 = 0\nx = 1/5\nx = -2"} {"input": "Find x in x^3 - 1/3x^2 - 25/12x + 1 = 0", "output": "x^3 - 1/3x^2 - 25/12x + 1 = 0\n(x - 4/3)(x - 1/2)(x - -3/2) = 0\nx - 4/3 = 0\nx - 1/2 = 0\nx - -3/2 = 0\nx = 4/3\nx = 1/2\nx = -3/2"} {"input": "Find x and y such that\n4x + 4y = -26\n4x + 10y = -59", "output": "4x + 4y = -26\n4x + 10y = -59\n\nUsing elimination\n4*(4x + 4y = -26)\n4*(4x + 10y = -59)\n16x + 16y = -104\n16x + 40y = -236\nSubtract equations\n-24y = 132\ny = 132/-24\ny = -11/2\n\nSubstitute y\n4x + 4(-11/2) = -26\n4x = -4\nx = -4/4\nx = -1"} {"input": "Solve 3x + 10 = 0", "output": "3x + 10 = 0\n3x = -10\nx = -10 / 3\nx = -10/3"} {"input": "Solve the equations:\n9x + 2y = 51\n8x + 9y = 67", "output": "9x + 2y = 51\n8x + 9y = 67\n\nUsing elimination\n8*(9x + 2y = 51)\n9*(8x + 9y = 67)\n72x + 16y = 408\n72x + 81y = 603\nSubtract equations\n-65y = -195\ny = -195/-65\ny = 3\n\nSubstitute y\n9x + 2(3) = 51\n9x = 45\nx = 45/9\nx = 5"} {"input": "Solve 2x + 17/2 = 0", "output": "2x + 17/2 = 0\n2x = -17/2\nx = -17/2 / 2\nx = -17/4"} {"input": "Solve quickly: x^2 + 26/15x - 96/5 = 0", "output": "x^2 + 26/15x - 96/5 = 0\n(x - 18/5)(x - -16/3) = 0\nx - 18/5 = 0 or x - -16/3 = 0\nx = 18/5\nx = -16/3"} {"input": "Find x for x^3 + 10/3x^2 - 397/75x - 104/25 = 0", "output": "x^3 + 10/3x^2 - 397/75x - 104/25 = 0\n(x - -3/5)(x - 8/5)(x - -13/3) = 0\nx - -3/5 = 0\nx - 8/5 = 0\nx - -13/3 = 0\nx = -3/5\nx = 8/5\nx = -13/3"} {"input": "Compute the solution of x^2 + 10/3x - 16 = 0", "output": "x^2 + 10/3x - 16 = 0\n(x - -6)(x - 8/3) = 0\nx - -6 = 0 or x - 8/3 = 0\nx = -6\nx = 8/3"} {"input": "Find x for x^2 - 139/28x + 171/28 = 0", "output": "x^2 - 139/28x + 171/28 = 0\n(x - 19/7)(x - 9/4) = 0\nx - 19/7 = 0 or x - 9/4 = 0\nx = 19/7\nx = 9/4"} {"input": "Solve simultaneously:\n8x + 7y = 475/8\n8x + 2y = 205/4", "output": "8x + 7y = 475/8\n8x + 2y = 205/4\n\nUsing elimination\n8*(8x + 7y = 475/8)\n8*(8x + 2y = 205/4)\n64x + 56y = 475\n64x + 16y = 410\nSubtract equations\n40y = 65\ny = 65/40\ny = 13/8\n\nSubstitute y\n8x + 7(13/8) = 475/8\n8x = 48\nx = 48/8\nx = 6"} {"input": "Solve the equations:\n5x + 8y = -3/2\n8x + 5y = -75/2", "output": "5x + 8y = -3/2\n8x + 5y = -75/2\n\nUsing elimination\n8*(5x + 8y = -3/2)\n5*(8x + 5y = -75/2)\n40x + 64y = -12\n40x + 25y = -375/2\nSubtract equations\n39y = 351/2\ny = 351/2/39\ny = 9/2\n\nSubstitute y\n5x + 8(9/2) = -3/2\n5x = -75/2\nx = -75/2/5\nx = -15/2"} {"input": "Solve quickly: 1x - 8/9 = 0", "output": "1x - 8/9 = 0\n1x = 8/9\nx = 8/9 / 1\nx = 8/9"} {"input": "Solve the system:\n3x + 1y = 43/4\n8x + 4y = 89/3", "output": "3x + 1y = 43/4\n8x + 4y = 89/3\n\nUsing elimination\n8*(3x + 1y = 43/4)\n3*(8x + 4y = 89/3)\n24x + 8y = 86\n24x + 12y = 89\nSubtract equations\n-4y = -3\ny = -3/-4\ny = 3/4\n\nSubstitute y\n3x + 1(3/4) = 43/4\n3x = 10\nx = 10/3\nx = 10/3"} {"input": "Solve the equation 10x - 55 = 0", "output": "10x - 55 = 0\n10x = 55\nx = 55 / 10\nx = 11/2"} {"input": "Compute the solution of x^2 + 19/21x - 170/21 = 0", "output": "x^2 + 19/21x - 170/21 = 0\n(x - 17/7)(x - -10/3) = 0\nx - 17/7 = 0 or x - -10/3 = 0\nx = 17/7\nx = -10/3"} {"input": "Determine x in x^3 - 1943/504x^2 + 229/56x - 221/252 = 0", "output": "x^3 - 1943/504x^2 + 229/56x - 221/252 = 0\n(x - 2/7)(x - 17/8)(x - 13/9) = 0\nx - 2/7 = 0\nx - 17/8 = 0\nx - 13/9 = 0\nx = 2/7\nx = 17/8\nx = 13/9"} {"input": "What value of x satisfies 4x + 80/3 = 0", "output": "4x + 80/3 = 0\n4x = -80/3\nx = -80/3 / 4\nx = -20/3"} {"input": "What value of x satisfies x^3 + 159/140x^2 - 139/280x - 33/56 = 0", "output": "x^3 + 159/140x^2 - 139/280x - 33/56 = 0\n(x - -11/10)(x - -3/4)(x - 5/7) = 0\nx - -11/10 = 0\nx - -3/4 = 0\nx - 5/7 = 0\nx = -11/10\nx = -3/4\nx = 5/7"} {"input": "Solve 1x - 13/4 = 0", "output": "1x - 13/4 = 0\n1x = 13/4\nx = 13/4 / 1\nx = 13/4"} {"input": "Solve the system:\n6x + 6y = -42\n9x + 6y = -129/2", "output": "6x + 6y = -42\n9x + 6y = -129/2\n\nUsing elimination\n9*(6x + 6y = -42)\n6*(9x + 6y = -129/2)\n54x + 54y = -378\n54x + 36y = -387\nSubtract equations\n18y = 9\ny = 9/18\ny = 1/2\n\nSubstitute y\n6x + 6(1/2) = -42\n6x = -45\nx = -45/6\nx = -15/2"} {"input": "Find x in x^3 + 139/10x^2 + 107/2x + 252/5 = 0", "output": "x^3 + 139/10x^2 + 107/2x + 252/5 = 0\n(x - -9/2)(x - -7/5)(x - -8) = 0\nx - -9/2 = 0\nx - -7/5 = 0\nx - -8 = 0\nx = -9/2\nx = -7/5\nx = -8"} {"input": "Find x and y such that\n4x + 3y = 129/5\n7x + 8y = 699/10", "output": "4x + 3y = 129/5\n7x + 8y = 699/10\n\nUsing elimination\n7*(4x + 3y = 129/5)\n4*(7x + 8y = 699/10)\n28x + 21y = 903/5\n28x + 32y = 1398/5\nSubtract equations\n-11y = -99\ny = -99/-11\ny = 9\n\nSubstitute y\n4x + 3(9) = 129/5\n4x = -6/5\nx = -6/5/4\nx = -3/10"} {"input": "Find the solution to x^3 - 115/72x^2 - 383/216x - 19/108 = 0", "output": "x^3 - 115/72x^2 - 383/216x - 19/108 = 0\n(x - 19/8)(x - -1/9)(x - -2/3) = 0\nx - 19/8 = 0\nx - -1/9 = 0\nx - -2/3 = 0\nx = 19/8\nx = -1/9\nx = -2/3"} {"input": "Solve 8x + 7 = 0", "output": "8x + 7 = 0\n8x = -7\nx = -7 / 8\nx = -7/8"} {"input": "Find x in x^2 + 111/56x + 27/28 = 0", "output": "x^2 + 111/56x + 27/28 = 0\n(x - -6/7)(x - -9/8) = 0\nx - -6/7 = 0 or x - -9/8 = 0\nx = -6/7\nx = -9/8"} {"input": "Solve the equation 5x + 65/4 = 0", "output": "5x + 65/4 = 0\n5x = -65/4\nx = -65/4 / 5\nx = -13/4"} {"input": "Find the solution to x^2 - 2/3x - 8/3 = 0", "output": "x^2 - 2/3x - 8/3 = 0\n(x - 2)(x - -4/3) = 0\nx - 2 = 0 or x - -4/3 = 0\nx = 2\nx = -4/3"} {"input": "Solve the equations:\n6x + 10y = 8/3\n8x + 4y = 104/3", "output": "6x + 10y = 8/3\n8x + 4y = 104/3\n\nUsing elimination\n8*(6x + 10y = 8/3)\n6*(8x + 4y = 104/3)\n48x + 80y = 64/3\n48x + 24y = 208\nSubtract equations\n56y = -560/3\ny = -560/3/56\ny = -10/3\n\nSubstitute y\n6x + 10(-10/3) = 8/3\n6x = 36\nx = 36/6\nx = 6"} {"input": "Find the solution to x^3 - 17/5x^2 - 193/25x - 7/5 = 0", "output": "x^3 - 17/5x^2 - 193/25x - 7/5 = 0\n(x - -7/5)(x - -1/5)(x - 5) = 0\nx - -7/5 = 0\nx - -1/5 = 0\nx - 5 = 0\nx = -7/5\nx = -1/5\nx = 5"} {"input": "Solve the equation x^3 - 151/24x^2 + 683/96x + 95/96 = 0", "output": "x^3 - 151/24x^2 + 683/96x + 95/96 = 0\n(x - 5/3)(x - -1/8)(x - 19/4) = 0\nx - 5/3 = 0\nx - -1/8 = 0\nx - 19/4 = 0\nx = 5/3\nx = -1/8\nx = 19/4"} {"input": "Compute the solution of x^2 - 19/6x + 13/6 = 0", "output": "x^2 - 19/6x + 13/6 = 0\n(x - 1)(x - 13/6) = 0\nx - 1 = 0 or x - 13/6 = 0\nx = 1\nx = 13/6"} {"input": "Determine x in 6x - 12/5 = 0", "output": "6x - 12/5 = 0\n6x = 12/5\nx = 12/5 / 6\nx = 2/5"} {"input": "Compute the solution of x^2 + 23/4x + 45/8 = 0", "output": "x^2 + 23/4x + 45/8 = 0\n(x - -5/4)(x - -9/2) = 0\nx - -5/4 = 0 or x - -9/2 = 0\nx = -5/4\nx = -9/2"} {"input": "Solve quickly: x^2 + 7/6x - 10/3 = 0", "output": "x^2 + 7/6x - 10/3 = 0\n(x - -5/2)(x - 4/3) = 0\nx - -5/2 = 0 or x - 4/3 = 0\nx = -5/2\nx = 4/3"} {"input": "Solve quickly: 6x + 22 = 0", "output": "6x + 22 = 0\n6x = -22\nx = -22 / 6\nx = -11/3"} {"input": "Find x and y such that\n2x + 1y = -8/5\n3x + 7y = 43/5", "output": "2x + 1y = -8/5\n3x + 7y = 43/5\n\nUsing elimination\n3*(2x + 1y = -8/5)\n2*(3x + 7y = 43/5)\n6x + 3y = -24/5\n6x + 14y = 86/5\nSubtract equations\n-11y = -22\ny = -22/-11\ny = 2\n\nSubstitute y\n2x + 1(2) = -8/5\n2x = -18/5\nx = -18/5/2\nx = -9/5"} {"input": "Find x and y such that\n4x + 10y = 788/45\n1x + 1y = 122/45", "output": "4x + 10y = 788/45\n1x + 1y = 122/45\n\nUsing elimination\n1*(4x + 10y = 788/45)\n4*(1x + 1y = 122/45)\n4x + 10y = 788/45\n4x + 4y = 488/45\nSubtract equations\n6y = 20/3\ny = 20/3/6\ny = 10/9\n\nSubstitute y\n4x + 10(10/9) = 788/45\n4x = 32/5\nx = 32/5/4\nx = 8/5"} {"input": "Solve quickly: 10x - 160 = 0", "output": "10x - 160 = 0\n10x = 160\nx = 160 / 10\nx = 16"} {"input": "Determine x in x^3 + 91/5x^2 + 14/5x - 72/5 = 0", "output": "x^3 + 91/5x^2 + 14/5x - 72/5 = 0\n(x - -1)(x - -18)(x - 4/5) = 0\nx - -1 = 0\nx - -18 = 0\nx - 4/5 = 0\nx = -1\nx = -18\nx = 4/5"} {"input": "Solve the equations:\n9x + 3y = 1/2\n7x + 3y = 5/2", "output": "9x + 3y = 1/2\n7x + 3y = 5/2\n\nUsing elimination\n7*(9x + 3y = 1/2)\n9*(7x + 3y = 5/2)\n63x + 21y = 7/2\n63x + 27y = 45/2\nSubtract equations\n-6y = -19\ny = -19/-6\ny = 19/6\n\nSubstitute y\n9x + 3(19/6) = 1/2\n9x = -9\nx = -9/9\nx = -1"} {"input": "Determine x in 2x - 15/4 = 0", "output": "2x - 15/4 = 0\n2x = 15/4\nx = 15/4 / 2\nx = 15/8"} {"input": "Solve the equation x^2 + 1/2x - 1/2 = 0", "output": "x^2 + 1/2x - 1/2 = 0\n(x - 1/2)(x - -1) = 0\nx - 1/2 = 0 or x - -1 = 0\nx = 1/2\nx = -1"} {"input": "Find the solution to 3x + 1/2 = 0", "output": "3x + 1/2 = 0\n3x = -1/2\nx = -1/2 / 3\nx = -1/6"} {"input": "Solve quickly: x^2 - 7/18x - 104/27 = 0", "output": "x^2 - 7/18x - 104/27 = 0\n(x - 13/6)(x - -16/9) = 0\nx - 13/6 = 0 or x - -16/9 = 0\nx = 13/6\nx = -16/9"} {"input": "Solve the equations:\n5x + 9y = 42\n4x + 4y = 296/9", "output": "5x + 9y = 42\n4x + 4y = 296/9\n\nUsing elimination\n4*(5x + 9y = 42)\n5*(4x + 4y = 296/9)\n20x + 36y = 168\n20x + 20y = 1480/9\nSubtract equations\n16y = 32/9\ny = 32/9/16\ny = 2/9\n\nSubstitute y\n5x + 9(2/9) = 42\n5x = 40\nx = 40/5\nx = 8"} {"input": "Solve quickly: x^3 - 20/3x^2 = 0", "output": "x^3 - 20/3x^2 = 0\n(x - 20/3)(x - 0)(x - 0) = 0\nx - 20/3 = 0\nx - 0 = 0\nx - 0 = 0\nx = 20/3\nx = 0\nx = 0"} {"input": "Compute the solution of x^2 + 5/2x - 25/2 = 0", "output": "x^2 + 5/2x - 25/2 = 0\n(x - 5/2)(x - -5) = 0\nx - 5/2 = 0 or x - -5 = 0\nx = 5/2\nx = -5"} {"input": "Solve 10x - 100 = 0", "output": "10x - 100 = 0\n10x = 100\nx = 100 / 10\nx = 10"} {"input": "Solve simultaneously:\n1x + 1y = -31/12\n1x + 9y = 41/12", "output": "1x + 1y = -31/12\n1x + 9y = 41/12\n\nUsing elimination\n1*(1x + 1y = -31/12)\n1*(1x + 9y = 41/12)\n1x + 1y = -31/12\n1x + 9y = 41/12\nSubtract equations\n-8y = -6\ny = -6/-8\ny = 3/4\n\nSubstitute y\n1x + 1(3/4) = -31/12\n1x = -10/3\nx = -10/3/1\nx = -10/3"} {"input": "Find x and y such that\n6x + 5y = 43/4\n2x + 4y = 3", "output": "6x + 5y = 43/4\n2x + 4y = 3\n\nUsing elimination\n2*(6x + 5y = 43/4)\n6*(2x + 4y = 3)\n12x + 10y = 43/2\n12x + 24y = 18\nSubtract equations\n-14y = 7/2\ny = 7/2/-14\ny = -1/4\n\nSubstitute y\n6x + 5(-1/4) = 43/4\n6x = 12\nx = 12/6\nx = 2"} {"input": "Solve quickly: x^3 - 17/7x^2 - 460/63x + 100/7 = 0", "output": "x^3 - 17/7x^2 - 460/63x + 100/7 = 0\n(x - 10/3)(x - -18/7)(x - 5/3) = 0\nx - 10/3 = 0\nx - -18/7 = 0\nx - 5/3 = 0\nx = 10/3\nx = -18/7\nx = 5/3"} {"input": "What value of x satisfies x^2 - 2/3x - 16/3 = 0", "output": "x^2 - 2/3x - 16/3 = 0\n(x - 8/3)(x - -2) = 0\nx - 8/3 = 0 or x - -2 = 0\nx = 8/3\nx = -2"} {"input": "Find x and y such that\n7x + 5y = 40/3\n5x + 7y = 80/3", "output": "7x + 5y = 40/3\n5x + 7y = 80/3\n\nUsing elimination\n5*(7x + 5y = 40/3)\n7*(5x + 7y = 80/3)\n35x + 25y = 200/3\n35x + 49y = 560/3\nSubtract equations\n-24y = -120\ny = -120/-24\ny = 5\n\nSubstitute y\n7x + 5(5) = 40/3\n7x = -35/3\nx = -35/3/7\nx = -5/3"} {"input": "What value of x satisfies x^2 + 61/5x - 52/5 = 0", "output": "x^2 + 61/5x - 52/5 = 0\n(x - -13)(x - 4/5) = 0\nx - -13 = 0 or x - 4/5 = 0\nx = -13\nx = 4/5"} {"input": "Solve the equations:\n4x + 9y = 26\n10x + 10y = 460/9", "output": "4x + 9y = 26\n10x + 10y = 460/9\n\nUsing elimination\n10*(4x + 9y = 26)\n4*(10x + 10y = 460/9)\n40x + 90y = 260\n40x + 40y = 1840/9\nSubtract equations\n50y = 500/9\ny = 500/9/50\ny = 10/9\n\nSubstitute y\n4x + 9(10/9) = 26\n4x = 16\nx = 16/4\nx = 4"} {"input": "Find x and y such that\n9x + 4y = 13/10\n7x + 1y = 241/40", "output": "9x + 4y = 13/10\n7x + 1y = 241/40\n\nUsing elimination\n7*(9x + 4y = 13/10)\n9*(7x + 1y = 241/40)\n63x + 28y = 91/10\n63x + 9y = 2169/40\nSubtract equations\n19y = -361/8\ny = -361/8/19\ny = -19/8\n\nSubstitute y\n9x + 4(-19/8) = 13/10\n9x = 54/5\nx = 54/5/9\nx = 6/5"} {"input": "Find x for x^2 + 82/5x - 51/5 = 0", "output": "x^2 + 82/5x - 51/5 = 0\n(x - -17)(x - 3/5) = 0\nx - -17 = 0 or x - 3/5 = 0\nx = -17\nx = 3/5"} {"input": "Solve x^2 + 1/2x - 1/2 = 0", "output": "x^2 + 1/2x - 1/2 = 0\n(x - 1/2)(x - -1) = 0\nx - 1/2 = 0 or x - -1 = 0\nx = 1/2\nx = -1"} {"input": "Find x for x^3 - 62/63x^2 - 655/189x + 100/63 = 0", "output": "x^3 - 62/63x^2 - 655/189x + 100/63 = 0\n(x - 20/9)(x - 3/7)(x - -5/3) = 0\nx - 20/9 = 0\nx - 3/7 = 0\nx - -5/3 = 0\nx = 20/9\nx = 3/7\nx = -5/3"} {"input": "Solve quickly: x^2 - 103/8x + 21/2 = 0", "output": "x^2 - 103/8x + 21/2 = 0\n(x - 12)(x - 7/8) = 0\nx - 12 = 0 or x - 7/8 = 0\nx = 12\nx = 7/8"} {"input": "Solve quickly: x^2 - 58/3x + 19/3 = 0", "output": "x^2 - 58/3x + 19/3 = 0\n(x - 1/3)(x - 19) = 0\nx - 1/3 = 0 or x - 19 = 0\nx = 1/3\nx = 19"} {"input": "Find x for x^3 - 281/120x^2 - 1283/240x + 143/80 = 0", "output": "x^3 - 281/120x^2 - 1283/240x + 143/80 = 0\n(x - 11/3)(x - 3/10)(x - -13/8) = 0\nx - 11/3 = 0\nx - 3/10 = 0\nx - -13/8 = 0\nx = 11/3\nx = 3/10\nx = -13/8"} {"input": "Find x for x^2 + 167/45x + 2/5 = 0", "output": "x^2 + 167/45x + 2/5 = 0\n(x - -18/5)(x - -1/9) = 0\nx - -18/5 = 0 or x - -1/9 = 0\nx = -18/5\nx = -1/9"} {"input": "Solve the equation x^2 - 5x - 39/4 = 0", "output": "x^2 - 5x - 39/4 = 0\n(x - -3/2)(x - 13/2) = 0\nx - -3/2 = 0 or x - 13/2 = 0\nx = -3/2\nx = 13/2"} {"input": "Solve quickly: 2x + 1/3 = 0", "output": "2x + 1/3 = 0\n2x = -1/3\nx = -1/3 / 2\nx = -1/6"} {"input": "What value of x satisfies 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Determine x in x^2 + 2/5x - 3/25 = 0", "output": "x^2 + 2/5x - 3/25 = 0\n(x - 1/5)(x - -3/5) = 0\nx - 1/5 = 0 or x - -3/5 = 0\nx = 1/5\nx = -3/5"} {"input": "Solve x^3 + 382/63x^2 + 760/189x + 128/189 = 0", "output": "x^3 + 382/63x^2 + 760/189x + 128/189 = 0\n(x - -4/9)(x - -2/7)(x - -16/3) = 0\nx - -4/9 = 0\nx - -2/7 = 0\nx - -16/3 = 0\nx = -4/9\nx = -2/7\nx = -16/3"} {"input": "Compute the solution of 3x - 33/4 = 0", "output": "3x - 33/4 = 0\n3x = 33/4\nx = 33/4 / 3\nx = 11/4"} {"input": "Solve the equations:\n10x + 6y = -39\n6x + 8y = -46/3", "output": "10x + 6y = -39\n6x + 8y = -46/3\n\nUsing elimination\n6*(10x + 6y = -39)\n10*(6x + 8y = -46/3)\n60x + 36y = -234\n60x + 80y = -460/3\nSubtract equations\n-44y = -242/3\ny = -242/3/-44\ny = 11/6\n\nSubstitute y\n10x + 6(11/6) = -39\n10x = -50\nx = -50/10\nx = -5"} {"input": "Solve the equation 9x - 45/4 = 0", "output": "9x - 45/4 = 0\n9x = 45/4\nx = 45/4 / 9\nx = 5/4"} {"input": "Find x and y such that\n10x + 10y = -210\n4x + 10y = -102", "output": "10x + 10y = -210\n4x + 10y = -102\n\nUsing elimination\n4*(10x + 10y = -210)\n10*(4x + 10y = -102)\n40x + 40y = -840\n40x + 100y = -1020\nSubtract equations\n-60y = 180\ny = 180/-60\ny = -3\n\nSubstitute y\n10x + 10(-3) = -210\n10x = -180\nx = -180/10\nx = -18"} {"input": "What value of x satisfies 9x + 45 = 0", "output": "9x + 45 = 0\n9x = -45\nx = -45 / 9\nx = -5"} {"input": "Determine x in 10x - 130/9 = 0", "output": "10x - 130/9 = 0\n10x = 130/9\nx = 130/9 / 10\nx = 13/9"} {"input": "Find x for x^2 + 5x - 75/4 = 0", "output": "x^2 + 5x - 75/4 = 0\n(x - -15/2)(x - 5/2) = 0\nx - -15/2 = 0 or x - 5/2 = 0\nx = -15/2\nx = 5/2"} {"input": "Solve the equations:\n9x + 1y = 27/4\n4x + 10y = 46", "output": "9x + 1y = 27/4\n4x + 10y = 46\n\nUsing elimination\n4*(9x + 1y = 27/4)\n9*(4x + 10y = 46)\n36x + 4y = 27\n36x + 90y = 414\nSubtract equations\n-86y = -387\ny = -387/-86\ny = 9/2\n\nSubstitute y\n9x + 1(9/2) = 27/4\n9x = 9/4\nx = 9/4/9\nx = 1/4"} {"input": "Solve x^3 - 18/7x^2 - 40/7x = 0", "output": "x^3 - 18/7x^2 - 40/7x = 0\n(x - 4)(x - -10/7)(x - 0) = 0\nx - 4 = 0\nx - -10/7 = 0\nx - 0 = 0\nx = 4\nx = -10/7\nx = 0"} {"input": "Solve the equations:\n2x + 9y = 242/35\n9x + 2y = -66/35", "output": "2x + 9y = 242/35\n9x + 2y = -66/35\n\nUsing elimination\n9*(2x + 9y = 242/35)\n2*(9x + 2y = -66/35)\n18x + 81y = 2178/35\n18x + 4y = -132/35\nSubtract equations\n77y = 66\ny = 66/77\ny = 6/7\n\nSubstitute y\n2x + 9(6/7) = 242/35\n2x = -4/5\nx = -4/5/2\nx = -2/5"} {"input": "Find x in x^3 - 41/6x^2 - 374/9x - 847/18 = 0", "output": "x^3 - 41/6x^2 - 374/9x - 847/18 = 0\n(x - -7/3)(x - 11)(x - -11/6) = 0\nx - -7/3 = 0\nx - 11 = 0\nx - -11/6 = 0\nx = -7/3\nx = 11\nx = -11/6"} {"input": "Find the solution to 4x - 36 = 0", "output": "4x - 36 = 0\n4x = 36\nx = 36 / 4\nx = 9"} {"input": "Solve the equations:\n3x + 7y = -14/5\n5x + 3y = 112/15", "output": "3x + 7y = -14/5\n5x + 3y = 112/15\n\nUsing elimination\n5*(3x + 7y = -14/5)\n3*(5x + 3y = 112/15)\n15x + 35y = -14\n15x + 9y = 112/5\nSubtract equations\n26y = -182/5\ny = -182/5/26\ny = -7/5\n\nSubstitute y\n3x + 7(-7/5) = -14/5\n3x = 7\nx = 7/3\nx = 7/3"} {"input": "Find the solution to 1x + 11/3 = 0", "output": "1x + 11/3 = 0\n1x = -11/3\nx = -11/3 / 1\nx = -11/3"} {"input": "Solve the system:\n3x + 9y = -28/3\n10x + 3y = -91/9", "output": "3x + 9y = -28/3\n10x + 3y = -91/9\n\nUsing elimination\n10*(3x + 9y = -28/3)\n3*(10x + 3y = -91/9)\n30x + 90y = -280/3\n30x + 9y = -91/3\nSubtract equations\n81y = -63\ny = -63/81\ny = -7/9\n\nSubstitute y\n3x + 9(-7/9) = -28/3\n3x = -7/3\nx = -7/3/3\nx = -7/9"} {"input": "Solve the system:\n1x + 8y = 70/3\n5x + 2y = -11/3", "output": "1x + 8y = 70/3\n5x + 2y = -11/3\n\nUsing elimination\n5*(1x + 8y = 70/3)\n1*(5x + 2y = -11/3)\n5x + 40y = 350/3\n5x + 2y = -11/3\nSubtract equations\n38y = 361/3\ny = 361/3/38\ny = 19/6\n\nSubstitute y\n1x + 8(19/6) = 70/3\n1x = -2\nx = -2/1\nx = -2"} {"input": "What value of x satisfies x^2 + 77/6x + 85/3 = 0", "output": "x^2 + 77/6x + 85/3 = 0\n(x - -10)(x - -17/6) = 0\nx - -10 = 0 or x - -17/6 = 0\nx = -10\nx = -17/6"} {"input": "Find x and y such that\n6x + 9y = -12\n9x + 1y = 13/9", "output": "6x + 9y = -12\n9x + 1y = 13/9\n\nUsing elimination\n9*(6x + 9y = -12)\n6*(9x + 1y = 13/9)\n54x + 81y = -108\n54x + 6y = 26/3\nSubtract equations\n75y = -350/3\ny = -350/3/75\ny = -14/9\n\nSubstitute y\n6x + 9(-14/9) = -12\n6x = 2\nx = 2/6\nx = 1/3"} {"input": "Solve the equations:\n10x + 5y = 245/18\n9x + 4y = 455/36", "output": "10x + 5y = 245/18\n9x + 4y = 455/36\n\nUsing elimination\n9*(10x + 5y = 245/18)\n10*(9x + 4y = 455/36)\n90x + 45y = 245/2\n90x + 40y = 2275/18\nSubtract equations\n5y = -35/9\ny = -35/9/5\ny = -7/9\n\nSubstitute y\n10x + 5(-7/9) = 245/18\n10x = 35/2\nx = 35/2/10\nx = 7/4"} {"input": "Solve the system:\n5x + 5y = -37/9\n8x + 4y = -436/45", "output": "5x + 5y = -37/9\n8x + 4y = -436/45\n\nUsing elimination\n8*(5x + 5y = -37/9)\n5*(8x + 4y = -436/45)\n40x + 40y = -296/9\n40x + 20y = -436/9\nSubtract equations\n20y = 140/9\ny = 140/9/20\ny = 7/9\n\nSubstitute y\n5x + 5(7/9) = -37/9\n5x = -8\nx = -8/5\nx = -8/5"} {"input": "Determine x in x^2 - 8/9x - 17/9 = 0", "output": "x^2 - 8/9x - 17/9 = 0\n(x - 17/9)(x - -1) = 0\nx - 17/9 = 0 or x - -1 = 0\nx = 17/9\nx = -1"} {"input": "Find x for x^3 + 3/4x^2 - 64/9x - 16/3 = 0", "output": "x^3 + 3/4x^2 - 64/9x - 16/3 = 0\n(x - 8/3)(x - -8/3)(x - -3/4) = 0\nx - 8/3 = 0\nx - -8/3 = 0\nx - -3/4 = 0\nx = 8/3\nx = -8/3\nx = -3/4"} {"input": "Solve quickly: x^2 - 13/15x + 2/15 = 0", "output": "x^2 - 13/15x + 2/15 = 0\n(x - 1/5)(x - 2/3) = 0\nx - 1/5 = 0 or x - 2/3 = 0\nx = 1/5\nx = 2/3"} {"input": "What value of x satisfies 8x - 80 = 0", "output": "8x - 80 = 0\n8x = 80\nx = 80 / 8\nx = 10"} {"input": "Solve simultaneously:\n5x + 7y = 227/3\n7x + 4y = 196/3", "output": "5x + 7y = 227/3\n7x + 4y = 196/3\n\nUsing elimination\n7*(5x + 7y = 227/3)\n5*(7x + 4y = 196/3)\n35x + 49y = 1589/3\n35x + 20y = 980/3\nSubtract equations\n29y = 203\ny = 203/29\ny = 7\n\nSubstitute y\n5x + 7(7) = 227/3\n5x = 80/3\nx = 80/3/5\nx = 16/3"} {"input": "Solve quickly: x^3 - 127/21x^2 + 220/21x - 100/21 = 0", "output": "x^3 - 127/21x^2 + 220/21x - 100/21 = 0\n(x - 5/7)(x - 2)(x - 10/3) = 0\nx - 5/7 = 0\nx - 2 = 0\nx - 10/3 = 0\nx = 5/7\nx = 2\nx = 10/3"} {"input": "Solve the equations:\n1x + 3y = 3\n10x + 7y = 44/3", "output": "1x + 3y = 3\n10x + 7y = 44/3\n\nUsing elimination\n10*(1x + 3y = 3)\n1*(10x + 7y = 44/3)\n10x + 30y = 30\n10x + 7y = 44/3\nSubtract equations\n23y = 46/3\ny = 46/3/23\ny = 2/3\n\nSubstitute y\n1x + 3(2/3) = 3\n1x = 1\nx = 1/1\nx = 1"} {"input": "Solve the system:\n7x + 7y = -490/9\n5x + 7y = -458/9", "output": "7x + 7y = -490/9\n5x + 7y = -458/9\n\nUsing elimination\n5*(7x + 7y = -490/9)\n7*(5x + 7y = -458/9)\n35x + 35y = -2450/9\n35x + 49y = -3206/9\nSubtract equations\n-14y = 84\ny = 84/-14\ny = -6\n\nSubstitute y\n7x + 7(-6) = -490/9\n7x = -112/9\nx = -112/9/7\nx = -16/9"} {"input": "Find the solution to 8x - 36 = 0", "output": "8x - 36 = 0\n8x = 36\nx = 36 / 8\nx = 9/2"} {"input": "What value of x satisfies x^3 - 7/2x^2 - 5/2x + 2 = 0", "output": "x^3 - 7/2x^2 - 5/2x + 2 = 0\n(x - 1/2)(x - -1)(x - 4) = 0\nx - 1/2 = 0\nx - -1 = 0\nx - 4 = 0\nx = 1/2\nx = -1\nx = 4"} {"input": "Find the solution to x^3 - 111/10x^2 + 81/2x - 243/5 = 0", "output": "x^3 - 111/10x^2 + 81/2x - 243/5 = 0\n(x - 9/2)(x - 18/5)(x - 3) = 0\nx - 9/2 = 0\nx - 18/5 = 0\nx - 3 = 0\nx = 9/2\nx = 18/5\nx = 3"} {"input": "Find x and y such that\n2x + 8y = -34\n3x + 10y = -45", "output": "2x + 8y = -34\n3x + 10y = -45\n\nUsing elimination\n3*(2x + 8y = -34)\n2*(3x + 10y = -45)\n6x + 24y = -102\n6x + 20y = -90\nSubtract equations\n4y = -12\ny = -12/4\ny = -3\n\nSubstitute y\n2x + 8(-3) = -34\n2x = -10\nx = -10/2\nx = -5"} {"input": "Find x for x^3 + 19/10x^2 - 76/5x + 3/2 = 0", "output": "x^3 + 19/10x^2 - 76/5x + 3/2 = 0\n(x - 1/10)(x - -5)(x - 3) = 0\nx - 1/10 = 0\nx - -5 = 0\nx - 3 = 0\nx = 1/10\nx = -5\nx = 3"} {"input": "Find the solution to x^2 + 91/9x + 10 = 0", "output": "x^2 + 91/9x + 10 = 0\n(x - -10/9)(x - -9) = 0\nx - -10/9 = 0 or x - -9 = 0\nx = -10/9\nx = -9"} {"input": "Compute the solution of x^2 + 46/9x - 280/27 = 0", "output": "x^2 + 46/9x - 280/27 = 0\n(x - -20/3)(x - 14/9) = 0\nx - -20/3 = 0 or x - 14/9 = 0\nx = -20/3\nx = 14/9"} {"input": "Solve the system:\n2x + 9y = -194/9\n7x + 4y = -184/9", "output": "2x + 9y = -194/9\n7x + 4y = -184/9\n\nUsing elimination\n7*(2x + 9y = -194/9)\n2*(7x + 4y = -184/9)\n14x + 63y = -1358/9\n14x + 8y = -368/9\nSubtract equations\n55y = -110\ny = -110/55\ny = -2\n\nSubstitute y\n2x + 9(-2) = -194/9\n2x = -32/9\nx = -32/9/2\nx = -16/9"} {"input": "Solve the equation 4x + 12 = 0", "output": "4x + 12 = 0\n4x = -12\nx = -12 / 4\nx = -3"} {"input": "Solve the system:\n9x + 10y = -248/7\n1x + 1y = -29/7", "output": "9x + 10y = -248/7\n1x + 1y = -29/7\n\nUsing elimination\n1*(9x + 10y = -248/7)\n9*(1x + 1y = -29/7)\n9x + 10y = -248/7\n9x + 9y = -261/7\nSubtract equations\n1y = 13/7\ny = 13/7/1\ny = 13/7\n\nSubstitute y\n9x + 10(13/7) = -248/7\n9x = -54\nx = -54/9\nx = -6"} {"input": "Solve the equations:\n5x + 10y = 137/7\n1x + 6y = 397/35", "output": "5x + 10y = 137/7\n1x + 6y = 397/35\n\nUsing elimination\n1*(5x + 10y = 137/7)\n5*(1x + 6y = 397/35)\n5x + 10y = 137/7\n5x + 30y = 397/7\nSubtract equations\n-20y = -260/7\ny = -260/7/-20\ny = 13/7\n\nSubstitute y\n5x + 10(13/7) = 137/7\n5x = 1\nx = 1/5\nx = 1/5"} {"input": "Find x for x^3 - 185/14x^2 - 163/14x + 9 = 0", "output": "x^3 - 185/14x^2 - 163/14x + 9 = 0\n(x - 1/2)(x - 14)(x - -9/7) = 0\nx - 1/2 = 0\nx - 14 = 0\nx - -9/7 = 0\nx = 1/2\nx = 14\nx = -9/7"} {"input": "Find x for 1x - 3/2 = 0", "output": "1x - 3/2 = 0\n1x = 3/2\nx = 3/2 / 1\nx = 3/2"} {"input": "Find x in x^2 - 5x - 24 = 0", "output": "x^2 - 5x - 24 = 0\n(x - -3)(x - 8) = 0\nx - -3 = 0 or x - 8 = 0\nx = -3\nx = 8"} {"input": "Solve the equations:\n2x + 1y = 58/21\n9x + 5y = 78/7", "output": "2x + 1y = 58/21\n9x + 5y = 78/7\n\nUsing elimination\n9*(2x + 1y = 58/21)\n2*(9x + 5y = 78/7)\n18x + 9y = 174/7\n18x + 10y = 156/7\nSubtract equations\n-1y = 18/7\ny = 18/7/-1\ny = -18/7\n\nSubstitute y\n2x + 1(-18/7) = 58/21\n2x = 16/3\nx = 16/3/2\nx = 8/3"} {"input": "Find x in x^2 + 3/4x = 0", "output": "x^2 + 3/4x = 0\n(x - -3/4)(x - 0) = 0\nx - -3/4 = 0 or x - 0 = 0\nx = -3/4\nx = 0"} {"input": "Solve simultaneously:\n5x + 7y = 179/5\n2x + 9y = 53/5", "output": "5x + 7y = 179/5\n2x + 9y = 53/5\n\nUsing elimination\n2*(5x + 7y = 179/5)\n5*(2x + 9y = 53/5)\n10x + 14y = 358/5\n10x + 45y = 53\nSubtract equations\n-31y = 93/5\ny = 93/5/-31\ny = -3/5\n\nSubstitute y\n5x + 7(-3/5) = 179/5\n5x = 40\nx = 40/5\nx = 8"} {"input": "Solve the equations:\n10x + 5y = -165/2\n10x + 9y = -233/2", "output": "10x + 5y = -165/2\n10x + 9y = -233/2\n\nUsing elimination\n10*(10x + 5y = -165/2)\n10*(10x + 9y = -233/2)\n100x + 50y = -825\n100x + 90y = -1165\nSubtract equations\n-40y = 340\ny = 340/-40\ny = -17/2\n\nSubstitute y\n10x + 5(-17/2) = -165/2\n10x = -40\nx = -40/10\nx = -4"} {"input": "Find x for x^2 - 17/6x + 5/3 = 0", "output": "x^2 - 17/6x + 5/3 = 0\n(x - 2)(x - 5/6) = 0\nx - 2 = 0 or x - 5/6 = 0\nx = 2\nx = 5/6"} {"input": "Solve quickly: x^3 - 139/30x^2 + 139/30x - 1 = 0", "output": "x^3 - 139/30x^2 + 139/30x - 1 = 0\n(x - 10/3)(x - 1)(x - 3/10) = 0\nx - 10/3 = 0\nx - 1 = 0\nx - 3/10 = 0\nx = 10/3\nx = 1\nx = 3/10"} {"input": "Find the solution to 8x + 8/3 = 0", "output": "8x + 8/3 = 0\n8x = -8/3\nx = -8/3 / 8\nx = -1/3"} {"input": "Solve x^2 - 8x + 95/9 = 0", "output": "x^2 - 8x + 95/9 = 0\n(x - 19/3)(x - 5/3) = 0\nx - 19/3 = 0 or x - 5/3 = 0\nx = 19/3\nx = 5/3"} {"input": "Find the solution to x^3 + 7x^2 - 105x + 225 = 0", "output": "x^3 + 7x^2 - 105x + 225 = 0\n(x - 5)(x - 3)(x - -15) = 0\nx - 5 = 0\nx - 3 = 0\nx - -15 = 0\nx = 5\nx = 3\nx = -15"} {"input": "Solve x^2 + 13/6x - 5/2 = 0", "output": "x^2 + 13/6x - 5/2 = 0\n(x - 5/6)(x - -3) = 0\nx - 5/6 = 0 or x - -3 = 0\nx = 5/6\nx = -3"} {"input": "Solve the system:\n5x + 4y = 71/28\n5x + 7y = 29/4", "output": "5x + 4y = 71/28\n5x + 7y = 29/4\n\nUsing elimination\n5*(5x + 4y = 71/28)\n5*(5x + 7y = 29/4)\n25x + 20y = 355/28\n25x + 35y = 145/4\nSubtract equations\n-15y = -165/7\ny = -165/7/-15\ny = 11/7\n\nSubstitute y\n5x + 4(11/7) = 71/28\n5x = -15/4\nx = -15/4/5\nx = -3/4"} {"input": "Find x and y such that\n3x + 6y = 53/21\n2x + 7y = 64/63", "output": "3x + 6y = 53/21\n2x + 7y = 64/63\n\nUsing elimination\n2*(3x + 6y = 53/21)\n3*(2x + 7y = 64/63)\n6x + 12y = 106/21\n6x + 21y = 64/21\nSubtract equations\n-9y = 2\ny = 2/-9\ny = -2/9\n\nSubstitute y\n3x + 6(-2/9) = 53/21\n3x = 27/7\nx = 27/7/3\nx = 9/7"} {"input": "What value of x satisfies x^3 - 409/70x^2 + 153/14x - 45/7 = 0", "output": "x^3 - 409/70x^2 + 153/14x - 45/7 = 0\n(x - 5/2)(x - 15/7)(x - 6/5) = 0\nx - 5/2 = 0\nx - 15/7 = 0\nx - 6/5 = 0\nx = 5/2\nx = 15/7\nx = 6/5"} {"input": "Solve the system:\n9x + 4y = -59/14\n3x + 4y = 39/14", "output": "9x + 4y = -59/14\n3x + 4y = 39/14\n\nUsing elimination\n3*(9x + 4y = -59/14)\n9*(3x + 4y = 39/14)\n27x + 12y = -177/14\n27x + 36y = 351/14\nSubtract equations\n-24y = -264/7\ny = -264/7/-24\ny = 11/7\n\nSubstitute y\n9x + 4(11/7) = -59/14\n9x = -21/2\nx = -21/2/9\nx = -7/6"} {"input": "Solve the equation x^3 - 5/2x^2 - 9/2x + 9 = 0", "output": "x^3 - 5/2x^2 - 9/2x + 9 = 0\n(x - -2)(x - 3)(x - 3/2) = 0\nx - -2 = 0\nx - 3 = 0\nx - 3/2 = 0\nx = -2\nx = 3\nx = 3/2"} {"input": "Determine x in 3x + 6 = 0", "output": "3x + 6 = 0\n3x = -6\nx = -6 / 3\nx = -2"} {"input": "Find x in x^2 + 3x + 2 = 0", "output": "x^2 + 3x + 2 = 0\n(x - -2)(x - -1) = 0\nx - -2 = 0 or x - -1 = 0\nx = -2\nx = -1"} {"input": "Solve simultaneously:\n8x + 5y = -76\n4x + 2y = -34", "output": "8x + 5y = -76\n4x + 2y = -34\n\nUsing elimination\n4*(8x + 5y = -76)\n8*(4x + 2y = -34)\n32x + 20y = -304\n32x + 16y = -272\nSubtract equations\n4y = -32\ny = -32/4\ny = -8\n\nSubstitute y\n8x + 5(-8) = -76\n8x = -36\nx = -36/8\nx = -9/2"} {"input": "Determine x in x^3 + 8/3x^2 - 157/12x - 85/12 = 0", "output": "x^3 + 8/3x^2 - 157/12x - 85/12 = 0\n(x - -5)(x - -1/2)(x - 17/6) = 0\nx - -5 = 0\nx - -1/2 = 0\nx - 17/6 = 0\nx = -5\nx = -1/2\nx = 17/6"} {"input": "Compute the solution of x^3 - 11/3x^2 - 32/9x + 140/9 = 0", "output": "x^3 - 11/3x^2 - 32/9x + 140/9 = 0\n(x - 7/3)(x - -2)(x - 10/3) = 0\nx - 7/3 = 0\nx - -2 = 0\nx - 10/3 = 0\nx = 7/3\nx = -2\nx = 10/3"} {"input": "Solve the equation x^3 + 92/21x^2 - 65/7x + 18/7 = 0", "output": "x^3 + 92/21x^2 - 65/7x + 18/7 = 0\n(x - -6)(x - 9/7)(x - 1/3) = 0\nx - -6 = 0\nx - 9/7 = 0\nx - 1/3 = 0\nx = -6\nx = 9/7\nx = 1/3"} {"input": "Find x in 1x + 2/7 = 0", "output": "1x + 2/7 = 0\n1x = -2/7\nx = -2/7 / 1\nx = -2/7"} {"input": "What value of x satisfies x^3 - 209/28x^2 - 367/28x + 494/7 = 0", "output": "x^3 - 209/28x^2 - 367/28x + 494/7 = 0\n(x - -13/4)(x - 8)(x - 19/7) = 0\nx - -13/4 = 0\nx - 8 = 0\nx - 19/7 = 0\nx = -13/4\nx = 8\nx = 19/7"} {"input": "Find x for x^3 - 191/45x^2 + 17/15x + 19/9 = 0", "output": "x^3 - 191/45x^2 + 17/15x + 19/9 = 0\n(x - 1)(x - -5/9)(x - 19/5) = 0\nx - 1 = 0\nx - -5/9 = 0\nx - 19/5 = 0\nx = 1\nx = -5/9\nx = 19/5"} {"input": "Solve the equations:\n1x + 2y = 3/14\n9x + 6y = 387/14", "output": "1x + 2y = 3/14\n9x + 6y = 387/14\n\nUsing elimination\n9*(1x + 2y = 3/14)\n1*(9x + 6y = 387/14)\n9x + 18y = 27/14\n9x + 6y = 387/14\nSubtract equations\n12y = -180/7\ny = -180/7/12\ny = -15/7\n\nSubstitute y\n1x + 2(-15/7) = 3/14\n1x = 9/2\nx = 9/2/1\nx = 9/2"} {"input": "Determine x in x^2 - 35/8x + 19/4 = 0", "output": "x^2 - 35/8x + 19/4 = 0\n(x - 19/8)(x - 2) = 0\nx - 19/8 = 0 or x - 2 = 0\nx = 19/8\nx = 2"} {"input": "Determine x in x^3 - 13x^2 + 47x - 35 = 0", "output": "x^3 - 13x^2 + 47x - 35 = 0\n(x - 5)(x - 1)(x - 7) = 0\nx - 5 = 0\nx - 1 = 0\nx - 7 = 0\nx = 5\nx = 1\nx = 7"} {"input": "What value of x satisfies x^2 - 171/10x - 81/5 = 0", "output": "x^2 - 171/10x - 81/5 = 0\n(x - -9/10)(x - 18) = 0\nx - -9/10 = 0 or x - 18 = 0\nx = -9/10\nx = 18"} {"input": "What value of x satisfies 7x - 63 = 0", "output": "7x - 63 = 0\n7x = 63\nx = 63 / 7\nx = 9"} {"input": "Find x in x^2 + 5/6x - 28/3 = 0", "output": "x^2 + 5/6x - 28/3 = 0\n(x - 8/3)(x - -7/2) = 0\nx - 8/3 = 0 or x - -7/2 = 0\nx = 8/3\nx = -7/2"} {"input": "Solve simultaneously:\n8x + 10y = -434/15\n4x + 9y = -79/5", "output": "8x + 10y = -434/15\n4x + 9y = -79/5\n\nUsing elimination\n4*(8x + 10y = -434/15)\n8*(4x + 9y = -79/5)\n32x + 40y = -1736/15\n32x + 72y = -632/5\nSubtract equations\n-32y = 32/3\ny = 32/3/-32\ny = -1/3\n\nSubstitute y\n8x + 10(-1/3) = -434/15\n8x = -128/5\nx = -128/5/8\nx = -16/5"} {"input": "Find x and y such that\n2x + 10y = -539/20\n9x + 6y = -573/20", "output": "2x + 10y = -539/20\n9x + 6y = -573/20\n\nUsing elimination\n9*(2x + 10y = -539/20)\n2*(9x + 6y = -573/20)\n18x + 90y = -4851/20\n18x + 12y = -573/10\nSubtract equations\n78y = -741/4\ny = -741/4/78\ny = -19/8\n\nSubstitute y\n2x + 10(-19/8) = -539/20\n2x = -16/5\nx = -16/5/2\nx = -8/5"} {"input": "Determine x in x^3 + 1/2x^2 - 31/9x - 28/9 = 0", "output": "x^3 + 1/2x^2 - 31/9x - 28/9 = 0\n(x - -7/6)(x - 2)(x - -4/3) = 0\nx - -7/6 = 0\nx - 2 = 0\nx - -4/3 = 0\nx = -7/6\nx = 2\nx = -4/3"} {"input": "What value of x satisfies 1x + 7/3 = 0", "output": "1x + 7/3 = 0\n1x = -7/3\nx = -7/3 / 1\nx = -7/3"} {"input": "Determine x in 9x - 60 = 0", "output": "9x - 60 = 0\n9x = 60\nx = 60 / 9\nx = 20/3"} {"input": "Solve quickly: x^2 + 23/3x + 20/3 = 0", "output": "x^2 + 23/3x + 20/3 = 0\n(x - -20/3)(x - -1) = 0\nx - -20/3 = 0 or x - -1 = 0\nx = -20/3\nx = -1"} {"input": "Compute the solution of 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Solve simultaneously:\n4x + 2y = -113/18\n6x + 5y = -167/12", "output": "4x + 2y = -113/18\n6x + 5y = -167/12\n\nUsing elimination\n6*(4x + 2y = -113/18)\n4*(6x + 5y = -167/12)\n24x + 12y = -113/3\n24x + 20y = -167/3\nSubtract equations\n-8y = 18\ny = 18/-8\ny = -9/4\n\nSubstitute y\n4x + 2(-9/4) = -113/18\n4x = -16/9\nx = -16/9/4\nx = -4/9"} {"input": "Compute the solution of x^2 - 23/10x - 34/5 = 0", "output": "x^2 - 23/10x - 34/5 = 0\n(x - 4)(x - -17/10) = 0\nx - 4 = 0 or x - -17/10 = 0\nx = 4\nx = -17/10"} {"input": "What value of x satisfies 2x - 12 = 0", "output": "2x - 12 = 0\n2x = 12\nx = 12 / 2\nx = 6"} {"input": "Solve the equation 1x + 5 = 0", "output": "1x + 5 = 0\n1x = -5\nx = -5 / 1\nx = -5"} {"input": "Solve quickly: 5x - 5/9 = 0", "output": "5x - 5/9 = 0\n5x = 5/9\nx = 5/9 / 5\nx = 1/9"} {"input": "Solve the equations:\n3x + 7y = -457/15\n3x + 4y = -304/15", "output": "3x + 7y = -457/15\n3x + 4y = -304/15\n\nUsing elimination\n3*(3x + 7y = -457/15)\n3*(3x + 4y = -304/15)\n9x + 21y = -457/5\n9x + 12y = -304/5\nSubtract equations\n9y = -153/5\ny = -153/5/9\ny = -17/5\n\nSubstitute y\n3x + 7(-17/5) = -457/15\n3x = -20/3\nx = -20/3/3\nx = -20/9"} {"input": "Find the solution to x^2 + 51/10x + 289/50 = 0", "output": "x^2 + 51/10x + 289/50 = 0\n(x - -17/10)(x - -17/5) = 0\nx - -17/10 = 0 or x - -17/5 = 0\nx = -17/10\nx = -17/5"} {"input": "Solve simultaneously:\n8x + 6y = -130/21\n7x + 1y = -101/21", "output": "8x + 6y = -130/21\n7x + 1y = -101/21\n\nUsing elimination\n7*(8x + 6y = -130/21)\n8*(7x + 1y = -101/21)\n56x + 42y = -130/3\n56x + 8y = -808/21\nSubtract equations\n34y = -34/7\ny = -34/7/34\ny = -1/7\n\nSubstitute y\n8x + 6(-1/7) = -130/21\n8x = -16/3\nx = -16/3/8\nx = -2/3"} {"input": "Compute the solution of x^3 - 1x^2 - 4x + 4 = 0", "output": "x^3 - 1x^2 - 4x + 4 = 0\n(x - 2)(x - 1)(x - -2) = 0\nx - 2 = 0\nx - 1 = 0\nx - -2 = 0\nx = 2\nx = 1\nx = -2"} {"input": "Determine x in x^3 - 91/90x^2 - 341/45x - 119/30 = 0", "output": "x^3 - 91/90x^2 - 341/45x - 119/30 = 0\n(x - 7/2)(x - -3/5)(x - -17/9) = 0\nx - 7/2 = 0\nx - -3/5 = 0\nx - -17/9 = 0\nx = 7/2\nx = -3/5\nx = -17/9"} {"input": "What value of x satisfies x^2 + 2/3x - 8/3 = 0", "output": "x^2 + 2/3x - 8/3 = 0\n(x - 4/3)(x - -2) = 0\nx - 4/3 = 0 or x - -2 = 0\nx = 4/3\nx = -2"} {"input": "Find x for x^3 - 5x^2 - 107/4x - 51/2 = 0", "output": "x^3 - 5x^2 - 107/4x - 51/2 = 0\n(x - -2)(x - -3/2)(x - 17/2) = 0\nx - -2 = 0\nx - -3/2 = 0\nx - 17/2 = 0\nx = -2\nx = -3/2\nx = 17/2"} {"input": "Compute the solution of x^2 + 22/5x + 21/5 = 0", "output": "x^2 + 22/5x + 21/5 = 0\n(x - -7/5)(x - -3) = 0\nx - -7/5 = 0 or x - -3 = 0\nx = -7/5\nx = -3"} {"input": "Find the solution to x^2 - 11/9x + 8/27 = 0", "output": "x^2 - 11/9x + 8/27 = 0\n(x - 8/9)(x - 1/3) = 0\nx - 8/9 = 0 or x - 1/3 = 0\nx = 8/9\nx = 1/3"} {"input": "Determine x in 10x - 45 = 0", "output": "10x - 45 = 0\n10x = 45\nx = 45 / 10\nx = 9/2"} {"input": "Find x for x^3 - 4/3x^2 - 25/3x + 14 = 0", "output": "x^3 - 4/3x^2 - 25/3x + 14 = 0\n(x - 7/3)(x - 2)(x - -3) = 0\nx - 7/3 = 0\nx - 2 = 0\nx - -3 = 0\nx = 7/3\nx = 2\nx = -3"} {"input": "Compute the solution of x^3 - 61/15x^2 + 29/15x + 17/15 = 0", "output": "x^3 - 61/15x^2 + 29/15x + 17/15 = 0\n(x - 17/5)(x - -1/3)(x - 1) = 0\nx - 17/5 = 0\nx - -1/3 = 0\nx - 1 = 0\nx = 17/5\nx = -1/3\nx = 1"} {"input": "Solve the equation x^3 + 325/72x^2 + 493/144x - 7/16 = 0", "output": "x^3 + 325/72x^2 + 493/144x - 7/16 = 0\n(x - -9/8)(x - -7/2)(x - 1/9) = 0\nx - -9/8 = 0\nx - -7/2 = 0\nx - 1/9 = 0\nx = -9/8\nx = -7/2\nx = 1/9"} {"input": "Solve x^3 + 49/18x^2 - 7/54x - 20/27 = 0", "output": "x^3 + 49/18x^2 - 7/54x - 20/27 = 0\n(x - 1/2)(x - -5/9)(x - -8/3) = 0\nx - 1/2 = 0\nx - -5/9 = 0\nx - -8/3 = 0\nx = 1/2\nx = -5/9\nx = -8/3"} {"input": "Find the solution to x^3 - 35/4x^2 + 137/8x - 15/4 = 0", "output": "x^3 - 35/4x^2 + 137/8x - 15/4 = 0\n(x - 5/2)(x - 6)(x - 1/4) = 0\nx - 5/2 = 0\nx - 6 = 0\nx - 1/4 = 0\nx = 5/2\nx = 6\nx = 1/4"} {"input": "Solve the equation x^3 - 47/4x^2 - 195/8x + 513/2 = 0", "output": "x^3 - 47/4x^2 - 195/8x + 513/2 = 0\n(x - 12)(x - 9/2)(x - -19/4) = 0\nx - 12 = 0\nx - 9/2 = 0\nx - -19/4 = 0\nx = 12\nx = 9/2\nx = -19/4"} {"input": "Find x in x^3 - 51/20x^2 - 27/5x + 243/20 = 0", "output": "x^3 - 51/20x^2 - 27/5x + 243/20 = 0\n(x - 9/5)(x - -9/4)(x - 3) = 0\nx - 9/5 = 0\nx - -9/4 = 0\nx - 3 = 0\nx = 9/5\nx = -9/4\nx = 3"} {"input": "Solve x^3 + 11/5x^2 - 16/5x - 36/5 = 0", "output": "x^3 + 11/5x^2 - 16/5x - 36/5 = 0\n(x - -2)(x - -2)(x - 9/5) = 0\nx - -2 = 0\nx - -2 = 0\nx - 9/5 = 0\nx = -2\nx = -2\nx = 9/5"} {"input": "Solve simultaneously:\n7x + 4y = -1139/36\n5x + 7y = -1145/36", "output": "7x + 4y = -1139/36\n5x + 7y = -1145/36\n\nUsing elimination\n5*(7x + 4y = -1139/36)\n7*(5x + 7y = -1145/36)\n35x + 20y = -5695/36\n35x + 49y = -8015/36\nSubtract equations\n-29y = 580/9\ny = 580/9/-29\ny = -20/9\n\nSubstitute y\n7x + 4(-20/9) = -1139/36\n7x = -91/4\nx = -91/4/7\nx = -13/4"} {"input": "Find x for x^3 - 41/5x^2 + 8/5x = 0", "output": "x^3 - 41/5x^2 + 8/5x = 0\n(x - 1/5)(x - 8)(x - 0) = 0\nx - 1/5 = 0\nx - 8 = 0\nx - 0 = 0\nx = 1/5\nx = 8\nx = 0"} {"input": "Find x in 7x = 0", "output": "7x = 0\n7x = 0\nx = 0 / 7\nx = 0"} {"input": "Compute the solution of x^2 - 128/7x - 240/7 = 0", "output": "x^2 - 128/7x - 240/7 = 0\n(x - -12/7)(x - 20) = 0\nx - -12/7 = 0 or x - 20 = 0\nx = -12/7\nx = 20"} {"input": "Find x in x^3 + 29/7x^2 + 38/7x + 16/7 = 0", "output": "x^3 + 29/7x^2 + 38/7x + 16/7 = 0\n(x - -8/7)(x - -2)(x - -1) = 0\nx - -8/7 = 0\nx - -2 = 0\nx - -1 = 0\nx = -8/7\nx = -2\nx = -1"} {"input": "Find x in x^2 - 47/12x - 17/12 = 0", "output": "x^2 - 47/12x - 17/12 = 0\n(x - 17/4)(x - -1/3) = 0\nx - 17/4 = 0 or x - -1/3 = 0\nx = 17/4\nx = -1/3"} {"input": "Determine x in 2x - 26/3 = 0", "output": "2x - 26/3 = 0\n2x = 26/3\nx = 26/3 / 2\nx = 13/3"} {"input": "Determine x in x^3 - 11/3x^2 - 58x - 160/3 = 0", "output": "x^3 - 11/3x^2 - 58x - 160/3 = 0\n(x - -16/3)(x - -1)(x - 10) = 0\nx - -16/3 = 0\nx - -1 = 0\nx - 10 = 0\nx = -16/3\nx = -1\nx = 10"} {"input": "Solve simultaneously:\n2x + 9y = 69\n7x + 1y = 28", "output": "2x + 9y = 69\n7x + 1y = 28\n\nUsing elimination\n7*(2x + 9y = 69)\n2*(7x + 1y = 28)\n14x + 63y = 483\n14x + 2y = 56\nSubtract equations\n61y = 427\ny = 427/61\ny = 7\n\nSubstitute y\n2x + 9(7) = 69\n2x = 6\nx = 6/2\nx = 3"} {"input": "Find x in 4x + 64/7 = 0", "output": "4x + 64/7 = 0\n4x = -64/7\nx = -64/7 / 4\nx = -16/7"} {"input": "Solve x^3 - 117/20x^2 + 13/8x + 33/20 = 0", "output": "x^3 - 117/20x^2 + 13/8x + 33/20 = 0\n(x - 11/2)(x - 3/4)(x - -2/5) = 0\nx - 11/2 = 0\nx - 3/4 = 0\nx - -2/5 = 0\nx = 11/2\nx = 3/4\nx = -2/5"} {"input": "Solve quickly: 2x + 2/3 = 0", "output": "2x + 2/3 = 0\n2x = -2/3\nx = -2/3 / 2\nx = -1/3"} {"input": "Find x and y such that\n3x + 4y = -17\n8x + 10y = -259/6", "output": "3x + 4y = -17\n8x + 10y = -259/6\n\nUsing elimination\n8*(3x + 4y = -17)\n3*(8x + 10y = -259/6)\n24x + 32y = -136\n24x + 30y = -259/2\nSubtract equations\n2y = -13/2\ny = -13/2/2\ny = -13/4\n\nSubstitute y\n3x + 4(-13/4) = -17\n3x = -4\nx = -4/3\nx = -4/3"} {"input": "Find x for x^3 - 29/30x^2 - 13/6x + 6/5 = 0", "output": "x^3 - 29/30x^2 - 13/6x + 6/5 = 0\n(x - 1/2)(x - -4/3)(x - 9/5) = 0\nx - 1/2 = 0\nx - -4/3 = 0\nx - 9/5 = 0\nx = 1/2\nx = -4/3\nx = 9/5"} {"input": "Determine x in 6x + 108/5 = 0", "output": "6x + 108/5 = 0\n6x = -108/5\nx = -108/5 / 6\nx = -18/5"} {"input": "Compute the solution of x^2 + 10/3x = 0", "output": "x^2 + 10/3x = 0\n(x - -10/3)(x - 0) = 0\nx - -10/3 = 0 or x - 0 = 0\nx = -10/3\nx = 0"} {"input": "Compute the solution of x^2 - 13x + 12 = 0", "output": "x^2 - 13x + 12 = 0\n(x - 1)(x - 12) = 0\nx - 1 = 0 or x - 12 = 0\nx = 1\nx = 12"} {"input": "Find x and y such that\n4x + 9y = 50\n3x + 5y = 88/3", "output": "4x + 9y = 50\n3x + 5y = 88/3\n\nUsing elimination\n3*(4x + 9y = 50)\n4*(3x + 5y = 88/3)\n12x + 27y = 150\n12x + 20y = 352/3\nSubtract equations\n7y = 98/3\ny = 98/3/7\ny = 14/3\n\nSubstitute y\n4x + 9(14/3) = 50\n4x = 8\nx = 8/4\nx = 2"} {"input": "Solve quickly: x^2 + 18/35x - 81/35 = 0", "output": "x^2 + 18/35x - 81/35 = 0\n(x - -9/5)(x - 9/7) = 0\nx - -9/5 = 0 or x - 9/7 = 0\nx = -9/5\nx = 9/7"} {"input": "Find the solution to 6x - 5 = 0", "output": "6x - 5 = 0\n6x = 5\nx = 5 / 6\nx = 5/6"} {"input": "Find x in x^3 - 31/60x^2 - 93/20x + 14/3 = 0", "output": "x^3 - 31/60x^2 - 93/20x + 14/3 = 0\n(x - -7/3)(x - 5/4)(x - 8/5) = 0\nx - -7/3 = 0\nx - 5/4 = 0\nx - 8/5 = 0\nx = -7/3\nx = 5/4\nx = 8/5"} {"input": "Solve the equations:\n1x + 9y = 56/5\n6x + 5y = -21", "output": "1x + 9y = 56/5\n6x + 5y = -21\n\nUsing elimination\n6*(1x + 9y = 56/5)\n1*(6x + 5y = -21)\n6x + 54y = 336/5\n6x + 5y = -21\nSubtract equations\n49y = 441/5\ny = 441/5/49\ny = 9/5\n\nSubstitute y\n1x + 9(9/5) = 56/5\n1x = -5\nx = -5/1\nx = -5"} {"input": "Solve 6x - 18 = 0", "output": "6x - 18 = 0\n6x = 18\nx = 18 / 6\nx = 3"} {"input": "Determine x in x^3 - 365/18x^2 + 628/27x + 1045/54 = 0", "output": "x^3 - 365/18x^2 + 628/27x + 1045/54 = 0\n(x - 11/6)(x - 19)(x - -5/9) = 0\nx - 11/6 = 0\nx - 19 = 0\nx - -5/9 = 0\nx = 11/6\nx = 19\nx = -5/9"} {"input": "Compute the solution of x^2 + 61/3x + 42 = 0", "output": "x^2 + 61/3x + 42 = 0\n(x - -7/3)(x - -18) = 0\nx - -7/3 = 0 or x - -18 = 0\nx = -7/3\nx = -18"} {"input": "Find x in 2x + 32 = 0", "output": "2x + 32 = 0\n2x = -32\nx = -32 / 2\nx = -16"} {"input": "Determine x in x^2 - 19/7x = 0", "output": "x^2 - 19/7x = 0\n(x - 19/7)(x - 0) = 0\nx - 19/7 = 0 or x - 0 = 0\nx = 19/7\nx = 0"} {"input": "Solve the system:\n2x + 6y = 15/2\n8x + 10y = 16", "output": "2x + 6y = 15/2\n8x + 10y = 16\n\nUsing elimination\n8*(2x + 6y = 15/2)\n2*(8x + 10y = 16)\n16x + 48y = 60\n16x + 20y = 32\nSubtract equations\n28y = 28\ny = 28/28\ny = 1\n\nSubstitute y\n2x + 6(1) = 15/2\n2x = 3/2\nx = 3/2/2\nx = 3/4"} {"input": "What value of x satisfies x^2 - 40/3x - 128/3 = 0", "output": "x^2 - 40/3x - 128/3 = 0\n(x - -8/3)(x - 16) = 0\nx - -8/3 = 0 or x - 16 = 0\nx = -8/3\nx = 16"} {"input": "Find the solution to x^2 - 36/5x - 32/5 = 0", "output": "x^2 - 36/5x - 32/5 = 0\n(x - -4/5)(x - 8) = 0\nx - -4/5 = 0 or x - 8 = 0\nx = -4/5\nx = 8"} {"input": "Find the solution to 2x - 10 = 0", "output": "2x - 10 = 0\n2x = 10\nx = 10 / 2\nx = 5"} {"input": "Solve x^3 + 71/14x^2 - 37x - 935/14 = 0", "output": "x^3 + 71/14x^2 - 37x - 935/14 = 0\n(x - -17/2)(x - 5)(x - -11/7) = 0\nx - -17/2 = 0\nx - 5 = 0\nx - -11/7 = 0\nx = -17/2\nx = 5\nx = -11/7"} {"input": "Find x and y such that\n1x + 5y = -101/7\n9x + 2y = -221/7", "output": "1x + 5y = -101/7\n9x + 2y = -221/7\n\nUsing elimination\n9*(1x + 5y = -101/7)\n1*(9x + 2y = -221/7)\n9x + 45y = -909/7\n9x + 2y = -221/7\nSubtract equations\n43y = -688/7\ny = -688/7/43\ny = -16/7\n\nSubstitute y\n1x + 5(-16/7) = -101/7\n1x = -3\nx = -3/1\nx = -3"} {"input": "Solve quickly: x^3 - 71/24x^2 - 37/32x + 65/96 = 0", "output": "x^3 - 71/24x^2 - 37/32x + 65/96 = 0\n(x - 13/4)(x - -5/8)(x - 1/3) = 0\nx - 13/4 = 0\nx - -5/8 = 0\nx - 1/3 = 0\nx = 13/4\nx = -5/8\nx = 1/3"} {"input": "Solve x^3 + 13/4x^2 - 165/8x - 513/8 = 0", "output": "x^3 + 13/4x^2 - 165/8x - 513/8 = 0\n(x - 9/2)(x - -19/4)(x - -3) = 0\nx - 9/2 = 0\nx - -19/4 = 0\nx - -3 = 0\nx = 9/2\nx = -19/4\nx = -3"} {"input": "Solve quickly: x^2 - 4x + 20/9 = 0", "output": "x^2 - 4x + 20/9 = 0\n(x - 10/3)(x - 2/3) = 0\nx - 10/3 = 0 or x - 2/3 = 0\nx = 10/3\nx = 2/3"} {"input": "Solve simultaneously:\n6x + 7y = -37/5\n5x + 10y = -12", "output": "6x + 7y = -37/5\n5x + 10y = -12\n\nUsing elimination\n5*(6x + 7y = -37/5)\n6*(5x + 10y = -12)\n30x + 35y = -37\n30x + 60y = -72\nSubtract equations\n-25y = 35\ny = 35/-25\ny = -7/5\n\nSubstitute y\n6x + 7(-7/5) = -37/5\n6x = 12/5\nx = 12/5/6\nx = 2/5"} {"input": "Find x and y such that\n4x + 4y = 38/3\n3x + 5y = 113/6", "output": "4x + 4y = 38/3\n3x + 5y = 113/6\n\nUsing elimination\n3*(4x + 4y = 38/3)\n4*(3x + 5y = 113/6)\n12x + 12y = 38\n12x + 20y = 226/3\nSubtract equations\n-8y = -112/3\ny = -112/3/-8\ny = 14/3\n\nSubstitute y\n4x + 4(14/3) = 38/3\n4x = -6\nx = -6/4\nx = -3/2"} {"input": "Find x in 10x + 20 = 0", "output": "10x + 20 = 0\n10x = -20\nx = -20 / 10\nx = -2"} {"input": "Find x for x^3 + 217/24x^2 + 413/18x + 152/9 = 0", "output": "x^3 + 217/24x^2 + 413/18x + 152/9 = 0\n(x - -16/3)(x - -4/3)(x - -19/8) = 0\nx - -16/3 = 0\nx - -4/3 = 0\nx - -19/8 = 0\nx = -16/3\nx = -4/3\nx = -19/8"} {"input": "Determine x in x^2 + 13/8x + 5/8 = 0", "output": "x^2 + 13/8x + 5/8 = 0\n(x - -1)(x - -5/8) = 0\nx - -1 = 0 or x - -5/8 = 0\nx = -1\nx = -5/8"} {"input": "Find x in x^3 + 493/84x^2 + 78/7x + 27/4 = 0", "output": "x^3 + 493/84x^2 + 78/7x + 27/4 = 0\n(x - -9/4)(x - -9/7)(x - -7/3) = 0\nx - -9/4 = 0\nx - -9/7 = 0\nx - -7/3 = 0\nx = -9/4\nx = -9/7\nx = -7/3"} {"input": "Solve the equation x^2 + 31/63x - 44/21 = 0", "output": "x^2 + 31/63x - 44/21 = 0\n(x - -12/7)(x - 11/9) = 0\nx - -12/7 = 0 or x - 11/9 = 0\nx = -12/7\nx = 11/9"} {"input": "Solve simultaneously:\n4x + 7y = 35\n10x + 6y = 53", "output": "4x + 7y = 35\n10x + 6y = 53\n\nUsing elimination\n10*(4x + 7y = 35)\n4*(10x + 6y = 53)\n40x + 70y = 350\n40x + 24y = 212\nSubtract equations\n46y = 138\ny = 138/46\ny = 3\n\nSubstitute y\n4x + 7(3) = 35\n4x = 14\nx = 14/4\nx = 7/2"} {"input": "Find the solution to x^2 - 167/42x + 68/21 = 0", "output": "x^2 - 167/42x + 68/21 = 0\n(x - 17/6)(x - 8/7) = 0\nx - 17/6 = 0 or x - 8/7 = 0\nx = 17/6\nx = 8/7"} {"input": "Solve 8x + 72/5 = 0", "output": "8x + 72/5 = 0\n8x = -72/5\nx = -72/5 / 8\nx = -9/5"} {"input": "Find x and y such that\n8x + 7y = -7\n5x + 8y = -535/56", "output": "8x + 7y = -7\n5x + 8y = -535/56\n\nUsing elimination\n5*(8x + 7y = -7)\n8*(5x + 8y = -535/56)\n40x + 35y = -35\n40x + 64y = -535/7\nSubtract equations\n-29y = 290/7\ny = 290/7/-29\ny = -10/7\n\nSubstitute y\n8x + 7(-10/7) = -7\n8x = 3\nx = 3/8\nx = 3/8"} {"input": "Solve quickly: x^3 - 18x^2 + 335/4x - 75/2 = 0", "output": "x^3 - 18x^2 + 335/4x - 75/2 = 0\n(x - 15/2)(x - 1/2)(x - 10) = 0\nx - 15/2 = 0\nx - 1/2 = 0\nx - 10 = 0\nx = 15/2\nx = 1/2\nx = 10"} {"input": "Solve the system:\n1x + 2y = -162/7\n1x + 5y = -393/7", "output": "1x + 2y = -162/7\n1x + 5y = -393/7\n\nUsing elimination\n1*(1x + 2y = -162/7)\n1*(1x + 5y = -393/7)\n1x + 2y = -162/7\n1x + 5y = -393/7\nSubtract equations\n-3y = 33\ny = 33/-3\ny = -11\n\nSubstitute y\n1x + 2(-11) = -162/7\n1x = -8/7\nx = -8/7/1\nx = -8/7"} {"input": "Solve quickly: x^3 + 25/4x^2 + 99/8x + 63/8 = 0", "output": "x^3 + 25/4x^2 + 99/8x + 63/8 = 0\n(x - -7/4)(x - -3/2)(x - -3) = 0\nx - -7/4 = 0\nx - -3/2 = 0\nx - -3 = 0\nx = -7/4\nx = -3/2\nx = -3"} {"input": "What value of x satisfies x^3 - 25/24x^2 - 57/32x + 65/48 = 0", "output": "x^3 - 25/24x^2 - 57/32x + 65/48 = 0\n(x - 13/8)(x - 2/3)(x - -5/4) = 0\nx - 13/8 = 0\nx - 2/3 = 0\nx - -5/4 = 0\nx = 13/8\nx = 2/3\nx = -5/4"} {"input": "Compute the solution of x^3 + 11x^2 + 36x + 36 = 0", "output": "x^3 + 11x^2 + 36x + 36 = 0\n(x - -2)(x - -3)(x - -6) = 0\nx - -2 = 0\nx - -3 = 0\nx - -6 = 0\nx = -2\nx = -3\nx = -6"} {"input": "Find x and y such that\n1x + 8y = 41/14\n6x + 4y = -9/7", "output": "1x + 8y = 41/14\n6x + 4y = -9/7\n\nUsing elimination\n6*(1x + 8y = 41/14)\n1*(6x + 4y = -9/7)\n6x + 48y = 123/7\n6x + 4y = -9/7\nSubtract equations\n44y = 132/7\ny = 132/7/44\ny = 3/7\n\nSubstitute y\n1x + 8(3/7) = 41/14\n1x = -1/2\nx = -1/2/1\nx = -1/2"} {"input": "Solve quickly: x^2 - 4x - 32 = 0", "output": "x^2 - 4x - 32 = 0\n(x - 8)(x - -4) = 0\nx - 8 = 0 or x - -4 = 0\nx = 8\nx = -4"} {"input": "Solve the equation 8x - 56/9 = 0", "output": "8x - 56/9 = 0\n8x = 56/9\nx = 56/9 / 8\nx = 7/9"} {"input": "What value of x satisfies 8x - 8 = 0", "output": "8x - 8 = 0\n8x = 8\nx = 8 / 8\nx = 1"} {"input": "Find the solution to x^2 - 2x = 0", "output": "x^2 - 2x = 0\n(x - 2)(x - 0) = 0\nx - 2 = 0 or x - 0 = 0\nx = 2\nx = 0"} {"input": "What value of x satisfies x^3 - 9/10x^2 - 661/10x - 741/5 = 0", "output": "x^3 - 9/10x^2 - 661/10x - 741/5 = 0\n(x - -13/5)(x - 19/2)(x - -6) = 0\nx - -13/5 = 0\nx - 19/2 = 0\nx - -6 = 0\nx = -13/5\nx = 19/2\nx = -6"} {"input": "What value of x satisfies 7x - 91/3 = 0", "output": "7x - 91/3 = 0\n7x = 91/3\nx = 91/3 / 7\nx = 13/3"} {"input": "Solve the equations:\n9x + 5y = -67/7\n4x + 4y = -92/7", "output": "9x + 5y = -67/7\n4x + 4y = -92/7\n\nUsing elimination\n4*(9x + 5y = -67/7)\n9*(4x + 4y = -92/7)\n36x + 20y = -268/7\n36x + 36y = -828/7\nSubtract equations\n-16y = 80\ny = 80/-16\ny = -5\n\nSubstitute y\n9x + 5(-5) = -67/7\n9x = 108/7\nx = 108/7/9\nx = 12/7"} {"input": "Find x in x^3 - 33/8x^2 - 45/4x = 0", "output": "x^3 - 33/8x^2 - 45/4x = 0\n(x - 6)(x - 0)(x - -15/8) = 0\nx - 6 = 0\nx - 0 = 0\nx - -15/8 = 0\nx = 6\nx = 0\nx = -15/8"} {"input": "Find the solution to x^3 + 37/90x^2 - 791/270x - 8/9 = 0", "output": "x^3 + 37/90x^2 - 791/270x - 8/9 = 0\n(x - 5/3)(x - -3/10)(x - -16/9) = 0\nx - 5/3 = 0\nx - -3/10 = 0\nx - -16/9 = 0\nx = 5/3\nx = -3/10\nx = -16/9"} {"input": "Solve quickly: 7x + 91/4 = 0", "output": "7x + 91/4 = 0\n7x = -91/4\nx = -91/4 / 7\nx = -13/4"} {"input": "Find the solution to x^2 - 27/28x - 9/7 = 0", "output": "x^2 - 27/28x - 9/7 = 0\n(x - -3/4)(x - 12/7) = 0\nx - -3/4 = 0 or x - 12/7 = 0\nx = -3/4\nx = 12/7"} {"input": "Solve the equation 4x + 52/7 = 0", "output": "4x + 52/7 = 0\n4x = -52/7\nx = -52/7 / 4\nx = -13/7"} {"input": "Determine x in x^2 - 149/72x + 13/18 = 0", "output": "x^2 - 149/72x + 13/18 = 0\n(x - 4/9)(x - 13/8) = 0\nx - 4/9 = 0 or x - 13/8 = 0\nx = 4/9\nx = 13/8"} {"input": "Solve quickly: 8x - 8/7 = 0", "output": "8x - 8/7 = 0\n8x = 8/7\nx = 8/7 / 8\nx = 1/7"} {"input": "Find the solution to 10x + 70/3 = 0", "output": "10x + 70/3 = 0\n10x = -70/3\nx = -70/3 / 10\nx = -7/3"} {"input": "Solve simultaneously:\n3x + 5y = 100/7\n6x + 9y = 180/7", "output": "3x + 5y = 100/7\n6x + 9y = 180/7\n\nUsing elimination\n6*(3x + 5y = 100/7)\n3*(6x + 9y = 180/7)\n18x + 30y = 600/7\n18x + 27y = 540/7\nSubtract equations\n3y = 60/7\ny = 60/7/3\ny = 20/7\n\nSubstitute y\n3x + 5(20/7) = 100/7\n3x = 0\nx = 0/3\nx = 0"} {"input": "Find x in 4x - 6 = 0", "output": "4x - 6 = 0\n4x = 6\nx = 6 / 4\nx = 3/2"} {"input": "Solve quickly: x^3 + 22/3x^2 - 76/3x + 40/3 = 0", "output": "x^3 + 22/3x^2 - 76/3x + 40/3 = 0\n(x - 2)(x - 2/3)(x - -10) = 0\nx - 2 = 0\nx - 2/3 = 0\nx - -10 = 0\nx = 2\nx = 2/3\nx = -10"} {"input": "Find the solution to x^3 - 23/4x^2 + 1123/200x + 323/100 = 0", "output": "x^3 - 23/4x^2 + 1123/200x + 323/100 = 0\n(x - 17/4)(x - -2/5)(x - 19/10) = 0\nx - 17/4 = 0\nx - -2/5 = 0\nx - 19/10 = 0\nx = 17/4\nx = -2/5\nx = 19/10"} {"input": "Solve simultaneously:\n1x + 3y = -81/8\n3x + 4y = -47/2", "output": "1x + 3y = -81/8\n3x + 4y = -47/2\n\nUsing elimination\n3*(1x + 3y = -81/8)\n1*(3x + 4y = -47/2)\n3x + 9y = -243/8\n3x + 4y = -47/2\nSubtract equations\n5y = -55/8\ny = -55/8/5\ny = -11/8\n\nSubstitute y\n1x + 3(-11/8) = -81/8\n1x = -6\nx = -6/1\nx = -6"} {"input": "Compute the solution of x^3 - 63/5x^2 - 272/5x = 0", "output": "x^3 - 63/5x^2 - 272/5x = 0\n(x - -17/5)(x - 0)(x - 16) = 0\nx - -17/5 = 0\nx - 0 = 0\nx - 16 = 0\nx = -17/5\nx = 0\nx = 16"} {"input": "What value of x satisfies x^3 + 17/60x^2 - 299/40x + 169/24 = 0", "output": "x^3 + 17/60x^2 - 299/40x + 169/24 = 0\n(x - 13/10)(x - -13/4)(x - 5/3) = 0\nx - 13/10 = 0\nx - -13/4 = 0\nx - 5/3 = 0\nx = 13/10\nx = -13/4\nx = 5/3"} {"input": "Compute the solution of 1x + 20 = 0", "output": "1x + 20 = 0\n1x = -20\nx = -20 / 1\nx = -20"} {"input": "Solve quickly: 6x - 24 = 0", "output": "6x - 24 = 0\n6x = 24\nx = 24 / 6\nx = 4"} {"input": "Determine x in x^2 - 3/4x - 5/2 = 0", "output": "x^2 - 3/4x - 5/2 = 0\n(x - -5/4)(x - 2) = 0\nx - -5/4 = 0 or x - 2 = 0\nx = -5/4\nx = 2"} {"input": "Solve quickly: 7x - 11 = 0", "output": "7x - 11 = 0\n7x = 11\nx = 11 / 7\nx = 11/7"} {"input": "Determine x in 2x + 1/2 = 0", "output": "2x + 1/2 = 0\n2x = -1/2\nx = -1/2 / 2\nx = -1/4"} {"input": "Solve the system:\n10x + 3y = 559/14\n6x + 9y = 249/14", "output": "10x + 3y = 559/14\n6x + 9y = 249/14\n\nUsing elimination\n6*(10x + 3y = 559/14)\n10*(6x + 9y = 249/14)\n60x + 18y = 1677/7\n60x + 90y = 1245/7\nSubtract equations\n-72y = 432/7\ny = 432/7/-72\ny = -6/7\n\nSubstitute y\n10x + 3(-6/7) = 559/14\n10x = 85/2\nx = 85/2/10\nx = 17/4"} {"input": "Find x in 6x - 15/2 = 0", "output": "6x - 15/2 = 0\n6x = 15/2\nx = 15/2 / 6\nx = 5/4"} {"input": "Solve the equation x^3 + 71/45x^2 - 52/27x - 76/45 = 0", "output": "x^3 + 71/45x^2 - 52/27x - 76/45 = 0\n(x - -2/3)(x - 6/5)(x - -19/9) = 0\nx - -2/3 = 0\nx - 6/5 = 0\nx - -19/9 = 0\nx = -2/3\nx = 6/5\nx = -19/9"} {"input": "Find x and y such that\n9x + 1y = -39/10\n9x + 9y = -279/10", "output": "9x + 1y = -39/10\n9x + 9y = -279/10\n\nUsing elimination\n9*(9x + 1y = -39/10)\n9*(9x + 9y = -279/10)\n81x + 9y = -351/10\n81x + 81y = -2511/10\nSubtract equations\n-72y = 216\ny = 216/-72\ny = -3\n\nSubstitute y\n9x + 1(-3) = -39/10\n9x = -9/10\nx = -9/10/9\nx = -1/10"} {"input": "Find x and y such that\n6x + 3y = 9\n4x + 6y = 66/5", "output": "6x + 3y = 9\n4x + 6y = 66/5\n\nUsing elimination\n4*(6x + 3y = 9)\n6*(4x + 6y = 66/5)\n24x + 12y = 36\n24x + 36y = 396/5\nSubtract equations\n-24y = -216/5\ny = -216/5/-24\ny = 9/5\n\nSubstitute y\n6x + 3(9/5) = 9\n6x = 18/5\nx = 18/5/6\nx = 3/5"} {"input": "Find x for x^3 + 63/8x^2 + 11/4x - 51 = 0", "output": "x^3 + 63/8x^2 + 11/4x - 51 = 0\n(x - 17/8)(x - -6)(x - -4) = 0\nx - 17/8 = 0\nx - -6 = 0\nx - -4 = 0\nx = 17/8\nx = -6\nx = -4"} {"input": "Solve quickly: 9x - 13 = 0", "output": "9x - 13 = 0\n9x = 13\nx = 13 / 9\nx = 13/9"} {"input": "Find x in x^3 + 9/10x^2 - 2/5x - 3/10 = 0", "output": "x^3 + 9/10x^2 - 2/5x - 3/10 = 0\n(x - -1/2)(x - -1)(x - 3/5) = 0\nx - -1/2 = 0\nx - -1 = 0\nx - 3/5 = 0\nx = -1/2\nx = -1\nx = 3/5"} {"input": "Find the solution to x^3 + 141/10x^2 - 71/5x - 21/2 = 0", "output": "x^3 + 141/10x^2 - 71/5x - 21/2 = 0\n(x - -15)(x - 7/5)(x - -1/2) = 0\nx - -15 = 0\nx - 7/5 = 0\nx - -1/2 = 0\nx = -15\nx = 7/5\nx = -1/2"} {"input": "Solve x^3 + 81/40x^2 - 177/20x - 19/5 = 0", "output": "x^3 + 81/40x^2 - 177/20x - 19/5 = 0\n(x - -4)(x - -2/5)(x - 19/8) = 0\nx - -4 = 0\nx - -2/5 = 0\nx - 19/8 = 0\nx = -4\nx = -2/5\nx = 19/8"} {"input": "Solve quickly: x^2 + 71/21x + 20/7 = 0", "output": "x^2 + 71/21x + 20/7 = 0\n(x - -5/3)(x - -12/7) = 0\nx - -5/3 = 0 or x - -12/7 = 0\nx = -5/3\nx = -12/7"} {"input": "Solve the equation x^3 + 12x^2 - 445/4x - 117/2 = 0", "output": "x^3 + 12x^2 - 445/4x - 117/2 = 0\n(x - -18)(x - 13/2)(x - -1/2) = 0\nx - -18 = 0\nx - 13/2 = 0\nx - -1/2 = 0\nx = -18\nx = 13/2\nx = -1/2"} {"input": "Find x for 8x + 4 = 0", "output": "8x + 4 = 0\n8x = -4\nx = -4 / 8\nx = -1/2"} {"input": "Solve the equations:\n5x + 6y = 49/4\n3x + 9y = 87/4", "output": "5x + 6y = 49/4\n3x + 9y = 87/4\n\nUsing elimination\n3*(5x + 6y = 49/4)\n5*(3x + 9y = 87/4)\n15x + 18y = 147/4\n15x + 45y = 435/4\nSubtract equations\n-27y = -72\ny = -72/-27\ny = 8/3\n\nSubstitute y\n5x + 6(8/3) = 49/4\n5x = -15/4\nx = -15/4/5\nx = -3/4"} {"input": "Solve x^3 - 7/4x^2 - 17/16x - 9/64 = 0", "output": "x^3 - 7/4x^2 - 17/16x - 9/64 = 0\n(x - 9/4)(x - -1/4)(x - -1/4) = 0\nx - 9/4 = 0\nx - -1/4 = 0\nx - -1/4 = 0\nx = 9/4\nx = -1/4\nx = -1/4"} {"input": "Solve the equation 9x - 19 = 0", "output": "9x - 19 = 0\n9x = 19\nx = 19 / 9\nx = 19/9"} {"input": "Find the solution to 1x - 3/2 = 0", "output": "1x - 3/2 = 0\n1x = 3/2\nx = 3/2 / 1\nx = 3/2"} {"input": "Compute the solution of x^3 + 197/168x^2 - 1/4x - 1/21 = 0", "output": "x^3 + 197/168x^2 - 1/4x - 1/21 = 0\n(x - -1/8)(x - -4/3)(x - 2/7) = 0\nx - -1/8 = 0\nx - -4/3 = 0\nx - 2/7 = 0\nx = -1/8\nx = -4/3\nx = 2/7"} {"input": "Solve the system:\n4x + 5y = -2/5\n1x + 10y = -141/10", "output": "4x + 5y = -2/5\n1x + 10y = -141/10\n\nUsing elimination\n1*(4x + 5y = -2/5)\n4*(1x + 10y = -141/10)\n4x + 5y = -2/5\n4x + 40y = -282/5\nSubtract equations\n-35y = 56\ny = 56/-35\ny = -8/5\n\nSubstitute y\n4x + 5(-8/5) = -2/5\n4x = 38/5\nx = 38/5/4\nx = 19/10"} {"input": "Solve the equations:\n7x + 3y = 16/5\n1x + 9y = 88/5", "output": "7x + 3y = 16/5\n1x + 9y = 88/5\n\nUsing elimination\n1*(7x + 3y = 16/5)\n7*(1x + 9y = 88/5)\n7x + 3y = 16/5\n7x + 63y = 616/5\nSubtract equations\n-60y = -120\ny = -120/-60\ny = 2\n\nSubstitute y\n7x + 3(2) = 16/5\n7x = -14/5\nx = -14/5/7\nx = -2/5"} {"input": "Find x and y such that\n7x + 3y = -1\n9x + 5y = -25/7", "output": "7x + 3y = -1\n9x + 5y = -25/7\n\nUsing elimination\n9*(7x + 3y = -1)\n7*(9x + 5y = -25/7)\n63x + 27y = -9\n63x + 35y = -25\nSubtract equations\n-8y = 16\ny = 16/-8\ny = -2\n\nSubstitute y\n7x + 3(-2) = -1\n7x = 5\nx = 5/7\nx = 5/7"} {"input": "Solve simultaneously:\n9x + 2y = -194/5\n2x + 1y = -47/5", "output": "9x + 2y = -194/5\n2x + 1y = -47/5\n\nUsing elimination\n2*(9x + 2y = -194/5)\n9*(2x + 1y = -47/5)\n18x + 4y = -388/5\n18x + 9y = -423/5\nSubtract equations\n-5y = 7\ny = 7/-5\ny = -7/5\n\nSubstitute y\n9x + 2(-7/5) = -194/5\n9x = -36\nx = -36/9\nx = -4"} {"input": "Find x for 6x - 54/5 = 0", "output": "6x - 54/5 = 0\n6x = 54/5\nx = 54/5 / 6\nx = 9/5"} {"input": "Compute the solution of x^3 + 1/8x^2 - 1/4x - 1/32 = 0", "output": "x^3 + 1/8x^2 - 1/4x - 1/32 = 0\n(x - 1/2)(x - -1/2)(x - -1/8) = 0\nx - 1/2 = 0\nx - -1/2 = 0\nx - -1/8 = 0\nx = 1/2\nx = -1/2\nx = -1/8"} {"input": "Find x for x^3 - 62/7x^2 + 47/7x + 8/7 = 0", "output": "x^3 - 62/7x^2 + 47/7x + 8/7 = 0\n(x - -1/7)(x - 1)(x - 8) = 0\nx - -1/7 = 0\nx - 1 = 0\nx - 8 = 0\nx = -1/7\nx = 1\nx = 8"} {"input": "Determine x in x^3 + 1487/180x^2 + 67/3x + 3553/180 = 0", "output": "x^3 + 1487/180x^2 + 67/3x + 3553/180 = 0\n(x - -17/5)(x - -11/4)(x - -19/9) = 0\nx - -17/5 = 0\nx - -11/4 = 0\nx - -19/9 = 0\nx = -17/5\nx = -11/4\nx = -19/9"} {"input": "Compute the solution of 3x - 9/5 = 0", "output": "3x - 9/5 = 0\n3x = 9/5\nx = 9/5 / 3\nx = 3/5"} {"input": "What value of x satisfies x^3 - 117/8x^2 - 653/8x - 57/2 = 0", "output": "x^3 - 117/8x^2 - 653/8x - 57/2 = 0\n(x - -3/8)(x - 19)(x - -4) = 0\nx - -3/8 = 0\nx - 19 = 0\nx - -4 = 0\nx = -3/8\nx = 19\nx = -4"} {"input": "Find x for x^3 - 144/35x^2 - 149/35x - 6/7 = 0", "output": "x^3 - 144/35x^2 - 149/35x - 6/7 = 0\n(x - -2/7)(x - 5)(x - -3/5) = 0\nx - -2/7 = 0\nx - 5 = 0\nx - -3/5 = 0\nx = -2/7\nx = 5\nx = -3/5"} {"input": "Find x for x^3 - 1853/315x^2 + 1199/105x - 2299/315 = 0", "output": "x^3 - 1853/315x^2 + 1199/105x - 2299/315 = 0\n(x - 19/9)(x - 11/7)(x - 11/5) = 0\nx - 19/9 = 0\nx - 11/7 = 0\nx - 11/5 = 0\nx = 19/9\nx = 11/7\nx = 11/5"} {"input": "What value of x satisfies 1x + 5/9 = 0", "output": "1x + 5/9 = 0\n1x = -5/9\nx = -5/9 / 1\nx = -5/9"} {"input": "Compute the solution of x^3 - 197/180x^2 - 5/12x + 5/18 = 0", "output": "x^3 - 197/180x^2 - 5/12x + 5/18 = 0\n(x - -5/9)(x - 5/4)(x - 2/5) = 0\nx - -5/9 = 0\nx - 5/4 = 0\nx - 2/5 = 0\nx = -5/9\nx = 5/4\nx = 2/5"} {"input": "Find x for x^2 + 9/2x + 45/16 = 0", "output": "x^2 + 9/2x + 45/16 = 0\n(x - -15/4)(x - -3/4) = 0\nx - -15/4 = 0 or x - -3/4 = 0\nx = -15/4\nx = -3/4"} {"input": "What value of x satisfies 9x - 27/4 = 0", "output": "9x - 27/4 = 0\n9x = 27/4\nx = 27/4 / 9\nx = 3/4"} {"input": "Solve the equation x^3 - 23/3x^2 + 22/3x + 16 = 0", "output": "x^3 - 23/3x^2 + 22/3x + 16 = 0\n(x - 6)(x - -1)(x - 8/3) = 0\nx - 6 = 0\nx - -1 = 0\nx - 8/3 = 0\nx = 6\nx = -1\nx = 8/3"} {"input": "What value of x satisfies x^2 - 34/9x + 280/81 = 0", "output": "x^2 - 34/9x + 280/81 = 0\n(x - 20/9)(x - 14/9) = 0\nx - 20/9 = 0 or x - 14/9 = 0\nx = 20/9\nx = 14/9"} {"input": "What value of x satisfies x^3 - 29/5x^2 - 86/5x - 16/5 = 0", "output": "x^3 - 29/5x^2 - 86/5x - 16/5 = 0\n(x - -2)(x - 8)(x - -1/5) = 0\nx - -2 = 0\nx - 8 = 0\nx - -1/5 = 0\nx = -2\nx = 8\nx = -1/5"} {"input": "Find x in x^3 + 859/90x^2 + 89/18x + 2/5 = 0", "output": "x^3 + 859/90x^2 + 89/18x + 2/5 = 0\n(x - -9)(x - -4/9)(x - -1/10) = 0\nx - -9 = 0\nx - -4/9 = 0\nx - -1/10 = 0\nx = -9\nx = -4/9\nx = -1/10"} {"input": "Find the solution to x^2 + 57/8x + 7/8 = 0", "output": "x^2 + 57/8x + 7/8 = 0\n(x - -1/8)(x - -7) = 0\nx - -1/8 = 0 or x - -7 = 0\nx = -1/8\nx = -7"} {"input": "Find x for 9x + 18 = 0", "output": "9x + 18 = 0\n9x = -18\nx = -18 / 9\nx = -2"} {"input": "Solve quickly: x^2 - 23x + 90 = 0", "output": "x^2 - 23x + 90 = 0\n(x - 18)(x - 5) = 0\nx - 18 = 0 or x - 5 = 0\nx = 18\nx = 5"} {"input": "Find the solution to x^3 - 91/5x^2 - 36x = 0", "output": "x^3 - 91/5x^2 - 36x = 0\n(x - 0)(x - -9/5)(x - 20) = 0\nx - 0 = 0\nx - -9/5 = 0\nx - 20 = 0\nx = 0\nx = -9/5\nx = 20"} {"input": "Solve quickly: x^3 - 403/84x^2 + 160/21x - 4 = 0", "output": "x^3 - 403/84x^2 + 160/21x - 4 = 0\n(x - 12/7)(x - 4/3)(x - 7/4) = 0\nx - 12/7 = 0\nx - 4/3 = 0\nx - 7/4 = 0\nx = 12/7\nx = 4/3\nx = 7/4"} {"input": "Solve the system:\n8x + 5y = -183/10\n5x + 7y = -157/10", "output": "8x + 5y = -183/10\n5x + 7y = -157/10\n\nUsing elimination\n5*(8x + 5y = -183/10)\n8*(5x + 7y = -157/10)\n40x + 25y = -183/2\n40x + 56y = -628/5\nSubtract equations\n-31y = 341/10\ny = 341/10/-31\ny = -11/10\n\nSubstitute y\n8x + 5(-11/10) = -183/10\n8x = -64/5\nx = -64/5/8\nx = -8/5"} {"input": "Solve the equations:\n3x + 9y = 3/28\n9x + 1y = 1153/28", "output": "3x + 9y = 3/28\n9x + 1y = 1153/28\n\nUsing elimination\n9*(3x + 9y = 3/28)\n3*(9x + 1y = 1153/28)\n27x + 81y = 27/28\n27x + 3y = 3459/28\nSubtract equations\n78y = -858/7\ny = -858/7/78\ny = -11/7\n\nSubstitute y\n3x + 9(-11/7) = 3/28\n3x = 57/4\nx = 57/4/3\nx = 19/4"} {"input": "Find x for x^2 + 97/45x - 26/5 = 0", "output": "x^2 + 97/45x - 26/5 = 0\n(x - 13/9)(x - -18/5) = 0\nx - 13/9 = 0 or x - -18/5 = 0\nx = 13/9\nx = -18/5"} {"input": "Solve the system:\n6x + 1y = 190/3\n3x + 8y = 170/3", "output": "6x + 1y = 190/3\n3x + 8y = 170/3\n\nUsing elimination\n3*(6x + 1y = 190/3)\n6*(3x + 8y = 170/3)\n18x + 3y = 190\n18x + 48y = 340\nSubtract equations\n-45y = -150\ny = -150/-45\ny = 10/3\n\nSubstitute y\n6x + 1(10/3) = 190/3\n6x = 60\nx = 60/6\nx = 10"} {"input": "Solve quickly: 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Solve x^2 - 39/20x - 11/5 = 0", "output": "x^2 - 39/20x - 11/5 = 0\n(x - -4/5)(x - 11/4) = 0\nx - -4/5 = 0 or x - 11/4 = 0\nx = -4/5\nx = 11/4"} {"input": "Find x for x^2 - 21x + 80 = 0", "output": "x^2 - 21x + 80 = 0\n(x - 5)(x - 16) = 0\nx - 5 = 0 or x - 16 = 0\nx = 5\nx = 16"} {"input": "Solve quickly: x^2 - 1/14x - 45/7 = 0", "output": "x^2 - 1/14x - 45/7 = 0\n(x - 18/7)(x - -5/2) = 0\nx - 18/7 = 0 or x - -5/2 = 0\nx = 18/7\nx = -5/2"} {"input": "Find x for 7x + 21/4 = 0", "output": "7x + 21/4 = 0\n7x = -21/4\nx = -21/4 / 7\nx = -3/4"} {"input": "Determine x in x^3 - 11/90x^2 - 998/135x - 221/270 = 0", "output": "x^3 - 11/90x^2 - 998/135x - 221/270 = 0\n(x - 17/6)(x - -1/9)(x - -13/5) = 0\nx - 17/6 = 0\nx - -1/9 = 0\nx - -13/5 = 0\nx = 17/6\nx = -1/9\nx = -13/5"} {"input": "Solve x^2 - 25/14x - 25/14 = 0", "output": "x^2 - 25/14x - 25/14 = 0\n(x - 5/2)(x - -5/7) = 0\nx - 5/2 = 0 or x - -5/7 = 0\nx = 5/2\nx = -5/7"} {"input": "Solve x^2 - 13/6x - 119/6 = 0", "output": "x^2 - 13/6x - 119/6 = 0\n(x - 17/3)(x - -7/2) = 0\nx - 17/3 = 0 or x - -7/2 = 0\nx = 17/3\nx = -7/2"} {"input": "Find x for x^2 - 1x - 8/49 = 0", "output": "x^2 - 1x - 8/49 = 0\n(x - -1/7)(x - 8/7) = 0\nx - -1/7 = 0 or x - 8/7 = 0\nx = -1/7\nx = 8/7"} {"input": "Find the solution to x^2 - 5x + 6 = 0", "output": "x^2 - 5x + 6 = 0\n(x - 3)(x - 2) = 0\nx - 3 = 0 or x - 2 = 0\nx = 3\nx = 2"} {"input": "Solve the equation x^3 - 25/2x^2 + 374/9x - 160/9 = 0", "output": "x^3 - 25/2x^2 + 374/9x - 160/9 = 0\n(x - 16/3)(x - 20/3)(x - 1/2) = 0\nx - 16/3 = 0\nx - 20/3 = 0\nx - 1/2 = 0\nx = 16/3\nx = 20/3\nx = 1/2"} {"input": "Solve the equation x^2 - 27/4x + 9/2 = 0", "output": "x^2 - 27/4x + 9/2 = 0\n(x - 6)(x - 3/4) = 0\nx - 6 = 0 or x - 3/4 = 0\nx = 6\nx = 3/4"} {"input": "Determine x in x^3 + 86/15x^2 - 11/15x - 442/15 = 0", "output": "x^3 + 86/15x^2 - 11/15x - 442/15 = 0\n(x - -17/5)(x - -13/3)(x - 2) = 0\nx - -17/5 = 0\nx - -13/3 = 0\nx - 2 = 0\nx = -17/5\nx = -13/3\nx = 2"} {"input": "Find x and y such that\n6x + 1y = -68/5\n2x + 5y = -116/5", "output": "6x + 1y = -68/5\n2x + 5y = -116/5\n\nUsing elimination\n2*(6x + 1y = -68/5)\n6*(2x + 5y = -116/5)\n12x + 2y = -136/5\n12x + 30y = -696/5\nSubtract equations\n-28y = 112\ny = 112/-28\ny = -4\n\nSubstitute y\n6x + 1(-4) = -68/5\n6x = -48/5\nx = -48/5/6\nx = -8/5"} {"input": "Determine x in x^3 + 1754/315x^2 + 1027/105x + 338/63 = 0", "output": "x^3 + 1754/315x^2 + 1027/105x + 338/63 = 0\n(x - -13/5)(x - -13/7)(x - -10/9) = 0\nx - -13/5 = 0\nx - -13/7 = 0\nx - -10/9 = 0\nx = -13/5\nx = -13/7\nx = -10/9"} {"input": "Find x for 2x - 38/7 = 0", "output": "2x - 38/7 = 0\n2x = 38/7\nx = 38/7 / 2\nx = 19/7"} {"input": "Find x and y such that\n8x + 4y = -44/3\n5x + 3y = -28/3", "output": "8x + 4y = -44/3\n5x + 3y = -28/3\n\nUsing elimination\n5*(8x + 4y = -44/3)\n8*(5x + 3y = -28/3)\n40x + 20y = -220/3\n40x + 24y = -224/3\nSubtract equations\n-4y = 4/3\ny = 4/3/-4\ny = -1/3\n\nSubstitute y\n8x + 4(-1/3) = -44/3\n8x = -40/3\nx = -40/3/8\nx = -5/3"} {"input": "Find x in x^3 + 1/60x^2 - 659/120x + 21/5 = 0", "output": "x^3 + 1/60x^2 - 659/120x + 21/5 = 0\n(x - 9/10)(x - 7/4)(x - -8/3) = 0\nx - 9/10 = 0\nx - 7/4 = 0\nx - -8/3 = 0\nx = 9/10\nx = 7/4\nx = -8/3"} {"input": "Solve the equations:\n9x + 9y = 67/2\n2x + 9y = 323/18", "output": "9x + 9y = 67/2\n2x + 9y = 323/18\n\nUsing elimination\n2*(9x + 9y = 67/2)\n9*(2x + 9y = 323/18)\n18x + 18y = 67\n18x + 81y = 323/2\nSubtract equations\n-63y = -189/2\ny = -189/2/-63\ny = 3/2\n\nSubstitute y\n9x + 9(3/2) = 67/2\n9x = 20\nx = 20/9\nx = 20/9"} {"input": "Find x and y such that\n6x + 6y = 177/4\n6x + 3y = 81/4", "output": "6x + 6y = 177/4\n6x + 3y = 81/4\n\nUsing elimination\n6*(6x + 6y = 177/4)\n6*(6x + 3y = 81/4)\n36x + 36y = 531/2\n36x + 18y = 243/2\nSubtract equations\n18y = 144\ny = 144/18\ny = 8\n\nSubstitute y\n6x + 6(8) = 177/4\n6x = -15/4\nx = -15/4/6\nx = -5/8"} {"input": "Solve simultaneously:\n5x + 6y = -296/15\n1x + 9y = -563/30", "output": "5x + 6y = -296/15\n1x + 9y = -563/30\n\nUsing elimination\n1*(5x + 6y = -296/15)\n5*(1x + 9y = -563/30)\n5x + 6y = -296/15\n5x + 45y = -563/6\nSubtract equations\n-39y = 741/10\ny = 741/10/-39\ny = -19/10\n\nSubstitute y\n5x + 6(-19/10) = -296/15\n5x = -25/3\nx = -25/3/5\nx = -5/3"} {"input": "Solve 4x + 8 = 0", "output": "4x + 8 = 0\n4x = -8\nx = -8 / 4\nx = -2"} {"input": "Compute the solution of 10x + 26 = 0", "output": "10x + 26 = 0\n10x = -26\nx = -26 / 10\nx = -13/5"} {"input": "Solve the system:\n9x + 4y = 148/5\n2x + 4y = 64/5", "output": "9x + 4y = 148/5\n2x + 4y = 64/5\n\nUsing elimination\n2*(9x + 4y = 148/5)\n9*(2x + 4y = 64/5)\n18x + 8y = 296/5\n18x + 36y = 576/5\nSubtract equations\n-28y = -56\ny = -56/-28\ny = 2\n\nSubstitute y\n9x + 4(2) = 148/5\n9x = 108/5\nx = 108/5/9\nx = 12/5"} {"input": "Solve x^3 + 41/4x^2 + 117/4x + 45/2 = 0", "output": "x^3 + 41/4x^2 + 117/4x + 45/2 = 0\n(x - -3)(x - -6)(x - -5/4) = 0\nx - -3 = 0\nx - -6 = 0\nx - -5/4 = 0\nx = -3\nx = -6\nx = -5/4"} {"input": "Find x in 10x - 40 = 0", "output": "10x - 40 = 0\n10x = 40\nx = 40 / 10\nx = 4"} {"input": "What value of x satisfies 8x - 20 = 0", "output": "8x - 20 = 0\n8x = 20\nx = 20 / 8\nx = 5/2"} {"input": "Compute the solution of 4x + 4 = 0", "output": "4x + 4 = 0\n4x = -4\nx = -4 / 4\nx = -1"} {"input": "Compute the solution of x^2 + 5/7x - 104/49 = 0", "output": "x^2 + 5/7x - 104/49 = 0\n(x - 8/7)(x - -13/7) = 0\nx - 8/7 = 0 or x - -13/7 = 0\nx = 8/7\nx = -13/7"} {"input": "Solve x^2 - 33/8x + 65/16 = 0", "output": "x^2 - 33/8x + 65/16 = 0\n(x - 13/8)(x - 5/2) = 0\nx - 13/8 = 0 or x - 5/2 = 0\nx = 13/8\nx = 5/2"} {"input": "Solve quickly: x^2 - 22/15x - 133/15 = 0", "output": "x^2 - 22/15x - 133/15 = 0\n(x - -7/3)(x - 19/5) = 0\nx - -7/3 = 0 or x - 19/5 = 0\nx = -7/3\nx = 19/5"} {"input": "Solve simultaneously:\n8x + 7y = 819/10\n9x + 10y = 551/5", "output": "8x + 7y = 819/10\n9x + 10y = 551/5\n\nUsing elimination\n9*(8x + 7y = 819/10)\n8*(9x + 10y = 551/5)\n72x + 63y = 7371/10\n72x + 80y = 4408/5\nSubtract equations\n-17y = -289/2\ny = -289/2/-17\ny = 17/2\n\nSubstitute y\n8x + 7(17/2) = 819/10\n8x = 112/5\nx = 112/5/8\nx = 14/5"} {"input": "Solve the equation x^3 - 36/7x^2 + 53/7x - 24/7 = 0", "output": "x^3 - 36/7x^2 + 53/7x - 24/7 = 0\n(x - 8/7)(x - 3)(x - 1) = 0\nx - 8/7 = 0\nx - 3 = 0\nx - 1 = 0\nx = 8/7\nx = 3\nx = 1"} {"input": "Find x in x^2 - 44/9x + 17/3 = 0", "output": "x^2 - 44/9x + 17/3 = 0\n(x - 17/9)(x - 3) = 0\nx - 17/9 = 0 or x - 3 = 0\nx = 17/9\nx = 3"} {"input": "Solve 8x - 104/9 = 0", "output": "8x - 104/9 = 0\n8x = 104/9\nx = 104/9 / 8\nx = 13/9"} {"input": "Find x for x^3 - 26/15x^2 - 49/15x + 4 = 0", "output": "x^3 - 26/15x^2 - 49/15x + 4 = 0\n(x - 12/5)(x - -5/3)(x - 1) = 0\nx - 12/5 = 0\nx - -5/3 = 0\nx - 1 = 0\nx = 12/5\nx = -5/3\nx = 1"} {"input": "Find x and y such that\n3x + 6y = -12\n10x + 10y = 20", "output": "3x + 6y = -12\n10x + 10y = 20\n\nUsing elimination\n10*(3x + 6y = -12)\n3*(10x + 10y = 20)\n30x + 60y = -120\n30x + 30y = 60\nSubtract equations\n30y = -180\ny = -180/30\ny = -6\n\nSubstitute y\n3x + 6(-6) = -12\n3x = 24\nx = 24/3\nx = 8"} {"input": "Solve simultaneously:\n6x + 5y = 65/14\n8x + 9y = 5/14", "output": "6x + 5y = 65/14\n8x + 9y = 5/14\n\nUsing elimination\n8*(6x + 5y = 65/14)\n6*(8x + 9y = 5/14)\n48x + 40y = 260/7\n48x + 54y = 15/7\nSubtract equations\n-14y = 35\ny = 35/-14\ny = -5/2\n\nSubstitute y\n6x + 5(-5/2) = 65/14\n6x = 120/7\nx = 120/7/6\nx = 20/7"} {"input": "Solve simultaneously:\n5x + 5y = 145/12\n3x + 8y = 367/12", "output": "5x + 5y = 145/12\n3x + 8y = 367/12\n\nUsing elimination\n3*(5x + 5y = 145/12)\n5*(3x + 8y = 367/12)\n15x + 15y = 145/4\n15x + 40y = 1835/12\nSubtract equations\n-25y = -350/3\ny = -350/3/-25\ny = 14/3\n\nSubstitute y\n5x + 5(14/3) = 145/12\n5x = -45/4\nx = -45/4/5\nx = -9/4"} {"input": "What value of x satisfies x^3 + 31/2x^2 - 225/2 = 0", "output": "x^3 + 31/2x^2 - 225/2 = 0\n(x - -3)(x - 5/2)(x - -15) = 0\nx - -3 = 0\nx - 5/2 = 0\nx - -15 = 0\nx = -3\nx = 5/2\nx = -15"} {"input": "Find x and y such that\n1x + 6y = 17/5\n10x + 3y = -65/2", "output": "1x + 6y = 17/5\n10x + 3y = -65/2\n\nUsing elimination\n10*(1x + 6y = 17/5)\n1*(10x + 3y = -65/2)\n10x + 60y = 34\n10x + 3y = -65/2\nSubtract equations\n57y = 133/2\ny = 133/2/57\ny = 7/6\n\nSubstitute y\n1x + 6(7/6) = 17/5\n1x = -18/5\nx = -18/5/1\nx = -18/5"} {"input": "Solve the system:\n2x + 4y = 57/2\n8x + 1y = 777/8", "output": "2x + 4y = 57/2\n8x + 1y = 777/8\n\nUsing elimination\n8*(2x + 4y = 57/2)\n2*(8x + 1y = 777/8)\n16x + 32y = 228\n16x + 2y = 777/4\nSubtract equations\n30y = 135/4\ny = 135/4/30\ny = 9/8\n\nSubstitute y\n2x + 4(9/8) = 57/2\n2x = 24\nx = 24/2\nx = 12"} {"input": "Solve the system:\n7x + 8y = -73/2\n1x + 5y = 5/2", "output": "7x + 8y = -73/2\n1x + 5y = 5/2\n\nUsing elimination\n1*(7x + 8y = -73/2)\n7*(1x + 5y = 5/2)\n7x + 8y = -73/2\n7x + 35y = 35/2\nSubtract equations\n-27y = -54\ny = -54/-27\ny = 2\n\nSubstitute y\n7x + 8(2) = -73/2\n7x = -105/2\nx = -105/2/7\nx = -15/2"} {"input": "Solve the system:\n3x + 8y = -259/10\n3x + 10y = -67/2", "output": "3x + 8y = -259/10\n3x + 10y = -67/2\n\nUsing elimination\n3*(3x + 8y = -259/10)\n3*(3x + 10y = -67/2)\n9x + 24y = -777/10\n9x + 30y = -201/2\nSubtract equations\n-6y = 114/5\ny = 114/5/-6\ny = -19/5\n\nSubstitute y\n3x + 8(-19/5) = -259/10\n3x = 9/2\nx = 9/2/3\nx = 3/2"} {"input": "Find x in x^2 + 7/2x = 0", "output": "x^2 + 7/2x = 0\n(x - -7/2)(x - 0) = 0\nx - -7/2 = 0 or x - 0 = 0\nx = -7/2\nx = 0"} {"input": "Solve quickly: x^2 + 29/42x - 130/21 = 0", "output": "x^2 + 29/42x - 130/21 = 0\n(x - 13/6)(x - -20/7) = 0\nx - 13/6 = 0 or x - -20/7 = 0\nx = 13/6\nx = -20/7"} {"input": "Solve quickly: x^3 + 10x^2 - 619/4x + 1235/4 = 0", "output": "x^3 + 10x^2 - 619/4x + 1235/4 = 0\n(x - 5/2)(x - -19)(x - 13/2) = 0\nx - 5/2 = 0\nx - -19 = 0\nx - 13/2 = 0\nx = 5/2\nx = -19\nx = 13/2"} {"input": "What value of x satisfies 2x + 13 = 0", "output": "2x + 13 = 0\n2x = -13\nx = -13 / 2\nx = -13/2"} {"input": "Solve 3x + 57/8 = 0", "output": "3x + 57/8 = 0\n3x = -57/8\nx = -57/8 / 3\nx = -19/8"} {"input": "Find x for x^2 - 97/6x + 8/3 = 0", "output": "x^2 - 97/6x + 8/3 = 0\n(x - 1/6)(x - 16) = 0\nx - 1/6 = 0 or x - 16 = 0\nx = 1/6\nx = 16"} {"input": "Find the solution to x^2 + 13/9x - 10/9 = 0", "output": "x^2 + 13/9x - 10/9 = 0\n(x - 5/9)(x - -2) = 0\nx - 5/9 = 0 or x - -2 = 0\nx = 5/9\nx = -2"} {"input": "Solve the equation 3x + 14 = 0", "output": "3x + 14 = 0\n3x = -14\nx = -14 / 3\nx = -14/3"} {"input": "Solve the equations:\n5x + 10y = -55\n7x + 5y = -127/2", "output": "5x + 10y = -55\n7x + 5y = -127/2\n\nUsing elimination\n7*(5x + 10y = -55)\n5*(7x + 5y = -127/2)\n35x + 70y = -385\n35x + 25y = -635/2\nSubtract equations\n45y = -135/2\ny = -135/2/45\ny = -3/2\n\nSubstitute y\n5x + 10(-3/2) = -55\n5x = -40\nx = -40/5\nx = -8"} {"input": "Solve quickly: x^2 + 5/9x - 50/27 = 0", "output": "x^2 + 5/9x - 50/27 = 0\n(x - 10/9)(x - -5/3) = 0\nx - 10/9 = 0 or x - -5/3 = 0\nx = 10/9\nx = -5/3"} {"input": "Determine x in x^3 - 123/28x^2 + 729/196x + 243/98 = 0", "output": "x^3 - 123/28x^2 + 729/196x + 243/98 = 0\n(x - 18/7)(x - -3/7)(x - 9/4) = 0\nx - 18/7 = 0\nx - -3/7 = 0\nx - 9/4 = 0\nx = 18/7\nx = -3/7\nx = 9/4"} {"input": "Find x and y such that\n6x + 10y = 0\n5x + 8y = 1", "output": "6x + 10y = 0\n5x + 8y = 1\n\nUsing elimination\n5*(6x + 10y = 0)\n6*(5x + 8y = 1)\n30x + 50y = 0\n30x + 48y = 6\nSubtract equations\n2y = -6\ny = -6/2\ny = -3\n\nSubstitute y\n6x + 10(-3) = 0\n6x = 30\nx = 30/6\nx = 5"} {"input": "Solve quickly: x^2 + 2/45x - 8/45 = 0", "output": "x^2 + 2/45x - 8/45 = 0\n(x - -4/9)(x - 2/5) = 0\nx - -4/9 = 0 or x - 2/5 = 0\nx = -4/9\nx = 2/5"} {"input": "What value of x satisfies x^2 + 98/15x + 19/15 = 0", "output": "x^2 + 98/15x + 19/15 = 0\n(x - -19/3)(x - -1/5) = 0\nx - -19/3 = 0 or x - -1/5 = 0\nx = -19/3\nx = -1/5"} {"input": "Solve the equation x^3 - 131/60x^2 - 157/20x - 119/30 = 0", "output": "x^3 - 131/60x^2 - 157/20x - 119/30 = 0\n(x - 17/4)(x - -7/5)(x - -2/3) = 0\nx - 17/4 = 0\nx - -7/5 = 0\nx - -2/3 = 0\nx = 17/4\nx = -7/5\nx = -2/3"} {"input": "Solve quickly: 8x - 20 = 0", "output": "8x - 20 = 0\n8x = 20\nx = 20 / 8\nx = 5/2"} {"input": "Solve the equations:\n1x + 9y = -137/6\n8x + 4y = -38/3", "output": "1x + 9y = -137/6\n8x + 4y = -38/3\n\nUsing elimination\n8*(1x + 9y = -137/6)\n1*(8x + 4y = -38/3)\n8x + 72y = -548/3\n8x + 4y = -38/3\nSubtract equations\n68y = -170\ny = -170/68\ny = -5/2\n\nSubstitute y\n1x + 9(-5/2) = -137/6\n1x = -1/3\nx = -1/3/1\nx = -1/3"} {"input": "Solve 3x + 36/7 = 0", "output": "3x + 36/7 = 0\n3x = -36/7\nx = -36/7 / 3\nx = -12/7"} {"input": "Find the solution to 7x + 70/9 = 0", "output": "7x + 70/9 = 0\n7x = -70/9\nx = -70/9 / 7\nx = -10/9"} {"input": "What value of x satisfies 5x - 45/8 = 0", "output": "5x - 45/8 = 0\n5x = 45/8\nx = 45/8 / 5\nx = 9/8"} {"input": "Compute the solution of x^3 + 169/24x^2 + 203/16x + 45/8 = 0", "output": "x^3 + 169/24x^2 + 203/16x + 45/8 = 0\n(x - -2/3)(x - -15/8)(x - -9/2) = 0\nx - -2/3 = 0\nx - -15/8 = 0\nx - -9/2 = 0\nx = -2/3\nx = -15/8\nx = -9/2"} {"input": "Find x and y such that\n6x + 5y = -38/5\n3x + 2y = -14/5", "output": "6x + 5y = -38/5\n3x + 2y = -14/5\n\nUsing elimination\n3*(6x + 5y = -38/5)\n6*(3x + 2y = -14/5)\n18x + 15y = -114/5\n18x + 12y = -84/5\nSubtract equations\n3y = -6\ny = -6/3\ny = -2\n\nSubstitute y\n6x + 5(-2) = -38/5\n6x = 12/5\nx = 12/5/6\nx = 2/5"} {"input": "Solve the equation 5x - 55/8 = 0", "output": "5x - 55/8 = 0\n5x = 55/8\nx = 55/8 / 5\nx = 11/8"} {"input": "Find x for x^2 + 11/14x - 15/14 = 0", "output": "x^2 + 11/14x - 15/14 = 0\n(x - 5/7)(x - -3/2) = 0\nx - 5/7 = 0 or x - -3/2 = 0\nx = 5/7\nx = -3/2"} {"input": "Find the solution to x^3 + 172/105x^2 - 44/15x - 48/35 = 0", "output": "x^3 + 172/105x^2 - 44/15x - 48/35 = 0\n(x - -2/5)(x - 4/3)(x - -18/7) = 0\nx - -2/5 = 0\nx - 4/3 = 0\nx - -18/7 = 0\nx = -2/5\nx = 4/3\nx = -18/7"} {"input": "Find x in x^3 - 267/40x^2 + 491/40x - 63/10 = 0", "output": "x^3 - 267/40x^2 + 491/40x - 63/10 = 0\n(x - 7/8)(x - 4)(x - 9/5) = 0\nx - 7/8 = 0\nx - 4 = 0\nx - 9/5 = 0\nx = 7/8\nx = 4\nx = 9/5"} {"input": "Find x for x^3 - 61/84x^2 - 261/56x + 195/56 = 0", "output": "x^3 - 61/84x^2 - 261/56x + 195/56 = 0\n(x - 15/7)(x - 3/4)(x - -13/6) = 0\nx - 15/7 = 0\nx - 3/4 = 0\nx - -13/6 = 0\nx = 15/7\nx = 3/4\nx = -13/6"} {"input": "Solve the equation x^2 - 11/2x - 3 = 0", "output": "x^2 - 11/2x - 3 = 0\n(x - 6)(x - -1/2) = 0\nx - 6 = 0 or x - -1/2 = 0\nx = 6\nx = -1/2"} {"input": "Solve the equation x^3 + 791/180x^2 + 2009/360x + 17/10 = 0", "output": "x^3 + 791/180x^2 + 2009/360x + 17/10 = 0\n(x - -17/10)(x - -4/9)(x - -9/4) = 0\nx - -17/10 = 0\nx - -4/9 = 0\nx - -9/4 = 0\nx = -17/10\nx = -4/9\nx = -9/4"} {"input": "Compute the solution of x^3 - 1/40x^2 - 1381/160x - 1547/160 = 0", "output": "x^3 - 1/40x^2 - 1381/160x - 1547/160 = 0\n(x - -7/4)(x - 17/5)(x - -13/8) = 0\nx - -7/4 = 0\nx - 17/5 = 0\nx - -13/8 = 0\nx = -7/4\nx = 17/5\nx = -13/8"} {"input": "Solve 5x - 10 = 0", "output": "5x - 10 = 0\n5x = 10\nx = 10 / 5\nx = 2"} {"input": "Solve x^2 - 11/10x - 7/2 = 0", "output": "x^2 - 11/10x - 7/2 = 0\n(x - -7/5)(x - 5/2) = 0\nx - -7/5 = 0 or x - 5/2 = 0\nx = -7/5\nx = 5/2"} {"input": "Determine x in x^2 - 74/15x + 91/15 = 0", "output": "x^2 - 74/15x + 91/15 = 0\n(x - 13/5)(x - 7/3) = 0\nx - 13/5 = 0 or x - 7/3 = 0\nx = 13/5\nx = 7/3"} {"input": "Find x in x^3 - 29/14x^2 - 2x + 30/7 = 0", "output": "x^3 - 29/14x^2 - 2x + 30/7 = 0\n(x - -10/7)(x - 3/2)(x - 2) = 0\nx - -10/7 = 0\nx - 3/2 = 0\nx - 2 = 0\nx = -10/7\nx = 3/2\nx = 2"} {"input": "Determine x in x^2 - 121/10x + 6/5 = 0", "output": "x^2 - 121/10x + 6/5 = 0\n(x - 1/10)(x - 12) = 0\nx - 1/10 = 0 or x - 12 = 0\nx = 1/10\nx = 12"} {"input": "Solve the equations:\n3x + 6y = 197/6\n9x + 9y = 157/2", "output": "3x + 6y = 197/6\n9x + 9y = 157/2\n\nUsing elimination\n9*(3x + 6y = 197/6)\n3*(9x + 9y = 157/2)\n27x + 54y = 591/2\n27x + 27y = 471/2\nSubtract equations\n27y = 60\ny = 60/27\ny = 20/9\n\nSubstitute y\n3x + 6(20/9) = 197/6\n3x = 39/2\nx = 39/2/3\nx = 13/2"} {"input": "Solve quickly: 3x + 6 = 0", "output": "3x + 6 = 0\n3x = -6\nx = -6 / 3\nx = -2"} {"input": "Solve the equation x^2 + 7/2x - 39/2 = 0", "output": "x^2 + 7/2x - 39/2 = 0\n(x - -13/2)(x - 3) = 0\nx - -13/2 = 0 or x - 3 = 0\nx = -13/2\nx = 3"} {"input": "Solve simultaneously:\n2x + 3y = -9/10\n8x + 5y = -71/10", "output": "2x + 3y = -9/10\n8x + 5y = -71/10\n\nUsing elimination\n8*(2x + 3y = -9/10)\n2*(8x + 5y = -71/10)\n16x + 24y = -36/5\n16x + 10y = -71/5\nSubtract equations\n14y = 7\ny = 7/14\ny = 1/2\n\nSubstitute y\n2x + 3(1/2) = -9/10\n2x = -12/5\nx = -12/5/2\nx = -6/5"} {"input": "Solve the equations:\n5x + 4y = 532/9\n7x + 10y = 736/9", "output": "5x + 4y = 532/9\n7x + 10y = 736/9\n\nUsing elimination\n7*(5x + 4y = 532/9)\n5*(7x + 10y = 736/9)\n35x + 28y = 3724/9\n35x + 50y = 3680/9\nSubtract equations\n-22y = 44/9\ny = 44/9/-22\ny = -2/9\n\nSubstitute y\n5x + 4(-2/9) = 532/9\n5x = 60\nx = 60/5\nx = 12"} {"input": "Solve the equation x^2 - 26x + 144 = 0", "output": "x^2 - 26x + 144 = 0\n(x - 8)(x - 18) = 0\nx - 8 = 0 or x - 18 = 0\nx = 8\nx = 18"} {"input": "What value of x satisfies x^3 + 71/4x^2 + 549/8x - 495/8 = 0", "output": "x^3 + 71/4x^2 + 549/8x - 495/8 = 0\n(x - -15/2)(x - -11)(x - 3/4) = 0\nx - -15/2 = 0\nx - -11 = 0\nx - 3/4 = 0\nx = -15/2\nx = -11\nx = 3/4"} {"input": "Find x for 4x + 2 = 0", "output": "4x + 2 = 0\n4x = -2\nx = -2 / 4\nx = -1/2"} {"input": "Solve 6x - 21/2 = 0", "output": "6x - 21/2 = 0\n6x = 21/2\nx = 21/2 / 6\nx = 7/4"} {"input": "Solve quickly: 8x + 56/5 = 0", "output": "8x + 56/5 = 0\n8x = -56/5\nx = -56/5 / 8\nx = -7/5"} {"input": "Find x for x^2 - 19/6x + 1/2 = 0", "output": "x^2 - 19/6x + 1/2 = 0\n(x - 1/6)(x - 3) = 0\nx - 1/6 = 0 or x - 3 = 0\nx = 1/6\nx = 3"} {"input": "Compute the solution of x^2 + 2/5x - 7/5 = 0", "output": "x^2 + 2/5x - 7/5 = 0\n(x - -7/5)(x - 1) = 0\nx - -7/5 = 0 or x - 1 = 0\nx = -7/5\nx = 1"} {"input": "Find x in x^2 + 13/4x - 45/8 = 0", "output": "x^2 + 13/4x - 45/8 = 0\n(x - 5/4)(x - -9/2) = 0\nx - 5/4 = 0 or x - -9/2 = 0\nx = 5/4\nx = -9/2"} {"input": "Find x and y such that\n5x + 2y = 10\n1x + 1y = 2", "output": "5x + 2y = 10\n1x + 1y = 2\n\nUsing elimination\n1*(5x + 2y = 10)\n5*(1x + 1y = 2)\n5x + 2y = 10\n5x + 5y = 10\nSubtract equations\n-3y = 0\ny = 0/-3\ny = 0\n\nSubstitute y\n5x + 2(0) = 10\n5x = 10\nx = 10/5\nx = 2"} {"input": "Solve the equation x^3 + 223/20x^2 + 133/4x + 147/5 = 0", "output": "x^3 + 223/20x^2 + 133/4x + 147/5 = 0\n(x - -12/5)(x - -7)(x - -7/4) = 0\nx - -12/5 = 0\nx - -7 = 0\nx - -7/4 = 0\nx = -12/5\nx = -7\nx = -7/4"} {"input": "Compute the solution of x^3 - 297/28x^2 - 1317/28x - 13/2 = 0", "output": "x^3 - 297/28x^2 - 1317/28x - 13/2 = 0\n(x - -13/4)(x - -1/7)(x - 14) = 0\nx - -13/4 = 0\nx - -1/7 = 0\nx - 14 = 0\nx = -13/4\nx = -1/7\nx = 14"} {"input": "Find x in x^2 + 7/2x - 2 = 0", "output": "x^2 + 7/2x - 2 = 0\n(x - 1/2)(x - -4) = 0\nx - 1/2 = 0 or x - -4 = 0\nx = 1/2\nx = -4"} {"input": "Solve x^2 + 8/9x - 17/9 = 0", "output": "x^2 + 8/9x - 17/9 = 0\n(x - 1)(x - -17/9) = 0\nx - 1 = 0 or x - -17/9 = 0\nx = 1\nx = -17/9"} {"input": "Solve 2x - 12 = 0", "output": "2x - 12 = 0\n2x = 12\nx = 12 / 2\nx = 6"} {"input": "What value of x satisfies x^2 + 23/12x - 95/3 = 0", "output": "x^2 + 23/12x - 95/3 = 0\n(x - 19/4)(x - -20/3) = 0\nx - 19/4 = 0 or x - -20/3 = 0\nx = 19/4\nx = -20/3"} {"input": "Solve the equations:\n3x + 10y = 49\n5x + 10y = 175/3", "output": "3x + 10y = 49\n5x + 10y = 175/3\n\nUsing elimination\n5*(3x + 10y = 49)\n3*(5x + 10y = 175/3)\n15x + 50y = 245\n15x + 30y = 175\nSubtract equations\n20y = 70\ny = 70/20\ny = 7/2\n\nSubstitute y\n3x + 10(7/2) = 49\n3x = 14\nx = 14/3\nx = 14/3"} {"input": "Solve x^3 - 13/6x^2 - 25/6x + 25/3 = 0", "output": "x^3 - 13/6x^2 - 25/6x + 25/3 = 0\n(x - -2)(x - 5/3)(x - 5/2) = 0\nx - -2 = 0\nx - 5/3 = 0\nx - 5/2 = 0\nx = -2\nx = 5/3\nx = 5/2"} {"input": "Solve the system:\n10x + 3y = -199/6\n7x + 5y = -61/6", "output": "10x + 3y = -199/6\n7x + 5y = -61/6\n\nUsing elimination\n7*(10x + 3y = -199/6)\n10*(7x + 5y = -61/6)\n70x + 21y = -1393/6\n70x + 50y = -305/3\nSubtract equations\n-29y = -261/2\ny = -261/2/-29\ny = 9/2\n\nSubstitute y\n10x + 3(9/2) = -199/6\n10x = -140/3\nx = -140/3/10\nx = -14/3"} {"input": "Find x and y such that\n3x + 3y = -10\n5x + 6y = -37/2", "output": "3x + 3y = -10\n5x + 6y = -37/2\n\nUsing elimination\n5*(3x + 3y = -10)\n3*(5x + 6y = -37/2)\n15x + 15y = -50\n15x + 18y = -111/2\nSubtract equations\n-3y = 11/2\ny = 11/2/-3\ny = -11/6\n\nSubstitute y\n3x + 3(-11/6) = -10\n3x = -9/2\nx = -9/2/3\nx = -3/2"} {"input": "Find x and y such that\n10x + 4y = 36\n6x + 9y = 174/5", "output": "10x + 4y = 36\n6x + 9y = 174/5\n\nUsing elimination\n6*(10x + 4y = 36)\n10*(6x + 9y = 174/5)\n60x + 24y = 216\n60x + 90y = 348\nSubtract equations\n-66y = -132\ny = -132/-66\ny = 2\n\nSubstitute y\n10x + 4(2) = 36\n10x = 28\nx = 28/10\nx = 14/5"} {"input": "Find x in x^3 + 43/6x^2 - 73/18x - 532/9 = 0", "output": "x^3 + 43/6x^2 - 73/18x - 532/9 = 0\n(x - -19/3)(x - 8/3)(x - -7/2) = 0\nx - -19/3 = 0\nx - 8/3 = 0\nx - -7/2 = 0\nx = -19/3\nx = 8/3\nx = -7/2"} {"input": "Solve the equation x^3 - 33/7x^2 - 103/7x - 9 = 0", "output": "x^3 - 33/7x^2 - 103/7x - 9 = 0\n(x - 7)(x - -1)(x - -9/7) = 0\nx - 7 = 0\nx - -1 = 0\nx - -9/7 = 0\nx = 7\nx = -1\nx = -9/7"} {"input": "Solve simultaneously:\n2x + 4y = -27/2\n4x + 10y = -29", "output": "2x + 4y = -27/2\n4x + 10y = -29\n\nUsing elimination\n4*(2x + 4y = -27/2)\n2*(4x + 10y = -29)\n8x + 16y = -54\n8x + 20y = -58\nSubtract equations\n-4y = 4\ny = 4/-4\ny = -1\n\nSubstitute y\n2x + 4(-1) = -27/2\n2x = -19/2\nx = -19/2/2\nx = -19/4"} {"input": "Solve simultaneously:\n6x + 4y = -54/7\n9x + 4y = -81/7", "output": "6x + 4y = -54/7\n9x + 4y = -81/7\n\nUsing elimination\n9*(6x + 4y = -54/7)\n6*(9x + 4y = -81/7)\n54x + 36y = -486/7\n54x + 24y = -486/7\nSubtract equations\n12y = 0\ny = 0/12\ny = 0\n\nSubstitute y\n6x + 4(0) = -54/7\n6x = -54/7\nx = -54/7/6\nx = -9/7"} {"input": "Solve the system:\n3x + 10y = 39/2\n3x + 7y = 111/8", "output": "3x + 10y = 39/2\n3x + 7y = 111/8\n\nUsing elimination\n3*(3x + 10y = 39/2)\n3*(3x + 7y = 111/8)\n9x + 30y = 117/2\n9x + 21y = 333/8\nSubtract equations\n9y = 135/8\ny = 135/8/9\ny = 15/8\n\nSubstitute y\n3x + 10(15/8) = 39/2\n3x = 3/4\nx = 3/4/3\nx = 1/4"} {"input": "Find x in 9x - 54 = 0", "output": "9x - 54 = 0\n9x = 54\nx = 54 / 9\nx = 6"} {"input": "Determine x in x^3 + 821/140x^2 + 603/70x + 18/7 = 0", "output": "x^3 + 821/140x^2 + 603/70x + 18/7 = 0\n(x - -12/7)(x - -2/5)(x - -15/4) = 0\nx - -12/7 = 0\nx - -2/5 = 0\nx - -15/4 = 0\nx = -12/7\nx = -2/5\nx = -15/4"} {"input": "Solve quickly: x^3 - 247/90x^2 - 52/9x + 136/45 = 0", "output": "x^3 - 247/90x^2 - 52/9x + 136/45 = 0\n(x - -17/10)(x - 4/9)(x - 4) = 0\nx - -17/10 = 0\nx - 4/9 = 0\nx - 4 = 0\nx = -17/10\nx = 4/9\nx = 4"} {"input": "Find x for 10x + 40 = 0", "output": "10x + 40 = 0\n10x = -40\nx = -40 / 10\nx = -4"} {"input": "Solve simultaneously:\n5x + 7y = 143/12\n6x + 1y = -39/4", "output": "5x + 7y = 143/12\n6x + 1y = -39/4\n\nUsing elimination\n6*(5x + 7y = 143/12)\n5*(6x + 1y = -39/4)\n30x + 42y = 143/2\n30x + 5y = -195/4\nSubtract equations\n37y = 481/4\ny = 481/4/37\ny = 13/4\n\nSubstitute y\n5x + 7(13/4) = 143/12\n5x = -65/6\nx = -65/6/5\nx = -13/6"} {"input": "Determine x in x^2 + 6x + 8 = 0", "output": "x^2 + 6x + 8 = 0\n(x - -2)(x - -4) = 0\nx - -2 = 0 or x - -4 = 0\nx = -2\nx = -4"} {"input": "Find the solution to x^3 - 209/70x^2 - 513/70x + 81/35 = 0", "output": "x^3 - 209/70x^2 - 513/70x + 81/35 = 0\n(x - 9/2)(x - -9/5)(x - 2/7) = 0\nx - 9/2 = 0\nx - -9/5 = 0\nx - 2/7 = 0\nx = 9/2\nx = -9/5\nx = 2/7"} {"input": "Find x and y such that\n9x + 9y = -63/4\n4x + 9y = -23/4", "output": "9x + 9y = -63/4\n4x + 9y = -23/4\n\nUsing elimination\n4*(9x + 9y = -63/4)\n9*(4x + 9y = -23/4)\n36x + 36y = -63\n36x + 81y = -207/4\nSubtract equations\n-45y = -45/4\ny = -45/4/-45\ny = 1/4\n\nSubstitute y\n9x + 9(1/4) = -63/4\n9x = -18\nx = -18/9\nx = -2"} {"input": "Find the solution to x^2 - 4 = 0", "output": "x^2 - 4 = 0\n(x - -2)(x - 2) = 0\nx - -2 = 0 or x - 2 = 0\nx = -2\nx = 2"} {"input": "Compute the solution of x^3 - 61/18x^2 + 55/18x - 34/81 = 0", "output": "x^3 - 61/18x^2 + 55/18x - 34/81 = 0\n(x - 17/9)(x - 1/6)(x - 4/3) = 0\nx - 17/9 = 0\nx - 1/6 = 0\nx - 4/3 = 0\nx = 17/9\nx = 1/6\nx = 4/3"} {"input": "Solve simultaneously:\n7x + 3y = -297/5\n5x + 8y = -177/5", "output": "7x + 3y = -297/5\n5x + 8y = -177/5\n\nUsing elimination\n5*(7x + 3y = -297/5)\n7*(5x + 8y = -177/5)\n35x + 15y = -297\n35x + 56y = -1239/5\nSubtract equations\n-41y = -246/5\ny = -246/5/-41\ny = 6/5\n\nSubstitute y\n7x + 3(6/5) = -297/5\n7x = -63\nx = -63/7\nx = -9"} {"input": "Compute the solution of 7x + 14 = 0", "output": "7x + 14 = 0\n7x = -14\nx = -14 / 7\nx = -2"} {"input": "Find x and y such that\n5x + 4y = 19\n2x + 2y = 42/5", "output": "5x + 4y = 19\n2x + 2y = 42/5\n\nUsing elimination\n2*(5x + 4y = 19)\n5*(2x + 2y = 42/5)\n10x + 8y = 38\n10x + 10y = 42\nSubtract equations\n-2y = -4\ny = -4/-2\ny = 2\n\nSubstitute y\n5x + 4(2) = 19\n5x = 11\nx = 11/5\nx = 11/5"} {"input": "Find x and y such that\n1x + 2y = 34/35\n10x + 1y = -103/7", "output": "1x + 2y = 34/35\n10x + 1y = -103/7\n\nUsing elimination\n10*(1x + 2y = 34/35)\n1*(10x + 1y = -103/7)\n10x + 20y = 68/7\n10x + 1y = -103/7\nSubtract equations\n19y = 171/7\ny = 171/7/19\ny = 9/7\n\nSubstitute y\n1x + 2(9/7) = 34/35\n1x = -8/5\nx = -8/5/1\nx = -8/5"} {"input": "Find x and y such that\n3x + 5y = 155/6\n2x + 6y = 77/3", "output": "3x + 5y = 155/6\n2x + 6y = 77/3\n\nUsing elimination\n2*(3x + 5y = 155/6)\n3*(2x + 6y = 77/3)\n6x + 10y = 155/3\n6x + 18y = 77\nSubtract equations\n-8y = -76/3\ny = -76/3/-8\ny = 19/6\n\nSubstitute y\n3x + 5(19/6) = 155/6\n3x = 10\nx = 10/3\nx = 10/3"} {"input": "Solve the equations:\n2x + 8y = 21/5\n9x + 8y = -28/5", "output": "2x + 8y = 21/5\n9x + 8y = -28/5\n\nUsing elimination\n9*(2x + 8y = 21/5)\n2*(9x + 8y = -28/5)\n18x + 72y = 189/5\n18x + 16y = -56/5\nSubtract equations\n56y = 49\ny = 49/56\ny = 7/8\n\nSubstitute y\n2x + 8(7/8) = 21/5\n2x = -14/5\nx = -14/5/2\nx = -7/5"} {"input": "Solve 2x + 9/5 = 0", "output": "2x + 9/5 = 0\n2x = -9/5\nx = -9/5 / 2\nx = -9/10"} {"input": "Find the solution to x^2 - 41/5x - 247/20 = 0", "output": "x^2 - 41/5x - 247/20 = 0\n(x - -13/10)(x - 19/2) = 0\nx - -13/10 = 0 or x - 19/2 = 0\nx = -13/10\nx = 19/2"} {"input": "Solve quickly: x^3 - 165/28x^2 + 233/28x - 15/14 = 0", "output": "x^3 - 165/28x^2 + 233/28x - 15/14 = 0\n(x - 2)(x - 15/4)(x - 1/7) = 0\nx - 2 = 0\nx - 15/4 = 0\nx - 1/7 = 0\nx = 2\nx = 15/4\nx = 1/7"} {"input": "Solve 2x - 2 = 0", "output": "2x - 2 = 0\n2x = 2\nx = 2 / 2\nx = 1"} {"input": "Find x in 1x - 19/10 = 0", "output": "1x - 19/10 = 0\n1x = 19/10\nx = 19/10 / 1\nx = 19/10"} {"input": "What value of x satisfies 10x - 70/3 = 0", "output": "10x - 70/3 = 0\n10x = 70/3\nx = 70/3 / 10\nx = 7/3"} {"input": "Find x and y such that\n3x + 9y = 9/4\n7x + 6y = 93/2", "output": "3x + 9y = 9/4\n7x + 6y = 93/2\n\nUsing elimination\n7*(3x + 9y = 9/4)\n3*(7x + 6y = 93/2)\n21x + 63y = 63/4\n21x + 18y = 279/2\nSubtract equations\n45y = -495/4\ny = -495/4/45\ny = -11/4\n\nSubstitute y\n3x + 9(-11/4) = 9/4\n3x = 27\nx = 27/3\nx = 9"} {"input": "Solve x^2 - 76/45x - 1/5 = 0", "output": "x^2 - 76/45x - 1/5 = 0\n(x - 9/5)(x - -1/9) = 0\nx - 9/5 = 0 or x - -1/9 = 0\nx = 9/5\nx = -1/9"} {"input": "What value of x satisfies x^3 - 12x^2 + 20x + 96 = 0", "output": "x^3 - 12x^2 + 20x + 96 = 0\n(x - -2)(x - 6)(x - 8) = 0\nx - -2 = 0\nx - 6 = 0\nx - 8 = 0\nx = -2\nx = 6\nx = 8"} {"input": "Find x for x^2 - 7x + 10 = 0", "output": "x^2 - 7x + 10 = 0\n(x - 2)(x - 5) = 0\nx - 2 = 0 or x - 5 = 0\nx = 2\nx = 5"} {"input": "Determine x in 6x + 4 = 0", "output": "6x + 4 = 0\n6x = -4\nx = -4 / 6\nx = -2/3"} {"input": "Solve the equation x^2 + 207/40x + 209/40 = 0", "output": "x^2 + 207/40x + 209/40 = 0\n(x - -11/8)(x - -19/5) = 0\nx - -11/8 = 0 or x - -19/5 = 0\nx = -11/8\nx = -19/5"} {"input": "Find x for x^2 + 9x + 65/4 = 0", "output": "x^2 + 9x + 65/4 = 0\n(x - -13/2)(x - -5/2) = 0\nx - -13/2 = 0 or x - -5/2 = 0\nx = -13/2\nx = -5/2"} {"input": "Find x for x^2 + 2/9x - 40/9 = 0", "output": "x^2 + 2/9x - 40/9 = 0\n(x - 2)(x - -20/9) = 0\nx - 2 = 0 or x - -20/9 = 0\nx = 2\nx = -20/9"} {"input": "Find x for x^2 - 63/10x + 22/5 = 0", "output": "x^2 - 63/10x + 22/5 = 0\n(x - 11/2)(x - 4/5) = 0\nx - 11/2 = 0 or x - 4/5 = 0\nx = 11/2\nx = 4/5"} {"input": "Find the solution to x^2 - 7x + 104/9 = 0", "output": "x^2 - 7x + 104/9 = 0\n(x - 8/3)(x - 13/3) = 0\nx - 8/3 = 0 or x - 13/3 = 0\nx = 8/3\nx = 13/3"} {"input": "Solve the equations:\n8x + 3y = 24\n2x + 3y = 51/4", "output": "8x + 3y = 24\n2x + 3y = 51/4\n\nUsing elimination\n2*(8x + 3y = 24)\n8*(2x + 3y = 51/4)\n16x + 6y = 48\n16x + 24y = 102\nSubtract equations\n-18y = -54\ny = -54/-18\ny = 3\n\nSubstitute y\n8x + 3(3) = 24\n8x = 15\nx = 15/8\nx = 15/8"} {"input": "Solve the equations:\n4x + 8y = 299/2\n5x + 8y = 1191/8", "output": "4x + 8y = 299/2\n5x + 8y = 1191/8\n\nUsing elimination\n5*(4x + 8y = 299/2)\n4*(5x + 8y = 1191/8)\n20x + 40y = 1495/2\n20x + 32y = 1191/2\nSubtract equations\n8y = 152\ny = 152/8\ny = 19\n\nSubstitute y\n4x + 8(19) = 299/2\n4x = -5/2\nx = -5/2/4\nx = -5/8"} {"input": "Solve x^3 - 35/6x^2 - 11x + 455/6 = 0", "output": "x^3 - 35/6x^2 - 11x + 455/6 = 0\n(x - -7/2)(x - 5)(x - 13/3) = 0\nx - -7/2 = 0\nx - 5 = 0\nx - 13/3 = 0\nx = -7/2\nx = 5\nx = 13/3"} {"input": "Solve the equation x^3 + 261/56x^2 + 801/112x + 405/112 = 0", "output": "x^3 + 261/56x^2 + 801/112x + 405/112 = 0\n(x - -15/8)(x - -9/7)(x - -3/2) = 0\nx - -15/8 = 0\nx - -9/7 = 0\nx - -3/2 = 0\nx = -15/8\nx = -9/7\nx = -3/2"} {"input": "What value of x satisfies 9x - 36 = 0", "output": "9x - 36 = 0\n9x = 36\nx = 36 / 9\nx = 4"} {"input": "Find x in 2x = 0", "output": "2x = 0\n2x = 0\nx = 0 / 2\nx = 0"} {"input": "Solve simultaneously:\n10x + 5y = -35/3\n10x + 4y = -37/3", "output": "10x + 5y = -35/3\n10x + 4y = -37/3\n\nUsing elimination\n10*(10x + 5y = -35/3)\n10*(10x + 4y = -37/3)\n100x + 50y = -350/3\n100x + 40y = -370/3\nSubtract equations\n10y = 20/3\ny = 20/3/10\ny = 2/3\n\nSubstitute y\n10x + 5(2/3) = -35/3\n10x = -15\nx = -15/10\nx = -3/2"} {"input": "Solve x^2 + 4x - 64/9 = 0", "output": "x^2 + 4x - 64/9 = 0\n(x - -16/3)(x - 4/3) = 0\nx - -16/3 = 0 or x - 4/3 = 0\nx = -16/3\nx = 4/3"} {"input": "What value of x satisfies x^2 - 27x + 182 = 0", "output": "x^2 - 27x + 182 = 0\n(x - 14)(x - 13) = 0\nx - 14 = 0 or x - 13 = 0\nx = 14\nx = 13"} {"input": "Solve simultaneously:\n4x + 8y = 34\n10x + 4y = 31/3", "output": "4x + 8y = 34\n10x + 4y = 31/3\n\nUsing elimination\n10*(4x + 8y = 34)\n4*(10x + 4y = 31/3)\n40x + 80y = 340\n40x + 16y = 124/3\nSubtract equations\n64y = 896/3\ny = 896/3/64\ny = 14/3\n\nSubstitute y\n4x + 8(14/3) = 34\n4x = -10/3\nx = -10/3/4\nx = -5/6"} {"input": "Solve the system:\n4x + 4y = 8\n2x + 1y = 3", "output": "4x + 4y = 8\n2x + 1y = 3\n\nUsing elimination\n2*(4x + 4y = 8)\n4*(2x + 1y = 3)\n8x + 8y = 16\n8x + 4y = 12\nSubtract equations\n4y = 4\ny = 4/4\ny = 1\n\nSubstitute y\n4x + 4(1) = 8\n4x = 4\nx = 4/4\nx = 1"} {"input": "Solve 7x - 133/9 = 0", "output": "7x - 133/9 = 0\n7x = 133/9\nx = 133/9 / 7\nx = 19/9"} {"input": "Solve x^3 + 181/42x^2 + 347/126x - 85/21 = 0", "output": "x^3 + 181/42x^2 + 347/126x - 85/21 = 0\n(x - 2/3)(x - -17/6)(x - -15/7) = 0\nx - 2/3 = 0\nx - -17/6 = 0\nx - -15/7 = 0\nx = 2/3\nx = -17/6\nx = -15/7"} {"input": "Find x for x^3 - 23/30x^2 - 733/150x - 12/25 = 0", "output": "x^3 - 23/30x^2 - 733/150x - 12/25 = 0\n(x - -9/5)(x - -1/10)(x - 8/3) = 0\nx - -9/5 = 0\nx - -1/10 = 0\nx - 8/3 = 0\nx = -9/5\nx = -1/10\nx = 8/3"} {"input": "Find the solution to x^3 + 14/5x^2 - 8/45x - 64/45 = 0", "output": "x^3 + 14/5x^2 - 8/45x - 64/45 = 0\n(x - 2/3)(x - -4/5)(x - -8/3) = 0\nx - 2/3 = 0\nx - -4/5 = 0\nx - -8/3 = 0\nx = 2/3\nx = -4/5\nx = -8/3"} {"input": "Find x in x^2 - 7/2x - 15/2 = 0", "output": "x^2 - 7/2x - 15/2 = 0\n(x - 5)(x - -3/2) = 0\nx - 5 = 0 or x - -3/2 = 0\nx = 5\nx = -3/2"} {"input": "Compute the solution of x^3 + 5/8x^2 - 51/32x - 27/64 = 0", "output": "x^3 + 5/8x^2 - 51/32x - 27/64 = 0\n(x - 9/8)(x - -1/4)(x - -3/2) = 0\nx - 9/8 = 0\nx - -1/4 = 0\nx - -3/2 = 0\nx = 9/8\nx = -1/4\nx = -3/2"} {"input": "Solve simultaneously:\n1x + 9y = -102/7\n5x + 3y = 162/7", "output": "1x + 9y = -102/7\n5x + 3y = 162/7\n\nUsing elimination\n5*(1x + 9y = -102/7)\n1*(5x + 3y = 162/7)\n5x + 45y = -510/7\n5x + 3y = 162/7\nSubtract equations\n42y = -96\ny = -96/42\ny = -16/7\n\nSubstitute y\n1x + 9(-16/7) = -102/7\n1x = 6\nx = 6/1\nx = 6"} {"input": "Find the solution to 4x - 32/3 = 0", "output": "4x - 32/3 = 0\n4x = 32/3\nx = 32/3 / 4\nx = 8/3"} {"input": "Compute the solution of 10x = 0", "output": "10x = 0\n10x = 0\nx = 0 / 10\nx = 0"} {"input": "Determine x in x^3 - 14/3x^2 - 5x + 50/3 = 0", "output": "x^3 - 14/3x^2 - 5x + 50/3 = 0\n(x - 5)(x - 5/3)(x - -2) = 0\nx - 5 = 0\nx - 5/3 = 0\nx - -2 = 0\nx = 5\nx = 5/3\nx = -2"} {"input": "What value of x satisfies x^3 + 56/15x^2 - 63/5x + 6 = 0", "output": "x^3 + 56/15x^2 - 63/5x + 6 = 0\n(x - -6)(x - 3/5)(x - 5/3) = 0\nx - -6 = 0\nx - 3/5 = 0\nx - 5/3 = 0\nx = -6\nx = 3/5\nx = 5/3"} {"input": "Solve the equation x^2 - 23/10x + 33/25 = 0", "output": "x^2 - 23/10x + 33/25 = 0\n(x - 6/5)(x - 11/10) = 0\nx - 6/5 = 0 or x - 11/10 = 0\nx = 6/5\nx = 11/10"} {"input": "Compute the solution of 9x + 90/7 = 0", "output": "9x + 90/7 = 0\n9x = -90/7\nx = -90/7 / 9\nx = -10/7"} {"input": "Compute the solution of 5x - 35 = 0", "output": "5x - 35 = 0\n5x = 35\nx = 35 / 5\nx = 7"} {"input": "Find x in x^3 + 553/24x^2 + 1273/16x + 2527/48 = 0", "output": "x^3 + 553/24x^2 + 1273/16x + 2527/48 = 0\n(x - -19)(x - -19/6)(x - -7/8) = 0\nx - -19 = 0\nx - -19/6 = 0\nx - -7/8 = 0\nx = -19\nx = -19/6\nx = -7/8"} {"input": "Solve 1x - 3/10 = 0", "output": "1x - 3/10 = 0\n1x = 3/10\nx = 3/10 / 1\nx = 3/10"} {"input": "Solve quickly: x^3 - 79/4x^2 + 223/2x - 140 = 0", "output": "x^3 - 79/4x^2 + 223/2x - 140 = 0\n(x - 7/4)(x - 10)(x - 8) = 0\nx - 7/4 = 0\nx - 10 = 0\nx - 8 = 0\nx = 7/4\nx = 10\nx = 8"} {"input": "Find x in x^3 - 619/210x^2 + 79/42x + 2/5 = 0", "output": "x^3 - 619/210x^2 + 79/42x + 2/5 = 0\n(x - 7/5)(x - -1/6)(x - 12/7) = 0\nx - 7/5 = 0\nx - -1/6 = 0\nx - 12/7 = 0\nx = 7/5\nx = -1/6\nx = 12/7"} {"input": "Find x and y such that\n8x + 8y = 168\n6x + 10y = 134", "output": "8x + 8y = 168\n6x + 10y = 134\n\nUsing elimination\n6*(8x + 8y = 168)\n8*(6x + 10y = 134)\n48x + 48y = 1008\n48x + 80y = 1072\nSubtract equations\n-32y = -64\ny = -64/-32\ny = 2\n\nSubstitute y\n8x + 8(2) = 168\n8x = 152\nx = 152/8\nx = 19"} {"input": "Find x for 10x + 40 = 0", "output": "10x + 40 = 0\n10x = -40\nx = -40 / 10\nx = -4"} {"input": "Solve the equation 9x + 153/4 = 0", "output": "9x + 153/4 = 0\n9x = -153/4\nx = -153/4 / 9\nx = -17/4"} {"input": "What value of x satisfies 9x + 27/8 = 0", "output": "9x + 27/8 = 0\n9x = -27/8\nx = -27/8 / 9\nx = -3/8"} {"input": "Find the solution to x^3 + 245/24x^2 + 679/24x + 95/4 = 0", "output": "x^3 + 245/24x^2 + 679/24x + 95/4 = 0\n(x - -19/3)(x - -2)(x - -15/8) = 0\nx - -19/3 = 0\nx - -2 = 0\nx - -15/8 = 0\nx = -19/3\nx = -2\nx = -15/8"} {"input": "Solve the equation x^3 - 53/252x^2 - 131/126x + 10/21 = 0", "output": "x^3 - 53/252x^2 - 131/126x + 10/21 = 0\n(x - 4/7)(x - 3/4)(x - -10/9) = 0\nx - 4/7 = 0\nx - 3/4 = 0\nx - -10/9 = 0\nx = 4/7\nx = 3/4\nx = -10/9"} {"input": "Solve the equations:\n4x + 10y = 108/5\n10x + 9y = 22", "output": "4x + 10y = 108/5\n10x + 9y = 22\n\nUsing elimination\n10*(4x + 10y = 108/5)\n4*(10x + 9y = 22)\n40x + 100y = 216\n40x + 36y = 88\nSubtract equations\n64y = 128\ny = 128/64\ny = 2\n\nSubstitute y\n4x + 10(2) = 108/5\n4x = 8/5\nx = 8/5/4\nx = 2/5"} {"input": "What value of x satisfies x^2 + 123/35x + 108/35 = 0", "output": "x^2 + 123/35x + 108/35 = 0\n(x - -12/7)(x - -9/5) = 0\nx - -12/7 = 0 or x - -9/5 = 0\nx = -12/7\nx = -9/5"} {"input": "Solve simultaneously:\n3x + 1y = 15/2\n5x + 4y = -5", "output": "3x + 1y = 15/2\n5x + 4y = -5\n\nUsing elimination\n5*(3x + 1y = 15/2)\n3*(5x + 4y = -5)\n15x + 5y = 75/2\n15x + 12y = -15\nSubtract equations\n-7y = 105/2\ny = 105/2/-7\ny = -15/2\n\nSubstitute y\n3x + 1(-15/2) = 15/2\n3x = 15\nx = 15/3\nx = 5"} {"input": "Compute the solution of 8x - 64/5 = 0", "output": "8x - 64/5 = 0\n8x = 64/5\nx = 64/5 / 8\nx = 8/5"} {"input": "Solve quickly: x^3 + 224/15x^2 - 263/15x - 112/15 = 0", "output": "x^3 + 224/15x^2 - 263/15x - 112/15 = 0\n(x - 7/5)(x - -1/3)(x - -16) = 0\nx - 7/5 = 0\nx - -1/3 = 0\nx - -16 = 0\nx = 7/5\nx = -1/3\nx = -16"} {"input": "Find x in x^3 - 34/9x^2 - 25/3x + 100/9 = 0", "output": "x^3 - 34/9x^2 - 25/3x + 100/9 = 0\n(x - -20/9)(x - 5)(x - 1) = 0\nx - -20/9 = 0\nx - 5 = 0\nx - 1 = 0\nx = -20/9\nx = 5\nx = 1"} {"input": "Solve the system:\n2x + 10y = 10\n8x + 7y = 499/10", "output": "2x + 10y = 10\n8x + 7y = 499/10\n\nUsing elimination\n8*(2x + 10y = 10)\n2*(8x + 7y = 499/10)\n16x + 80y = 80\n16x + 14y = 499/5\nSubtract equations\n66y = -99/5\ny = -99/5/66\ny = -3/10\n\nSubstitute y\n2x + 10(-3/10) = 10\n2x = 13\nx = 13/2\nx = 13/2"} {"input": "Solve x^3 - 23/4x^2 + 9/2x + 45/4 = 0", "output": "x^3 - 23/4x^2 + 9/2x + 45/4 = 0\n(x - -1)(x - 15/4)(x - 3) = 0\nx - -1 = 0\nx - 15/4 = 0\nx - 3 = 0\nx = -1\nx = 15/4\nx = 3"} {"input": "Solve 5x + 55/3 = 0", "output": "5x + 55/3 = 0\n5x = -55/3\nx = -55/3 / 5\nx = -11/3"} {"input": "Find the solution to x^2 - 7/2x - 15/2 = 0", "output": "x^2 - 7/2x - 15/2 = 0\n(x - -3/2)(x - 5) = 0\nx - -3/2 = 0 or x - 5 = 0\nx = -3/2\nx = 5"} {"input": "Solve 4x + 76/7 = 0", "output": "4x + 76/7 = 0\n4x = -76/7\nx = -76/7 / 4\nx = -19/7"} {"input": "Find the solution to 10x - 90/7 = 0", "output": "10x - 90/7 = 0\n10x = 90/7\nx = 90/7 / 10\nx = 9/7"} {"input": "Find x for x^2 + 11/3x + 19/12 = 0", "output": "x^2 + 11/3x + 19/12 = 0\n(x - -1/2)(x - -19/6) = 0\nx - -1/2 = 0 or x - -19/6 = 0\nx = -1/2\nx = -19/6"} {"input": "Find the solution to 10x + 70/3 = 0", "output": "10x + 70/3 = 0\n10x = -70/3\nx = -70/3 / 10\nx = -7/3"} {"input": "Determine x in x^3 + 5/72x^2 - 29/48x - 7/36 = 0", "output": "x^3 + 5/72x^2 - 29/48x - 7/36 = 0\n(x - -1/2)(x - 7/8)(x - -4/9) = 0\nx - -1/2 = 0\nx - 7/8 = 0\nx - -4/9 = 0\nx = -1/2\nx = 7/8\nx = -4/9"} {"input": "Find x in x^3 + 767/280x^2 + 219/280x - 117/70 = 0", "output": "x^3 + 767/280x^2 + 219/280x - 117/70 = 0\n(x - -13/8)(x - 3/5)(x - -12/7) = 0\nx - -13/8 = 0\nx - 3/5 = 0\nx - -12/7 = 0\nx = -13/8\nx = 3/5\nx = -12/7"} {"input": "Solve the equation 2x + 12 = 0", "output": "2x + 12 = 0\n2x = -12\nx = -12 / 2\nx = -6"} {"input": "Solve the system:\n3x + 2y = -47/4\n8x + 8y = -34", "output": "3x + 2y = -47/4\n8x + 8y = -34\n\nUsing elimination\n8*(3x + 2y = -47/4)\n3*(8x + 8y = -34)\n24x + 16y = -94\n24x + 24y = -102\nSubtract equations\n-8y = 8\ny = 8/-8\ny = -1\n\nSubstitute y\n3x + 2(-1) = -47/4\n3x = -39/4\nx = -39/4/3\nx = -13/4"} {"input": "Solve the equation x^2 + 164/9x - 320/9 = 0", "output": "x^2 + 164/9x - 320/9 = 0\n(x - -20)(x - 16/9) = 0\nx - -20 = 0 or x - 16/9 = 0\nx = -20\nx = 16/9"} {"input": "Solve the equation 7x - 126/5 = 0", "output": "7x - 126/5 = 0\n7x = 126/5\nx = 126/5 / 7\nx = 18/5"} {"input": "Solve the equation 7x - 7 = 0", "output": "7x - 7 = 0\n7x = 7\nx = 7 / 7\nx = 1"} {"input": "Find x for 3x + 57/7 = 0", "output": "3x + 57/7 = 0\n3x = -57/7\nx = -57/7 / 3\nx = -19/7"} {"input": "Determine x in 5x + 25/6 = 0", "output": "5x + 25/6 = 0\n5x = -25/6\nx = -25/6 / 5\nx = -5/6"} {"input": "Solve simultaneously:\n7x + 10y = 61/2\n2x + 5y = 409/28", "output": "7x + 10y = 61/2\n2x + 5y = 409/28\n\nUsing elimination\n2*(7x + 10y = 61/2)\n7*(2x + 5y = 409/28)\n14x + 20y = 61\n14x + 35y = 409/4\nSubtract equations\n-15y = -165/4\ny = -165/4/-15\ny = 11/4\n\nSubstitute y\n7x + 10(11/4) = 61/2\n7x = 3\nx = 3/7\nx = 3/7"} {"input": "Solve quickly: x^2 + 37/4x + 85/4 = 0", "output": "x^2 + 37/4x + 85/4 = 0\n(x - -5)(x - -17/4) = 0\nx - -5 = 0 or x - -17/4 = 0\nx = -5\nx = -17/4"} {"input": "Solve the equations:\n2x + 9y = -141/28\n8x + 7y = -16", "output": "2x + 9y = -141/28\n8x + 7y = -16\n\nUsing elimination\n8*(2x + 9y = -141/28)\n2*(8x + 7y = -16)\n16x + 72y = -282/7\n16x + 14y = -32\nSubtract equations\n58y = -58/7\ny = -58/7/58\ny = -1/7\n\nSubstitute y\n2x + 9(-1/7) = -141/28\n2x = -15/4\nx = -15/4/2\nx = -15/8"} {"input": "Solve quickly: x^3 + 25/14x^2 - 37/14x - 24/7 = 0", "output": "x^3 + 25/14x^2 - 37/14x - 24/7 = 0\n(x - 3/2)(x - -1)(x - -16/7) = 0\nx - 3/2 = 0\nx - -1 = 0\nx - -16/7 = 0\nx = 3/2\nx = -1\nx = -16/7"} {"input": "Find x for x^3 + 107/20x^2 - 389/20x + 14 = 0", "output": "x^3 + 107/20x^2 - 389/20x + 14 = 0\n(x - -8)(x - 5/4)(x - 7/5) = 0\nx - -8 = 0\nx - 5/4 = 0\nx - 7/5 = 0\nx = -8\nx = 5/4\nx = 7/5"} {"input": "Compute the solution of x^3 - 19/4x^2 + 395/64x - 323/256 = 0", "output": "x^3 - 19/4x^2 + 395/64x - 323/256 = 0\n(x - 17/8)(x - 19/8)(x - 1/4) = 0\nx - 17/8 = 0\nx - 19/8 = 0\nx - 1/4 = 0\nx = 17/8\nx = 19/8\nx = 1/4"} {"input": "Solve quickly: x^2 - 19/4x + 11/2 = 0", "output": "x^2 - 19/4x + 11/2 = 0\n(x - 11/4)(x - 2) = 0\nx - 11/4 = 0 or x - 2 = 0\nx = 11/4\nx = 2"} {"input": "Find x and y such that\n5x + 5y = -260/7\n6x + 3y = -207/7", "output": "5x + 5y = -260/7\n6x + 3y = -207/7\n\nUsing elimination\n6*(5x + 5y = -260/7)\n5*(6x + 3y = -207/7)\n30x + 30y = -1560/7\n30x + 15y = -1035/7\nSubtract equations\n15y = -75\ny = -75/15\ny = -5\n\nSubstitute y\n5x + 5(-5) = -260/7\n5x = -85/7\nx = -85/7/5\nx = -17/7"} {"input": "What value of x satisfies x^2 - 23/8x - 285/32 = 0", "output": "x^2 - 23/8x - 285/32 = 0\n(x - 19/4)(x - -15/8) = 0\nx - 19/4 = 0 or x - -15/8 = 0\nx = 19/4\nx = -15/8"} {"input": "Compute the solution of x^3 + 3/2x^2 - 305/98x - 102/49 = 0", "output": "x^3 + 3/2x^2 - 305/98x - 102/49 = 0\n(x - -4/7)(x - 3/2)(x - -17/7) = 0\nx - -4/7 = 0\nx - 3/2 = 0\nx - -17/7 = 0\nx = -4/7\nx = 3/2\nx = -17/7"} {"input": "Solve the equation 3x - 21 = 0", "output": "3x - 21 = 0\n3x = 21\nx = 21 / 3\nx = 7"} {"input": "Find x and y such that\n2x + 10y = 167/7\n2x + 2y = 27/7", "output": "2x + 10y = 167/7\n2x + 2y = 27/7\n\nUsing elimination\n2*(2x + 10y = 167/7)\n2*(2x + 2y = 27/7)\n4x + 20y = 334/7\n4x + 4y = 54/7\nSubtract equations\n16y = 40\ny = 40/16\ny = 5/2\n\nSubstitute y\n2x + 10(5/2) = 167/7\n2x = -8/7\nx = -8/7/2\nx = -4/7"} {"input": "Find x in 9x + 171/10 = 0", "output": "9x + 171/10 = 0\n9x = -171/10\nx = -171/10 / 9\nx = -19/10"} {"input": "Find x and y such that\n9x + 8y = 9/5\n7x + 3y = -8/15", "output": "9x + 8y = 9/5\n7x + 3y = -8/15\n\nUsing elimination\n7*(9x + 8y = 9/5)\n9*(7x + 3y = -8/15)\n63x + 56y = 63/5\n63x + 27y = -24/5\nSubtract equations\n29y = 87/5\ny = 87/5/29\ny = 3/5\n\nSubstitute y\n9x + 8(3/5) = 9/5\n9x = -3\nx = -3/9\nx = -1/3"} {"input": "Solve simultaneously:\n4x + 2y = 282/35\n6x + 2y = 338/35", "output": "4x + 2y = 282/35\n6x + 2y = 338/35\n\nUsing elimination\n6*(4x + 2y = 282/35)\n4*(6x + 2y = 338/35)\n24x + 12y = 1692/35\n24x + 8y = 1352/35\nSubtract equations\n4y = 68/7\ny = 68/7/4\ny = 17/7\n\nSubstitute y\n4x + 2(17/7) = 282/35\n4x = 16/5\nx = 16/5/4\nx = 4/5"} {"input": "Solve simultaneously:\n7x + 2y = 130/9\n3x + 2y = 262/63", "output": "7x + 2y = 130/9\n3x + 2y = 262/63\n\nUsing elimination\n3*(7x + 2y = 130/9)\n7*(3x + 2y = 262/63)\n21x + 6y = 130/3\n21x + 14y = 262/9\nSubtract equations\n-8y = 128/9\ny = 128/9/-8\ny = -16/9\n\nSubstitute y\n7x + 2(-16/9) = 130/9\n7x = 18\nx = 18/7\nx = 18/7"} {"input": "Solve quickly: x^2 + 17/6x - 1/2 = 0", "output": "x^2 + 17/6x - 1/2 = 0\n(x - 1/6)(x - -3) = 0\nx - 1/6 = 0 or x - -3 = 0\nx = 1/6\nx = -3"} {"input": "Solve x^2 + 17/12x - 33/4 = 0", "output": "x^2 + 17/12x - 33/4 = 0\n(x - -11/3)(x - 9/4) = 0\nx - -11/3 = 0 or x - 9/4 = 0\nx = -11/3\nx = 9/4"} {"input": "Solve x^3 + 5/3x^2 - 33/4x - 51/4 = 0", "output": "x^3 + 5/3x^2 - 33/4x - 51/4 = 0\n(x - -3)(x - -3/2)(x - 17/6) = 0\nx - -3 = 0\nx - -3/2 = 0\nx - 17/6 = 0\nx = -3\nx = -3/2\nx = 17/6"} {"input": "Solve quickly: x^2 + 7/2x + 3 = 0", "output": "x^2 + 7/2x + 3 = 0\n(x - -3/2)(x - -2) = 0\nx - -3/2 = 0 or x - -2 = 0\nx = -3/2\nx = -2"} {"input": "Compute the solution of x^2 - 10/9x - 19/9 = 0", "output": "x^2 - 10/9x - 19/9 = 0\n(x - 19/9)(x - -1) = 0\nx - 19/9 = 0 or x - -1 = 0\nx = 19/9\nx = -1"} {"input": "What value of x satisfies x^3 + 197/30x^2 + 761/60x + 273/40 = 0", "output": "x^3 + 197/30x^2 + 761/60x + 273/40 = 0\n(x - -7/2)(x - -13/6)(x - -9/10) = 0\nx - -7/2 = 0\nx - -13/6 = 0\nx - -9/10 = 0\nx = -7/2\nx = -13/6\nx = -9/10"} {"input": "Solve the equation 4x - 7/2 = 0", "output": "4x - 7/2 = 0\n4x = 7/2\nx = 7/2 / 4\nx = 7/8"} {"input": "Find the solution to 1x + 10/3 = 0", "output": "1x + 10/3 = 0\n1x = -10/3\nx = -10/3 / 1\nx = -10/3"} {"input": "Find x and y such that\n7x + 5y = -191/4\n7x + 6y = -51", "output": "7x + 5y = -191/4\n7x + 6y = -51\n\nUsing elimination\n7*(7x + 5y = -191/4)\n7*(7x + 6y = -51)\n49x + 35y = -1337/4\n49x + 42y = -357\nSubtract equations\n-7y = 91/4\ny = 91/4/-7\ny = -13/4\n\nSubstitute y\n7x + 5(-13/4) = -191/4\n7x = -63/2\nx = -63/2/7\nx = -9/2"} {"input": "Find the solution to 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Find x in x^3 + 17/9x^2 - 56/81x - 128/81 = 0", "output": "x^3 + 17/9x^2 - 56/81x - 128/81 = 0\n(x - 8/9)(x - -16/9)(x - -1) = 0\nx - 8/9 = 0\nx - -16/9 = 0\nx - -1 = 0\nx = 8/9\nx = -16/9\nx = -1"} {"input": "Find the solution to 1x + 15 = 0", "output": "1x + 15 = 0\n1x = -15\nx = -15 / 1\nx = -15"} {"input": "Solve simultaneously:\n8x + 5y = 667/28\n6x + 9y = 831/28", "output": "8x + 5y = 667/28\n6x + 9y = 831/28\n\nUsing elimination\n6*(8x + 5y = 667/28)\n8*(6x + 9y = 831/28)\n48x + 30y = 2001/14\n48x + 72y = 1662/7\nSubtract equations\n-42y = -189/2\ny = -189/2/-42\ny = 9/4\n\nSubstitute y\n8x + 5(9/4) = 667/28\n8x = 88/7\nx = 88/7/8\nx = 11/7"} {"input": "Compute the solution of x^3 - 133/12x^2 + 203/8x - 17/3 = 0", "output": "x^3 - 133/12x^2 + 203/8x - 17/3 = 0\n(x - 8)(x - 1/4)(x - 17/6) = 0\nx - 8 = 0\nx - 1/4 = 0\nx - 17/6 = 0\nx = 8\nx = 1/4\nx = 17/6"} {"input": "Find x and y such that\n8x + 1y = -171/7\n5x + 5y = -260/7", "output": "8x + 1y = -171/7\n5x + 5y = -260/7\n\nUsing elimination\n5*(8x + 1y = -171/7)\n8*(5x + 5y = -260/7)\n40x + 5y = -855/7\n40x + 40y = -2080/7\nSubtract equations\n-35y = 175\ny = 175/-35\ny = -5\n\nSubstitute y\n8x + 1(-5) = -171/7\n8x = -136/7\nx = -136/7/8\nx = -17/7"} {"input": "Solve simultaneously:\n6x + 5y = -24/5\n5x + 10y = -4", "output": "6x + 5y = -24/5\n5x + 10y = -4\n\nUsing elimination\n5*(6x + 5y = -24/5)\n6*(5x + 10y = -4)\n30x + 25y = -24\n30x + 60y = -24\nSubtract equations\n-35y = 0\ny = 0/-35\ny = 0\n\nSubstitute y\n6x + 5(0) = -24/5\n6x = -24/5\nx = -24/5/6\nx = -4/5"} {"input": "Solve quickly: 4x - 68/9 = 0", "output": "4x - 68/9 = 0\n4x = 68/9\nx = 68/9 / 4\nx = 17/9"} {"input": "Find x and y such that\n3x + 2y = -38/5\n7x + 10y = -38", "output": "3x + 2y = -38/5\n7x + 10y = -38\n\nUsing elimination\n7*(3x + 2y = -38/5)\n3*(7x + 10y = -38)\n21x + 14y = -266/5\n21x + 30y = -114\nSubtract equations\n-16y = 304/5\ny = 304/5/-16\ny = -19/5\n\nSubstitute y\n3x + 2(-19/5) = -38/5\n3x = 0\nx = 0/3\nx = 0"} {"input": "Compute the solution of 10x + 10 = 0", "output": "10x + 10 = 0\n10x = -10\nx = -10 / 10\nx = -1"} {"input": "Determine x in x^3 - 73/4x^2 - 16x + 133/4 = 0", "output": "x^3 - 73/4x^2 - 16x + 133/4 = 0\n(x - 19)(x - -7/4)(x - 1) = 0\nx - 19 = 0\nx - -7/4 = 0\nx - 1 = 0\nx = 19\nx = -7/4\nx = 1"} {"input": "Find x and y such that\n5x + 2y = 131/5\n3x + 1y = 78/5", "output": "5x + 2y = 131/5\n3x + 1y = 78/5\n\nUsing elimination\n3*(5x + 2y = 131/5)\n5*(3x + 1y = 78/5)\n15x + 6y = 393/5\n15x + 5y = 78\nSubtract equations\n1y = 3/5\ny = 3/5/1\ny = 3/5\n\nSubstitute y\n5x + 2(3/5) = 131/5\n5x = 25\nx = 25/5\nx = 5"} {"input": "Find x and y such that\n2x + 5y = 53/4\n1x + 2y = 197/40", "output": "2x + 5y = 53/4\n1x + 2y = 197/40\n\nUsing elimination\n1*(2x + 5y = 53/4)\n2*(1x + 2y = 197/40)\n2x + 5y = 53/4\n2x + 4y = 197/20\nSubtract equations\n1y = 17/5\ny = 17/5/1\ny = 17/5\n\nSubstitute y\n2x + 5(17/5) = 53/4\n2x = -15/4\nx = -15/4/2\nx = -15/8"} {"input": "Solve simultaneously:\n6x + 7y = -497/5\n8x + 2y = -186/5", "output": "6x + 7y = -497/5\n8x + 2y = -186/5\n\nUsing elimination\n8*(6x + 7y = -497/5)\n6*(8x + 2y = -186/5)\n48x + 56y = -3976/5\n48x + 12y = -1116/5\nSubtract equations\n44y = -572\ny = -572/44\ny = -13\n\nSubstitute y\n6x + 7(-13) = -497/5\n6x = -42/5\nx = -42/5/6\nx = -7/5"} {"input": "Solve the equation x^2 - 1/3x - 14/3 = 0", "output": "x^2 - 1/3x - 14/3 = 0\n(x - 7/3)(x - -2) = 0\nx - 7/3 = 0 or x - -2 = 0\nx = 7/3\nx = -2"} {"input": "Find x and y such that\n2x + 7y = 247/35\n8x + 9y = 589/35", "output": "2x + 7y = 247/35\n8x + 9y = 589/35\n\nUsing elimination\n8*(2x + 7y = 247/35)\n2*(8x + 9y = 589/35)\n16x + 56y = 1976/35\n16x + 18y = 1178/35\nSubtract equations\n38y = 114/5\ny = 114/5/38\ny = 3/5\n\nSubstitute y\n2x + 7(3/5) = 247/35\n2x = 20/7\nx = 20/7/2\nx = 10/7"} {"input": "Solve quickly: 7x - 7/5 = 0", "output": "7x - 7/5 = 0\n7x = 7/5\nx = 7/5 / 7\nx = 1/5"} {"input": "Solve the equations:\n1x + 8y = 12\n5x + 9y = -2", "output": "1x + 8y = 12\n5x + 9y = -2\n\nUsing elimination\n5*(1x + 8y = 12)\n1*(5x + 9y = -2)\n5x + 40y = 60\n5x + 9y = -2\nSubtract equations\n31y = 62\ny = 62/31\ny = 2\n\nSubstitute y\n1x + 8(2) = 12\n1x = -4\nx = -4/1\nx = -4"} {"input": "Find x in 9x + 99/8 = 0", "output": "9x + 99/8 = 0\n9x = -99/8\nx = -99/8 / 9\nx = -11/8"} {"input": "Solve simultaneously:\n3x + 6y = 93/7\n5x + 7y = 17", "output": "3x + 6y = 93/7\n5x + 7y = 17\n\nUsing elimination\n5*(3x + 6y = 93/7)\n3*(5x + 7y = 17)\n15x + 30y = 465/7\n15x + 21y = 51\nSubtract equations\n9y = 108/7\ny = 108/7/9\ny = 12/7\n\nSubstitute y\n3x + 6(12/7) = 93/7\n3x = 3\nx = 3/3\nx = 1"} {"input": "Compute the solution of 8x - 26 = 0", "output": "8x - 26 = 0\n8x = 26\nx = 26 / 8\nx = 13/4"} {"input": "Solve quickly: x^2 + 151/72x + 77/72 = 0", "output": "x^2 + 151/72x + 77/72 = 0\n(x - -11/9)(x - -7/8) = 0\nx - -11/9 = 0 or x - -7/8 = 0\nx = -11/9\nx = -7/8"} {"input": "Find x for x^2 - 37/6x - 10/3 = 0", "output": "x^2 - 37/6x - 10/3 = 0\n(x - -1/2)(x - 20/3) = 0\nx - -1/2 = 0 or x - 20/3 = 0\nx = -1/2\nx = 20/3"} {"input": "Find x for x^3 - 27/4x^2 - 19x - 45/4 = 0", "output": "x^3 - 27/4x^2 - 19x - 45/4 = 0\n(x - -5/4)(x - -1)(x - 9) = 0\nx - -5/4 = 0\nx - -1 = 0\nx - 9 = 0\nx = -5/4\nx = -1\nx = 9"} {"input": "Find x and y such that\n8x + 10y = -346/3\n9x + 6y = -128", "output": "8x + 10y = -346/3\n9x + 6y = -128\n\nUsing elimination\n9*(8x + 10y = -346/3)\n8*(9x + 6y = -128)\n72x + 90y = -1038\n72x + 48y = -1024\nSubtract equations\n42y = -14\ny = -14/42\ny = -1/3\n\nSubstitute y\n8x + 10(-1/3) = -346/3\n8x = -112\nx = -112/8\nx = -14"} {"input": "Solve quickly: x^2 - 81/70x - 13/70 = 0", "output": "x^2 - 81/70x - 13/70 = 0\n(x - 13/10)(x - -1/7) = 0\nx - 13/10 = 0 or x - -1/7 = 0\nx = 13/10\nx = -1/7"} {"input": "Find the solution to x^2 + 5/3x - 2/3 = 0", "output": "x^2 + 5/3x - 2/3 = 0\n(x - 1/3)(x - -2) = 0\nx - 1/3 = 0 or x - -2 = 0\nx = 1/3\nx = -2"} {"input": "Find x and y such that\n9x + 6y = -123/5\n3x + 9y = -174/5", "output": "9x + 6y = -123/5\n3x + 9y = -174/5\n\nUsing elimination\n3*(9x + 6y = -123/5)\n9*(3x + 9y = -174/5)\n27x + 18y = -369/5\n27x + 81y = -1566/5\nSubtract equations\n-63y = 1197/5\ny = 1197/5/-63\ny = -19/5\n\nSubstitute y\n9x + 6(-19/5) = -123/5\n9x = -9/5\nx = -9/5/9\nx = -1/5"} {"input": "Find x for x^3 - 943/315x^2 + 64/35x - 16/63 = 0", "output": "x^3 - 943/315x^2 + 64/35x - 16/63 = 0\n(x - 1/5)(x - 4/7)(x - 20/9) = 0\nx - 1/5 = 0\nx - 4/7 = 0\nx - 20/9 = 0\nx = 1/5\nx = 4/7\nx = 20/9"} {"input": "Find the solution to x^3 + 37/5x^2 + 99/20x - 117/20 = 0", "output": "x^3 + 37/5x^2 + 99/20x - 117/20 = 0\n(x - 3/5)(x - -13/2)(x - -3/2) = 0\nx - 3/5 = 0\nx - -13/2 = 0\nx - -3/2 = 0\nx = 3/5\nx = -13/2\nx = -3/2"} {"input": "Solve the system:\n9x + 6y = 62\n8x + 2y = 112/3", "output": "9x + 6y = 62\n8x + 2y = 112/3\n\nUsing elimination\n8*(9x + 6y = 62)\n9*(8x + 2y = 112/3)\n72x + 48y = 496\n72x + 18y = 336\nSubtract equations\n30y = 160\ny = 160/30\ny = 16/3\n\nSubstitute y\n9x + 6(16/3) = 62\n9x = 30\nx = 30/9\nx = 10/3"} {"input": "Determine x in x^3 + 61/9x^2 - 86/9x + 16/9 = 0", "output": "x^3 + 61/9x^2 - 86/9x + 16/9 = 0\n(x - -8)(x - 1)(x - 2/9) = 0\nx - -8 = 0\nx - 1 = 0\nx - 2/9 = 0\nx = -8\nx = 1\nx = 2/9"} {"input": "Solve the equations:\n9x + 10y = -3\n8x + 1y = 173/15", "output": "9x + 10y = -3\n8x + 1y = 173/15\n\nUsing elimination\n8*(9x + 10y = -3)\n9*(8x + 1y = 173/15)\n72x + 80y = -24\n72x + 9y = 519/5\nSubtract equations\n71y = -639/5\ny = -639/5/71\ny = -9/5\n\nSubstitute y\n9x + 10(-9/5) = -3\n9x = 15\nx = 15/9\nx = 5/3"} {"input": "Determine x in 2x + 8/3 = 0", "output": "2x + 8/3 = 0\n2x = -8/3\nx = -8/3 / 2\nx = -4/3"} {"input": "Find x in 10x - 12 = 0", "output": "10x - 12 = 0\n10x = 12\nx = 12 / 10\nx = 6/5"} {"input": "Determine x in x^3 - 83/35x^2 - 452/245x + 608/245 = 0", "output": "x^3 - 83/35x^2 - 452/245x + 608/245 = 0\n(x - 19/7)(x - -8/7)(x - 4/5) = 0\nx - 19/7 = 0\nx - -8/7 = 0\nx - 4/5 = 0\nx = 19/7\nx = -8/7\nx = 4/5"} {"input": "Solve the equations:\n4x + 3y = -11/9\n5x + 7y = 1", "output": "4x + 3y = -11/9\n5x + 7y = 1\n\nUsing elimination\n5*(4x + 3y = -11/9)\n4*(5x + 7y = 1)\n20x + 15y = -55/9\n20x + 28y = 4\nSubtract equations\n-13y = -91/9\ny = -91/9/-13\ny = 7/9\n\nSubstitute y\n4x + 3(7/9) = -11/9\n4x = -32/9\nx = -32/9/4\nx = -8/9"} {"input": "Find x for x^3 - 27/10x^2 - 53/20x - 21/40 = 0", "output": "x^3 - 27/10x^2 - 53/20x - 21/40 = 0\n(x - -3/10)(x - 7/2)(x - -1/2) = 0\nx - -3/10 = 0\nx - 7/2 = 0\nx - -1/2 = 0\nx = -3/10\nx = 7/2\nx = -1/2"} {"input": "What value of x satisfies x^2 - 64/25 = 0", "output": "x^2 - 64/25 = 0\n(x - 8/5)(x - -8/5) = 0\nx - 8/5 = 0 or x - -8/5 = 0\nx = 8/5\nx = -8/5"} {"input": "Find x for 2x - 1/5 = 0", "output": "2x - 1/5 = 0\n2x = 1/5\nx = 1/5 / 2\nx = 1/10"} {"input": "Solve quickly: 1x - 3 = 0", "output": "1x - 3 = 0\n1x = 3\nx = 3 / 1\nx = 3"} {"input": "Find x and y such that\n2x + 7y = 61/5\n3x + 10y = 71/4", "output": "2x + 7y = 61/5\n3x + 10y = 71/4\n\nUsing elimination\n3*(2x + 7y = 61/5)\n2*(3x + 10y = 71/4)\n6x + 21y = 183/5\n6x + 20y = 71/2\nSubtract equations\n1y = 11/10\ny = 11/10/1\ny = 11/10\n\nSubstitute y\n2x + 7(11/10) = 61/5\n2x = 9/2\nx = 9/2/2\nx = 9/4"} {"input": "Solve x^3 + 89/30x^2 + 19/15x - 3/2 = 0", "output": "x^3 + 89/30x^2 + 19/15x - 3/2 = 0\n(x - -9/5)(x - -5/3)(x - 1/2) = 0\nx - -9/5 = 0\nx - -5/3 = 0\nx - 1/2 = 0\nx = -9/5\nx = -5/3\nx = 1/2"} {"input": "Compute the solution of x^2 + 3x - 40 = 0", "output": "x^2 + 3x - 40 = 0\n(x - -8)(x - 5) = 0\nx - -8 = 0 or x - 5 = 0\nx = -8\nx = 5"} {"input": "Solve quickly: 8x + 128/3 = 0", "output": "8x + 128/3 = 0\n8x = -128/3\nx = -128/3 / 8\nx = -16/3"} {"input": "Find the solution to x^2 - 2/5x - 3/25 = 0", "output": "x^2 - 2/5x - 3/25 = 0\n(x - 3/5)(x - -1/5) = 0\nx - 3/5 = 0 or x - -1/5 = 0\nx = 3/5\nx = -1/5"} {"input": "Find x and y such that\n1x + 5y = -161/8\n9x + 6y = -201/8", "output": "1x + 5y = -161/8\n9x + 6y = -201/8\n\nUsing elimination\n9*(1x + 5y = -161/8)\n1*(9x + 6y = -201/8)\n9x + 45y = -1449/8\n9x + 6y = -201/8\nSubtract equations\n39y = -156\ny = -156/39\ny = -4\n\nSubstitute y\n1x + 5(-4) = -161/8\n1x = -1/8\nx = -1/8/1\nx = -1/8"} {"input": "Compute the solution of x^2 - 19/6x - 6 = 0", "output": "x^2 - 19/6x - 6 = 0\n(x - 9/2)(x - -4/3) = 0\nx - 9/2 = 0 or x - -4/3 = 0\nx = 9/2\nx = -4/3"} {"input": "Find x in x^2 - 47/18x + 5/18 = 0", "output": "x^2 - 47/18x + 5/18 = 0\n(x - 1/9)(x - 5/2) = 0\nx - 1/9 = 0 or x - 5/2 = 0\nx = 1/9\nx = 5/2"} {"input": "Find x for 6x - 3/4 = 0", "output": "6x - 3/4 = 0\n6x = 3/4\nx = 3/4 / 6\nx = 1/8"} {"input": "Solve quickly: 6x + 26 = 0", "output": "6x + 26 = 0\n6x = -26\nx = -26 / 6\nx = -13/3"} {"input": "Solve the equation x^2 - 73/45x + 22/45 = 0", "output": "x^2 - 73/45x + 22/45 = 0\n(x - 2/5)(x - 11/9) = 0\nx - 2/5 = 0 or x - 11/9 = 0\nx = 2/5\nx = 11/9"} {"input": "Solve the system:\n4x + 7y = -692/15\n9x + 10y = -1097/15", "output": "4x + 7y = -692/15\n9x + 10y = -1097/15\n\nUsing elimination\n9*(4x + 7y = -692/15)\n4*(9x + 10y = -1097/15)\n36x + 63y = -2076/5\n36x + 40y = -4388/15\nSubtract equations\n23y = -368/3\ny = -368/3/23\ny = -16/3\n\nSubstitute y\n4x + 7(-16/3) = -692/15\n4x = -44/5\nx = -44/5/4\nx = -11/5"} {"input": "Find the solution to x^3 - 7/2x^2 + 189/64x - 171/256 = 0", "output": "x^3 - 7/2x^2 + 189/64x - 171/256 = 0\n(x - 3/8)(x - 3/4)(x - 19/8) = 0\nx - 3/8 = 0\nx - 3/4 = 0\nx - 19/8 = 0\nx = 3/8\nx = 3/4\nx = 19/8"} {"input": "Find the solution to x^3 - 125/7x^2 - 26/7x + 144/7 = 0", "output": "x^3 - 125/7x^2 - 26/7x + 144/7 = 0\n(x - -8/7)(x - 1)(x - 18) = 0\nx - -8/7 = 0\nx - 1 = 0\nx - 18 = 0\nx = -8/7\nx = 1\nx = 18"} {"input": "Solve quickly: x^3 - 160/9x^2 - 43/9x + 14 = 0", "output": "x^3 - 160/9x^2 - 43/9x + 14 = 0\n(x - -1)(x - 7/9)(x - 18) = 0\nx - -1 = 0\nx - 7/9 = 0\nx - 18 = 0\nx = -1\nx = 7/9\nx = 18"} {"input": "Compute the solution of x^2 - 62/45x + 7/15 = 0", "output": "x^2 - 62/45x + 7/15 = 0\n(x - 3/5)(x - 7/9) = 0\nx - 3/5 = 0 or x - 7/9 = 0\nx = 3/5\nx = 7/9"} {"input": "Solve quickly: 3x + 33/7 = 0", "output": "3x + 33/7 = 0\n3x = -33/7\nx = -33/7 / 3\nx = -11/7"} {"input": "Find x in x^3 - 73/12x^2 - 35/8x + 117/4 = 0", "output": "x^3 - 73/12x^2 - 35/8x + 117/4 = 0\n(x - 6)(x - -13/6)(x - 9/4) = 0\nx - 6 = 0\nx - -13/6 = 0\nx - 9/4 = 0\nx = 6\nx = -13/6\nx = 9/4"} {"input": "Find x in 5x + 45/4 = 0", "output": "5x + 45/4 = 0\n5x = -45/4\nx = -45/4 / 5\nx = -9/4"} {"input": "Compute the solution of x^3 + 33/5x^2 - 437/5x - 273/5 = 0", "output": "x^3 + 33/5x^2 - 437/5x - 273/5 = 0\n(x - 7)(x - -13)(x - -3/5) = 0\nx - 7 = 0\nx - -13 = 0\nx - -3/5 = 0\nx = 7\nx = -13\nx = -3/5"} {"input": "Find the solution to x^3 + 134/21x^2 - 289/147x - 20/49 = 0", "output": "x^3 + 134/21x^2 - 289/147x - 20/49 = 0\n(x - -1/7)(x - 3/7)(x - -20/3) = 0\nx - -1/7 = 0\nx - 3/7 = 0\nx - -20/3 = 0\nx = -1/7\nx = 3/7\nx = -20/3"} {"input": "Determine x in x^2 - 4x + 3 = 0", "output": "x^2 - 4x + 3 = 0\n(x - 3)(x - 1) = 0\nx - 3 = 0 or x - 1 = 0\nx = 3\nx = 1"} {"input": "Compute the solution of x^3 + 56/15x^2 + 191/75x - 42/25 = 0", "output": "x^3 + 56/15x^2 + 191/75x - 42/25 = 0\n(x - 2/5)(x - -7/3)(x - -9/5) = 0\nx - 2/5 = 0\nx - -7/3 = 0\nx - -9/5 = 0\nx = 2/5\nx = -7/3\nx = -9/5"} {"input": "Solve 6x + 24/5 = 0", "output": "6x + 24/5 = 0\n6x = -24/5\nx = -24/5 / 6\nx = -4/5"} {"input": "Solve 9x - 72 = 0", "output": "9x - 72 = 0\n9x = 72\nx = 72 / 9\nx = 8"} {"input": "Find the solution to 6x = 0", "output": "6x = 0\n6x = 0\nx = 0 / 6\nx = 0"} {"input": "Find x and y such that\n6x + 6y = 172/15\n5x + 7y = 502/45", "output": "6x + 6y = 172/15\n5x + 7y = 502/45\n\nUsing elimination\n5*(6x + 6y = 172/15)\n6*(5x + 7y = 502/45)\n30x + 30y = 172/3\n30x + 42y = 1004/15\nSubtract equations\n-12y = -48/5\ny = -48/5/-12\ny = 4/5\n\nSubstitute y\n6x + 6(4/5) = 172/15\n6x = 20/3\nx = 20/3/6\nx = 10/9"} {"input": "Find x for x^2 + 13/10x = 0", "output": "x^2 + 13/10x = 0\n(x - 0)(x - -13/10) = 0\nx - 0 = 0 or x - -13/10 = 0\nx = 0\nx = -13/10"} {"input": "Determine x in x^2 + 14x + 40 = 0", "output": "x^2 + 14x + 40 = 0\n(x - -10)(x - -4) = 0\nx - -10 = 0 or x - -4 = 0\nx = -10\nx = -4"} {"input": "Determine x in 5x + 10/7 = 0", "output": "5x + 10/7 = 0\n5x = -10/7\nx = -10/7 / 5\nx = -2/7"} {"input": "Determine x in 3x + 27/10 = 0", "output": "3x + 27/10 = 0\n3x = -27/10\nx = -27/10 / 3\nx = -9/10"} {"input": "Find x and y such that\n8x + 4y = 520/7\n6x + 7y = 894/7", "output": "8x + 4y = 520/7\n6x + 7y = 894/7\n\nUsing elimination\n6*(8x + 4y = 520/7)\n8*(6x + 7y = 894/7)\n48x + 24y = 3120/7\n48x + 56y = 7152/7\nSubtract equations\n-32y = -576\ny = -576/-32\ny = 18\n\nSubstitute y\n8x + 4(18) = 520/7\n8x = 16/7\nx = 16/7/8\nx = 2/7"} {"input": "Solve quickly: x^2 - 67/15x - 44/3 = 0", "output": "x^2 - 67/15x - 44/3 = 0\n(x - 20/3)(x - -11/5) = 0\nx - 20/3 = 0 or x - -11/5 = 0\nx = 20/3\nx = -11/5"} {"input": "Compute the solution of 8x - 8/3 = 0", "output": "8x - 8/3 = 0\n8x = 8/3\nx = 8/3 / 8\nx = 1/3"} {"input": "Compute the solution of x^2 - 41/14x + 15/7 = 0", "output": "x^2 - 41/14x + 15/7 = 0\n(x - 3/2)(x - 10/7) = 0\nx - 3/2 = 0 or x - 10/7 = 0\nx = 3/2\nx = 10/7"} {"input": "Compute the solution of x^2 - 4/9x = 0", "output": "x^2 - 4/9x = 0\n(x - 0)(x - 4/9) = 0\nx - 0 = 0 or x - 4/9 = 0\nx = 0\nx = 4/9"} {"input": "Find x in x^2 - 16/9x + 5/27 = 0", "output": "x^2 - 16/9x + 5/27 = 0\n(x - 1/9)(x - 5/3) = 0\nx - 1/9 = 0 or x - 5/3 = 0\nx = 1/9\nx = 5/3"} {"input": "Find x for 6x + 12/5 = 0", "output": "6x + 12/5 = 0\n6x = -12/5\nx = -12/5 / 6\nx = -2/5"} {"input": "Find x for 10x + 170/9 = 0", "output": "10x + 170/9 = 0\n10x = -170/9\nx = -170/9 / 10\nx = -17/9"} {"input": "Solve x^2 - 68/15x + 64/15 = 0", "output": "x^2 - 68/15x + 64/15 = 0\n(x - 16/5)(x - 4/3) = 0\nx - 16/5 = 0 or x - 4/3 = 0\nx = 16/5\nx = 4/3"} {"input": "Solve the system:\n3x + 8y = -54\n4x + 8y = -72", "output": "3x + 8y = -54\n4x + 8y = -72\n\nUsing elimination\n4*(3x + 8y = -54)\n3*(4x + 8y = -72)\n12x + 32y = -216\n12x + 24y = -216\nSubtract equations\n8y = 0\ny = 0/8\ny = 0\n\nSubstitute y\n3x + 8(0) = -54\n3x = -54\nx = -54/3\nx = -18"} {"input": "Find x in 9x - 63/2 = 0", "output": "9x - 63/2 = 0\n9x = 63/2\nx = 63/2 / 9\nx = 7/2"} {"input": "What value of x satisfies 2x - 7 = 0", "output": "2x - 7 = 0\n2x = 7\nx = 7 / 2\nx = 7/2"} {"input": "Find the solution to x^3 - 27/2x^2 + 207/4x - 405/8 = 0", "output": "x^3 - 27/2x^2 + 207/4x - 405/8 = 0\n(x - 3/2)(x - 15/2)(x - 9/2) = 0\nx - 3/2 = 0\nx - 15/2 = 0\nx - 9/2 = 0\nx = 3/2\nx = 15/2\nx = 9/2"} {"input": "Solve the system:\n2x + 8y = -6\n7x + 2y = -55/2", "output": "2x + 8y = -6\n7x + 2y = -55/2\n\nUsing elimination\n7*(2x + 8y = -6)\n2*(7x + 2y = -55/2)\n14x + 56y = -42\n14x + 4y = -55\nSubtract equations\n52y = 13\ny = 13/52\ny = 1/4\n\nSubstitute y\n2x + 8(1/4) = -6\n2x = -8\nx = -8/2\nx = -4"} {"input": "Find x and y such that\n3x + 1y = -71/5\n2x + 8y = -634/5", "output": "3x + 1y = -71/5\n2x + 8y = -634/5\n\nUsing elimination\n2*(3x + 1y = -71/5)\n3*(2x + 8y = -634/5)\n6x + 2y = -142/5\n6x + 24y = -1902/5\nSubtract equations\n-22y = 352\ny = 352/-22\ny = -16\n\nSubstitute y\n3x + 1(-16) = -71/5\n3x = 9/5\nx = 9/5/3\nx = 3/5"} {"input": "Solve the equations:\n10x + 9y = -86\n4x + 9y = -110", "output": "10x + 9y = -86\n4x + 9y = -110\n\nUsing elimination\n4*(10x + 9y = -86)\n10*(4x + 9y = -110)\n40x + 36y = -344\n40x + 90y = -1100\nSubtract equations\n-54y = 756\ny = 756/-54\ny = -14\n\nSubstitute y\n10x + 9(-14) = -86\n10x = 40\nx = 40/10\nx = 4"} {"input": "Determine x in 1x - 4 = 0", "output": "1x - 4 = 0\n1x = 4\nx = 4 / 1\nx = 4"} {"input": "Solve x^2 + 61/28x - 17/28 = 0", "output": "x^2 + 61/28x - 17/28 = 0\n(x - 1/4)(x - -17/7) = 0\nx - 1/4 = 0 or x - -17/7 = 0\nx = 1/4\nx = -17/7"} {"input": "Find x in 9x + 9 = 0", "output": "9x + 9 = 0\n9x = -9\nx = -9 / 9\nx = -1"} {"input": "Find x for x^2 + 39/10x + 27/10 = 0", "output": "x^2 + 39/10x + 27/10 = 0\n(x - -9/10)(x - -3) = 0\nx - -9/10 = 0 or x - -3 = 0\nx = -9/10\nx = -3"} {"input": "Solve x^3 + 83/9x^2 + 250/27x - 112/27 = 0", "output": "x^3 + 83/9x^2 + 250/27x - 112/27 = 0\n(x - 1/3)(x - -14/9)(x - -8) = 0\nx - 1/3 = 0\nx - -14/9 = 0\nx - -8 = 0\nx = 1/3\nx = -14/9\nx = -8"} {"input": "Solve the equation 2x - 5/4 = 0", "output": "2x - 5/4 = 0\n2x = 5/4\nx = 5/4 / 2\nx = 5/8"} {"input": "Solve quickly: x^3 - 7/15x^2 - 31/3x - 133/15 = 0", "output": "x^3 - 7/15x^2 - 31/3x - 133/15 = 0\n(x - -1)(x - 19/5)(x - -7/3) = 0\nx - -1 = 0\nx - 19/5 = 0\nx - -7/3 = 0\nx = -1\nx = 19/5\nx = -7/3"} {"input": "Solve simultaneously:\n7x + 3y = -1067/42\n5x + 10y = -1375/42", "output": "7x + 3y = -1067/42\n5x + 10y = -1375/42\n\nUsing elimination\n5*(7x + 3y = -1067/42)\n7*(5x + 10y = -1375/42)\n35x + 15y = -5335/42\n35x + 70y = -1375/6\nSubtract equations\n-55y = 715/7\ny = 715/7/-55\ny = -13/7\n\nSubstitute y\n7x + 3(-13/7) = -1067/42\n7x = -119/6\nx = -119/6/7\nx = -17/6"} {"input": "Find x in 7x + 35 = 0", "output": "7x + 35 = 0\n7x = -35\nx = -35 / 7\nx = -5"} {"input": "Solve the equation 10x + 6 = 0", "output": "10x + 6 = 0\n10x = -6\nx = -6 / 10\nx = -3/5"} {"input": "Find x in x^3 - 35/36x^2 - 49/36x = 0", "output": "x^3 - 35/36x^2 - 49/36x = 0\n(x - 0)(x - -7/9)(x - 7/4) = 0\nx - 0 = 0\nx - -7/9 = 0\nx - 7/4 = 0\nx = 0\nx = -7/9\nx = 7/4"} {"input": "Compute the solution of x^3 - 64x = 0", "output": "x^3 - 64x = 0\n(x - 0)(x - 8)(x - -8) = 0\nx - 0 = 0\nx - 8 = 0\nx - -8 = 0\nx = 0\nx = 8\nx = -8"} {"input": "Solve x^2 - 16 = 0", "output": "x^2 - 16 = 0\n(x - 4)(x - -4) = 0\nx - 4 = 0 or x - -4 = 0\nx = 4\nx = -4"} {"input": "Solve simultaneously:\n7x + 2y = -55/3\n2x + 1y = -14/3", "output": "7x + 2y = -55/3\n2x + 1y = -14/3\n\nUsing elimination\n2*(7x + 2y = -55/3)\n7*(2x + 1y = -14/3)\n14x + 4y = -110/3\n14x + 7y = -98/3\nSubtract equations\n-3y = -4\ny = -4/-3\ny = 4/3\n\nSubstitute y\n7x + 2(4/3) = -55/3\n7x = -21\nx = -21/7\nx = -3"} {"input": "Solve the system:\n2x + 9y = 49/9\n9x + 4y = -12", "output": "2x + 9y = 49/9\n9x + 4y = -12\n\nUsing elimination\n9*(2x + 9y = 49/9)\n2*(9x + 4y = -12)\n18x + 81y = 49\n18x + 8y = -24\nSubtract equations\n73y = 73\ny = 73/73\ny = 1\n\nSubstitute y\n2x + 9(1) = 49/9\n2x = -32/9\nx = -32/9/2\nx = -16/9"} {"input": "Find x for x^3 - 1/2x^2 - 4x + 2 = 0", "output": "x^3 - 1/2x^2 - 4x + 2 = 0\n(x - 2)(x - -2)(x - 1/2) = 0\nx - 2 = 0\nx - -2 = 0\nx - 1/2 = 0\nx = 2\nx = -2\nx = 1/2"} {"input": "Solve the equations:\n5x + 5y = -770/9\n6x + 3y = -298/3", "output": "5x + 5y = -770/9\n6x + 3y = -298/3\n\nUsing elimination\n6*(5x + 5y = -770/9)\n5*(6x + 3y = -298/3)\n30x + 30y = -1540/3\n30x + 15y = -1490/3\nSubtract equations\n15y = -50/3\ny = -50/3/15\ny = -10/9\n\nSubstitute y\n5x + 5(-10/9) = -770/9\n5x = -80\nx = -80/5\nx = -16"} {"input": "Solve quickly: x^3 - 82/21x^2 + 229/84x + 55/28 = 0", "output": "x^3 - 82/21x^2 + 229/84x + 55/28 = 0\n(x - 5/2)(x - 11/6)(x - -3/7) = 0\nx - 5/2 = 0\nx - 11/6 = 0\nx - -3/7 = 0\nx = 5/2\nx = 11/6\nx = -3/7"} {"input": "Find the solution to x^2 + 4/15x - 7/3 = 0", "output": "x^2 + 4/15x - 7/3 = 0\n(x - -5/3)(x - 7/5) = 0\nx - -5/3 = 0 or x - 7/5 = 0\nx = -5/3\nx = 7/5"} {"input": "Solve quickly: 4x + 4 = 0", "output": "4x + 4 = 0\n4x = -4\nx = -4 / 4\nx = -1"} {"input": "Find x in x^3 - 229/30x^2 - 251/10x + 2261/15 = 0", "output": "x^3 - 229/30x^2 - 251/10x + 2261/15 = 0\n(x - 19/5)(x - 17/2)(x - -14/3) = 0\nx - 19/5 = 0\nx - 17/2 = 0\nx - -14/3 = 0\nx = 19/5\nx = 17/2\nx = -14/3"} {"input": "Solve x^2 + 121/35x + 78/35 = 0", "output": "x^2 + 121/35x + 78/35 = 0\n(x - -6/7)(x - -13/5) = 0\nx - -6/7 = 0 or x - -13/5 = 0\nx = -6/7\nx = -13/5"} {"input": "Find the solution to 10x - 9 = 0", "output": "10x - 9 = 0\n10x = 9\nx = 9 / 10\nx = 9/10"} {"input": "What value of x satisfies x^2 - 47/30x - 187/30 = 0", "output": "x^2 - 47/30x - 187/30 = 0\n(x - 17/5)(x - -11/6) = 0\nx - 17/5 = 0 or x - -11/6 = 0\nx = 17/5\nx = -11/6"} {"input": "Find the solution to x^3 + 32/35x^2 - 2031/700x - 459/175 = 0", "output": "x^3 + 32/35x^2 - 2031/700x - 459/175 = 0\n(x - -9/10)(x - -12/7)(x - 17/10) = 0\nx - -9/10 = 0\nx - -12/7 = 0\nx - 17/10 = 0\nx = -9/10\nx = -12/7\nx = 17/10"} {"input": "Solve the system:\n3x + 4y = 43/5\n1x + 4y = -7/5", "output": "3x + 4y = 43/5\n1x + 4y = -7/5\n\nUsing elimination\n1*(3x + 4y = 43/5)\n3*(1x + 4y = -7/5)\n3x + 4y = 43/5\n3x + 12y = -21/5\nSubtract equations\n-8y = 64/5\ny = 64/5/-8\ny = -8/5\n\nSubstitute y\n3x + 4(-8/5) = 43/5\n3x = 15\nx = 15/3\nx = 5"} {"input": "Solve quickly: 3x + 3/8 = 0", "output": "3x + 3/8 = 0\n3x = -3/8\nx = -3/8 / 3\nx = -1/8"} {"input": "Solve quickly: x^2 + 55/8x - 9 = 0", "output": "x^2 + 55/8x - 9 = 0\n(x - -8)(x - 9/8) = 0\nx - -8 = 0 or x - 9/8 = 0\nx = -8\nx = 9/8"} {"input": "What value of x satisfies x^2 + 5/2x - 39/16 = 0", "output": "x^2 + 5/2x - 39/16 = 0\n(x - -13/4)(x - 3/4) = 0\nx - -13/4 = 0 or x - 3/4 = 0\nx = -13/4\nx = 3/4"} {"input": "Determine x in 6x - 3 = 0", "output": "6x - 3 = 0\n6x = 3\nx = 3 / 6\nx = 1/2"} {"input": "Determine x in x^2 + 226/45x + 209/45 = 0", "output": "x^2 + 226/45x + 209/45 = 0\n(x - -11/9)(x - -19/5) = 0\nx - -11/9 = 0 or x - -19/5 = 0\nx = -11/9\nx = -19/5"} {"input": "Compute the solution of x^3 - 11/10x^2 - 114/25x + 297/50 = 0", "output": "x^3 - 11/10x^2 - 114/25x + 297/50 = 0\n(x - 9/5)(x - 3/2)(x - -11/5) = 0\nx - 9/5 = 0\nx - 3/2 = 0\nx - -11/5 = 0\nx = 9/5\nx = 3/2\nx = -11/5"} {"input": "Find x for 5x - 55/3 = 0", "output": "5x - 55/3 = 0\n5x = 55/3\nx = 55/3 / 5\nx = 11/3"} {"input": "Find the solution to x^3 - 4/5x^2 - 73/100x + 11/25 = 0", "output": "x^3 - 4/5x^2 - 73/100x + 11/25 = 0\n(x - 11/10)(x - 1/2)(x - -4/5) = 0\nx - 11/10 = 0\nx - 1/2 = 0\nx - -4/5 = 0\nx = 11/10\nx = 1/2\nx = -4/5"} {"input": "Determine x in x^3 + 137/45x^2 + 124/45x + 32/45 = 0", "output": "x^3 + 137/45x^2 + 124/45x + 32/45 = 0\n(x - -1)(x - -8/5)(x - -4/9) = 0\nx - -1 = 0\nx - -8/5 = 0\nx - -4/9 = 0\nx = -1\nx = -8/5\nx = -4/9"} {"input": "Solve the equation x^3 + 34/21x^2 + 3/7x = 0", "output": "x^3 + 34/21x^2 + 3/7x = 0\n(x - -1/3)(x - -9/7)(x - 0) = 0\nx - -1/3 = 0\nx - -9/7 = 0\nx - 0 = 0\nx = -1/3\nx = -9/7\nx = 0"} {"input": "Solve x^3 + 15/4x^2 - 17/2x - 45/4 = 0", "output": "x^3 + 15/4x^2 - 17/2x - 45/4 = 0\n(x - -5)(x - 9/4)(x - -1) = 0\nx - -5 = 0\nx - 9/4 = 0\nx - -1 = 0\nx = -5\nx = 9/4\nx = -1"} {"input": "Compute the solution of x^2 - 9/2x + 5 = 0", "output": "x^2 - 9/2x + 5 = 0\n(x - 5/2)(x - 2) = 0\nx - 5/2 = 0 or x - 2 = 0\nx = 5/2\nx = 2"} {"input": "Solve the equation x^2 + 29/4x + 15/2 = 0", "output": "x^2 + 29/4x + 15/2 = 0\n(x - -6)(x - -5/4) = 0\nx - -6 = 0 or x - -5/4 = 0\nx = -6\nx = -5/4"} {"input": "Find x and y such that\n9x + 8y = 671/6\n7x + 2y = 353/6", "output": "9x + 8y = 671/6\n7x + 2y = 353/6\n\nUsing elimination\n7*(9x + 8y = 671/6)\n9*(7x + 2y = 353/6)\n63x + 56y = 4697/6\n63x + 18y = 1059/2\nSubtract equations\n38y = 760/3\ny = 760/3/38\ny = 20/3\n\nSubstitute y\n9x + 8(20/3) = 671/6\n9x = 117/2\nx = 117/2/9\nx = 13/2"} {"input": "What value of x satisfies 4x + 28/3 = 0", "output": "4x + 28/3 = 0\n4x = -28/3\nx = -28/3 / 4\nx = -7/3"} {"input": "Find x and y such that\n8x + 2y = 109/15\n1x + 5y = -43/6", "output": "8x + 2y = 109/15\n1x + 5y = -43/6\n\nUsing elimination\n1*(8x + 2y = 109/15)\n8*(1x + 5y = -43/6)\n8x + 2y = 109/15\n8x + 40y = -172/3\nSubtract equations\n-38y = 323/5\ny = 323/5/-38\ny = -17/10\n\nSubstitute y\n8x + 2(-17/10) = 109/15\n8x = 32/3\nx = 32/3/8\nx = 4/3"} {"input": "Solve x^2 - 41/5x + 42/5 = 0", "output": "x^2 - 41/5x + 42/5 = 0\n(x - 7)(x - 6/5) = 0\nx - 7 = 0 or x - 6/5 = 0\nx = 7\nx = 6/5"} {"input": "What value of x satisfies 4x + 18 = 0", "output": "4x + 18 = 0\n4x = -18\nx = -18 / 4\nx = -9/2"} {"input": "Solve the system:\n3x + 1y = 48/5\n8x + 6y = 148/5", "output": "3x + 1y = 48/5\n8x + 6y = 148/5\n\nUsing elimination\n8*(3x + 1y = 48/5)\n3*(8x + 6y = 148/5)\n24x + 8y = 384/5\n24x + 18y = 444/5\nSubtract equations\n-10y = -12\ny = -12/-10\ny = 6/5\n\nSubstitute y\n3x + 1(6/5) = 48/5\n3x = 42/5\nx = 42/5/3\nx = 14/5"} {"input": "Solve x^2 + 55/28x - 68/7 = 0", "output": "x^2 + 55/28x - 68/7 = 0\n(x - 16/7)(x - -17/4) = 0\nx - 16/7 = 0 or x - -17/4 = 0\nx = 16/7\nx = -17/4"} {"input": "Find x and y such that\n2x + 8y = -49/5\n8x + 4y = -56/5", "output": "2x + 8y = -49/5\n8x + 4y = -56/5\n\nUsing elimination\n8*(2x + 8y = -49/5)\n2*(8x + 4y = -56/5)\n16x + 64y = -392/5\n16x + 8y = -112/5\nSubtract equations\n56y = -56\ny = -56/56\ny = -1\n\nSubstitute y\n2x + 8(-1) = -49/5\n2x = -9/5\nx = -9/5/2\nx = -9/10"} {"input": "Find x and y such that\n5x + 1y = 80/3\n7x + 8y = 244/3", "output": "5x + 1y = 80/3\n7x + 8y = 244/3\n\nUsing elimination\n7*(5x + 1y = 80/3)\n5*(7x + 8y = 244/3)\n35x + 7y = 560/3\n35x + 40y = 1220/3\nSubtract equations\n-33y = -220\ny = -220/-33\ny = 20/3\n\nSubstitute y\n5x + 1(20/3) = 80/3\n5x = 20\nx = 20/5\nx = 4"} {"input": "Solve the system:\n2x + 7y = -18\n2x + 5y = -27/2", "output": "2x + 7y = -18\n2x + 5y = -27/2\n\nUsing elimination\n2*(2x + 7y = -18)\n2*(2x + 5y = -27/2)\n4x + 14y = -36\n4x + 10y = -27\nSubtract equations\n4y = -9\ny = -9/4\ny = -9/4\n\nSubstitute y\n2x + 7(-9/4) = -18\n2x = -9/4\nx = -9/4/2\nx = -9/8"} {"input": "Solve the equation x^3 - 191/84x^2 - 43/24x + 5/14 = 0", "output": "x^3 - 191/84x^2 - 43/24x + 5/14 = 0\n(x - 20/7)(x - -3/4)(x - 1/6) = 0\nx - 20/7 = 0\nx - -3/4 = 0\nx - 1/6 = 0\nx = 20/7\nx = -3/4\nx = 1/6"} {"input": "Find x for 10x + 5/4 = 0", "output": "10x + 5/4 = 0\n10x = -5/4\nx = -5/4 / 10\nx = -1/8"} {"input": "Solve the system:\n1x + 1y = -239/63\n8x + 9y = -228/7", "output": "1x + 1y = -239/63\n8x + 9y = -228/7\n\nUsing elimination\n8*(1x + 1y = -239/63)\n1*(8x + 9y = -228/7)\n8x + 8y = -1912/63\n8x + 9y = -228/7\nSubtract equations\n-1y = 20/9\ny = 20/9/-1\ny = -20/9\n\nSubstitute y\n1x + 1(-20/9) = -239/63\n1x = -11/7\nx = -11/7/1\nx = -11/7"} {"input": "Solve simultaneously:\n4x + 6y = 146/3\n5x + 3y = 203/6", "output": "4x + 6y = 146/3\n5x + 3y = 203/6\n\nUsing elimination\n5*(4x + 6y = 146/3)\n4*(5x + 3y = 203/6)\n20x + 30y = 730/3\n20x + 12y = 406/3\nSubtract equations\n18y = 108\ny = 108/18\ny = 6\n\nSubstitute y\n4x + 6(6) = 146/3\n4x = 38/3\nx = 38/3/4\nx = 19/6"} {"input": "Solve the equation 5x - 5 = 0", "output": "5x - 5 = 0\n5x = 5\nx = 5 / 5\nx = 1"} {"input": "Solve the equations:\n5x + 1y = 88/3\n6x + 10y = 88/3", "output": "5x + 1y = 88/3\n6x + 10y = 88/3\n\nUsing elimination\n6*(5x + 1y = 88/3)\n5*(6x + 10y = 88/3)\n30x + 6y = 176\n30x + 50y = 440/3\nSubtract equations\n-44y = 88/3\ny = 88/3/-44\ny = -2/3\n\nSubstitute y\n5x + 1(-2/3) = 88/3\n5x = 30\nx = 30/5\nx = 6"} {"input": "Solve x^3 + 149/45x^2 - 61/12x + 6/5 = 0", "output": "x^3 + 149/45x^2 - 61/12x + 6/5 = 0\n(x - 3/10)(x - -9/2)(x - 8/9) = 0\nx - 3/10 = 0\nx - -9/2 = 0\nx - 8/9 = 0\nx = 3/10\nx = -9/2\nx = 8/9"} {"input": "Solve the equations:\n5x + 3y = -3/2\n2x + 8y = -29/3", "output": "5x + 3y = -3/2\n2x + 8y = -29/3\n\nUsing elimination\n2*(5x + 3y = -3/2)\n5*(2x + 8y = -29/3)\n10x + 6y = -3\n10x + 40y = -145/3\nSubtract equations\n-34y = 136/3\ny = 136/3/-34\ny = -4/3\n\nSubstitute y\n5x + 3(-4/3) = -3/2\n5x = 5/2\nx = 5/2/5\nx = 1/2"} {"input": "Solve quickly: 3x + 9 = 0", "output": "3x + 9 = 0\n3x = -9\nx = -9 / 3\nx = -3"} {"input": "Find x in 1x - 9/5 = 0", "output": "1x - 9/5 = 0\n1x = 9/5\nx = 9/5 / 1\nx = 9/5"} {"input": "Solve quickly: x^2 + 49/18x + 49/27 = 0", "output": "x^2 + 49/18x + 49/27 = 0\n(x - -14/9)(x - -7/6) = 0\nx - -14/9 = 0 or x - -7/6 = 0\nx = -14/9\nx = -7/6"} {"input": "Solve the equation 8x + 13 = 0", "output": "8x + 13 = 0\n8x = -13\nx = -13 / 8\nx = -13/8"} {"input": "Find x in x^2 + 37/6x - 13/6 = 0", "output": "x^2 + 37/6x - 13/6 = 0\n(x - 1/3)(x - -13/2) = 0\nx - 1/3 = 0 or x - -13/2 = 0\nx = 1/3\nx = -13/2"} {"input": "Compute the solution of x^3 + 17/3x^2 + 28/3x + 4 = 0", "output": "x^3 + 17/3x^2 + 28/3x + 4 = 0\n(x - -3)(x - -2/3)(x - -2) = 0\nx - -3 = 0\nx - -2/3 = 0\nx - -2 = 0\nx = -3\nx = -2/3\nx = -2"} {"input": "Solve the equations:\n8x + 7y = 114/5\n7x + 6y = 199/10", "output": "8x + 7y = 114/5\n7x + 6y = 199/10\n\nUsing elimination\n7*(8x + 7y = 114/5)\n8*(7x + 6y = 199/10)\n56x + 49y = 798/5\n56x + 48y = 796/5\nSubtract equations\n1y = 2/5\ny = 2/5/1\ny = 2/5\n\nSubstitute y\n8x + 7(2/5) = 114/5\n8x = 20\nx = 20/8\nx = 5/2"} {"input": "Find x for x^3 + 21/4x^2 - 103/4x - 30 = 0", "output": "x^3 + 21/4x^2 - 103/4x - 30 = 0\n(x - -8)(x - 15/4)(x - -1) = 0\nx - -8 = 0\nx - 15/4 = 0\nx - -1 = 0\nx = -8\nx = 15/4\nx = -1"} {"input": "Solve the equation 2x + 4 = 0", "output": "2x + 4 = 0\n2x = -4\nx = -4 / 2\nx = -2"} {"input": "Find x for x^2 + 2/3x - 5/3 = 0", "output": "x^2 + 2/3x - 5/3 = 0\n(x - 1)(x - -5/3) = 0\nx - 1 = 0 or x - -5/3 = 0\nx = 1\nx = -5/3"} {"input": "Find the solution to 3x - 24/5 = 0", "output": "3x - 24/5 = 0\n3x = 24/5\nx = 24/5 / 3\nx = 8/5"} {"input": "Find x in x^3 + 9/5x^2 - 3/100x - 17/50 = 0", "output": "x^3 + 9/5x^2 - 3/100x - 17/50 = 0\n(x - -1/2)(x - -17/10)(x - 2/5) = 0\nx - -1/2 = 0\nx - -17/10 = 0\nx - 2/5 = 0\nx = -1/2\nx = -17/10\nx = 2/5"} {"input": "Find x for 6x - 30 = 0", "output": "6x - 30 = 0\n6x = 30\nx = 30 / 6\nx = 5"} {"input": "Determine x in x^2 + 5/6x - 1/6 = 0", "output": "x^2 + 5/6x - 1/6 = 0\n(x - 1/6)(x - -1) = 0\nx - 1/6 = 0 or x - -1 = 0\nx = 1/6\nx = -1"} {"input": "Solve the equations:\n5x + 8y = -455/72\n10x + 6y = -85/12", "output": "5x + 8y = -455/72\n10x + 6y = -85/12\n\nUsing elimination\n10*(5x + 8y = -455/72)\n5*(10x + 6y = -85/12)\n50x + 80y = -2275/36\n50x + 30y = -425/12\nSubtract equations\n50y = -250/9\ny = -250/9/50\ny = -5/9\n\nSubstitute y\n5x + 8(-5/9) = -455/72\n5x = -15/8\nx = -15/8/5\nx = -3/8"} {"input": "Solve the equations:\n7x + 6y = 39/4\n9x + 1y = 419/12", "output": "7x + 6y = 39/4\n9x + 1y = 419/12\n\nUsing elimination\n9*(7x + 6y = 39/4)\n7*(9x + 1y = 419/12)\n63x + 54y = 351/4\n63x + 7y = 2933/12\nSubtract equations\n47y = -470/3\ny = -470/3/47\ny = -10/3\n\nSubstitute y\n7x + 6(-10/3) = 39/4\n7x = 119/4\nx = 119/4/7\nx = 17/4"} {"input": "Solve x^2 - 27/20x - 7/10 = 0", "output": "x^2 - 27/20x - 7/10 = 0\n(x - -2/5)(x - 7/4) = 0\nx - -2/5 = 0 or x - 7/4 = 0\nx = -2/5\nx = 7/4"} {"input": "What value of x satisfies 10x - 4 = 0", "output": "10x - 4 = 0\n10x = 4\nx = 4 / 10\nx = 2/5"} {"input": "Find the solution to x^2 + 11/21x - 2/21 = 0", "output": "x^2 + 11/21x - 2/21 = 0\n(x - 1/7)(x - -2/3) = 0\nx - 1/7 = 0 or x - -2/3 = 0\nx = 1/7\nx = -2/3"} {"input": "Solve the equation x^2 + 25/4x + 63/8 = 0", "output": "x^2 + 25/4x + 63/8 = 0\n(x - -7/4)(x - -9/2) = 0\nx - -7/4 = 0 or x - -9/2 = 0\nx = -7/4\nx = -9/2"} {"input": "Find the solution to x^3 + 97/45x^2 + 206/135x + 16/45 = 0", "output": "x^3 + 97/45x^2 + 206/135x + 16/45 = 0\n(x - -3/5)(x - -2/3)(x - -8/9) = 0\nx - -3/5 = 0\nx - -2/3 = 0\nx - -8/9 = 0\nx = -3/5\nx = -2/3\nx = -8/9"} {"input": "Compute the solution of x^2 - 5x - 6 = 0", "output": "x^2 - 5x - 6 = 0\n(x - 6)(x - -1) = 0\nx - 6 = 0 or x - -1 = 0\nx = 6\nx = -1"} {"input": "Find the solution to x^2 - 23/8x + 15/8 = 0", "output": "x^2 - 23/8x + 15/8 = 0\n(x - 1)(x - 15/8) = 0\nx - 1 = 0 or x - 15/8 = 0\nx = 1\nx = 15/8"} {"input": "Solve the equations:\n7x + 2y = -121/5\n5x + 5y = -18", "output": "7x + 2y = -121/5\n5x + 5y = -18\n\nUsing elimination\n5*(7x + 2y = -121/5)\n7*(5x + 5y = -18)\n35x + 10y = -121\n35x + 35y = -126\nSubtract equations\n-25y = 5\ny = 5/-25\ny = -1/5\n\nSubstitute y\n7x + 2(-1/5) = -121/5\n7x = -119/5\nx = -119/5/7\nx = -17/5"} {"input": "Determine x in x^2 - 14/5x + 8/5 = 0", "output": "x^2 - 14/5x + 8/5 = 0\n(x - 4/5)(x - 2) = 0\nx - 4/5 = 0 or x - 2 = 0\nx = 4/5\nx = 2"} {"input": "Find x for 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Find x and y such that\n8x + 3y = 41/6\n4x + 7y = 27/2", "output": "8x + 3y = 41/6\n4x + 7y = 27/2\n\nUsing elimination\n4*(8x + 3y = 41/6)\n8*(4x + 7y = 27/2)\n32x + 12y = 82/3\n32x + 56y = 108\nSubtract equations\n-44y = -242/3\ny = -242/3/-44\ny = 11/6\n\nSubstitute y\n8x + 3(11/6) = 41/6\n8x = 4/3\nx = 4/3/8\nx = 1/6"} {"input": "What value of x satisfies x^2 + 7/3x - 10/3 = 0", "output": "x^2 + 7/3x - 10/3 = 0\n(x - 1)(x - -10/3) = 0\nx - 1 = 0 or x - -10/3 = 0\nx = 1\nx = -10/3"} {"input": "Find x for x^2 - 21/8x - 49/16 = 0", "output": "x^2 - 21/8x - 49/16 = 0\n(x - 7/2)(x - -7/8) = 0\nx - 7/2 = 0 or x - -7/8 = 0\nx = 7/2\nx = -7/8"} {"input": "Find x and y such that\n8x + 1y = -99/5\n5x + 1y = -63/5", "output": "8x + 1y = -99/5\n5x + 1y = -63/5\n\nUsing elimination\n5*(8x + 1y = -99/5)\n8*(5x + 1y = -63/5)\n40x + 5y = -99\n40x + 8y = -504/5\nSubtract equations\n-3y = 9/5\ny = 9/5/-3\ny = -3/5\n\nSubstitute y\n8x + 1(-3/5) = -99/5\n8x = -96/5\nx = -96/5/8\nx = -12/5"} {"input": "Solve the equation 1x + 3/5 = 0", "output": "1x + 3/5 = 0\n1x = -3/5\nx = -3/5 / 1\nx = -3/5"} {"input": "Solve quickly: x^2 - 82/15x + 112/15 = 0", "output": "x^2 - 82/15x + 112/15 = 0\n(x - 8/3)(x - 14/5) = 0\nx - 8/3 = 0 or x - 14/5 = 0\nx = 8/3\nx = 14/5"} {"input": "What value of x satisfies x^3 + 493/140x^2 + 467/140x + 33/35 = 0", "output": "x^3 + 493/140x^2 + 467/140x + 33/35 = 0\n(x - -4/7)(x - -11/5)(x - -3/4) = 0\nx - -4/7 = 0\nx - -11/5 = 0\nx - -3/4 = 0\nx = -4/7\nx = -11/5\nx = -3/4"} {"input": "Solve x^3 + 212/15x^2 + 9/5x - 14/15 = 0", "output": "x^3 + 212/15x^2 + 9/5x - 14/15 = 0\n(x - -1/3)(x - -14)(x - 1/5) = 0\nx - -1/3 = 0\nx - -14 = 0\nx - 1/5 = 0\nx = -1/3\nx = -14\nx = 1/5"} {"input": "Solve the equation 7x - 77 = 0", "output": "7x - 77 = 0\n7x = 77\nx = 77 / 7\nx = 11"} {"input": "Determine x in 6x - 36/5 = 0", "output": "6x - 36/5 = 0\n6x = 36/5\nx = 36/5 / 6\nx = 6/5"} {"input": "Solve the equations:\n4x + 9y = 8\n7x + 4y = -19/2", "output": "4x + 9y = 8\n7x + 4y = -19/2\n\nUsing elimination\n7*(4x + 9y = 8)\n4*(7x + 4y = -19/2)\n28x + 63y = 56\n28x + 16y = -38\nSubtract equations\n47y = 94\ny = 94/47\ny = 2\n\nSubstitute y\n4x + 9(2) = 8\n4x = -10\nx = -10/4\nx = -5/2"} {"input": "Find x and y such that\n7x + 9y = -115/8\n10x + 9y = -1069/56", "output": "7x + 9y = -115/8\n10x + 9y = -1069/56\n\nUsing elimination\n10*(7x + 9y = -115/8)\n7*(10x + 9y = -1069/56)\n70x + 90y = -575/4\n70x + 63y = -1069/8\nSubtract equations\n27y = -81/8\ny = -81/8/27\ny = -3/8\n\nSubstitute y\n7x + 9(-3/8) = -115/8\n7x = -11\nx = -11/7\nx = -11/7"} {"input": "Compute the solution of x^2 - 5/6x - 13/2 = 0", "output": "x^2 - 5/6x - 13/2 = 0\n(x - 3)(x - -13/6) = 0\nx - 3 = 0 or x - -13/6 = 0\nx = 3\nx = -13/6"} {"input": "Solve the equation 8x + 28/3 = 0", "output": "8x + 28/3 = 0\n8x = -28/3\nx = -28/3 / 8\nx = -7/6"} {"input": "Determine x in x^3 - 53/12x^2 - 14/3x + 49/3 = 0", "output": "x^3 - 53/12x^2 - 14/3x + 49/3 = 0\n(x - 14/3)(x - -2)(x - 7/4) = 0\nx - 14/3 = 0\nx - -2 = 0\nx - 7/4 = 0\nx = 14/3\nx = -2\nx = 7/4"} {"input": "Solve x^2 - 44/3x - 60 = 0", "output": "x^2 - 44/3x - 60 = 0\n(x - 18)(x - -10/3) = 0\nx - 18 = 0 or x - -10/3 = 0\nx = 18\nx = -10/3"} {"input": "Determine x in 9x - 27 = 0", "output": "9x - 27 = 0\n9x = 27\nx = 27 / 9\nx = 3"} {"input": "Solve quickly: x^3 - 17/6x^2 - 11/6x + 7 = 0", "output": "x^3 - 17/6x^2 - 11/6x + 7 = 0\n(x - -3/2)(x - 2)(x - 7/3) = 0\nx - -3/2 = 0\nx - 2 = 0\nx - 7/3 = 0\nx = -3/2\nx = 2\nx = 7/3"} {"input": "Solve quickly: x^2 + 25/2x - 75/2 = 0", "output": "x^2 + 25/2x - 75/2 = 0\n(x - 5/2)(x - -15) = 0\nx - 5/2 = 0 or x - -15 = 0\nx = 5/2\nx = -15"} {"input": "Solve the equation x^2 + 13/5x - 63/20 = 0", "output": "x^2 + 13/5x - 63/20 = 0\n(x - 9/10)(x - -7/2) = 0\nx - 9/10 = 0 or x - -7/2 = 0\nx = 9/10\nx = -7/2"} {"input": "Compute the solution of x^3 - 10/7x^2 - 11/49x = 0", "output": "x^3 - 10/7x^2 - 11/49x = 0\n(x - 0)(x - 11/7)(x - -1/7) = 0\nx - 0 = 0\nx - 11/7 = 0\nx - -1/7 = 0\nx = 0\nx = 11/7\nx = -1/7"} {"input": "Solve the system:\n1x + 9y = 225/4\n8x + 7y = 60", "output": "1x + 9y = 225/4\n8x + 7y = 60\n\nUsing elimination\n8*(1x + 9y = 225/4)\n1*(8x + 7y = 60)\n8x + 72y = 450\n8x + 7y = 60\nSubtract equations\n65y = 390\ny = 390/65\ny = 6\n\nSubstitute y\n1x + 9(6) = 225/4\n1x = 9/4\nx = 9/4/1\nx = 9/4"} {"input": "Solve the system:\n3x + 6y = 36/5\n3x + 7y = 41/5", "output": "3x + 6y = 36/5\n3x + 7y = 41/5\n\nUsing elimination\n3*(3x + 6y = 36/5)\n3*(3x + 7y = 41/5)\n9x + 18y = 108/5\n9x + 21y = 123/5\nSubtract equations\n-3y = -3\ny = -3/-3\ny = 1\n\nSubstitute y\n3x + 6(1) = 36/5\n3x = 6/5\nx = 6/5/3\nx = 2/5"} {"input": "Find x and y such that\n3x + 7y = -15/2\n10x + 1y = 185/6", "output": "3x + 7y = -15/2\n10x + 1y = 185/6\n\nUsing elimination\n10*(3x + 7y = -15/2)\n3*(10x + 1y = 185/6)\n30x + 70y = -75\n30x + 3y = 185/2\nSubtract equations\n67y = -335/2\ny = -335/2/67\ny = -5/2\n\nSubstitute y\n3x + 7(-5/2) = -15/2\n3x = 10\nx = 10/3\nx = 10/3"} {"input": "Solve the equations:\n1x + 8y = -97/10\n4x + 5y = -37/10", "output": "1x + 8y = -97/10\n4x + 5y = -37/10\n\nUsing elimination\n4*(1x + 8y = -97/10)\n1*(4x + 5y = -37/10)\n4x + 32y = -194/5\n4x + 5y = -37/10\nSubtract equations\n27y = -351/10\ny = -351/10/27\ny = -13/10\n\nSubstitute y\n1x + 8(-13/10) = -97/10\n1x = 7/10\nx = 7/10/1\nx = 7/10"} {"input": "What value of x satisfies 2x - 36/5 = 0", "output": "2x - 36/5 = 0\n2x = 36/5\nx = 36/5 / 2\nx = 18/5"} {"input": "Solve the system:\n10x + 4y = 120\n2x + 10y = 24", "output": "10x + 4y = 120\n2x + 10y = 24\n\nUsing elimination\n2*(10x + 4y = 120)\n10*(2x + 10y = 24)\n20x + 8y = 240\n20x + 100y = 240\nSubtract equations\n-92y = 0\ny = 0/-92\ny = 0\n\nSubstitute y\n10x + 4(0) = 120\n10x = 120\nx = 120/10\nx = 12"} {"input": "Solve simultaneously:\n5x + 4y = 137/5\n5x + 6y = 143/5", "output": "5x + 4y = 137/5\n5x + 6y = 143/5\n\nUsing elimination\n5*(5x + 4y = 137/5)\n5*(5x + 6y = 143/5)\n25x + 20y = 137\n25x + 30y = 143\nSubtract equations\n-10y = -6\ny = -6/-10\ny = 3/5\n\nSubstitute y\n5x + 4(3/5) = 137/5\n5x = 25\nx = 25/5\nx = 5"} {"input": "Find x and y such that\n1x + 5y = -87/40\n8x + 7y = -201/40", "output": "1x + 5y = -87/40\n8x + 7y = -201/40\n\nUsing elimination\n8*(1x + 5y = -87/40)\n1*(8x + 7y = -201/40)\n8x + 40y = -87/5\n8x + 7y = -201/40\nSubtract equations\n33y = -99/8\ny = -99/8/33\ny = -3/8\n\nSubstitute y\n1x + 5(-3/8) = -87/40\n1x = -3/10\nx = -3/10/1\nx = -3/10"} {"input": "Find x for 6x + 102/5 = 0", "output": "6x + 102/5 = 0\n6x = -102/5\nx = -102/5 / 6\nx = -17/5"} {"input": "Solve x^2 - 32/7x + 256/49 = 0", "output": "x^2 - 32/7x + 256/49 = 0\n(x - 16/7)(x - 16/7) = 0\nx - 16/7 = 0 or x - 16/7 = 0\nx = 16/7\nx = 16/7"} {"input": "Solve simultaneously:\n3x + 8y = 25/7\n8x + 7y = -13", "output": "3x + 8y = 25/7\n8x + 7y = -13\n\nUsing elimination\n8*(3x + 8y = 25/7)\n3*(8x + 7y = -13)\n24x + 64y = 200/7\n24x + 21y = -39\nSubtract equations\n43y = 473/7\ny = 473/7/43\ny = 11/7\n\nSubstitute y\n3x + 8(11/7) = 25/7\n3x = -9\nx = -9/3\nx = -3"} {"input": "Solve simultaneously:\n6x + 1y = -146/5\n5x + 4y = -517/15", "output": "6x + 1y = -146/5\n5x + 4y = -517/15\n\nUsing elimination\n5*(6x + 1y = -146/5)\n6*(5x + 4y = -517/15)\n30x + 5y = -146\n30x + 24y = -1034/5\nSubtract equations\n-19y = 304/5\ny = 304/5/-19\ny = -16/5\n\nSubstitute y\n6x + 1(-16/5) = -146/5\n6x = -26\nx = -26/6\nx = -13/3"} {"input": "Find the solution to x^3 - 9x^2 - 57x + 65 = 0", "output": "x^3 - 9x^2 - 57x + 65 = 0\n(x - -5)(x - 13)(x - 1) = 0\nx - -5 = 0\nx - 13 = 0\nx - 1 = 0\nx = -5\nx = 13\nx = 1"} {"input": "Solve quickly: x^2 - 2/3x - 5/3 = 0", "output": "x^2 - 2/3x - 5/3 = 0\n(x - -1)(x - 5/3) = 0\nx - -1 = 0 or x - 5/3 = 0\nx = -1\nx = 5/3"} {"input": "Find x and y such that\n9x + 8y = -111\n2x + 3y = -43", "output": "9x + 8y = -111\n2x + 3y = -43\n\nUsing elimination\n2*(9x + 8y = -111)\n9*(2x + 3y = -43)\n18x + 16y = -222\n18x + 27y = -387\nSubtract equations\n-11y = 165\ny = 165/-11\ny = -15\n\nSubstitute y\n9x + 8(-15) = -111\n9x = 9\nx = 9/9\nx = 1"} {"input": "Compute the solution of 1x - 7/2 = 0", "output": "1x - 7/2 = 0\n1x = 7/2\nx = 7/2 / 1\nx = 7/2"} {"input": "Find x for x^2 + 41/24x + 1/2 = 0", "output": "x^2 + 41/24x + 1/2 = 0\n(x - -3/8)(x - -4/3) = 0\nx - -3/8 = 0 or x - -4/3 = 0\nx = -3/8\nx = -4/3"} {"input": "Compute the solution of x^2 - 73/4x + 195/4 = 0", "output": "x^2 - 73/4x + 195/4 = 0\n(x - 13/4)(x - 15) = 0\nx - 13/4 = 0 or x - 15 = 0\nx = 13/4\nx = 15"} {"input": "Solve x^2 + 83/9x + 88/9 = 0", "output": "x^2 + 83/9x + 88/9 = 0\n(x - -8)(x - -11/9) = 0\nx - -8 = 0 or x - -11/9 = 0\nx = -8\nx = -11/9"} {"input": "What value of x satisfies x^3 + 128/7x^2 + 452/7x + 64 = 0", "output": "x^3 + 128/7x^2 + 452/7x + 64 = 0\n(x - -2)(x - -14)(x - -16/7) = 0\nx - -2 = 0\nx - -14 = 0\nx - -16/7 = 0\nx = -2\nx = -14\nx = -16/7"} {"input": "Find x and y such that\n3x + 9y = -117/5\n3x + 1y = -133/5", "output": "3x + 9y = -117/5\n3x + 1y = -133/5\n\nUsing elimination\n3*(3x + 9y = -117/5)\n3*(3x + 1y = -133/5)\n9x + 27y = -351/5\n9x + 3y = -399/5\nSubtract equations\n24y = 48/5\ny = 48/5/24\ny = 2/5\n\nSubstitute y\n3x + 9(2/5) = -117/5\n3x = -27\nx = -27/3\nx = -9"} {"input": "What value of x satisfies 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Compute the solution of x^2 + 7/5x - 34/5 = 0", "output": "x^2 + 7/5x - 34/5 = 0\n(x - -17/5)(x - 2) = 0\nx - -17/5 = 0 or x - 2 = 0\nx = -17/5\nx = 2"} {"input": "Solve the equation 7x + 63/5 = 0", "output": "7x + 63/5 = 0\n7x = -63/5\nx = -63/5 / 7\nx = -9/5"} {"input": "Find x and y such that\n6x + 8y = 160\n4x + 6y = 113", "output": "6x + 8y = 160\n4x + 6y = 113\n\nUsing elimination\n4*(6x + 8y = 160)\n6*(4x + 6y = 113)\n24x + 32y = 640\n24x + 36y = 678\nSubtract equations\n-4y = -38\ny = -38/-4\ny = 19/2\n\nSubstitute y\n6x + 8(19/2) = 160\n6x = 84\nx = 84/6\nx = 14"} {"input": "Solve the system:\n1x + 2y = 8\n3x + 1y = 23/2", "output": "1x + 2y = 8\n3x + 1y = 23/2\n\nUsing elimination\n3*(1x + 2y = 8)\n1*(3x + 1y = 23/2)\n3x + 6y = 24\n3x + 1y = 23/2\nSubtract equations\n5y = 25/2\ny = 25/2/5\ny = 5/2\n\nSubstitute y\n1x + 2(5/2) = 8\n1x = 3\nx = 3/1\nx = 3"} {"input": "Determine x in x^3 - 183/70x^2 - 422/245x + 144/49 = 0", "output": "x^3 - 183/70x^2 - 422/245x + 144/49 = 0\n(x - -8/7)(x - 20/7)(x - 9/10) = 0\nx - -8/7 = 0\nx - 20/7 = 0\nx - 9/10 = 0\nx = -8/7\nx = 20/7\nx = 9/10"} {"input": "Find x in x^2 + 43/9x + 52/27 = 0", "output": "x^2 + 43/9x + 52/27 = 0\n(x - -4/9)(x - -13/3) = 0\nx - -4/9 = 0 or x - -13/3 = 0\nx = -4/9\nx = -13/3"} {"input": "Find x for x^2 + 23/21x - 10/21 = 0", "output": "x^2 + 23/21x - 10/21 = 0\n(x - 1/3)(x - -10/7) = 0\nx - 1/3 = 0 or x - -10/7 = 0\nx = 1/3\nx = -10/7"} {"input": "Solve the equation x^2 - 10x + 200/9 = 0", "output": "x^2 - 10x + 200/9 = 0\n(x - 20/3)(x - 10/3) = 0\nx - 20/3 = 0 or x - 10/3 = 0\nx = 20/3\nx = 10/3"} {"input": "Solve quickly: x^3 + 493/126x^2 - 25/42x - 650/63 = 0", "output": "x^3 + 493/126x^2 - 25/42x - 650/63 = 0\n(x - -5/2)(x - 13/9)(x - -20/7) = 0\nx - -5/2 = 0\nx - 13/9 = 0\nx - -20/7 = 0\nx = -5/2\nx = 13/9\nx = -20/7"} {"input": "Solve quickly: x^2 + 5/3x - 19/4 = 0", "output": "x^2 + 5/3x - 19/4 = 0\n(x - -19/6)(x - 3/2) = 0\nx - -19/6 = 0 or x - 3/2 = 0\nx = -19/6\nx = 3/2"} {"input": "Compute the solution of x^3 + 23/2x^2 - 2x - 165/2 = 0", "output": "x^3 + 23/2x^2 - 2x - 165/2 = 0\n(x - 5/2)(x - -3)(x - -11) = 0\nx - 5/2 = 0\nx - -3 = 0\nx - -11 = 0\nx = 5/2\nx = -3\nx = -11"} {"input": "Find the solution to 6x + 16 = 0", "output": "6x + 16 = 0\n6x = -16\nx = -16 / 6\nx = -8/3"} {"input": "Solve the equation 8x - 12/5 = 0", "output": "8x - 12/5 = 0\n8x = 12/5\nx = 12/5 / 8\nx = 3/10"} {"input": "Determine x in x^3 - 197/210x^2 - 79/70x + 22/105 = 0", "output": "x^3 - 197/210x^2 - 79/70x + 22/105 = 0\n(x - -4/5)(x - 1/6)(x - 11/7) = 0\nx - -4/5 = 0\nx - 1/6 = 0\nx - 11/7 = 0\nx = -4/5\nx = 1/6\nx = 11/7"} {"input": "Find x for 2x - 38/9 = 0", "output": "2x - 38/9 = 0\n2x = 38/9\nx = 38/9 / 2\nx = 19/9"} {"input": "Solve the system:\n2x + 1y = -1/2\n8x + 8y = -14", "output": "2x + 1y = -1/2\n8x + 8y = -14\n\nUsing elimination\n8*(2x + 1y = -1/2)\n2*(8x + 8y = -14)\n16x + 8y = -4\n16x + 16y = -28\nSubtract equations\n-8y = 24\ny = 24/-8\ny = -3\n\nSubstitute y\n2x + 1(-3) = -1/2\n2x = 5/2\nx = 5/2/2\nx = 5/4"} {"input": "Compute the solution of 7x + 42 = 0", "output": "7x + 42 = 0\n7x = -42\nx = -42 / 7\nx = -6"} {"input": "Find x for x^3 + 179/28x^2 + 93/8x + 45/7 = 0", "output": "x^3 + 179/28x^2 + 93/8x + 45/7 = 0\n(x - -3/2)(x - -15/4)(x - -8/7) = 0\nx - -3/2 = 0\nx - -15/4 = 0\nx - -8/7 = 0\nx = -3/2\nx = -15/4\nx = -8/7"} {"input": "Find the solution to x^3 + 1x^2 - 253/4x - 595/4 = 0", "output": "x^3 + 1x^2 - 253/4x - 595/4 = 0\n(x - -5/2)(x - 17/2)(x - -7) = 0\nx - -5/2 = 0\nx - 17/2 = 0\nx - -7 = 0\nx = -5/2\nx = 17/2\nx = -7"} {"input": "Solve simultaneously:\n5x + 6y = 4\n10x + 4y = 28/3", "output": "5x + 6y = 4\n10x + 4y = 28/3\n\nUsing elimination\n10*(5x + 6y = 4)\n5*(10x + 4y = 28/3)\n50x + 60y = 40\n50x + 20y = 140/3\nSubtract equations\n40y = -20/3\ny = -20/3/40\ny = -1/6\n\nSubstitute y\n5x + 6(-1/6) = 4\n5x = 5\nx = 5/5\nx = 1"} {"input": "Compute the solution of x^3 + 541/35x^2 - 328/35x - 384/35 = 0", "output": "x^3 + 541/35x^2 - 328/35x - 384/35 = 0\n(x - -16)(x - 8/7)(x - -3/5) = 0\nx - -16 = 0\nx - 8/7 = 0\nx - -3/5 = 0\nx = -16\nx = 8/7\nx = -3/5"} {"input": "Solve 8x + 24 = 0", "output": "8x + 24 = 0\n8x = -24\nx = -24 / 8\nx = -3"} {"input": "Solve simultaneously:\n5x + 3y = -32\n4x + 4y = -208/5", "output": "5x + 3y = -32\n4x + 4y = -208/5\n\nUsing elimination\n4*(5x + 3y = -32)\n5*(4x + 4y = -208/5)\n20x + 12y = -128\n20x + 20y = -208\nSubtract equations\n-8y = 80\ny = 80/-8\ny = -10\n\nSubstitute y\n5x + 3(-10) = -32\n5x = -2\nx = -2/5\nx = -2/5"} {"input": "Find x in 7x - 112/3 = 0", "output": "7x - 112/3 = 0\n7x = 112/3\nx = 112/3 / 7\nx = 16/3"} {"input": "Determine x in x^3 + 367/56x^2 + 27/8x + 9/28 = 0", "output": "x^3 + 367/56x^2 + 27/8x + 9/28 = 0\n(x - -6)(x - -1/8)(x - -3/7) = 0\nx - -6 = 0\nx - -1/8 = 0\nx - -3/7 = 0\nx = -6\nx = -1/8\nx = -3/7"} {"input": "What value of x satisfies x^2 - 5/2x = 0", "output": "x^2 - 5/2x = 0\n(x - 5/2)(x - 0) = 0\nx - 5/2 = 0 or x - 0 = 0\nx = 5/2\nx = 0"} {"input": "Compute the solution of x^2 + 67/70x + 3/35 = 0", "output": "x^2 + 67/70x + 3/35 = 0\n(x - -6/7)(x - -1/10) = 0\nx - -6/7 = 0 or x - -1/10 = 0\nx = -6/7\nx = -1/10"} {"input": "Find x for x^3 + 1/5x^2 - 33/20x + 9/20 = 0", "output": "x^3 + 1/5x^2 - 33/20x + 9/20 = 0\n(x - 3/10)(x - 1)(x - -3/2) = 0\nx - 3/10 = 0\nx - 1 = 0\nx - -3/2 = 0\nx = 3/10\nx = 1\nx = -3/2"} {"input": "Solve simultaneously:\n10x + 8y = 22\n5x + 1y = -1", "output": "10x + 8y = 22\n5x + 1y = -1\n\nUsing elimination\n5*(10x + 8y = 22)\n10*(5x + 1y = -1)\n50x + 40y = 110\n50x + 10y = -10\nSubtract equations\n30y = 120\ny = 120/30\ny = 4\n\nSubstitute y\n10x + 8(4) = 22\n10x = -10\nx = -10/10\nx = -1"} {"input": "Solve the system:\n1x + 3y = -9/5\n4x + 3y = -21/5", "output": "1x + 3y = -9/5\n4x + 3y = -21/5\n\nUsing elimination\n4*(1x + 3y = -9/5)\n1*(4x + 3y = -21/5)\n4x + 12y = -36/5\n4x + 3y = -21/5\nSubtract equations\n9y = -3\ny = -3/9\ny = -1/3\n\nSubstitute y\n1x + 3(-1/3) = -9/5\n1x = -4/5\nx = -4/5/1\nx = -4/5"} {"input": "Find x in 5x + 65 = 0", "output": "5x + 65 = 0\n5x = -65\nx = -65 / 5\nx = -13"} {"input": "Find the solution to 7x - 35/2 = 0", "output": "7x - 35/2 = 0\n7x = 35/2\nx = 35/2 / 7\nx = 5/2"} {"input": "Determine x in 7x + 35/3 = 0", "output": "7x + 35/3 = 0\n7x = -35/3\nx = -35/3 / 7\nx = -5/3"} {"input": "Solve the equation x^2 - 13/5x + 6/5 = 0", "output": "x^2 - 13/5x + 6/5 = 0\n(x - 2)(x - 3/5) = 0\nx - 2 = 0 or x - 3/5 = 0\nx = 2\nx = 3/5"} {"input": "Determine x in x^2 + 191/9x + 380/9 = 0", "output": "x^2 + 191/9x + 380/9 = 0\n(x - -20/9)(x - -19) = 0\nx - -20/9 = 0 or x - -19 = 0\nx = -20/9\nx = -19"} {"input": "Find the solution to x^3 + 988/45x^2 + 2459/45x - 1292/45 = 0", "output": "x^3 + 988/45x^2 + 2459/45x - 1292/45 = 0\n(x - 4/9)(x - -17/5)(x - -19) = 0\nx - 4/9 = 0\nx - -17/5 = 0\nx - -19 = 0\nx = 4/9\nx = -17/5\nx = -19"} {"input": "What value of x satisfies x^3 - 149/120x^2 - 467/240x + 119/60 = 0", "output": "x^3 - 149/120x^2 - 467/240x + 119/60 = 0\n(x - 17/10)(x - 7/8)(x - -4/3) = 0\nx - 17/10 = 0\nx - 7/8 = 0\nx - -4/3 = 0\nx = 17/10\nx = 7/8\nx = -4/3"} {"input": "Solve x^2 - 5/6x - 2/3 = 0", "output": "x^2 - 5/6x - 2/3 = 0\n(x - 4/3)(x - -1/2) = 0\nx - 4/3 = 0 or x - -1/2 = 0\nx = 4/3\nx = -1/2"} {"input": "Find the solution to x^3 - 7x - 6 = 0", "output": "x^3 - 7x - 6 = 0\n(x - -1)(x - 3)(x - -2) = 0\nx - -1 = 0\nx - 3 = 0\nx - -2 = 0\nx = -1\nx = 3\nx = -2"} {"input": "Find x and y such that\n4x + 5y = 1/3\n6x + 9y = 0", "output": "4x + 5y = 1/3\n6x + 9y = 0\n\nUsing elimination\n6*(4x + 5y = 1/3)\n4*(6x + 9y = 0)\n24x + 30y = 2\n24x + 36y = 0\nSubtract equations\n-6y = 2\ny = 2/-6\ny = -1/3\n\nSubstitute y\n4x + 5(-1/3) = 1/3\n4x = 2\nx = 2/4\nx = 1/2"} {"input": "Determine x in x^2 + 74/45x + 13/45 = 0", "output": "x^2 + 74/45x + 13/45 = 0\n(x - -13/9)(x - -1/5) = 0\nx - -13/9 = 0 or x - -1/5 = 0\nx = -13/9\nx = -1/5"} {"input": "Find x in x^3 - 9/2x^2 - 3x + 20 = 0", "output": "x^3 - 9/2x^2 - 3x + 20 = 0\n(x - -2)(x - 5/2)(x - 4) = 0\nx - -2 = 0\nx - 5/2 = 0\nx - 4 = 0\nx = -2\nx = 5/2\nx = 4"} {"input": "Find x for x^3 + 5/2x^2 - 261/2x - 198 = 0", "output": "x^3 + 5/2x^2 - 261/2x - 198 = 0\n(x - -12)(x - 11)(x - -3/2) = 0\nx - -12 = 0\nx - 11 = 0\nx - -3/2 = 0\nx = -12\nx = 11\nx = -3/2"} {"input": "Solve quickly: x^2 + 25/3x + 52/3 = 0", "output": "x^2 + 25/3x + 52/3 = 0\n(x - -4)(x - -13/3) = 0\nx - -4 = 0 or x - -13/3 = 0\nx = -4\nx = -13/3"} {"input": "Find x for 4x - 24/7 = 0", "output": "4x - 24/7 = 0\n4x = 24/7\nx = 24/7 / 4\nx = 6/7"} {"input": "What value of x satisfies 3x + 9/2 = 0", "output": "3x + 9/2 = 0\n3x = -9/2\nx = -9/2 / 3\nx = -3/2"} {"input": "Solve the system:\n6x + 9y = 21/20\n4x + 5y = 1", "output": "6x + 9y = 21/20\n4x + 5y = 1\n\nUsing elimination\n4*(6x + 9y = 21/20)\n6*(4x + 5y = 1)\n24x + 36y = 21/5\n24x + 30y = 6\nSubtract equations\n6y = -9/5\ny = -9/5/6\ny = -3/10\n\nSubstitute y\n6x + 9(-3/10) = 21/20\n6x = 15/4\nx = 15/4/6\nx = 5/8"} {"input": "Solve the system:\n6x + 2y = -349/14\n7x + 9y = -1321/28", "output": "6x + 2y = -349/14\n7x + 9y = -1321/28\n\nUsing elimination\n7*(6x + 2y = -349/14)\n6*(7x + 9y = -1321/28)\n42x + 14y = -349/2\n42x + 54y = -3963/14\nSubtract equations\n-40y = 760/7\ny = 760/7/-40\ny = -19/7\n\nSubstitute y\n6x + 2(-19/7) = -349/14\n6x = -39/2\nx = -39/2/6\nx = -13/4"} {"input": "Find x for x^2 + 15/2x = 0", "output": "x^2 + 15/2x = 0\n(x - 0)(x - -15/2) = 0\nx - 0 = 0 or x - -15/2 = 0\nx = 0\nx = -15/2"} {"input": "Solve x^2 + 104/63x - 17/9 = 0", "output": "x^2 + 104/63x - 17/9 = 0\n(x - 7/9)(x - -17/7) = 0\nx - 7/9 = 0 or x - -17/7 = 0\nx = 7/9\nx = -17/7"} {"input": "Solve simultaneously:\n6x + 6y = 204/5\n2x + 1y = 38/5", "output": "6x + 6y = 204/5\n2x + 1y = 38/5\n\nUsing elimination\n2*(6x + 6y = 204/5)\n6*(2x + 1y = 38/5)\n12x + 12y = 408/5\n12x + 6y = 228/5\nSubtract equations\n6y = 36\ny = 36/6\ny = 6\n\nSubstitute y\n6x + 6(6) = 204/5\n6x = 24/5\nx = 24/5/6\nx = 4/5"} {"input": "Solve the equation x^2 + 12/35x - 36/35 = 0", "output": "x^2 + 12/35x - 36/35 = 0\n(x - -6/5)(x - 6/7) = 0\nx - -6/5 = 0 or x - 6/7 = 0\nx = -6/5\nx = 6/7"} {"input": "Find x and y such that\n4x + 8y = -16/7\n10x + 6y = 9/7", "output": "4x + 8y = -16/7\n10x + 6y = 9/7\n\nUsing elimination\n10*(4x + 8y = -16/7)\n4*(10x + 6y = 9/7)\n40x + 80y = -160/7\n40x + 24y = 36/7\nSubtract equations\n56y = -28\ny = -28/56\ny = -1/2\n\nSubstitute y\n4x + 8(-1/2) = -16/7\n4x = 12/7\nx = 12/7/4\nx = 3/7"} {"input": "Compute the solution of x^3 - 1091/360x^2 + 21/20x + 13/72 = 0", "output": "x^3 - 1091/360x^2 + 21/20x + 13/72 = 0\n(x - 13/5)(x - 5/9)(x - -1/8) = 0\nx - 13/5 = 0\nx - 5/9 = 0\nx - -1/8 = 0\nx = 13/5\nx = 5/9\nx = -1/8"} {"input": "Solve the system:\n5x + 4y = 43\n6x + 5y = 52", "output": "5x + 4y = 43\n6x + 5y = 52\n\nUsing elimination\n6*(5x + 4y = 43)\n5*(6x + 5y = 52)\n30x + 24y = 258\n30x + 25y = 260\nSubtract equations\n-1y = -2\ny = -2/-1\ny = 2\n\nSubstitute y\n5x + 4(2) = 43\n5x = 35\nx = 35/5\nx = 7"} {"input": "What value of x satisfies x^3 - 89/63x^2 - 38/21x + 80/63 = 0", "output": "x^3 - 89/63x^2 - 38/21x + 80/63 = 0\n(x - -8/7)(x - 5/9)(x - 2) = 0\nx - -8/7 = 0\nx - 5/9 = 0\nx - 2 = 0\nx = -8/7\nx = 5/9\nx = 2"} {"input": "Find x in 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "What value of x satisfies x^3 + 187/35x^2 + 28/5x + 32/35 = 0", "output": "x^3 + 187/35x^2 + 28/5x + 32/35 = 0\n(x - -8/7)(x - -1/5)(x - -4) = 0\nx - -8/7 = 0\nx - -1/5 = 0\nx - -4 = 0\nx = -8/7\nx = -1/5\nx = -4"} {"input": "Determine x in x^3 + 23/2x^2 - 15/2x - 18 = 0", "output": "x^3 + 23/2x^2 - 15/2x - 18 = 0\n(x - -1)(x - 3/2)(x - -12) = 0\nx - -1 = 0\nx - 3/2 = 0\nx - -12 = 0\nx = -1\nx = 3/2\nx = -12"} {"input": "Find x for x^3 + 6x^2 + 17/4x - 15/4 = 0", "output": "x^3 + 6x^2 + 17/4x - 15/4 = 0\n(x - -5)(x - 1/2)(x - -3/2) = 0\nx - -5 = 0\nx - 1/2 = 0\nx - -3/2 = 0\nx = -5\nx = 1/2\nx = -3/2"} {"input": "Solve quickly: 4x - 34 = 0", "output": "4x - 34 = 0\n4x = 34\nx = 34 / 4\nx = 17/2"} {"input": "What value of x satisfies x^2 - 68/9x + 209/27 = 0", "output": "x^2 - 68/9x + 209/27 = 0\n(x - 11/9)(x - 19/3) = 0\nx - 11/9 = 0 or x - 19/3 = 0\nx = 11/9\nx = 19/3"} {"input": "Solve quickly: 4x - 3 = 0", "output": "4x - 3 = 0\n4x = 3\nx = 3 / 4\nx = 3/4"} {"input": "Compute the solution of x^2 + 55/9x + 76/9 = 0", "output": "x^2 + 55/9x + 76/9 = 0\n(x - -4)(x - -19/9) = 0\nx - -4 = 0 or x - -19/9 = 0\nx = -4\nx = -19/9"} {"input": "Solve the equations:\n8x + 2y = 50/7\n8x + 4y = 36/7", "output": "8x + 2y = 50/7\n8x + 4y = 36/7\n\nUsing elimination\n8*(8x + 2y = 50/7)\n8*(8x + 4y = 36/7)\n64x + 16y = 400/7\n64x + 32y = 288/7\nSubtract equations\n-16y = 16\ny = 16/-16\ny = -1\n\nSubstitute y\n8x + 2(-1) = 50/7\n8x = 64/7\nx = 64/7/8\nx = 8/7"} {"input": "Solve the equation x^2 - 41/6x + 35/3 = 0", "output": "x^2 - 41/6x + 35/3 = 0\n(x - 10/3)(x - 7/2) = 0\nx - 10/3 = 0 or x - 7/2 = 0\nx = 10/3\nx = 7/2"} {"input": "Solve quickly: x^3 + 247/12x^2 + 943/12x + 84 = 0", "output": "x^3 + 247/12x^2 + 943/12x + 84 = 0\n(x - -9/4)(x - -16)(x - -7/3) = 0\nx - -9/4 = 0\nx - -16 = 0\nx - -7/3 = 0\nx = -9/4\nx = -16\nx = -7/3"} {"input": "Solve the equation 5x - 7 = 0", "output": "5x - 7 = 0\n5x = 7\nx = 7 / 5\nx = 7/5"} {"input": "Determine x in x^3 - 87/40x^2 - 111/20x - 19/8 = 0", "output": "x^3 - 87/40x^2 - 111/20x - 19/8 = 0\n(x - 19/5)(x - -1)(x - -5/8) = 0\nx - 19/5 = 0\nx - -1 = 0\nx - -5/8 = 0\nx = 19/5\nx = -1\nx = -5/8"} {"input": "Solve the equation 6x - 7 = 0", "output": "6x - 7 = 0\n6x = 7\nx = 7 / 6\nx = 7/6"} {"input": "What value of x satisfies x^2 - 23/24x - 85/16 = 0", "output": "x^2 - 23/24x - 85/16 = 0\n(x - -15/8)(x - 17/6) = 0\nx - -15/8 = 0 or x - 17/6 = 0\nx = -15/8\nx = 17/6"} {"input": "What value of x satisfies x^2 - 8/3x + 7/9 = 0", "output": "x^2 - 8/3x + 7/9 = 0\n(x - 7/3)(x - 1/3) = 0\nx - 7/3 = 0 or x - 1/3 = 0\nx = 7/3\nx = 1/3"} {"input": "Solve 1x + 7/5 = 0", "output": "1x + 7/5 = 0\n1x = -7/5\nx = -7/5 / 1\nx = -7/5"} {"input": "Find x in x^3 - 194/15x^2 - 53/15x + 104/3 = 0", "output": "x^3 - 194/15x^2 - 53/15x + 104/3 = 0\n(x - 8/5)(x - -5/3)(x - 13) = 0\nx - 8/5 = 0\nx - -5/3 = 0\nx - 13 = 0\nx = 8/5\nx = -5/3\nx = 13"} {"input": "What value of x satisfies x^2 + 49/8x + 45/8 = 0", "output": "x^2 + 49/8x + 45/8 = 0\n(x - -9/8)(x - -5) = 0\nx - -9/8 = 0 or x - -5 = 0\nx = -9/8\nx = -5"} {"input": "What value of x satisfies x^2 + 3x + 2 = 0", "output": "x^2 + 3x + 2 = 0\n(x - -1)(x - -2) = 0\nx - -1 = 0 or x - -2 = 0\nx = -1\nx = -2"} {"input": "Solve the equation x^3 - 1/4x^2 - 19/4x - 35/16 = 0", "output": "x^3 - 1/4x^2 - 19/4x - 35/16 = 0\n(x - 5/2)(x - -1/2)(x - -7/4) = 0\nx - 5/2 = 0\nx - -1/2 = 0\nx - -7/4 = 0\nx = 5/2\nx = -1/2\nx = -7/4"} {"input": "Find the solution to x^3 + 55/12x^2 + 53/8x + 35/12 = 0", "output": "x^3 + 55/12x^2 + 53/8x + 35/12 = 0\n(x - -7/4)(x - -5/6)(x - -2) = 0\nx - -7/4 = 0\nx - -5/6 = 0\nx - -2 = 0\nx = -7/4\nx = -5/6\nx = -2"} {"input": "Solve the equation x^3 - 407/84x^2 + 123/28x - 15/14 = 0", "output": "x^3 - 407/84x^2 + 123/28x - 15/14 = 0\n(x - 15/4)(x - 2/3)(x - 3/7) = 0\nx - 15/4 = 0\nx - 2/3 = 0\nx - 3/7 = 0\nx = 15/4\nx = 2/3\nx = 3/7"} {"input": "Solve the equations:\n5x + 5y = 235/6\n1x + 7y = 317/6", "output": "5x + 5y = 235/6\n1x + 7y = 317/6\n\nUsing elimination\n1*(5x + 5y = 235/6)\n5*(1x + 7y = 317/6)\n5x + 5y = 235/6\n5x + 35y = 1585/6\nSubtract equations\n-30y = -225\ny = -225/-30\ny = 15/2\n\nSubstitute y\n5x + 5(15/2) = 235/6\n5x = 5/3\nx = 5/3/5\nx = 1/3"} {"input": "Solve the equation 6x + 18/5 = 0", "output": "6x + 18/5 = 0\n6x = -18/5\nx = -18/5 / 6\nx = -3/5"} {"input": "Solve x^2 - 163/63x + 20/21 = 0", "output": "x^2 - 163/63x + 20/21 = 0\n(x - 15/7)(x - 4/9) = 0\nx - 15/7 = 0 or x - 4/9 = 0\nx = 15/7\nx = 4/9"} {"input": "Solve simultaneously:\n4x + 1y = 211/42\n10x + 1y = 643/42", "output": "4x + 1y = 211/42\n10x + 1y = 643/42\n\nUsing elimination\n10*(4x + 1y = 211/42)\n4*(10x + 1y = 643/42)\n40x + 10y = 1055/21\n40x + 4y = 1286/21\nSubtract equations\n6y = -11\ny = -11/6\ny = -11/6\n\nSubstitute y\n4x + 1(-11/6) = 211/42\n4x = 48/7\nx = 48/7/4\nx = 12/7"} {"input": "Solve the equations:\n2x + 5y = -29/10\n6x + 1y = 67/10", "output": "2x + 5y = -29/10\n6x + 1y = 67/10\n\nUsing elimination\n6*(2x + 5y = -29/10)\n2*(6x + 1y = 67/10)\n12x + 30y = -87/5\n12x + 2y = 67/5\nSubtract equations\n28y = -154/5\ny = -154/5/28\ny = -11/10\n\nSubstitute y\n2x + 5(-11/10) = -29/10\n2x = 13/5\nx = 13/5/2\nx = 13/10"} {"input": "Find x for 1x - 9/10 = 0", "output": "1x - 9/10 = 0\n1x = 9/10\nx = 9/10 / 1\nx = 9/10"} {"input": "Compute the solution of 1x + 13/5 = 0", "output": "1x + 13/5 = 0\n1x = -13/5\nx = -13/5 / 1\nx = -13/5"} {"input": "Solve the equations:\n9x + 3y = 251/3\n5x + 4y = 374/9", "output": "9x + 3y = 251/3\n5x + 4y = 374/9\n\nUsing elimination\n5*(9x + 3y = 251/3)\n9*(5x + 4y = 374/9)\n45x + 15y = 1255/3\n45x + 36y = 374\nSubtract equations\n-21y = 133/3\ny = 133/3/-21\ny = -19/9\n\nSubstitute y\n9x + 3(-19/9) = 251/3\n9x = 90\nx = 90/9\nx = 10"} {"input": "Solve simultaneously:\n3x + 9y = -5/2\n7x + 6y = 65/6", "output": "3x + 9y = -5/2\n7x + 6y = 65/6\n\nUsing elimination\n7*(3x + 9y = -5/2)\n3*(7x + 6y = 65/6)\n21x + 63y = -35/2\n21x + 18y = 65/2\nSubtract equations\n45y = -50\ny = -50/45\ny = -10/9\n\nSubstitute y\n3x + 9(-10/9) = -5/2\n3x = 15/2\nx = 15/2/3\nx = 5/2"} {"input": "Find the solution to x^3 - 163/12x^2 + 515/12x - 627/16 = 0", "output": "x^3 - 163/12x^2 + 515/12x - 627/16 = 0\n(x - 11/6)(x - 19/2)(x - 9/4) = 0\nx - 11/6 = 0\nx - 19/2 = 0\nx - 9/4 = 0\nx = 11/6\nx = 19/2\nx = 9/4"} {"input": "Compute the solution of 10x - 50/3 = 0", "output": "10x - 50/3 = 0\n10x = 50/3\nx = 50/3 / 10\nx = 5/3"} {"input": "Find x in x^2 + 111/28x + 95/28 = 0", "output": "x^2 + 111/28x + 95/28 = 0\n(x - -5/4)(x - -19/7) = 0\nx - -5/4 = 0 or x - -19/7 = 0\nx = -5/4\nx = -19/7"} {"input": "Solve the equations:\n1x + 7y = -121/10\n7x + 4y = 53/10", "output": "1x + 7y = -121/10\n7x + 4y = 53/10\n\nUsing elimination\n7*(1x + 7y = -121/10)\n1*(7x + 4y = 53/10)\n7x + 49y = -847/10\n7x + 4y = 53/10\nSubtract equations\n45y = -90\ny = -90/45\ny = -2\n\nSubstitute y\n1x + 7(-2) = -121/10\n1x = 19/10\nx = 19/10/1\nx = 19/10"} {"input": "Find x for x^2 + 197/36x + 187/36 = 0", "output": "x^2 + 197/36x + 187/36 = 0\n(x - -11/9)(x - -17/4) = 0\nx - -11/9 = 0 or x - -17/4 = 0\nx = -11/9\nx = -17/4"} {"input": "Find the solution to 3x - 27/4 = 0", "output": "3x - 27/4 = 0\n3x = 27/4\nx = 27/4 / 3\nx = 9/4"} {"input": "Solve simultaneously:\n10x + 5y = 55\n10x + 1y = 35", "output": "10x + 5y = 55\n10x + 1y = 35\n\nUsing elimination\n10*(10x + 5y = 55)\n10*(10x + 1y = 35)\n100x + 50y = 550\n100x + 10y = 350\nSubtract equations\n40y = 200\ny = 200/40\ny = 5\n\nSubstitute y\n10x + 5(5) = 55\n10x = 30\nx = 30/10\nx = 3"} {"input": "Determine x in x^2 - 27/4x + 81/8 = 0", "output": "x^2 - 27/4x + 81/8 = 0\n(x - 9/4)(x - 9/2) = 0\nx - 9/4 = 0 or x - 9/2 = 0\nx = 9/4\nx = 9/2"} {"input": "Solve quickly: x^3 + 23/10x^2 - 202/5x - 546/5 = 0", "output": "x^3 + 23/10x^2 - 202/5x - 546/5 = 0\n(x - -6)(x - 13/2)(x - -14/5) = 0\nx - -6 = 0\nx - 13/2 = 0\nx - -14/5 = 0\nx = -6\nx = 13/2\nx = -14/5"} {"input": "Solve x^2 - 181/30x - 19/10 = 0", "output": "x^2 - 181/30x - 19/10 = 0\n(x - -3/10)(x - 19/3) = 0\nx - -3/10 = 0 or x - 19/3 = 0\nx = -3/10\nx = 19/3"} {"input": "Find x in x^2 - 38/5x + 48/5 = 0", "output": "x^2 - 38/5x + 48/5 = 0\n(x - 6)(x - 8/5) = 0\nx - 6 = 0 or x - 8/5 = 0\nx = 6\nx = 8/5"} {"input": "Find x for x^3 + 503/180x^2 - 13/10x - 169/36 = 0", "output": "x^3 + 503/180x^2 - 13/10x - 169/36 = 0\n(x - -13/5)(x - 5/4)(x - -13/9) = 0\nx - -13/5 = 0\nx - 5/4 = 0\nx - -13/9 = 0\nx = -13/5\nx = 5/4\nx = -13/9"} {"input": "Find the solution to 5x - 12 = 0", "output": "5x - 12 = 0\n5x = 12\nx = 12 / 5\nx = 12/5"} {"input": "Find x and y such that\n1x + 2y = -22/9\n2x + 3y = -17/3", "output": "1x + 2y = -22/9\n2x + 3y = -17/3\n\nUsing elimination\n2*(1x + 2y = -22/9)\n1*(2x + 3y = -17/3)\n2x + 4y = -44/9\n2x + 3y = -17/3\nSubtract equations\n1y = 7/9\ny = 7/9/1\ny = 7/9\n\nSubstitute y\n1x + 2(7/9) = -22/9\n1x = -4\nx = -4/1\nx = -4"} {"input": "Solve quickly: x^2 - 31/7x - 20/7 = 0", "output": "x^2 - 31/7x - 20/7 = 0\n(x - -4/7)(x - 5) = 0\nx - -4/7 = 0 or x - 5 = 0\nx = -4/7\nx = 5"} {"input": "Find x and y such that\n2x + 7y = 27\n5x + 9y = 328/7", "output": "2x + 7y = 27\n5x + 9y = 328/7\n\nUsing elimination\n5*(2x + 7y = 27)\n2*(5x + 9y = 328/7)\n10x + 35y = 135\n10x + 18y = 656/7\nSubtract equations\n17y = 289/7\ny = 289/7/17\ny = 17/7\n\nSubstitute y\n2x + 7(17/7) = 27\n2x = 10\nx = 10/2\nx = 5"} {"input": "Find the solution to 1x - 15/4 = 0", "output": "1x - 15/4 = 0\n1x = 15/4\nx = 15/4 / 1\nx = 15/4"} {"input": "Solve the system:\n8x + 2y = -25/3\n4x + 9y = -11/2", "output": "8x + 2y = -25/3\n4x + 9y = -11/2\n\nUsing elimination\n4*(8x + 2y = -25/3)\n8*(4x + 9y = -11/2)\n32x + 8y = -100/3\n32x + 72y = -44\nSubtract equations\n-64y = 32/3\ny = 32/3/-64\ny = -1/6\n\nSubstitute y\n8x + 2(-1/6) = -25/3\n8x = -8\nx = -8/8\nx = -1"} {"input": "Solve the system:\n2x + 5y = -22\n10x + 1y = -118/5", "output": "2x + 5y = -22\n10x + 1y = -118/5\n\nUsing elimination\n10*(2x + 5y = -22)\n2*(10x + 1y = -118/5)\n20x + 50y = -220\n20x + 2y = -236/5\nSubtract equations\n48y = -864/5\ny = -864/5/48\ny = -18/5\n\nSubstitute y\n2x + 5(-18/5) = -22\n2x = -4\nx = -4/2\nx = -2"} {"input": "What value of x satisfies x^2 + 23/8x + 15/8 = 0", "output": "x^2 + 23/8x + 15/8 = 0\n(x - -15/8)(x - -1) = 0\nx - -15/8 = 0 or x - -1 = 0\nx = -15/8\nx = -1"} {"input": "Solve the equation x^2 - 29/10x - 24/25 = 0", "output": "x^2 - 29/10x - 24/25 = 0\n(x - -3/10)(x - 16/5) = 0\nx - -3/10 = 0 or x - 16/5 = 0\nx = -3/10\nx = 16/5"} {"input": "Find x and y such that\n7x + 2y = -218/15\n7x + 4y = -296/15", "output": "7x + 2y = -218/15\n7x + 4y = -296/15\n\nUsing elimination\n7*(7x + 2y = -218/15)\n7*(7x + 4y = -296/15)\n49x + 14y = -1526/15\n49x + 28y = -2072/15\nSubtract equations\n-14y = 182/5\ny = 182/5/-14\ny = -13/5\n\nSubstitute y\n7x + 2(-13/5) = -218/15\n7x = -28/3\nx = -28/3/7\nx = -4/3"} {"input": "What value of x satisfies x^3 - 79/8x^2 + 15x = 0", "output": "x^3 - 79/8x^2 + 15x = 0\n(x - 15/8)(x - 8)(x - 0) = 0\nx - 15/8 = 0\nx - 8 = 0\nx - 0 = 0\nx = 15/8\nx = 8\nx = 0"} {"input": "Compute the solution of 7x + 28/3 = 0", "output": "7x + 28/3 = 0\n7x = -28/3\nx = -28/3 / 7\nx = -4/3"} {"input": "Solve the equation x^2 + 83/20x + 117/40 = 0", "output": "x^2 + 83/20x + 117/40 = 0\n(x - -9/10)(x - -13/4) = 0\nx - -9/10 = 0 or x - -13/4 = 0\nx = -9/10\nx = -13/4"} {"input": "Solve quickly: x^3 + 17/12x^2 - 25/4x - 9/2 = 0", "output": "x^3 + 17/12x^2 - 25/4x - 9/2 = 0\n(x - -2/3)(x - 9/4)(x - -3) = 0\nx - -2/3 = 0\nx - 9/4 = 0\nx - -3 = 0\nx = -2/3\nx = 9/4\nx = -3"} {"input": "What value of x satisfies x^3 - 1081/72x^2 + 515/36x - 14/9 = 0", "output": "x^3 - 1081/72x^2 + 515/36x - 14/9 = 0\n(x - 8/9)(x - 1/8)(x - 14) = 0\nx - 8/9 = 0\nx - 1/8 = 0\nx - 14 = 0\nx = 8/9\nx = 1/8\nx = 14"} {"input": "Solve the equation x^2 - 1/4 = 0", "output": "x^2 - 1/4 = 0\n(x - 1/2)(x - -1/2) = 0\nx - 1/2 = 0 or x - -1/2 = 0\nx = 1/2\nx = -1/2"} {"input": "Solve the equations:\n9x + 1y = -8\n2x + 3y = -491/9", "output": "9x + 1y = -8\n2x + 3y = -491/9\n\nUsing elimination\n2*(9x + 1y = -8)\n9*(2x + 3y = -491/9)\n18x + 2y = -16\n18x + 27y = -491\nSubtract equations\n-25y = 475\ny = 475/-25\ny = -19\n\nSubstitute y\n9x + 1(-19) = -8\n9x = 11\nx = 11/9\nx = 11/9"} {"input": "What value of x satisfies x^2 + 63/4x + 45/4 = 0", "output": "x^2 + 63/4x + 45/4 = 0\n(x - -3/4)(x - -15) = 0\nx - -3/4 = 0 or x - -15 = 0\nx = -3/4\nx = -15"} {"input": "Find x for x^2 - 7/18x - 4/9 = 0", "output": "x^2 - 7/18x - 4/9 = 0\n(x - 8/9)(x - -1/2) = 0\nx - 8/9 = 0 or x - -1/2 = 0\nx = 8/9\nx = -1/2"} {"input": "Find x for x^3 + 155/18x^2 - 1453/9x + 136 = 0", "output": "x^3 + 155/18x^2 - 1453/9x + 136 = 0\n(x - 17/2)(x - -18)(x - 8/9) = 0\nx - 17/2 = 0\nx - -18 = 0\nx - 8/9 = 0\nx = 17/2\nx = -18\nx = 8/9"} {"input": "Solve x^3 + 7/10x^2 - 11/25x = 0", "output": "x^3 + 7/10x^2 - 11/25x = 0\n(x - 0)(x - 2/5)(x - -11/10) = 0\nx - 0 = 0\nx - 2/5 = 0\nx - -11/10 = 0\nx = 0\nx = 2/5\nx = -11/10"} {"input": "Find x for x^3 - 35/9x^2 - 379/27x - 247/27 = 0", "output": "x^3 - 35/9x^2 - 379/27x - 247/27 = 0\n(x - -13/9)(x - 19/3)(x - -1) = 0\nx - -13/9 = 0\nx - 19/3 = 0\nx - -1 = 0\nx = -13/9\nx = 19/3\nx = -1"} {"input": "Compute the solution of x^3 + 281/30x^2 + 811/30x + 119/5 = 0", "output": "x^3 + 281/30x^2 + 811/30x + 119/5 = 0\n(x - -14/3)(x - -17/10)(x - -3) = 0\nx - -14/3 = 0\nx - -17/10 = 0\nx - -3 = 0\nx = -14/3\nx = -17/10\nx = -3"} {"input": "Find x for 10x - 110 = 0", "output": "10x - 110 = 0\n10x = 110\nx = 110 / 10\nx = 11"} {"input": "Compute the solution of x^2 - 10/3x = 0", "output": "x^2 - 10/3x = 0\n(x - 10/3)(x - 0) = 0\nx - 10/3 = 0 or x - 0 = 0\nx = 10/3\nx = 0"} {"input": "Solve the equation 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Solve 9x + 27/2 = 0", "output": "9x + 27/2 = 0\n9x = -27/2\nx = -27/2 / 9\nx = -3/2"} {"input": "Solve quickly: x^2 + 8x - 180 = 0", "output": "x^2 + 8x - 180 = 0\n(x - 10)(x - -18) = 0\nx - 10 = 0 or x - -18 = 0\nx = 10\nx = -18"} {"input": "Solve 8x - 72 = 0", "output": "8x - 72 = 0\n8x = 72\nx = 72 / 8\nx = 9"} {"input": "What value of x satisfies x^3 + 249/70x^2 + 1233/490x - 54/49 = 0", "output": "x^3 + 249/70x^2 + 1233/490x - 54/49 = 0\n(x - -12/7)(x - -15/7)(x - 3/10) = 0\nx - -12/7 = 0\nx - -15/7 = 0\nx - 3/10 = 0\nx = -12/7\nx = -15/7\nx = 3/10"} {"input": "Solve the equations:\n1x + 4y = -19/7\n9x + 5y = -33/28", "output": "1x + 4y = -19/7\n9x + 5y = -33/28\n\nUsing elimination\n9*(1x + 4y = -19/7)\n1*(9x + 5y = -33/28)\n9x + 36y = -171/7\n9x + 5y = -33/28\nSubtract equations\n31y = -93/4\ny = -93/4/31\ny = -3/4\n\nSubstitute y\n1x + 4(-3/4) = -19/7\n1x = 2/7\nx = 2/7/1\nx = 2/7"} {"input": "Find x for x^2 - 43/18x + 17/18 = 0", "output": "x^2 - 43/18x + 17/18 = 0\n(x - 17/9)(x - 1/2) = 0\nx - 17/9 = 0 or x - 1/2 = 0\nx = 17/9\nx = 1/2"} {"input": "Find x for x^2 + 67/24x - 19/16 = 0", "output": "x^2 + 67/24x - 19/16 = 0\n(x - 3/8)(x - -19/6) = 0\nx - 3/8 = 0 or x - -19/6 = 0\nx = 3/8\nx = -19/6"} {"input": "Solve the equations:\n8x + 5y = -255/7\n4x + 6y = -250/7", "output": "8x + 5y = -255/7\n4x + 6y = -250/7\n\nUsing elimination\n4*(8x + 5y = -255/7)\n8*(4x + 6y = -250/7)\n32x + 20y = -1020/7\n32x + 48y = -2000/7\nSubtract equations\n-28y = 140\ny = 140/-28\ny = -5\n\nSubstitute y\n8x + 5(-5) = -255/7\n8x = -80/7\nx = -80/7/8\nx = -10/7"} {"input": "Solve x^3 + 69/5x^2 + 27x - 209/5 = 0", "output": "x^3 + 69/5x^2 + 27x - 209/5 = 0\n(x - -11)(x - -19/5)(x - 1) = 0\nx - -11 = 0\nx - -19/5 = 0\nx - 1 = 0\nx = -11\nx = -19/5\nx = 1"} {"input": "Compute the solution of 7x - 49/3 = 0", "output": "7x - 49/3 = 0\n7x = 49/3\nx = 49/3 / 7\nx = 7/3"} {"input": "Find x for 9x + 13 = 0", "output": "9x + 13 = 0\n9x = -13\nx = -13 / 9\nx = -13/9"} {"input": "Solve 5x + 65/2 = 0", "output": "5x + 65/2 = 0\n5x = -65/2\nx = -65/2 / 5\nx = -13/2"} {"input": "Solve the equations:\n2x + 2y = -3\n7x + 4y = -9", "output": "2x + 2y = -3\n7x + 4y = -9\n\nUsing elimination\n7*(2x + 2y = -3)\n2*(7x + 4y = -9)\n14x + 14y = -21\n14x + 8y = -18\nSubtract equations\n6y = -3\ny = -3/6\ny = -1/2\n\nSubstitute y\n2x + 2(-1/2) = -3\n2x = -2\nx = -2/2\nx = -1"} {"input": "Find x in x^3 + 16/21x^2 - 5/63x - 2/21 = 0", "output": "x^3 + 16/21x^2 - 5/63x - 2/21 = 0\n(x - 1/3)(x - -2/3)(x - -3/7) = 0\nx - 1/3 = 0\nx - -2/3 = 0\nx - -3/7 = 0\nx = 1/3\nx = -2/3\nx = -3/7"} {"input": "Determine x in 6x - 18 = 0", "output": "6x - 18 = 0\n6x = 18\nx = 18 / 6\nx = 3"} {"input": "Solve the equations:\n10x + 3y = 259/5\n10x + 7y = 271/5", "output": "10x + 3y = 259/5\n10x + 7y = 271/5\n\nUsing elimination\n10*(10x + 3y = 259/5)\n10*(10x + 7y = 271/5)\n100x + 30y = 518\n100x + 70y = 542\nSubtract equations\n-40y = -24\ny = -24/-40\ny = 3/5\n\nSubstitute y\n10x + 3(3/5) = 259/5\n10x = 50\nx = 50/10\nx = 5"} {"input": "Find x in 5x + 5 = 0", "output": "5x + 5 = 0\n5x = -5\nx = -5 / 5\nx = -1"} {"input": "What value of x satisfies x^3 + 18/5x^2 - 273/25x - 98/5 = 0", "output": "x^3 + 18/5x^2 - 273/25x - 98/5 = 0\n(x - -5)(x - -7/5)(x - 14/5) = 0\nx - -5 = 0\nx - -7/5 = 0\nx - 14/5 = 0\nx = -5\nx = -7/5\nx = 14/5"} {"input": "Determine x in 4x - 6 = 0", "output": "4x - 6 = 0\n4x = 6\nx = 6 / 4\nx = 3/2"} {"input": "Solve the equations:\n5x + 2y = -32\n10x + 2y = -32", "output": "5x + 2y = -32\n10x + 2y = -32\n\nUsing elimination\n10*(5x + 2y = -32)\n5*(10x + 2y = -32)\n50x + 20y = -320\n50x + 10y = -160\nSubtract equations\n10y = -160\ny = -160/10\ny = -16\n\nSubstitute y\n5x + 2(-16) = -32\n5x = 0\nx = 0/5\nx = 0"} {"input": "Solve the system:\n6x + 7y = -125/3\n2x + 7y = -65/3", "output": "6x + 7y = -125/3\n2x + 7y = -65/3\n\nUsing elimination\n2*(6x + 7y = -125/3)\n6*(2x + 7y = -65/3)\n12x + 14y = -250/3\n12x + 42y = -130\nSubtract equations\n-28y = 140/3\ny = 140/3/-28\ny = -5/3\n\nSubstitute y\n6x + 7(-5/3) = -125/3\n6x = -30\nx = -30/6\nx = -5"} {"input": "Compute the solution of x^2 + 3/4x - 5/2 = 0", "output": "x^2 + 3/4x - 5/2 = 0\n(x - -2)(x - 5/4) = 0\nx - -2 = 0 or x - 5/4 = 0\nx = -2\nx = 5/4"} {"input": "Determine x in x^3 + 7/4x^2 + 21/25x + 27/400 = 0", "output": "x^3 + 7/4x^2 + 21/25x + 27/400 = 0\n(x - -1/10)(x - -9/10)(x - -3/4) = 0\nx - -1/10 = 0\nx - -9/10 = 0\nx - -3/4 = 0\nx = -1/10\nx = -9/10\nx = -3/4"} {"input": "Find x in x^2 + 31/15x + 14/15 = 0", "output": "x^2 + 31/15x + 14/15 = 0\n(x - -2/3)(x - -7/5) = 0\nx - -2/3 = 0 or x - -7/5 = 0\nx = -2/3\nx = -7/5"} {"input": "Compute the solution of x^3 + 26/45x^2 - 4009/405x + 722/81 = 0", "output": "x^3 + 26/45x^2 - 4009/405x + 722/81 = 0\n(x - 10/9)(x - 19/9)(x - -19/5) = 0\nx - 10/9 = 0\nx - 19/9 = 0\nx - -19/5 = 0\nx = 10/9\nx = 19/9\nx = -19/5"} {"input": "Determine x in 9x + 6 = 0", "output": "9x + 6 = 0\n9x = -6\nx = -6 / 9\nx = -2/3"} {"input": "Solve the equation x^3 - 24/35x^2 - 43/28x + 33/70 = 0", "output": "x^3 - 24/35x^2 - 43/28x + 33/70 = 0\n(x - 2/7)(x - -11/10)(x - 3/2) = 0\nx - 2/7 = 0\nx - -11/10 = 0\nx - 3/2 = 0\nx = 2/7\nx = -11/10\nx = 3/2"} {"input": "Find the solution to 3x - 12 = 0", "output": "3x - 12 = 0\n3x = 12\nx = 12 / 3\nx = 4"} {"input": "Solve the equation x^2 + 61/18x + 17/6 = 0", "output": "x^2 + 61/18x + 17/6 = 0\n(x - -17/9)(x - -3/2) = 0\nx - -17/9 = 0 or x - -3/2 = 0\nx = -17/9\nx = -3/2"} {"input": "What value of x satisfies x^2 - 11/5x + 2/5 = 0", "output": "x^2 - 11/5x + 2/5 = 0\n(x - 2)(x - 1/5) = 0\nx - 2 = 0 or x - 1/5 = 0\nx = 2\nx = 1/5"} {"input": "Solve the system:\n2x + 7y = 41\n5x + 2y = 131/4", "output": "2x + 7y = 41\n5x + 2y = 131/4\n\nUsing elimination\n5*(2x + 7y = 41)\n2*(5x + 2y = 131/4)\n10x + 35y = 205\n10x + 4y = 131/2\nSubtract equations\n31y = 279/2\ny = 279/2/31\ny = 9/2\n\nSubstitute y\n2x + 7(9/2) = 41\n2x = 19/2\nx = 19/2/2\nx = 19/4"} {"input": "Solve the equation x^2 + 29/9x - 44/27 = 0", "output": "x^2 + 29/9x - 44/27 = 0\n(x - -11/3)(x - 4/9) = 0\nx - -11/3 = 0 or x - 4/9 = 0\nx = -11/3\nx = 4/9"} {"input": "Solve quickly: x^2 + 27/14x + 5/7 = 0", "output": "x^2 + 27/14x + 5/7 = 0\n(x - -1/2)(x - -10/7) = 0\nx - -1/2 = 0 or x - -10/7 = 0\nx = -1/2\nx = -10/7"} {"input": "Determine x in 4x - 8 = 0", "output": "4x - 8 = 0\n4x = 8\nx = 8 / 4\nx = 2"} {"input": "Solve x^3 - 107/63x^2 + 106/189x + 16/189 = 0", "output": "x^3 - 107/63x^2 + 106/189x + 16/189 = 0\n(x - 8/7)(x - -1/9)(x - 2/3) = 0\nx - 8/7 = 0\nx - -1/9 = 0\nx - 2/3 = 0\nx = 8/7\nx = -1/9\nx = 2/3"} {"input": "Solve x^2 - 1x - 42 = 0", "output": "x^2 - 1x - 42 = 0\n(x - -6)(x - 7) = 0\nx - -6 = 0 or x - 7 = 0\nx = -6\nx = 7"} {"input": "Find x for 9x = 0", "output": "9x = 0\n9x = 0\nx = 0 / 9\nx = 0"} {"input": "Determine x in x^2 + 97/5x - 12 = 0", "output": "x^2 + 97/5x - 12 = 0\n(x - -20)(x - 3/5) = 0\nx - -20 = 0 or x - 3/5 = 0\nx = -20\nx = 3/5"} {"input": "Solve x^2 - 79/45x + 2/3 = 0", "output": "x^2 - 79/45x + 2/3 = 0\n(x - 5/9)(x - 6/5) = 0\nx - 5/9 = 0 or x - 6/5 = 0\nx = 5/9\nx = 6/5"} {"input": "Find x and y such that\n4x + 5y = -1/5\n1x + 2y = 11/5", "output": "4x + 5y = -1/5\n1x + 2y = 11/5\n\nUsing elimination\n1*(4x + 5y = -1/5)\n4*(1x + 2y = 11/5)\n4x + 5y = -1/5\n4x + 8y = 44/5\nSubtract equations\n-3y = -9\ny = -9/-3\ny = 3\n\nSubstitute y\n4x + 5(3) = -1/5\n4x = -76/5\nx = -76/5/4\nx = -19/5"} {"input": "Solve the equation 9x - 18 = 0", "output": "9x - 18 = 0\n9x = 18\nx = 18 / 9\nx = 2"} {"input": "Solve x^3 - 1555/72x^2 + 275/9x + 250/9 = 0", "output": "x^3 - 1555/72x^2 + 275/9x + 250/9 = 0\n(x - 20/9)(x - -5/8)(x - 20) = 0\nx - 20/9 = 0\nx - -5/8 = 0\nx - 20 = 0\nx = 20/9\nx = -5/8\nx = 20"} {"input": "Find the solution to x^3 - 113/20x^2 - 133/10x + 539/20 = 0", "output": "x^3 - 113/20x^2 - 133/10x + 539/20 = 0\n(x - -11/4)(x - 7/5)(x - 7) = 0\nx - -11/4 = 0\nx - 7/5 = 0\nx - 7 = 0\nx = -11/4\nx = 7/5\nx = 7"} {"input": "Find x in x^2 + 11/8x - 5/4 = 0", "output": "x^2 + 11/8x - 5/4 = 0\n(x - 5/8)(x - -2) = 0\nx - 5/8 = 0 or x - -2 = 0\nx = 5/8\nx = -2"} {"input": "Solve the system:\n1x + 7y = -103/10\n1x + 4y = -32/5", "output": "1x + 7y = -103/10\n1x + 4y = -32/5\n\nUsing elimination\n1*(1x + 7y = -103/10)\n1*(1x + 4y = -32/5)\n1x + 7y = -103/10\n1x + 4y = -32/5\nSubtract equations\n3y = -39/10\ny = -39/10/3\ny = -13/10\n\nSubstitute y\n1x + 7(-13/10) = -103/10\n1x = -6/5\nx = -6/5/1\nx = -6/5"} {"input": "Find the solution to x^3 + 17/6x^2 - 99/16x + 65/48 = 0", "output": "x^3 + 17/6x^2 - 99/16x + 65/48 = 0\n(x - 5/4)(x - 1/4)(x - -13/3) = 0\nx - 5/4 = 0\nx - 1/4 = 0\nx - -13/3 = 0\nx = 5/4\nx = 1/4\nx = -13/3"} {"input": "Solve the equations:\n10x + 1y = 361/9\n4x + 3y = 49/3", "output": "10x + 1y = 361/9\n4x + 3y = 49/3\n\nUsing elimination\n4*(10x + 1y = 361/9)\n10*(4x + 3y = 49/3)\n40x + 4y = 1444/9\n40x + 30y = 490/3\nSubtract equations\n-26y = -26/9\ny = -26/9/-26\ny = 1/9\n\nSubstitute y\n10x + 1(1/9) = 361/9\n10x = 40\nx = 40/10\nx = 4"} {"input": "Find x for x^3 + 39/10x^2 + 19/20x - 63/40 = 0", "output": "x^3 + 39/10x^2 + 19/20x - 63/40 = 0\n(x - -7/2)(x - 1/2)(x - -9/10) = 0\nx - -7/2 = 0\nx - 1/2 = 0\nx - -9/10 = 0\nx = -7/2\nx = 1/2\nx = -9/10"} {"input": "Find x for x^3 - 12x^2 + 41x - 42 = 0", "output": "x^3 - 12x^2 + 41x - 42 = 0\n(x - 3)(x - 7)(x - 2) = 0\nx - 3 = 0\nx - 7 = 0\nx - 2 = 0\nx = 3\nx = 7\nx = 2"} {"input": "What value of x satisfies x^2 - 13/4x + 21/8 = 0", "output": "x^2 - 13/4x + 21/8 = 0\n(x - 3/2)(x - 7/4) = 0\nx - 3/2 = 0 or x - 7/4 = 0\nx = 3/2\nx = 7/4"} {"input": "Find x in x^3 + 179/36x^2 - 7/36x - 5/18 = 0", "output": "x^3 + 179/36x^2 - 7/36x - 5/18 = 0\n(x - -5)(x - -2/9)(x - 1/4) = 0\nx - -5 = 0\nx - -2/9 = 0\nx - 1/4 = 0\nx = -5\nx = -2/9\nx = 1/4"} {"input": "Solve the system:\n10x + 9y = 60\n10x + 5y = 36", "output": "10x + 9y = 60\n10x + 5y = 36\n\nUsing elimination\n10*(10x + 9y = 60)\n10*(10x + 5y = 36)\n100x + 90y = 600\n100x + 50y = 360\nSubtract equations\n40y = 240\ny = 240/40\ny = 6\n\nSubstitute y\n10x + 9(6) = 60\n10x = 6\nx = 6/10\nx = 3/5"} {"input": "Solve the system:\n6x + 10y = 62\n3x + 6y = 38", "output": "6x + 10y = 62\n3x + 6y = 38\n\nUsing elimination\n3*(6x + 10y = 62)\n6*(3x + 6y = 38)\n18x + 30y = 186\n18x + 36y = 228\nSubtract equations\n-6y = -42\ny = -42/-6\ny = 7\n\nSubstitute y\n6x + 10(7) = 62\n6x = -8\nx = -8/6\nx = -4/3"} {"input": "What value of x satisfies x^2 + 9/2x + 85/18 = 0", "output": "x^2 + 9/2x + 85/18 = 0\n(x - -17/6)(x - -5/3) = 0\nx - -17/6 = 0 or x - -5/3 = 0\nx = -17/6\nx = -5/3"} {"input": "What value of x satisfies 2x + 4/5 = 0", "output": "2x + 4/5 = 0\n2x = -4/5\nx = -4/5 / 2\nx = -2/5"} {"input": "Solve x^3 + 37/5x^2 + 51/4x - 27/20 = 0", "output": "x^3 + 37/5x^2 + 51/4x - 27/20 = 0\n(x - 1/10)(x - -9/2)(x - -3) = 0\nx - 1/10 = 0\nx - -9/2 = 0\nx - -3 = 0\nx = 1/10\nx = -9/2\nx = -3"} {"input": "Find x in 7x + 35/3 = 0", "output": "7x + 35/3 = 0\n7x = -35/3\nx = -35/3 / 7\nx = -5/3"} {"input": "Compute the solution of x^2 - 311/90x + 133/45 = 0", "output": "x^2 - 311/90x + 133/45 = 0\n(x - 14/9)(x - 19/10) = 0\nx - 14/9 = 0 or x - 19/10 = 0\nx = 14/9\nx = 19/10"} {"input": "Solve simultaneously:\n1x + 5y = -71/24\n10x + 10y = -35/12", "output": "1x + 5y = -71/24\n10x + 10y = -35/12\n\nUsing elimination\n10*(1x + 5y = -71/24)\n1*(10x + 10y = -35/12)\n10x + 50y = -355/12\n10x + 10y = -35/12\nSubtract equations\n40y = -80/3\ny = -80/3/40\ny = -2/3\n\nSubstitute y\n1x + 5(-2/3) = -71/24\n1x = 3/8\nx = 3/8/1\nx = 3/8"} {"input": "Determine x in x^3 + 155/8x^2 + 451/8x + 38 = 0", "output": "x^3 + 155/8x^2 + 451/8x + 38 = 0\n(x - -1)(x - -16)(x - -19/8) = 0\nx - -1 = 0\nx - -16 = 0\nx - -19/8 = 0\nx = -1\nx = -16\nx = -19/8"} {"input": "Find the solution to x^2 + 19/6x = 0", "output": "x^2 + 19/6x = 0\n(x - 0)(x - -19/6) = 0\nx - 0 = 0 or x - -19/6 = 0\nx = 0\nx = -19/6"} {"input": "Find x for x^3 - 111/10x^2 - 279/5x - 81/2 = 0", "output": "x^3 - 111/10x^2 - 279/5x - 81/2 = 0\n(x - 15)(x - -3)(x - -9/10) = 0\nx - 15 = 0\nx - -3 = 0\nx - -9/10 = 0\nx = 15\nx = -3\nx = -9/10"} {"input": "Find x for x^2 + 4/3x - 32/9 = 0", "output": "x^2 + 4/3x - 32/9 = 0\n(x - 4/3)(x - -8/3) = 0\nx - 4/3 = 0 or x - -8/3 = 0\nx = 4/3\nx = -8/3"} {"input": "Find x for x^3 - 299/63x^2 - 464/63x - 20/21 = 0", "output": "x^3 - 299/63x^2 - 464/63x - 20/21 = 0\n(x - 6)(x - -10/9)(x - -1/7) = 0\nx - 6 = 0\nx - -10/9 = 0\nx - -1/7 = 0\nx = 6\nx = -10/9\nx = -1/7"} {"input": "Solve the equation x^3 + 7/3x^2 - 7/3x - 1 = 0", "output": "x^3 + 7/3x^2 - 7/3x - 1 = 0\n(x - -1/3)(x - 1)(x - -3) = 0\nx - -1/3 = 0\nx - 1 = 0\nx - -3 = 0\nx = -1/3\nx = 1\nx = -3"} {"input": "Solve the equation x^2 + 19/30x + 1/10 = 0", "output": "x^2 + 19/30x + 1/10 = 0\n(x - -1/3)(x - -3/10) = 0\nx - -1/3 = 0 or x - -3/10 = 0\nx = -1/3\nx = -3/10"} {"input": "Find x in 9x + 10 = 0", "output": "9x + 10 = 0\n9x = -10\nx = -10 / 9\nx = -10/9"} {"input": "Determine x in x^3 + 5/7x^2 - 191/448x + 9/224 = 0", "output": "x^3 + 5/7x^2 - 191/448x + 9/224 = 0\n(x - 1/8)(x - -9/8)(x - 2/7) = 0\nx - 1/8 = 0\nx - -9/8 = 0\nx - 2/7 = 0\nx = 1/8\nx = -9/8\nx = 2/7"} {"input": "Find x for x^3 - 481/24x^2 - 23/48x + 105/4 = 0", "output": "x^3 - 481/24x^2 - 23/48x + 105/4 = 0\n(x - -9/8)(x - 7/6)(x - 20) = 0\nx - -9/8 = 0\nx - 7/6 = 0\nx - 20 = 0\nx = -9/8\nx = 7/6\nx = 20"} {"input": "Find x and y such that\n3x + 5y = 193/21\n1x + 3y = 37/7", "output": "3x + 5y = 193/21\n1x + 3y = 37/7\n\nUsing elimination\n1*(3x + 5y = 193/21)\n3*(1x + 3y = 37/7)\n3x + 5y = 193/21\n3x + 9y = 111/7\nSubtract equations\n-4y = -20/3\ny = -20/3/-4\ny = 5/3\n\nSubstitute y\n3x + 5(5/3) = 193/21\n3x = 6/7\nx = 6/7/3\nx = 2/7"} {"input": "Solve the system:\n10x + 2y = -221/6\n6x + 8y = -17/6", "output": "10x + 2y = -221/6\n6x + 8y = -17/6\n\nUsing elimination\n6*(10x + 2y = -221/6)\n10*(6x + 8y = -17/6)\n60x + 12y = -221\n60x + 80y = -85/3\nSubtract equations\n-68y = -578/3\ny = -578/3/-68\ny = 17/6\n\nSubstitute y\n10x + 2(17/6) = -221/6\n10x = -85/2\nx = -85/2/10\nx = -17/4"} {"input": "Solve the system:\n8x + 9y = 69\n5x + 2y = 25", "output": "8x + 9y = 69\n5x + 2y = 25\n\nUsing elimination\n5*(8x + 9y = 69)\n8*(5x + 2y = 25)\n40x + 45y = 345\n40x + 16y = 200\nSubtract equations\n29y = 145\ny = 145/29\ny = 5\n\nSubstitute y\n8x + 9(5) = 69\n8x = 24\nx = 24/8\nx = 3"} {"input": "Solve the equations:\n6x + 7y = 72\n8x + 1y = 46", "output": "6x + 7y = 72\n8x + 1y = 46\n\nUsing elimination\n8*(6x + 7y = 72)\n6*(8x + 1y = 46)\n48x + 56y = 576\n48x + 6y = 276\nSubtract equations\n50y = 300\ny = 300/50\ny = 6\n\nSubstitute y\n6x + 7(6) = 72\n6x = 30\nx = 30/6\nx = 5"} {"input": "Find x for 10x + 5 = 0", "output": "10x + 5 = 0\n10x = -5\nx = -5 / 10\nx = -1/2"} {"input": "Find x in x^2 - 23/3x + 20/3 = 0", "output": "x^2 - 23/3x + 20/3 = 0\n(x - 1)(x - 20/3) = 0\nx - 1 = 0 or x - 20/3 = 0\nx = 1\nx = 20/3"} {"input": "Solve x^3 - 12/5x^2 - 273/5x + 392/5 = 0", "output": "x^3 - 12/5x^2 - 273/5x + 392/5 = 0\n(x - -7)(x - 8)(x - 7/5) = 0\nx - -7 = 0\nx - 8 = 0\nx - 7/5 = 0\nx = -7\nx = 8\nx = 7/5"} {"input": "Compute the solution of x^2 - 49/20x + 3/2 = 0", "output": "x^2 - 49/20x + 3/2 = 0\n(x - 5/4)(x - 6/5) = 0\nx - 5/4 = 0 or x - 6/5 = 0\nx = 5/4\nx = 6/5"} {"input": "Find the solution to 1x - 7/5 = 0", "output": "1x - 7/5 = 0\n1x = 7/5\nx = 7/5 / 1\nx = 7/5"} {"input": "Solve the equations:\n3x + 1y = 11/5\n3x + 8y = 256/5", "output": "3x + 1y = 11/5\n3x + 8y = 256/5\n\nUsing elimination\n3*(3x + 1y = 11/5)\n3*(3x + 8y = 256/5)\n9x + 3y = 33/5\n9x + 24y = 768/5\nSubtract equations\n-21y = -147\ny = -147/-21\ny = 7\n\nSubstitute y\n3x + 1(7) = 11/5\n3x = -24/5\nx = -24/5/3\nx = -8/5"} {"input": "What value of x satisfies x^3 + 397/36x^2 - 157/2x + 152/9 = 0", "output": "x^3 + 397/36x^2 - 157/2x + 152/9 = 0\n(x - -16)(x - 2/9)(x - 19/4) = 0\nx - -16 = 0\nx - 2/9 = 0\nx - 19/4 = 0\nx = -16\nx = 2/9\nx = 19/4"} {"input": "Solve simultaneously:\n8x + 10y = 68/3\n3x + 1y = 14", "output": "8x + 10y = 68/3\n3x + 1y = 14\n\nUsing elimination\n3*(8x + 10y = 68/3)\n8*(3x + 1y = 14)\n24x + 30y = 68\n24x + 8y = 112\nSubtract equations\n22y = -44\ny = -44/22\ny = -2\n\nSubstitute y\n8x + 10(-2) = 68/3\n8x = 128/3\nx = 128/3/8\nx = 16/3"} {"input": "Solve simultaneously:\n5x + 1y = -6\n1x + 2y = 0", "output": "5x + 1y = -6\n1x + 2y = 0\n\nUsing elimination\n1*(5x + 1y = -6)\n5*(1x + 2y = 0)\n5x + 1y = -6\n5x + 10y = 0\nSubtract equations\n-9y = -6\ny = -6/-9\ny = 2/3\n\nSubstitute y\n5x + 1(2/3) = -6\n5x = -20/3\nx = -20/3/5\nx = -4/3"} {"input": "Find x in 1x + 2 = 0", "output": "1x + 2 = 0\n1x = -2\nx = -2 / 1\nx = -2"} {"input": "Find x in x^2 + 2/5x - 57/20 = 0", "output": "x^2 + 2/5x - 57/20 = 0\n(x - 3/2)(x - -19/10) = 0\nx - 3/2 = 0 or x - -19/10 = 0\nx = 3/2\nx = -19/10"} {"input": "Solve the equation x^3 - 17x^2 + 47x + 65 = 0", "output": "x^3 - 17x^2 + 47x + 65 = 0\n(x - 13)(x - 5)(x - -1) = 0\nx - 13 = 0\nx - 5 = 0\nx - -1 = 0\nx = 13\nx = 5\nx = -1"} {"input": "Find x for x^2 + 14/9x = 0", "output": "x^2 + 14/9x = 0\n(x - 0)(x - -14/9) = 0\nx - 0 = 0 or x - -14/9 = 0\nx = 0\nx = -14/9"} {"input": "Compute the solution of x^2 - 1/30x - 26/15 = 0", "output": "x^2 - 1/30x - 26/15 = 0\n(x - 4/3)(x - -13/10) = 0\nx - 4/3 = 0 or x - -13/10 = 0\nx = 4/3\nx = -13/10"} {"input": "Solve the system:\n4x + 7y = 917/45\n6x + 7y = 259/15", "output": "4x + 7y = 917/45\n6x + 7y = 259/15\n\nUsing elimination\n6*(4x + 7y = 917/45)\n4*(6x + 7y = 259/15)\n24x + 42y = 1834/15\n24x + 28y = 1036/15\nSubtract equations\n14y = 266/5\ny = 266/5/14\ny = 19/5\n\nSubstitute y\n4x + 7(19/5) = 917/45\n4x = -56/9\nx = -56/9/4\nx = -14/9"} {"input": "Compute the solution of x^2 + 4/5x - 153/100 = 0", "output": "x^2 + 4/5x - 153/100 = 0\n(x - -17/10)(x - 9/10) = 0\nx - -17/10 = 0 or x - 9/10 = 0\nx = -17/10\nx = 9/10"} {"input": "Find x in 2x - 4 = 0", "output": "2x - 4 = 0\n2x = 4\nx = 4 / 2\nx = 2"} {"input": "Find x in 1x - 7/9 = 0", "output": "1x - 7/9 = 0\n1x = 7/9\nx = 7/9 / 1\nx = 7/9"} {"input": "Find x in x^2 + 1/56x - 1/56 = 0", "output": "x^2 + 1/56x - 1/56 = 0\n(x - -1/7)(x - 1/8) = 0\nx - -1/7 = 0 or x - 1/8 = 0\nx = -1/7\nx = 1/8"} {"input": "Solve the equations:\n9x + 5y = 229/28\n3x + 9y = 135/28", "output": "9x + 5y = 229/28\n3x + 9y = 135/28\n\nUsing elimination\n3*(9x + 5y = 229/28)\n9*(3x + 9y = 135/28)\n27x + 15y = 687/28\n27x + 81y = 1215/28\nSubtract equations\n-66y = -132/7\ny = -132/7/-66\ny = 2/7\n\nSubstitute y\n9x + 5(2/7) = 229/28\n9x = 27/4\nx = 27/4/9\nx = 3/4"} {"input": "Solve the system:\n4x + 7y = -58/15\n8x + 10y = -28/3", "output": "4x + 7y = -58/15\n8x + 10y = -28/3\n\nUsing elimination\n8*(4x + 7y = -58/15)\n4*(8x + 10y = -28/3)\n32x + 56y = -464/15\n32x + 40y = -112/3\nSubtract equations\n16y = 32/5\ny = 32/5/16\ny = 2/5\n\nSubstitute y\n4x + 7(2/5) = -58/15\n4x = -20/3\nx = -20/3/4\nx = -5/3"} {"input": "Solve the equations:\n4x + 6y = -590/7\n3x + 5y = -495/7", "output": "4x + 6y = -590/7\n3x + 5y = -495/7\n\nUsing elimination\n3*(4x + 6y = -590/7)\n4*(3x + 5y = -495/7)\n12x + 18y = -1770/7\n12x + 20y = -1980/7\nSubtract equations\n-2y = 30\ny = 30/-2\ny = -15\n\nSubstitute y\n4x + 6(-15) = -590/7\n4x = 40/7\nx = 40/7/4\nx = 10/7"} {"input": "Find x in x^3 + 3x^2 - 295/4x - 75/2 = 0", "output": "x^3 + 3x^2 - 295/4x - 75/2 = 0\n(x - 15/2)(x - -1/2)(x - -10) = 0\nx - 15/2 = 0\nx - -1/2 = 0\nx - -10 = 0\nx = 15/2\nx = -1/2\nx = -10"} {"input": "Find the solution to x^2 - 49/8x - 323/16 = 0", "output": "x^2 - 49/8x - 323/16 = 0\n(x - 17/2)(x - -19/8) = 0\nx - 17/2 = 0 or x - -19/8 = 0\nx = 17/2\nx = -19/8"} {"input": "Compute the solution of x^2 + 1/9x - 8/9 = 0", "output": "x^2 + 1/9x - 8/9 = 0\n(x - -1)(x - 8/9) = 0\nx - -1 = 0 or x - 8/9 = 0\nx = -1\nx = 8/9"} {"input": "Solve 3x + 45 = 0", "output": "3x + 45 = 0\n3x = -45\nx = -45 / 3\nx = -15"} {"input": "Solve the system:\n8x + 4y = 88/63\n2x + 6y = -16/21", "output": "8x + 4y = 88/63\n2x + 6y = -16/21\n\nUsing elimination\n2*(8x + 4y = 88/63)\n8*(2x + 6y = -16/21)\n16x + 8y = 176/63\n16x + 48y = -128/21\nSubtract equations\n-40y = 80/9\ny = 80/9/-40\ny = -2/9\n\nSubstitute y\n8x + 4(-2/9) = 88/63\n8x = 16/7\nx = 16/7/8\nx = 2/7"} {"input": "Compute the solution of x^2 + 169/21x + 304/21 = 0", "output": "x^2 + 169/21x + 304/21 = 0\n(x - -16/3)(x - -19/7) = 0\nx - -16/3 = 0 or x - -19/7 = 0\nx = -16/3\nx = -19/7"} {"input": "Determine x in x^2 - 37/5x - 72/5 = 0", "output": "x^2 - 37/5x - 72/5 = 0\n(x - -8/5)(x - 9) = 0\nx - -8/5 = 0 or x - 9 = 0\nx = -8/5\nx = 9"} {"input": "Solve x^3 + 67/12x^2 - 1097/12x + 65 = 0", "output": "x^3 + 67/12x^2 - 1097/12x + 65 = 0\n(x - -13)(x - 3/4)(x - 20/3) = 0\nx - -13 = 0\nx - 3/4 = 0\nx - 20/3 = 0\nx = -13\nx = 3/4\nx = 20/3"} {"input": "Compute the solution of x^2 + 37/3x - 102 = 0", "output": "x^2 + 37/3x - 102 = 0\n(x - 17/3)(x - -18) = 0\nx - 17/3 = 0 or x - -18 = 0\nx = 17/3\nx = -18"} {"input": "Compute the solution of 4x + 4/9 = 0", "output": "4x + 4/9 = 0\n4x = -4/9\nx = -4/9 / 4\nx = -1/9"} {"input": "Find the solution to 4x + 4/5 = 0", "output": "4x + 4/5 = 0\n4x = -4/5\nx = -4/5 / 4\nx = -1/5"} {"input": "Find x for 8x + 6 = 0", "output": "8x + 6 = 0\n8x = -6\nx = -6 / 8\nx = -3/4"} {"input": "Determine x in x^2 + 24/5x - 128/5 = 0", "output": "x^2 + 24/5x - 128/5 = 0\n(x - 16/5)(x - -8) = 0\nx - 16/5 = 0 or x - -8 = 0\nx = 16/5\nx = -8"} {"input": "Solve the system:\n7x + 4y = -211/10\n1x + 1y = -97/40", "output": "7x + 4y = -211/10\n1x + 1y = -97/40\n\nUsing elimination\n1*(7x + 4y = -211/10)\n7*(1x + 1y = -97/40)\n7x + 4y = -211/10\n7x + 7y = -679/40\nSubtract equations\n-3y = -33/8\ny = -33/8/-3\ny = 11/8\n\nSubstitute y\n7x + 4(11/8) = -211/10\n7x = -133/5\nx = -133/5/7\nx = -19/5"} {"input": "Compute the solution of 4x + 3 = 0", "output": "4x + 3 = 0\n4x = -3\nx = -3 / 4\nx = -3/4"} {"input": "Solve the system:\n1x + 7y = -23\n10x + 10y = -110", "output": "1x + 7y = -23\n10x + 10y = -110\n\nUsing elimination\n10*(1x + 7y = -23)\n1*(10x + 10y = -110)\n10x + 70y = -230\n10x + 10y = -110\nSubtract equations\n60y = -120\ny = -120/60\ny = -2\n\nSubstitute y\n1x + 7(-2) = -23\n1x = -9\nx = -9/1\nx = -9"} {"input": "What value of x satisfies 9x - 42 = 0", "output": "9x - 42 = 0\n9x = 42\nx = 42 / 9\nx = 14/3"} {"input": "Solve the system:\n10x + 8y = -28/3\n3x + 3y = -8/3", "output": "10x + 8y = -28/3\n3x + 3y = -8/3\n\nUsing elimination\n3*(10x + 8y = -28/3)\n10*(3x + 3y = -8/3)\n30x + 24y = -28\n30x + 30y = -80/3\nSubtract equations\n-6y = -4/3\ny = -4/3/-6\ny = 2/9\n\nSubstitute y\n10x + 8(2/9) = -28/3\n10x = -100/9\nx = -100/9/10\nx = -10/9"} {"input": "Compute the solution of 6x - 84 = 0", "output": "6x - 84 = 0\n6x = 84\nx = 84 / 6\nx = 14"} {"input": "Find x for x^3 + 133/12x^2 - 679/12x + 65/2 = 0", "output": "x^3 + 133/12x^2 - 679/12x + 65/2 = 0\n(x - -15)(x - 13/4)(x - 2/3) = 0\nx - -15 = 0\nx - 13/4 = 0\nx - 2/3 = 0\nx = -15\nx = 13/4\nx = 2/3"} {"input": "Find x in x^2 - 111/10x + 76/5 = 0", "output": "x^2 - 111/10x + 76/5 = 0\n(x - 19/2)(x - 8/5) = 0\nx - 19/2 = 0 or x - 8/5 = 0\nx = 19/2\nx = 8/5"} {"input": "Find x in 8x - 12 = 0", "output": "8x - 12 = 0\n8x = 12\nx = 12 / 8\nx = 3/2"} {"input": "Solve simultaneously:\n4x + 2y = -152/3\n4x + 9y = -551/3", "output": "4x + 2y = -152/3\n4x + 9y = -551/3\n\nUsing elimination\n4*(4x + 2y = -152/3)\n4*(4x + 9y = -551/3)\n16x + 8y = -608/3\n16x + 36y = -2204/3\nSubtract equations\n-28y = 532\ny = 532/-28\ny = -19\n\nSubstitute y\n4x + 2(-19) = -152/3\n4x = -38/3\nx = -38/3/4\nx = -19/6"} {"input": "What value of x satisfies 6x + 108/5 = 0", "output": "6x + 108/5 = 0\n6x = -108/5\nx = -108/5 / 6\nx = -18/5"} {"input": "Solve the equation 9x + 117 = 0", "output": "9x + 117 = 0\n9x = -117\nx = -117 / 9\nx = -13"} {"input": "Solve the equation 4x = 0", "output": "4x = 0\n4x = 0\nx = 0 / 4\nx = 0"} {"input": "Find x and y such that\n10x + 8y = 199/3\n5x + 1y = 151/6", "output": "10x + 8y = 199/3\n5x + 1y = 151/6\n\nUsing elimination\n5*(10x + 8y = 199/3)\n10*(5x + 1y = 151/6)\n50x + 40y = 995/3\n50x + 10y = 755/3\nSubtract equations\n30y = 80\ny = 80/30\ny = 8/3\n\nSubstitute y\n10x + 8(8/3) = 199/3\n10x = 45\nx = 45/10\nx = 9/2"} {"input": "Solve simultaneously:\n1x + 10y = 1/2\n10x + 8y = 117/5", "output": "1x + 10y = 1/2\n10x + 8y = 117/5\n\nUsing elimination\n10*(1x + 10y = 1/2)\n1*(10x + 8y = 117/5)\n10x + 100y = 5\n10x + 8y = 117/5\nSubtract equations\n92y = -92/5\ny = -92/5/92\ny = -1/5\n\nSubstitute y\n1x + 10(-1/5) = 1/2\n1x = 5/2\nx = 5/2/1\nx = 5/2"} {"input": "Find x for x^2 + 24x + 108 = 0", "output": "x^2 + 24x + 108 = 0\n(x - -6)(x - -18) = 0\nx - -6 = 0 or x - -18 = 0\nx = -6\nx = -18"} {"input": "Solve x^3 + 15/8x^2 - 27/8x = 0", "output": "x^3 + 15/8x^2 - 27/8x = 0\n(x - 9/8)(x - -3)(x - 0) = 0\nx - 9/8 = 0\nx - -3 = 0\nx - 0 = 0\nx = 9/8\nx = -3\nx = 0"} {"input": "Solve the equations:\n9x + 5y = 23\n5x + 4y = 59/5", "output": "9x + 5y = 23\n5x + 4y = 59/5\n\nUsing elimination\n5*(9x + 5y = 23)\n9*(5x + 4y = 59/5)\n45x + 25y = 115\n45x + 36y = 531/5\nSubtract equations\n-11y = 44/5\ny = 44/5/-11\ny = -4/5\n\nSubstitute y\n9x + 5(-4/5) = 23\n9x = 27\nx = 27/9\nx = 3"} {"input": "Solve the system:\n5x + 3y = 17\n10x + 7y = 71/2", "output": "5x + 3y = 17\n10x + 7y = 71/2\n\nUsing elimination\n10*(5x + 3y = 17)\n5*(10x + 7y = 71/2)\n50x + 30y = 170\n50x + 35y = 355/2\nSubtract equations\n-5y = -15/2\ny = -15/2/-5\ny = 3/2\n\nSubstitute y\n5x + 3(3/2) = 17\n5x = 25/2\nx = 25/2/5\nx = 5/2"} {"input": "Solve the equation 7x + 21/8 = 0", "output": "7x + 21/8 = 0\n7x = -21/8\nx = -21/8 / 7\nx = -3/8"} {"input": "What value of x satisfies x^2 + 21x + 38 = 0", "output": "x^2 + 21x + 38 = 0\n(x - -19)(x - -2) = 0\nx - -19 = 0 or x - -2 = 0\nx = -19\nx = -2"} {"input": "What value of x satisfies x^3 - 77/72x^2 - 17/6x + 35/18 = 0", "output": "x^3 - 77/72x^2 - 17/6x + 35/18 = 0\n(x - -14/9)(x - 2)(x - 5/8) = 0\nx - -14/9 = 0\nx - 2 = 0\nx - 5/8 = 0\nx = -14/9\nx = 2\nx = 5/8"} {"input": "Solve the equation 4x - 64/3 = 0", "output": "4x - 64/3 = 0\n4x = 64/3\nx = 64/3 / 4\nx = 16/3"} {"input": "Find x in x^2 + 6x + 8 = 0", "output": "x^2 + 6x + 8 = 0\n(x - -2)(x - -4) = 0\nx - -2 = 0 or x - -4 = 0\nx = -2\nx = -4"} {"input": "Solve x^2 + 97/30x - 1/3 = 0", "output": "x^2 + 97/30x - 1/3 = 0\n(x - 1/10)(x - -10/3) = 0\nx - 1/10 = 0 or x - -10/3 = 0\nx = 1/10\nx = -10/3"} {"input": "Find x and y such that\n1x + 8y = 51/2\n3x + 2y = -1/2", "output": "1x + 8y = 51/2\n3x + 2y = -1/2\n\nUsing elimination\n3*(1x + 8y = 51/2)\n1*(3x + 2y = -1/2)\n3x + 24y = 153/2\n3x + 2y = -1/2\nSubtract equations\n22y = 77\ny = 77/22\ny = 7/2\n\nSubstitute y\n1x + 8(7/2) = 51/2\n1x = -5/2\nx = -5/2/1\nx = -5/2"} {"input": "Compute the solution of x^3 - 31/6x^2 - 29/2x + 35/3 = 0", "output": "x^3 - 31/6x^2 - 29/2x + 35/3 = 0\n(x - 2/3)(x - -5/2)(x - 7) = 0\nx - 2/3 = 0\nx - -5/2 = 0\nx - 7 = 0\nx = 2/3\nx = -5/2\nx = 7"} {"input": "Solve quickly: 1x - 5/6 = 0", "output": "1x - 5/6 = 0\n1x = 5/6\nx = 5/6 / 1\nx = 5/6"} {"input": "Solve x^3 + 43/10x^2 - 11/5x - 68/5 = 0", "output": "x^3 + 43/10x^2 - 11/5x - 68/5 = 0\n(x - 17/10)(x - -4)(x - -2) = 0\nx - 17/10 = 0\nx - -4 = 0\nx - -2 = 0\nx = 17/10\nx = -4\nx = -2"} {"input": "Find x in x^2 + 37/10x - 99/10 = 0", "output": "x^2 + 37/10x - 99/10 = 0\n(x - -11/2)(x - 9/5) = 0\nx - -11/2 = 0 or x - 9/5 = 0\nx = -11/2\nx = 9/5"} {"input": "Find x in x^2 - 16/5x - 9 = 0", "output": "x^2 - 16/5x - 9 = 0\n(x - -9/5)(x - 5) = 0\nx - -9/5 = 0 or x - 5 = 0\nx = -9/5\nx = 5"} {"input": "Find x in x^3 - 25/4x^2 - 23x - 63/4 = 0", "output": "x^3 - 25/4x^2 - 23x - 63/4 = 0\n(x - 9)(x - -1)(x - -7/4) = 0\nx - 9 = 0\nx - -1 = 0\nx - -7/4 = 0\nx = 9\nx = -1\nx = -7/4"} {"input": "Find the solution to x^2 + 124/15x + 84/5 = 0", "output": "x^2 + 124/15x + 84/5 = 0\n(x - -14/3)(x - -18/5) = 0\nx - -14/3 = 0 or x - -18/5 = 0\nx = -14/3\nx = -18/5"} {"input": "Solve the equation x^3 + 419/72x^2 + 797/72x + 247/36 = 0", "output": "x^3 + 419/72x^2 + 797/72x + 247/36 = 0\n(x - -13/9)(x - -2)(x - -19/8) = 0\nx - -13/9 = 0\nx - -2 = 0\nx - -19/8 = 0\nx = -13/9\nx = -2\nx = -19/8"} {"input": "Compute the solution of 5x + 5 = 0", "output": "5x + 5 = 0\n5x = -5\nx = -5 / 5\nx = -1"} {"input": "Determine x in x^2 + 16/9x - 4/9 = 0", "output": "x^2 + 16/9x - 4/9 = 0\n(x - -2)(x - 2/9) = 0\nx - -2 = 0 or x - 2/9 = 0\nx = -2\nx = 2/9"} {"input": "Find the solution to 7x - 28/9 = 0", "output": "7x - 28/9 = 0\n7x = 28/9\nx = 28/9 / 7\nx = 4/9"} {"input": "Find x in 4x - 64/3 = 0", "output": "4x - 64/3 = 0\n4x = 64/3\nx = 64/3 / 4\nx = 16/3"} {"input": "Find x and y such that\n2x + 4y = -80/3\n8x + 8y = -256/3", "output": "2x + 4y = -80/3\n8x + 8y = -256/3\n\nUsing elimination\n8*(2x + 4y = -80/3)\n2*(8x + 8y = -256/3)\n16x + 32y = -640/3\n16x + 16y = -512/3\nSubtract equations\n16y = -128/3\ny = -128/3/16\ny = -8/3\n\nSubstitute y\n2x + 4(-8/3) = -80/3\n2x = -16\nx = -16/2\nx = -8"} {"input": "Solve the equation x^3 + 2/3x^2 = 0", "output": "x^3 + 2/3x^2 = 0\n(x - 0)(x - -2/3)(x - 0) = 0\nx - 0 = 0\nx - -2/3 = 0\nx - 0 = 0\nx = 0\nx = -2/3\nx = 0"} {"input": "Find x for 7x - 14 = 0", "output": "7x - 14 = 0\n7x = 14\nx = 14 / 7\nx = 2"} {"input": "Find x and y such that\n8x + 7y = -115/4\n5x + 3y = -65/4", "output": "8x + 7y = -115/4\n5x + 3y = -65/4\n\nUsing elimination\n5*(8x + 7y = -115/4)\n8*(5x + 3y = -65/4)\n40x + 35y = -575/4\n40x + 24y = -130\nSubtract equations\n11y = -55/4\ny = -55/4/11\ny = -5/4\n\nSubstitute y\n8x + 7(-5/4) = -115/4\n8x = -20\nx = -20/8\nx = -5/2"} {"input": "Determine x in x^3 + 53/6x^2 + 29/12x - 85/24 = 0", "output": "x^3 + 53/6x^2 + 29/12x - 85/24 = 0\n(x - -17/2)(x - -5/6)(x - 1/2) = 0\nx - -17/2 = 0\nx - -5/6 = 0\nx - 1/2 = 0\nx = -17/2\nx = -5/6\nx = 1/2"} {"input": "Solve quickly: 4x - 4/9 = 0", "output": "4x - 4/9 = 0\n4x = 4/9\nx = 4/9 / 4\nx = 1/9"} {"input": "Compute the solution of 3x - 48 = 0", "output": "3x - 48 = 0\n3x = 48\nx = 48 / 3\nx = 16"} {"input": "Solve the equation x^2 + 27/10x + 11/10 = 0", "output": "x^2 + 27/10x + 11/10 = 0\n(x - -1/2)(x - -11/5) = 0\nx - -1/2 = 0 or x - -11/5 = 0\nx = -1/2\nx = -11/5"} {"input": "Solve quickly: 8x + 16 = 0", "output": "8x + 16 = 0\n8x = -16\nx = -16 / 8\nx = -2"} {"input": "Solve the equation 4x + 8/9 = 0", "output": "4x + 8/9 = 0\n4x = -8/9\nx = -8/9 / 4\nx = -2/9"} {"input": "Solve the equation 9x - 81/4 = 0", "output": "9x - 81/4 = 0\n9x = 81/4\nx = 81/4 / 9\nx = 9/4"} {"input": "Solve quickly: x^3 + 227/56x^2 - 1627/112x + 143/16 = 0", "output": "x^3 + 227/56x^2 - 1627/112x + 143/16 = 0\n(x - -13/2)(x - 11/7)(x - 7/8) = 0\nx - -13/2 = 0\nx - 11/7 = 0\nx - 7/8 = 0\nx = -13/2\nx = 11/7\nx = 7/8"} {"input": "Find the solution to x^3 - 143/36x^2 + 167/36x - 5/3 = 0", "output": "x^3 - 143/36x^2 + 167/36x - 5/3 = 0\n(x - 1)(x - 20/9)(x - 3/4) = 0\nx - 1 = 0\nx - 20/9 = 0\nx - 3/4 = 0\nx = 1\nx = 20/9\nx = 3/4"} {"input": "Solve the equations:\n1x + 10y = -163/9\n2x + 7y = -131/9", "output": "1x + 10y = -163/9\n2x + 7y = -131/9\n\nUsing elimination\n2*(1x + 10y = -163/9)\n1*(2x + 7y = -131/9)\n2x + 20y = -326/9\n2x + 7y = -131/9\nSubtract equations\n13y = -65/3\ny = -65/3/13\ny = -5/3\n\nSubstitute y\n1x + 10(-5/3) = -163/9\n1x = -13/9\nx = -13/9/1\nx = -13/9"} {"input": "What value of x satisfies x^2 - 5x + 6 = 0", "output": "x^2 - 5x + 6 = 0\n(x - 2)(x - 3) = 0\nx - 2 = 0 or x - 3 = 0\nx = 2\nx = 3"} {"input": "Solve x^3 - 18x^2 - 19x = 0", "output": "x^3 - 18x^2 - 19x = 0\n(x - 0)(x - 19)(x - -1) = 0\nx - 0 = 0\nx - 19 = 0\nx - -1 = 0\nx = 0\nx = 19\nx = -1"} {"input": "Solve simultaneously:\n4x + 4y = 4\n8x + 10y = 34/3", "output": "4x + 4y = 4\n8x + 10y = 34/3\n\nUsing elimination\n8*(4x + 4y = 4)\n4*(8x + 10y = 34/3)\n32x + 32y = 32\n32x + 40y = 136/3\nSubtract equations\n-8y = -40/3\ny = -40/3/-8\ny = 5/3\n\nSubstitute y\n4x + 4(5/3) = 4\n4x = -8/3\nx = -8/3/4\nx = -2/3"} {"input": "Find x and y such that\n6x + 2y = -102/35\n4x + 6y = 282/35", "output": "6x + 2y = -102/35\n4x + 6y = 282/35\n\nUsing elimination\n4*(6x + 2y = -102/35)\n6*(4x + 6y = 282/35)\n24x + 8y = -408/35\n24x + 36y = 1692/35\nSubtract equations\n-28y = -60\ny = -60/-28\ny = 15/7\n\nSubstitute y\n6x + 2(15/7) = -102/35\n6x = -36/5\nx = -36/5/6\nx = -6/5"} {"input": "Solve the equations:\n1x + 4y = -38/3\n7x + 9y = -19", "output": "1x + 4y = -38/3\n7x + 9y = -19\n\nUsing elimination\n7*(1x + 4y = -38/3)\n1*(7x + 9y = -19)\n7x + 28y = -266/3\n7x + 9y = -19\nSubtract equations\n19y = -209/3\ny = -209/3/19\ny = -11/3\n\nSubstitute y\n1x + 4(-11/3) = -38/3\n1x = 2\nx = 2/1\nx = 2"} {"input": "Solve x^3 - 2x^2 - 16x + 32 = 0", "output": "x^3 - 2x^2 - 16x + 32 = 0\n(x - 4)(x - 2)(x - -4) = 0\nx - 4 = 0\nx - 2 = 0\nx - -4 = 0\nx = 4\nx = 2\nx = -4"} {"input": "Determine x in x^3 + 217/40x^2 - 309/40x - 513/20 = 0", "output": "x^3 + 217/40x^2 - 309/40x - 513/20 = 0\n(x - 19/8)(x - -9/5)(x - -6) = 0\nx - 19/8 = 0\nx - -9/5 = 0\nx - -6 = 0\nx = 19/8\nx = -9/5\nx = -6"} {"input": "Compute the solution of x^3 - 9/4x^2 + 3/2x - 1/4 = 0", "output": "x^3 - 9/4x^2 + 3/2x - 1/4 = 0\n(x - 1)(x - 1/4)(x - 1) = 0\nx - 1 = 0\nx - 1/4 = 0\nx - 1 = 0\nx = 1\nx = 1/4\nx = 1"} {"input": "What value of x satisfies 7x - 119/10 = 0", "output": "7x - 119/10 = 0\n7x = 119/10\nx = 119/10 / 7\nx = 17/10"} {"input": "Find x for x^2 - 43/30x - 4/15 = 0", "output": "x^2 - 43/30x - 4/15 = 0\n(x - -1/6)(x - 8/5) = 0\nx - -1/6 = 0 or x - 8/5 = 0\nx = -1/6\nx = 8/5"} {"input": "Find x for x^2 + 19/5x + 12/5 = 0", "output": "x^2 + 19/5x + 12/5 = 0\n(x - -4/5)(x - -3) = 0\nx - -4/5 = 0 or x - -3 = 0\nx = -4/5\nx = -3"} {"input": "Find x and y such that\n6x + 9y = 207/5\n3x + 7y = 86/5", "output": "6x + 9y = 207/5\n3x + 7y = 86/5\n\nUsing elimination\n3*(6x + 9y = 207/5)\n6*(3x + 7y = 86/5)\n18x + 27y = 621/5\n18x + 42y = 516/5\nSubtract equations\n-15y = 21\ny = 21/-15\ny = -7/5\n\nSubstitute y\n6x + 9(-7/5) = 207/5\n6x = 54\nx = 54/6\nx = 9"} {"input": "What value of x satisfies x^3 + 121/20x^2 + 5x - 5/4 = 0", "output": "x^3 + 121/20x^2 + 5x - 5/4 = 0\n(x - -5/4)(x - 1/5)(x - -5) = 0\nx - -5/4 = 0\nx - 1/5 = 0\nx - -5 = 0\nx = -5/4\nx = 1/5\nx = -5"} {"input": "Find x for 10x - 20 = 0", "output": "10x - 20 = 0\n10x = 20\nx = 20 / 10\nx = 2"} {"input": "Find x for 7x + 119/9 = 0", "output": "7x + 119/9 = 0\n7x = -119/9\nx = -119/9 / 7\nx = -17/9"} {"input": "Find x for x^3 - 233/20x^2 - 2163/40x + 459/8 = 0", "output": "x^3 - 233/20x^2 - 2163/40x + 459/8 = 0\n(x - 15)(x - 9/10)(x - -17/4) = 0\nx - 15 = 0\nx - 9/10 = 0\nx - -17/4 = 0\nx = 15\nx = 9/10\nx = -17/4"} {"input": "Compute the solution of 8x + 19 = 0", "output": "8x + 19 = 0\n8x = -19\nx = -19 / 8\nx = -19/8"} {"input": "Find the solution to x^3 - 37/14x^2 - 27/7x + 117/14 = 0", "output": "x^3 - 37/14x^2 - 27/7x + 117/14 = 0\n(x - 3/2)(x - 3)(x - -13/7) = 0\nx - 3/2 = 0\nx - 3 = 0\nx - -13/7 = 0\nx = 3/2\nx = 3\nx = -13/7"} {"input": "Solve the equation 8x - 112/3 = 0", "output": "8x - 112/3 = 0\n8x = 112/3\nx = 112/3 / 8\nx = 14/3"} {"input": "Solve the system:\n6x + 10y = -19/4\n1x + 5y = -3/8", "output": "6x + 10y = -19/4\n1x + 5y = -3/8\n\nUsing elimination\n1*(6x + 10y = -19/4)\n6*(1x + 5y = -3/8)\n6x + 10y = -19/4\n6x + 30y = -9/4\nSubtract equations\n-20y = -5/2\ny = -5/2/-20\ny = 1/8\n\nSubstitute y\n6x + 10(1/8) = -19/4\n6x = -6\nx = -6/6\nx = -1"} {"input": "Find x in x^3 + 10/9x^2 - 101/27x + 88/81 = 0", "output": "x^3 + 10/9x^2 - 101/27x + 88/81 = 0\n(x - 1/3)(x - -8/3)(x - 11/9) = 0\nx - 1/3 = 0\nx - -8/3 = 0\nx - 11/9 = 0\nx = 1/3\nx = -8/3\nx = 11/9"} {"input": "Solve x^2 - 98/9x + 80/9 = 0", "output": "x^2 - 98/9x + 80/9 = 0\n(x - 10)(x - 8/9) = 0\nx - 10 = 0 or x - 8/9 = 0\nx = 10\nx = 8/9"} {"input": "Solve simultaneously:\n6x + 2y = 97\n9x + 4y = 149", "output": "6x + 2y = 97\n9x + 4y = 149\n\nUsing elimination\n9*(6x + 2y = 97)\n6*(9x + 4y = 149)\n54x + 18y = 873\n54x + 24y = 894\nSubtract equations\n-6y = -21\ny = -21/-6\ny = 7/2\n\nSubstitute y\n6x + 2(7/2) = 97\n6x = 90\nx = 90/6\nx = 15"} {"input": "Compute the solution of x^2 - 104/5x + 252/5 = 0", "output": "x^2 - 104/5x + 252/5 = 0\n(x - 14/5)(x - 18) = 0\nx - 14/5 = 0 or x - 18 = 0\nx = 14/5\nx = 18"} {"input": "Find the solution to x^2 + 45/14x - 81/14 = 0", "output": "x^2 + 45/14x - 81/14 = 0\n(x - 9/7)(x - -9/2) = 0\nx - 9/7 = 0 or x - -9/2 = 0\nx = 9/7\nx = -9/2"} {"input": "Find x for 4x - 32 = 0", "output": "4x - 32 = 0\n4x = 32\nx = 32 / 4\nx = 8"} {"input": "Solve x^2 - 63/40x - 11/8 = 0", "output": "x^2 - 63/40x - 11/8 = 0\n(x - 11/5)(x - -5/8) = 0\nx - 11/5 = 0 or x - -5/8 = 0\nx = 11/5\nx = -5/8"} {"input": "What value of x satisfies 5x - 35/9 = 0", "output": "5x - 35/9 = 0\n5x = 35/9\nx = 35/9 / 5\nx = 7/9"} {"input": "Find x and y such that\n6x + 3y = -69/2\n9x + 1y = -51/2", "output": "6x + 3y = -69/2\n9x + 1y = -51/2\n\nUsing elimination\n9*(6x + 3y = -69/2)\n6*(9x + 1y = -51/2)\n54x + 27y = -621/2\n54x + 6y = -153\nSubtract equations\n21y = -315/2\ny = -315/2/21\ny = -15/2\n\nSubstitute y\n6x + 3(-15/2) = -69/2\n6x = -12\nx = -12/6\nx = -2"} {"input": "Find the solution to x^3 - 143/24x^2 + 31/3x - 35/8 = 0", "output": "x^3 - 143/24x^2 + 31/3x - 35/8 = 0\n(x - 7/3)(x - 3)(x - 5/8) = 0\nx - 7/3 = 0\nx - 3 = 0\nx - 5/8 = 0\nx = 7/3\nx = 3\nx = 5/8"} {"input": "What value of x satisfies 6x + 32/3 = 0", "output": "6x + 32/3 = 0\n6x = -32/3\nx = -32/3 / 6\nx = -16/9"} {"input": "Solve the equations:\n7x + 4y = -101/10\n7x + 8y = -237/10", "output": "7x + 4y = -101/10\n7x + 8y = -237/10\n\nUsing elimination\n7*(7x + 4y = -101/10)\n7*(7x + 8y = -237/10)\n49x + 28y = -707/10\n49x + 56y = -1659/10\nSubtract equations\n-28y = 476/5\ny = 476/5/-28\ny = -17/5\n\nSubstitute y\n7x + 4(-17/5) = -101/10\n7x = 7/2\nx = 7/2/7\nx = 1/2"} {"input": "Find x in x^3 - 13/15x^2 - 674/15x - 1456/15 = 0", "output": "x^3 - 13/15x^2 - 674/15x - 1456/15 = 0\n(x - 8)(x - -14/5)(x - -13/3) = 0\nx - 8 = 0\nx - -14/5 = 0\nx - -13/3 = 0\nx = 8\nx = -14/5\nx = -13/3"} {"input": "Solve simultaneously:\n1x + 6y = 187/15\n1x + 10y = 71/3", "output": "1x + 6y = 187/15\n1x + 10y = 71/3\n\nUsing elimination\n1*(1x + 6y = 187/15)\n1*(1x + 10y = 71/3)\n1x + 6y = 187/15\n1x + 10y = 71/3\nSubtract equations\n-4y = -56/5\ny = -56/5/-4\ny = 14/5\n\nSubstitute y\n1x + 6(14/5) = 187/15\n1x = -13/3\nx = -13/3/1\nx = -13/3"} {"input": "Find the solution to x^2 + 18/7x - 85/7 = 0", "output": "x^2 + 18/7x - 85/7 = 0\n(x - -5)(x - 17/7) = 0\nx - -5 = 0 or x - 17/7 = 0\nx = -5\nx = 17/7"} {"input": "Find x for 5x + 55/2 = 0", "output": "5x + 55/2 = 0\n5x = -55/2\nx = -55/2 / 5\nx = -11/2"} {"input": "Solve the equation 5x + 80/3 = 0", "output": "5x + 80/3 = 0\n5x = -80/3\nx = -80/3 / 5\nx = -16/3"} {"input": "Determine x in x^3 + 669/40x^2 + 2489/40x + 663/10 = 0", "output": "x^3 + 669/40x^2 + 2489/40x + 663/10 = 0\n(x - -17/8)(x - -13/5)(x - -12) = 0\nx - -17/8 = 0\nx - -13/5 = 0\nx - -12 = 0\nx = -17/8\nx = -13/5\nx = -12"} {"input": "Solve 6x - 114/7 = 0", "output": "6x - 114/7 = 0\n6x = 114/7\nx = 114/7 / 6\nx = 19/7"} {"input": "Solve the equations:\n9x + 7y = 58/5\n3x + 8y = 127/5", "output": "9x + 7y = 58/5\n3x + 8y = 127/5\n\nUsing elimination\n3*(9x + 7y = 58/5)\n9*(3x + 8y = 127/5)\n27x + 21y = 174/5\n27x + 72y = 1143/5\nSubtract equations\n-51y = -969/5\ny = -969/5/-51\ny = 19/5\n\nSubstitute y\n9x + 7(19/5) = 58/5\n9x = -15\nx = -15/9\nx = -5/3"} {"input": "Compute the solution of x^2 - 19/5x - 4/5 = 0", "output": "x^2 - 19/5x - 4/5 = 0\n(x - -1/5)(x - 4) = 0\nx - -1/5 = 0 or x - 4 = 0\nx = -1/5\nx = 4"} {"input": "What value of x satisfies x^2 + 3/2x - 10 = 0", "output": "x^2 + 3/2x - 10 = 0\n(x - 5/2)(x - -4) = 0\nx - 5/2 = 0 or x - -4 = 0\nx = 5/2\nx = -4"} {"input": "Solve x^3 + 116/15x^2 + 239/15x + 26/5 = 0", "output": "x^3 + 116/15x^2 + 239/15x + 26/5 = 0\n(x - -13/3)(x - -2/5)(x - -3) = 0\nx - -13/3 = 0\nx - -2/5 = 0\nx - -3 = 0\nx = -13/3\nx = -2/5\nx = -3"} {"input": "Solve quickly: x^2 - 12/5x - 9/5 = 0", "output": "x^2 - 12/5x - 9/5 = 0\n(x - 3)(x - -3/5) = 0\nx - 3 = 0 or x - -3/5 = 0\nx = 3\nx = -3/5"} {"input": "Find x for x^3 - 101/6x^2 + 43x + 760/3 = 0", "output": "x^3 - 101/6x^2 + 43x + 760/3 = 0\n(x - 19/2)(x - -8/3)(x - 10) = 0\nx - 19/2 = 0\nx - -8/3 = 0\nx - 10 = 0\nx = 19/2\nx = -8/3\nx = 10"} {"input": "Solve quickly: x^3 + 5/3x^2 - 17x - 39 = 0", "output": "x^3 + 5/3x^2 - 17x - 39 = 0\n(x - -3)(x - -3)(x - 13/3) = 0\nx - -3 = 0\nx - -3 = 0\nx - 13/3 = 0\nx = -3\nx = -3\nx = 13/3"} {"input": "Compute the solution of 5x + 75/7 = 0", "output": "5x + 75/7 = 0\n5x = -75/7\nx = -75/7 / 5\nx = -15/7"} {"input": "Solve the system:\n6x + 1y = -20\n5x + 4y = -23", "output": "6x + 1y = -20\n5x + 4y = -23\n\nUsing elimination\n5*(6x + 1y = -20)\n6*(5x + 4y = -23)\n30x + 5y = -100\n30x + 24y = -138\nSubtract equations\n-19y = 38\ny = 38/-19\ny = -2\n\nSubstitute y\n6x + 1(-2) = -20\n6x = -18\nx = -18/6\nx = -3"} {"input": "Solve the system:\n8x + 5y = 200/3\n8x + 3y = 64", "output": "8x + 5y = 200/3\n8x + 3y = 64\n\nUsing elimination\n8*(8x + 5y = 200/3)\n8*(8x + 3y = 64)\n64x + 40y = 1600/3\n64x + 24y = 512\nSubtract equations\n16y = 64/3\ny = 64/3/16\ny = 4/3\n\nSubstitute y\n8x + 5(4/3) = 200/3\n8x = 60\nx = 60/8\nx = 15/2"} {"input": "Find x for x^3 - 143/70x^2 - 491/50x + 418/35 = 0", "output": "x^3 - 143/70x^2 - 491/50x + 418/35 = 0\n(x - -20/7)(x - 19/5)(x - 11/10) = 0\nx - -20/7 = 0\nx - 19/5 = 0\nx - 11/10 = 0\nx = -20/7\nx = 19/5\nx = 11/10"} {"input": "Find x in x^3 - 14/3x^2 - 139/4x - 153/4 = 0", "output": "x^3 - 14/3x^2 - 139/4x - 153/4 = 0\n(x - 9)(x - -17/6)(x - -3/2) = 0\nx - 9 = 0\nx - -17/6 = 0\nx - -3/2 = 0\nx = 9\nx = -17/6\nx = -3/2"} {"input": "Determine x in 5x - 65/3 = 0", "output": "5x - 65/3 = 0\n5x = 65/3\nx = 65/3 / 5\nx = 13/3"} {"input": "Solve simultaneously:\n1x + 7y = -122/35\n6x + 7y = 3/35", "output": "1x + 7y = -122/35\n6x + 7y = 3/35\n\nUsing elimination\n6*(1x + 7y = -122/35)\n1*(6x + 7y = 3/35)\n6x + 42y = -732/35\n6x + 7y = 3/35\nSubtract equations\n35y = -21\ny = -21/35\ny = -3/5\n\nSubstitute y\n1x + 7(-3/5) = -122/35\n1x = 5/7\nx = 5/7/1\nx = 5/7"} {"input": "Find x in 10x + 10/3 = 0", "output": "10x + 10/3 = 0\n10x = -10/3\nx = -10/3 / 10\nx = -1/3"} {"input": "Find x and y such that\n4x + 9y = -33/10\n1x + 6y = 81/20", "output": "4x + 9y = -33/10\n1x + 6y = 81/20\n\nUsing elimination\n1*(4x + 9y = -33/10)\n4*(1x + 6y = 81/20)\n4x + 9y = -33/10\n4x + 24y = 81/5\nSubtract equations\n-15y = -39/2\ny = -39/2/-15\ny = 13/10\n\nSubstitute y\n4x + 9(13/10) = -33/10\n4x = -15\nx = -15/4\nx = -15/4"} {"input": "Compute the solution of x^2 + 131/56x + 15/14 = 0", "output": "x^2 + 131/56x + 15/14 = 0\n(x - -12/7)(x - -5/8) = 0\nx - -12/7 = 0 or x - -5/8 = 0\nx = -12/7\nx = -5/8"} {"input": "Solve the equations:\n10x + 8y = -208/35\n8x + 3y = -71/70", "output": "10x + 8y = -208/35\n8x + 3y = -71/70\n\nUsing elimination\n8*(10x + 8y = -208/35)\n10*(8x + 3y = -71/70)\n80x + 64y = -1664/35\n80x + 30y = -71/7\nSubtract equations\n34y = -187/5\ny = -187/5/34\ny = -11/10\n\nSubstitute y\n10x + 8(-11/10) = -208/35\n10x = 20/7\nx = 20/7/10\nx = 2/7"} {"input": "Solve the equations:\n9x + 8y = 37\n6x + 9y = 21", "output": "9x + 8y = 37\n6x + 9y = 21\n\nUsing elimination\n6*(9x + 8y = 37)\n9*(6x + 9y = 21)\n54x + 48y = 222\n54x + 81y = 189\nSubtract equations\n-33y = 33\ny = 33/-33\ny = -1\n\nSubstitute y\n9x + 8(-1) = 37\n9x = 45\nx = 45/9\nx = 5"} {"input": "Find x and y such that\n1x + 10y = -289/7\n4x + 6y = -204/7", "output": "1x + 10y = -289/7\n4x + 6y = -204/7\n\nUsing elimination\n4*(1x + 10y = -289/7)\n1*(4x + 6y = -204/7)\n4x + 40y = -1156/7\n4x + 6y = -204/7\nSubtract equations\n34y = -136\ny = -136/34\ny = -4\n\nSubstitute y\n1x + 10(-4) = -289/7\n1x = -9/7\nx = -9/7/1\nx = -9/7"} {"input": "Solve the system:\n2x + 5y = -20/9\n2x + 10y = -20/9", "output": "2x + 5y = -20/9\n2x + 10y = -20/9\n\nUsing elimination\n2*(2x + 5y = -20/9)\n2*(2x + 10y = -20/9)\n4x + 10y = -40/9\n4x + 20y = -40/9\nSubtract equations\n-10y = 0\ny = 0/-10\ny = 0\n\nSubstitute y\n2x + 5(0) = -20/9\n2x = -20/9\nx = -20/9/2\nx = -10/9"} {"input": "What value of x satisfies 5x - 5/6 = 0", "output": "5x - 5/6 = 0\n5x = 5/6\nx = 5/6 / 5\nx = 1/6"} {"input": "Solve the equations:\n8x + 4y = 176/45\n8x + 10y = -154/45", "output": "8x + 4y = 176/45\n8x + 10y = -154/45\n\nUsing elimination\n8*(8x + 4y = 176/45)\n8*(8x + 10y = -154/45)\n64x + 32y = 1408/45\n64x + 80y = -1232/45\nSubtract equations\n-48y = 176/3\ny = 176/3/-48\ny = -11/9\n\nSubstitute y\n8x + 4(-11/9) = 176/45\n8x = 44/5\nx = 44/5/8\nx = 11/10"} {"input": "Find x for 10x - 20/9 = 0", "output": "10x - 20/9 = 0\n10x = 20/9\nx = 20/9 / 10\nx = 2/9"} {"input": "Solve the equation x^3 - 46/3x^2 + 17x + 520/3 = 0", "output": "x^3 - 46/3x^2 + 17x + 520/3 = 0\n(x - -8/3)(x - 13)(x - 5) = 0\nx - -8/3 = 0\nx - 13 = 0\nx - 5 = 0\nx = -8/3\nx = 13\nx = 5"} {"input": "Solve the equation x^3 + 297/20x^2 - 51/20x - 2023/10 = 0", "output": "x^3 + 297/20x^2 - 51/20x - 2023/10 = 0\n(x - 17/5)(x - -14)(x - -17/4) = 0\nx - 17/5 = 0\nx - -14 = 0\nx - -17/4 = 0\nx = 17/5\nx = -14\nx = -17/4"} {"input": "What value of x satisfies x^3 - 814/45x^2 + 17x + 1156/45 = 0", "output": "x^3 - 814/45x^2 + 17x + 1156/45 = 0\n(x - 17/9)(x - -4/5)(x - 17) = 0\nx - 17/9 = 0\nx - -4/5 = 0\nx - 17 = 0\nx = 17/9\nx = -4/5\nx = 17"} {"input": "Solve quickly: x^2 + 57/14x + 55/14 = 0", "output": "x^2 + 57/14x + 55/14 = 0\n(x - -11/7)(x - -5/2) = 0\nx - -11/7 = 0 or x - -5/2 = 0\nx = -11/7\nx = -5/2"} {"input": "Solve simultaneously:\n6x + 5y = 74/3\n10x + 8y = 122/3", "output": "6x + 5y = 74/3\n10x + 8y = 122/3\n\nUsing elimination\n10*(6x + 5y = 74/3)\n6*(10x + 8y = 122/3)\n60x + 50y = 740/3\n60x + 48y = 244\nSubtract equations\n2y = 8/3\ny = 8/3/2\ny = 4/3\n\nSubstitute y\n6x + 5(4/3) = 74/3\n6x = 18\nx = 18/6\nx = 3"} {"input": "Solve simultaneously:\n8x + 10y = 54\n2x + 3y = 16", "output": "8x + 10y = 54\n2x + 3y = 16\n\nUsing elimination\n2*(8x + 10y = 54)\n8*(2x + 3y = 16)\n16x + 20y = 108\n16x + 24y = 128\nSubtract equations\n-4y = -20\ny = -20/-4\ny = 5\n\nSubstitute y\n8x + 10(5) = 54\n8x = 4\nx = 4/8\nx = 1/2"} {"input": "Find x for x^3 - 181/12x^2 - 311/6x - 12 = 0", "output": "x^3 - 181/12x^2 - 311/6x - 12 = 0\n(x - -8/3)(x - -1/4)(x - 18) = 0\nx - -8/3 = 0\nx - -1/4 = 0\nx - 18 = 0\nx = -8/3\nx = -1/4\nx = 18"} {"input": "Find x and y such that\n7x + 5y = -319/10\n10x + 8y = -49", "output": "7x + 5y = -319/10\n10x + 8y = -49\n\nUsing elimination\n10*(7x + 5y = -319/10)\n7*(10x + 8y = -49)\n70x + 50y = -319\n70x + 56y = -343\nSubtract equations\n-6y = 24\ny = 24/-6\ny = -4\n\nSubstitute y\n7x + 5(-4) = -319/10\n7x = -119/10\nx = -119/10/7\nx = -17/10"} {"input": "Determine x in 5x + 75/8 = 0", "output": "5x + 75/8 = 0\n5x = -75/8\nx = -75/8 / 5\nx = -15/8"} {"input": "Solve simultaneously:\n4x + 1y = -57/4\n7x + 8y = -39", "output": "4x + 1y = -57/4\n7x + 8y = -39\n\nUsing elimination\n7*(4x + 1y = -57/4)\n4*(7x + 8y = -39)\n28x + 7y = -399/4\n28x + 32y = -156\nSubtract equations\n-25y = 225/4\ny = 225/4/-25\ny = -9/4\n\nSubstitute y\n4x + 1(-9/4) = -57/4\n4x = -12\nx = -12/4\nx = -3"} {"input": "Solve quickly: x^3 + 65/8x^2 - 171/4x + 45 = 0", "output": "x^3 + 65/8x^2 - 171/4x + 45 = 0\n(x - -12)(x - 2)(x - 15/8) = 0\nx - -12 = 0\nx - 2 = 0\nx - 15/8 = 0\nx = -12\nx = 2\nx = 15/8"} {"input": "Find x in x^3 + 61/10x^2 - 1/5x - 57/2 = 0", "output": "x^3 + 61/10x^2 - 1/5x - 57/2 = 0\n(x - -5)(x - 19/10)(x - -3) = 0\nx - -5 = 0\nx - 19/10 = 0\nx - -3 = 0\nx = -5\nx = 19/10\nx = -3"} {"input": "Find x in x^2 - 39/28x + 5/28 = 0", "output": "x^2 - 39/28x + 5/28 = 0\n(x - 1/7)(x - 5/4) = 0\nx - 1/7 = 0 or x - 5/4 = 0\nx = 1/7\nx = 5/4"} {"input": "Solve x^3 - 133/24x^2 + 6583/648x - 665/108 = 0", "output": "x^3 - 133/24x^2 + 6583/648x - 665/108 = 0\n(x - 15/8)(x - 19/9)(x - 14/9) = 0\nx - 15/8 = 0\nx - 19/9 = 0\nx - 14/9 = 0\nx = 15/8\nx = 19/9\nx = 14/9"} {"input": "Find the solution to 7x + 1 = 0", "output": "7x + 1 = 0\n7x = -1\nx = -1 / 7\nx = -1/7"} {"input": "Compute the solution of 4x + 38 = 0", "output": "4x + 38 = 0\n4x = -38\nx = -38 / 4\nx = -19/2"} {"input": "Find the solution to x^2 - 7/2x - 2 = 0", "output": "x^2 - 7/2x - 2 = 0\n(x - 4)(x - -1/2) = 0\nx - 4 = 0 or x - -1/2 = 0\nx = 4\nx = -1/2"} {"input": "What value of x satisfies x^3 + 682/105x^2 + 397/35x + 374/105 = 0", "output": "x^3 + 682/105x^2 + 397/35x + 374/105 = 0\n(x - -11/3)(x - -17/7)(x - -2/5) = 0\nx - -11/3 = 0\nx - -17/7 = 0\nx - -2/5 = 0\nx = -11/3\nx = -17/7\nx = -2/5"} {"input": "What value of x satisfies x^2 + 41/14x + 15/14 = 0", "output": "x^2 + 41/14x + 15/14 = 0\n(x - -3/7)(x - -5/2) = 0\nx - -3/7 = 0 or x - -5/2 = 0\nx = -3/7\nx = -5/2"} {"input": "Solve the system:\n4x + 5y = -15/2\n5x + 1y = -69/4", "output": "4x + 5y = -15/2\n5x + 1y = -69/4\n\nUsing elimination\n5*(4x + 5y = -15/2)\n4*(5x + 1y = -69/4)\n20x + 25y = -75/2\n20x + 4y = -69\nSubtract equations\n21y = 63/2\ny = 63/2/21\ny = 3/2\n\nSubstitute y\n4x + 5(3/2) = -15/2\n4x = -15\nx = -15/4\nx = -15/4"} {"input": "Find the solution to x^3 + 109/18x^2 - 457/18x + 10 = 0", "output": "x^3 + 109/18x^2 - 457/18x + 10 = 0\n(x - 5/2)(x - 4/9)(x - -9) = 0\nx - 5/2 = 0\nx - 4/9 = 0\nx - -9 = 0\nx = 5/2\nx = 4/9\nx = -9"} {"input": "Find x for 5x + 10 = 0", "output": "5x + 10 = 0\n5x = -10\nx = -10 / 5\nx = -2"} {"input": "What value of x satisfies 10x + 2 = 0", "output": "10x + 2 = 0\n10x = -2\nx = -2 / 10\nx = -1/5"} {"input": "Solve quickly: x^2 - 1/3x - 80/3 = 0", "output": "x^2 - 1/3x - 80/3 = 0\n(x - 16/3)(x - -5) = 0\nx - 16/3 = 0 or x - -5 = 0\nx = 16/3\nx = -5"} {"input": "Find x in 3x + 27/4 = 0", "output": "3x + 27/4 = 0\n3x = -27/4\nx = -27/4 / 3\nx = -9/4"} {"input": "Find x for x^3 + 29/12x^2 - 55/4x - 91/6 = 0", "output": "x^3 + 29/12x^2 - 55/4x - 91/6 = 0\n(x - 13/4)(x - -14/3)(x - -1) = 0\nx - 13/4 = 0\nx - -14/3 = 0\nx - -1 = 0\nx = 13/4\nx = -14/3\nx = -1"} {"input": "Find x in x^3 + 55/3x^2 + 637/12x - 845/4 = 0", "output": "x^3 + 55/3x^2 + 637/12x - 845/4 = 0\n(x - -13)(x - -15/2)(x - 13/6) = 0\nx - -13 = 0\nx - -15/2 = 0\nx - 13/6 = 0\nx = -13\nx = -15/2\nx = 13/6"} {"input": "Find x in x^3 + 69/8x^2 + 727/32x + 1197/64 = 0", "output": "x^3 + 69/8x^2 + 727/32x + 1197/64 = 0\n(x - -19/8)(x - -7/4)(x - -9/2) = 0\nx - -19/8 = 0\nx - -7/4 = 0\nx - -9/2 = 0\nx = -19/8\nx = -7/4\nx = -9/2"} {"input": "Solve quickly: x^3 + 91/72x^2 - 161/288x + 13/288 = 0", "output": "x^3 + 91/72x^2 - 161/288x + 13/288 = 0\n(x - -13/8)(x - 1/4)(x - 1/9) = 0\nx - -13/8 = 0\nx - 1/4 = 0\nx - 1/9 = 0\nx = -13/8\nx = 1/4\nx = 1/9"} {"input": "Find x and y such that\n7x + 5y = 32\n10x + 4y = 254/7", "output": "7x + 5y = 32\n10x + 4y = 254/7\n\nUsing elimination\n10*(7x + 5y = 32)\n7*(10x + 4y = 254/7)\n70x + 50y = 320\n70x + 28y = 254\nSubtract equations\n22y = 66\ny = 66/22\ny = 3\n\nSubstitute y\n7x + 5(3) = 32\n7x = 17\nx = 17/7\nx = 17/7"} {"input": "Find x in x^2 - 183/70x + 19/14 = 0", "output": "x^2 - 183/70x + 19/14 = 0\n(x - 5/7)(x - 19/10) = 0\nx - 5/7 = 0 or x - 19/10 = 0\nx = 5/7\nx = 19/10"} {"input": "Find x in x^3 - 38/3x^2 - 409/12x - 55/4 = 0", "output": "x^3 - 38/3x^2 - 409/12x - 55/4 = 0\n(x - 15)(x - -11/6)(x - -1/2) = 0\nx - 15 = 0\nx - -11/6 = 0\nx - -1/2 = 0\nx = 15\nx = -11/6\nx = -1/2"} {"input": "Determine x in 9x + 45 = 0", "output": "9x + 45 = 0\n9x = -45\nx = -45 / 9\nx = -5"} {"input": "Solve the system:\n3x + 8y = -749/40\n4x + 4y = -103/10", "output": "3x + 8y = -749/40\n4x + 4y = -103/10\n\nUsing elimination\n4*(3x + 8y = -749/40)\n3*(4x + 4y = -103/10)\n12x + 32y = -749/10\n12x + 12y = -309/10\nSubtract equations\n20y = -44\ny = -44/20\ny = -11/5\n\nSubstitute y\n3x + 8(-11/5) = -749/40\n3x = -9/8\nx = -9/8/3\nx = -3/8"} {"input": "Find x for x^2 - 25/18x - 133/18 = 0", "output": "x^2 - 25/18x - 133/18 = 0\n(x - -19/9)(x - 7/2) = 0\nx - -19/9 = 0 or x - 7/2 = 0\nx = -19/9\nx = 7/2"} {"input": "Solve simultaneously:\n8x + 4y = 10/3\n8x + 8y = 32/3", "output": "8x + 4y = 10/3\n8x + 8y = 32/3\n\nUsing elimination\n8*(8x + 4y = 10/3)\n8*(8x + 8y = 32/3)\n64x + 32y = 80/3\n64x + 64y = 256/3\nSubtract equations\n-32y = -176/3\ny = -176/3/-32\ny = 11/6\n\nSubstitute y\n8x + 4(11/6) = 10/3\n8x = -4\nx = -4/8\nx = -1/2"} {"input": "What value of x satisfies x^3 + 10/63x^2 - 17/189x - 2/189 = 0", "output": "x^3 + 10/63x^2 - 17/189x - 2/189 = 0\n(x - -1/3)(x - -1/9)(x - 2/7) = 0\nx - -1/3 = 0\nx - -1/9 = 0\nx - 2/7 = 0\nx = -1/3\nx = -1/9\nx = 2/7"} {"input": "Find x for x^3 - 152/21x^2 + 31/3x + 30/7 = 0", "output": "x^3 - 152/21x^2 + 31/3x + 30/7 = 0\n(x - 5)(x - -1/3)(x - 18/7) = 0\nx - 5 = 0\nx - -1/3 = 0\nx - 18/7 = 0\nx = 5\nx = -1/3\nx = 18/7"} {"input": "Find x and y such that\n7x + 4y = -74/5\n6x + 3y = -867/70", "output": "7x + 4y = -74/5\n6x + 3y = -867/70\n\nUsing elimination\n6*(7x + 4y = -74/5)\n7*(6x + 3y = -867/70)\n42x + 24y = -444/5\n42x + 21y = -867/10\nSubtract equations\n3y = -21/10\ny = -21/10/3\ny = -7/10\n\nSubstitute y\n7x + 4(-7/10) = -74/5\n7x = -12\nx = -12/7\nx = -12/7"} {"input": "Solve simultaneously:\n7x + 4y = -129/5\n8x + 3y = -138/5", "output": "7x + 4y = -129/5\n8x + 3y = -138/5\n\nUsing elimination\n8*(7x + 4y = -129/5)\n7*(8x + 3y = -138/5)\n56x + 32y = -1032/5\n56x + 21y = -966/5\nSubtract equations\n11y = -66/5\ny = -66/5/11\ny = -6/5\n\nSubstitute y\n7x + 4(-6/5) = -129/5\n7x = -21\nx = -21/7\nx = -3"} {"input": "Determine x in x^3 - 227/72x^2 + 515/288x + 7/6 = 0", "output": "x^3 - 227/72x^2 + 515/288x + 7/6 = 0\n(x - 7/4)(x - -3/8)(x - 16/9) = 0\nx - 7/4 = 0\nx - -3/8 = 0\nx - 16/9 = 0\nx = 7/4\nx = -3/8\nx = 16/9"} {"input": "Find the solution to 1x - 14/9 = 0", "output": "1x - 14/9 = 0\n1x = 14/9\nx = 14/9 / 1\nx = 14/9"} {"input": "Determine x in x^3 - 129/8x^2 - 599/8x - 105/2 = 0", "output": "x^3 - 129/8x^2 - 599/8x - 105/2 = 0\n(x - -7/8)(x - -3)(x - 20) = 0\nx - -7/8 = 0\nx - -3 = 0\nx - 20 = 0\nx = -7/8\nx = -3\nx = 20"} {"input": "Find x and y such that\n1x + 8y = -50\n3x + 5y = -53/2", "output": "1x + 8y = -50\n3x + 5y = -53/2\n\nUsing elimination\n3*(1x + 8y = -50)\n1*(3x + 5y = -53/2)\n3x + 24y = -150\n3x + 5y = -53/2\nSubtract equations\n19y = -247/2\ny = -247/2/19\ny = -13/2\n\nSubstitute y\n1x + 8(-13/2) = -50\n1x = 2\nx = 2/1\nx = 2"} {"input": "Solve x^3 + 61/14x^2 + 25/14x - 50/7 = 0", "output": "x^3 + 61/14x^2 + 25/14x - 50/7 = 0\n(x - 1)(x - -20/7)(x - -5/2) = 0\nx - 1 = 0\nx - -20/7 = 0\nx - -5/2 = 0\nx = 1\nx = -20/7\nx = -5/2"} {"input": "Find x in 9x + 21 = 0", "output": "9x + 21 = 0\n9x = -21\nx = -21 / 9\nx = -7/3"} {"input": "Solve the system:\n9x + 6y = -5\n5x + 6y = -61/9", "output": "9x + 6y = -5\n5x + 6y = -61/9\n\nUsing elimination\n5*(9x + 6y = -5)\n9*(5x + 6y = -61/9)\n45x + 30y = -25\n45x + 54y = -61\nSubtract equations\n-24y = 36\ny = 36/-24\ny = -3/2\n\nSubstitute y\n9x + 6(-3/2) = -5\n9x = 4\nx = 4/9\nx = 4/9"} {"input": "Solve x^2 - 21/10x + 11/10 = 0", "output": "x^2 - 21/10x + 11/10 = 0\n(x - 11/10)(x - 1) = 0\nx - 11/10 = 0 or x - 1 = 0\nx = 11/10\nx = 1"} {"input": "Find x in 10x + 160 = 0", "output": "10x + 160 = 0\n10x = -160\nx = -160 / 10\nx = -16"} {"input": "Solve the equation x^3 + 115/42x^2 - 401/42x - 51/7 = 0", "output": "x^3 + 115/42x^2 - 401/42x - 51/7 = 0\n(x - 17/7)(x - -9/2)(x - -2/3) = 0\nx - 17/7 = 0\nx - -9/2 = 0\nx - -2/3 = 0\nx = 17/7\nx = -9/2\nx = -2/3"} {"input": "Determine x in x^3 - 176/21x^2 + 1459/63x - 190/9 = 0", "output": "x^3 - 176/21x^2 + 1459/63x - 190/9 = 0\n(x - 7/3)(x - 10/3)(x - 19/7) = 0\nx - 7/3 = 0\nx - 10/3 = 0\nx - 19/7 = 0\nx = 7/3\nx = 10/3\nx = 19/7"} {"input": "Find x and y such that\n4x + 4y = 20\n1x + 3y = 7", "output": "4x + 4y = 20\n1x + 3y = 7\n\nUsing elimination\n1*(4x + 4y = 20)\n4*(1x + 3y = 7)\n4x + 4y = 20\n4x + 12y = 28\nSubtract equations\n-8y = -8\ny = -8/-8\ny = 1\n\nSubstitute y\n4x + 4(1) = 20\n4x = 16\nx = 16/4\nx = 4"}