input stringlengths 13 66 | output stringlengths 30 276 |
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Solve 3x - 5/3 = 0 | 3x - 5/3 = 0
3x = 5/3
x = 5/3 / 3
x = 5/9 |
Solve quickly: x^2 + 4/5x - 12/5 = 0 | x^2 + 4/5x - 12/5 = 0
(x - 6/5)(x - -2) = 0
x - 6/5 = 0 or x - -2 = 0
x = 6/5
x = -2 |
Compute the solution of x^2 + 1/4x - 9/2 = 0 | x^2 + 1/4x - 9/2 = 0
(x - -9/4)(x - 2) = 0
x - -9/4 = 0 or x - 2 = 0
x = -9/4
x = 2 |
Find x and y such that
5x + 2y = 41/3
3x + 10y = -5 | 5x + 2y = 41/3
3x + 10y = -5
Using elimination
3*(5x + 2y = 41/3)
5*(3x + 10y = -5)
15x + 6y = 41
15x + 50y = -25
Subtract equations
-44y = 66
y = 66/-44
y = -3/2
Substitute y
5x + 2(-3/2) = 41/3
5x = 50/3
x = 50/3/5
x = 10/3 |
Determine x in x^3 - 241/70x^2 + 113/35x - 24/35 = 0 | x^3 - 241/70x^2 + 113/35x - 24/35 = 0
(x - 2)(x - 8/7)(x - 3/10) = 0
x - 2 = 0
x - 8/7 = 0
x - 3/10 = 0
x = 2
x = 8/7
x = 3/10 |
Solve x^2 + 97/6x + 247/6 = 0 | x^2 + 97/6x + 247/6 = 0
(x - -19/6)(x - -13) = 0
x - -19/6 = 0 or x - -13 = 0
x = -19/6
x = -13 |
Find x in x^3 - 277/40x^2 + 91/16x + 1881/80 = 0 | x^3 - 277/40x^2 + 91/16x + 1881/80 = 0
(x - -11/8)(x - 19/5)(x - 9/2) = 0
x - -11/8 = 0
x - 19/5 = 0
x - 9/2 = 0
x = -11/8
x = 19/5
x = 9/2 |
Determine x in x^2 + 50/63x - 32/7 = 0 | x^2 + 50/63x - 32/7 = 0
(x - -18/7)(x - 16/9) = 0
x - -18/7 = 0 or x - 16/9 = 0
x = -18/7
x = 16/9 |
Find x and y such that
6x + 9y = -18
8x + 4y = -40/3 | 6x + 9y = -18
8x + 4y = -40/3
Using elimination
8*(6x + 9y = -18)
6*(8x + 4y = -40/3)
48x + 72y = -144
48x + 24y = -80
Subtract equations
48y = -64
y = -64/48
y = -4/3
Substitute y
6x + 9(-4/3) = -18
6x = -6
x = -6/6
x = -1 |
Find the solution to x^3 - 7/12x^2 - 77/3x + 221/4 = 0 | x^3 - 7/12x^2 - 77/3x + 221/4 = 0
(x - 13/4)(x - 3)(x - -17/3) = 0
x - 13/4 = 0
x - 3 = 0
x - -17/3 = 0
x = 13/4
x = 3
x = -17/3 |
Compute the solution of 2x + 17/3 = 0 | 2x + 17/3 = 0
2x = -17/3
x = -17/3 / 2
x = -17/6 |
Compute the solution of x^2 - 47/20x - 11/10 = 0 | x^2 - 47/20x - 11/10 = 0
(x - -2/5)(x - 11/4) = 0
x - -2/5 = 0 or x - 11/4 = 0
x = -2/5
x = 11/4 |
Solve x^3 - 9x^2 + 74/9x + 544/9 = 0 | x^3 - 9x^2 + 74/9x + 544/9 = 0
(x - -2)(x - 17/3)(x - 16/3) = 0
x - -2 = 0
x - 17/3 = 0
x - 16/3 = 0
x = -2
x = 17/3
x = 16/3 |
Solve the equations:
7x + 3y = 38
3x + 8y = 93/2 | 7x + 3y = 38
3x + 8y = 93/2
Using elimination
3*(7x + 3y = 38)
7*(3x + 8y = 93/2)
21x + 9y = 114
21x + 56y = 651/2
Subtract equations
-47y = -423/2
y = -423/2/-47
y = 9/2
Substitute y
7x + 3(9/2) = 38
7x = 49/2
x = 49/2/7
x = 7/2 |
Solve quickly: x^2 + 13/5x - 6/5 = 0 | x^2 + 13/5x - 6/5 = 0
(x - -3)(x - 2/5) = 0
x - -3 = 0 or x - 2/5 = 0
x = -3
x = 2/5 |
Solve the system:
6x + 9y = 21/2
1x + 4y = 1/2 | 6x + 9y = 21/2
1x + 4y = 1/2
Using elimination
1*(6x + 9y = 21/2)
6*(1x + 4y = 1/2)
6x + 9y = 21/2
6x + 24y = 3
Subtract equations
-15y = 15/2
y = 15/2/-15
y = -1/2
Substitute y
6x + 9(-1/2) = 21/2
6x = 15
x = 15/6
x = 5/2 |
Solve the equation x^3 + 15/4x^2 + 13/8x = 0 | x^3 + 15/4x^2 + 13/8x = 0
(x - -13/4)(x - -1/2)(x - 0) = 0
x - -13/4 = 0
x - -1/2 = 0
x - 0 = 0
x = -13/4
x = -1/2
x = 0 |
Find the solution to 6x + 24/5 = 0 | 6x + 24/5 = 0
6x = -24/5
x = -24/5 / 6
x = -4/5 |
Solve the equations:
5x + 8y = -161/5
10x + 2y = -84/5 | 5x + 8y = -161/5
10x + 2y = -84/5
Using elimination
10*(5x + 8y = -161/5)
5*(10x + 2y = -84/5)
50x + 80y = -322
50x + 10y = -84
Subtract equations
70y = -238
y = -238/70
y = -17/5
Substitute y
5x + 8(-17/5) = -161/5
5x = -5
x = -5/5
x = -1 |
Find x for 5x + 65/8 = 0 | 5x + 65/8 = 0
5x = -65/8
x = -65/8 / 5
x = -13/8 |
Find x in 2x + 2/3 = 0 | 2x + 2/3 = 0
2x = -2/3
x = -2/3 / 2
x = -1/3 |
Solve the equation x^3 - 557/28x^2 - 195/28x + 675/7 = 0 | x^3 - 557/28x^2 - 195/28x + 675/7 = 0
(x - -9/4)(x - 15/7)(x - 20) = 0
x - -9/4 = 0
x - 15/7 = 0
x - 20 = 0
x = -9/4
x = 15/7
x = 20 |
Solve the system:
6x + 10y = -97/7
3x + 1y = 31/14 | 6x + 10y = -97/7
3x + 1y = 31/14
Using elimination
3*(6x + 10y = -97/7)
6*(3x + 1y = 31/14)
18x + 30y = -291/7
18x + 6y = 93/7
Subtract equations
24y = -384/7
y = -384/7/24
y = -16/7
Substitute y
6x + 10(-16/7) = -97/7
6x = 9
x = 9/6
x = 3/2 |
Find the solution to 9x + 36/5 = 0 | 9x + 36/5 = 0
9x = -36/5
x = -36/5 / 9
x = -4/5 |
Find x for x^2 + 81/4x + 95/4 = 0 | x^2 + 81/4x + 95/4 = 0
(x - -5/4)(x - -19) = 0
x - -5/4 = 0 or x - -19 = 0
x = -5/4
x = -19 |
Compute the solution of x^3 - 1/15x^2 - 1321/300x + 91/25 = 0 | x^3 - 1/15x^2 - 1321/300x + 91/25 = 0
(x - 13/10)(x - 7/6)(x - -12/5) = 0
x - 13/10 = 0
x - 7/6 = 0
x - -12/5 = 0
x = 13/10
x = 7/6
x = -12/5 |
Solve the equations:
7x + 2y = 35
5x + 10y = 25 | 7x + 2y = 35
5x + 10y = 25
Using elimination
5*(7x + 2y = 35)
7*(5x + 10y = 25)
35x + 10y = 175
35x + 70y = 175
Subtract equations
-60y = 0
y = 0/-60
y = 0
Substitute y
7x + 2(0) = 35
7x = 35
x = 35/7
x = 5 |
Solve simultaneously:
7x + 4y = -119/30
2x + 5y = -23/6 | 7x + 4y = -119/30
2x + 5y = -23/6
Using elimination
2*(7x + 4y = -119/30)
7*(2x + 5y = -23/6)
14x + 8y = -119/15
14x + 35y = -161/6
Subtract equations
-27y = 189/10
y = 189/10/-27
y = -7/10
Substitute y
7x + 4(-7/10) = -119/30
7x = -7/6
x = -7/6/7
x = -1/6 |
Find x and y such that
6x + 8y = -179/20
6x + 1y = -193/20 | 6x + 8y = -179/20
6x + 1y = -193/20
Using elimination
6*(6x + 8y = -179/20)
6*(6x + 1y = -193/20)
36x + 48y = -537/10
36x + 6y = -579/10
Subtract equations
42y = 21/5
y = 21/5/42
y = 1/10
Substitute y
6x + 8(1/10) = -179/20
6x = -39/4
x = -39/4/6
x = -13/8 |
Solve x^3 - 139/72x^2 - 19/18x = 0 | x^3 - 139/72x^2 - 19/18x = 0
(x - 0)(x - -4/9)(x - 19/8) = 0
x - 0 = 0
x - -4/9 = 0
x - 19/8 = 0
x = 0
x = -4/9
x = 19/8 |
Solve the equation x^2 - 7x - 30 = 0 | x^2 - 7x - 30 = 0
(x - -3)(x - 10) = 0
x - -3 = 0 or x - 10 = 0
x = -3
x = 10 |
Solve quickly: 1x + 15 = 0 | 1x + 15 = 0
1x = -15
x = -15 / 1
x = -15 |
Determine x in x^3 + 305/56x^2 - 291/28x + 27/8 = 0 | x^3 + 305/56x^2 - 291/28x + 27/8 = 0
(x - 9/8)(x - 3/7)(x - -7) = 0
x - 9/8 = 0
x - 3/7 = 0
x - -7 = 0
x = 9/8
x = 3/7
x = -7 |
Solve quickly: 3x - 42 = 0 | 3x - 42 = 0
3x = 42
x = 42 / 3
x = 14 |
Find x in 8x + 32 = 0 | 8x + 32 = 0
8x = -32
x = -32 / 8
x = -4 |
Find x for 2x - 36 = 0 | 2x - 36 = 0
2x = 36
x = 36 / 2
x = 18 |
Solve the system:
3x + 6y = -3
6x + 5y = -13 | 3x + 6y = -3
6x + 5y = -13
Using elimination
6*(3x + 6y = -3)
3*(6x + 5y = -13)
18x + 36y = -18
18x + 15y = -39
Subtract equations
21y = 21
y = 21/21
y = 1
Substitute y
3x + 6(1) = -3
3x = -9
x = -9/3
x = -3 |
Solve x^3 - 41/14x^2 - 34/7x + 10 = 0 | x^3 - 41/14x^2 - 34/7x + 10 = 0
(x - 7/2)(x - 10/7)(x - -2) = 0
x - 7/2 = 0
x - 10/7 = 0
x - -2 = 0
x = 7/2
x = 10/7
x = -2 |
Find x and y such that
1x + 7y = 23/4
5x + 6y = 7 | 1x + 7y = 23/4
5x + 6y = 7
Using elimination
5*(1x + 7y = 23/4)
1*(5x + 6y = 7)
5x + 35y = 115/4
5x + 6y = 7
Subtract equations
29y = 87/4
y = 87/4/29
y = 3/4
Substitute y
1x + 7(3/4) = 23/4
1x = 1/2
x = 1/2/1
x = 1/2 |
Solve the equation x^2 + 31/7x + 12/7 = 0 | x^2 + 31/7x + 12/7 = 0
(x - -3/7)(x - -4) = 0
x - -3/7 = 0 or x - -4 = 0
x = -3/7
x = -4 |
Compute the solution of x^2 + 133/45x - 68/45 = 0 | x^2 + 133/45x - 68/45 = 0
(x - 4/9)(x - -17/5) = 0
x - 4/9 = 0 or x - -17/5 = 0
x = 4/9
x = -17/5 |
Find x and y such that
9x + 4y = 117
2x + 4y = 26 | 9x + 4y = 117
2x + 4y = 26
Using elimination
2*(9x + 4y = 117)
9*(2x + 4y = 26)
18x + 8y = 234
18x + 36y = 234
Subtract equations
-28y = 0
y = 0/-28
y = 0
Substitute y
9x + 4(0) = 117
9x = 117
x = 117/9
x = 13 |
Find x for x^3 - 83/30x^2 - 35/12x + 209/40 = 0 | x^3 - 83/30x^2 - 35/12x + 209/40 = 0
(x - 11/10)(x - 19/6)(x - -3/2) = 0
x - 11/10 = 0
x - 19/6 = 0
x - -3/2 = 0
x = 11/10
x = 19/6
x = -3/2 |
Find the solution to x^2 - 4 = 0 | x^2 - 4 = 0
(x - -2)(x - 2) = 0
x - -2 = 0 or x - 2 = 0
x = -2
x = 2 |
Find x for 3x + 21/2 = 0 | 3x + 21/2 = 0
3x = -21/2
x = -21/2 / 3
x = -7/2 |
Solve quickly: 5x + 5/2 = 0 | 5x + 5/2 = 0
5x = -5/2
x = -5/2 / 5
x = -1/2 |
Find x and y such that
1x + 3y = 24/5
9x + 9y = 297/5 | 1x + 3y = 24/5
9x + 9y = 297/5
Using elimination
9*(1x + 3y = 24/5)
1*(9x + 9y = 297/5)
9x + 27y = 216/5
9x + 9y = 297/5
Subtract equations
18y = -81/5
y = -81/5/18
y = -9/10
Substitute y
1x + 3(-9/10) = 24/5
1x = 15/2
x = 15/2/1
x = 15/2 |
Solve simultaneously:
1x + 9y = 453/20
2x + 9y = 219/10 | 1x + 9y = 453/20
2x + 9y = 219/10
Using elimination
2*(1x + 9y = 453/20)
1*(2x + 9y = 219/10)
2x + 18y = 453/10
2x + 9y = 219/10
Subtract equations
9y = 117/5
y = 117/5/9
y = 13/5
Substitute y
1x + 9(13/5) = 453/20
1x = -3/4
x = -3/4/1
x = -3/4 |
Determine x in 1x + 3/7 = 0 | 1x + 3/7 = 0
1x = -3/7
x = -3/7 / 1
x = -3/7 |
Solve the equations:
4x + 10y = -206/3
1x + 5y = -94/3 | 4x + 10y = -206/3
1x + 5y = -94/3
Using elimination
1*(4x + 10y = -206/3)
4*(1x + 5y = -94/3)
4x + 10y = -206/3
4x + 20y = -376/3
Subtract equations
-10y = 170/3
y = 170/3/-10
y = -17/3
Substitute y
4x + 10(-17/3) = -206/3
4x = -12
x = -12/4
x = -3 |
Compute the solution of x^3 - 16/7x^2 - 95/7x = 0 | x^3 - 16/7x^2 - 95/7x = 0
(x - 5)(x - -19/7)(x - 0) = 0
x - 5 = 0
x - -19/7 = 0
x - 0 = 0
x = 5
x = -19/7
x = 0 |
Compute the solution of 6x + 48 = 0 | 6x + 48 = 0
6x = -48
x = -48 / 6
x = -8 |
Find x in x^3 - 17x^2 + 134/25x + 4256/25 = 0 | x^3 - 17x^2 + 134/25x + 4256/25 = 0
(x - 19/5)(x - 16)(x - -14/5) = 0
x - 19/5 = 0
x - 16 = 0
x - -14/5 = 0
x = 19/5
x = 16
x = -14/5 |
Find the solution to 10x - 50/3 = 0 | 10x - 50/3 = 0
10x = 50/3
x = 50/3 / 10
x = 5/3 |
Find x for 1x - 8/3 = 0 | 1x - 8/3 = 0
1x = 8/3
x = 8/3 / 1
x = 8/3 |
Determine x in x^3 + 179/30x^2 + 57/5x + 104/15 = 0 | x^3 + 179/30x^2 + 57/5x + 104/15 = 0
(x - -2)(x - -8/3)(x - -13/10) = 0
x - -2 = 0
x - -8/3 = 0
x - -13/10 = 0
x = -2
x = -8/3
x = -13/10 |
Solve 10x + 130/9 = 0 | 10x + 130/9 = 0
10x = -130/9
x = -130/9 / 10
x = -13/9 |
Solve x^2 - 14/9x + 13/81 = 0 | x^2 - 14/9x + 13/81 = 0
(x - 13/9)(x - 1/9) = 0
x - 13/9 = 0 or x - 1/9 = 0
x = 13/9
x = 1/9 |
Solve 7x + 2 = 0 | 7x + 2 = 0
7x = -2
x = -2 / 7
x = -2/7 |
Find the solution to x^3 + 149/40x^2 + 201/200x - 54/25 = 0 | x^3 + 149/40x^2 + 201/200x - 54/25 = 0
(x - 3/5)(x - -16/5)(x - -9/8) = 0
x - 3/5 = 0
x - -16/5 = 0
x - -9/8 = 0
x = 3/5
x = -16/5
x = -9/8 |
What value of x satisfies 5x - 90 = 0 | 5x - 90 = 0
5x = 90
x = 90 / 5
x = 18 |
What value of x satisfies x^3 - 16/3x^2 + 13/9x + 10/9 = 0 | x^3 - 16/3x^2 + 13/9x + 10/9 = 0
(x - -1/3)(x - 5)(x - 2/3) = 0
x - -1/3 = 0
x - 5 = 0
x - 2/3 = 0
x = -1/3
x = 5
x = 2/3 |
Solve the system:
7x + 1y = -51/8
7x + 2y = -53/8 | 7x + 1y = -51/8
7x + 2y = -53/8
Using elimination
7*(7x + 1y = -51/8)
7*(7x + 2y = -53/8)
49x + 7y = -357/8
49x + 14y = -371/8
Subtract equations
-7y = 7/4
y = 7/4/-7
y = -1/4
Substitute y
7x + 1(-1/4) = -51/8
7x = -49/8
x = -49/8/7
x = -7/8 |
Solve x^2 - 9/2x + 5 = 0 | x^2 - 9/2x + 5 = 0
(x - 5/2)(x - 2) = 0
x - 5/2 = 0 or x - 2 = 0
x = 5/2
x = 2 |
Find x and y such that
1x + 7y = -173/4
8x + 2y = -22 | 1x + 7y = -173/4
8x + 2y = -22
Using elimination
8*(1x + 7y = -173/4)
1*(8x + 2y = -22)
8x + 56y = -346
8x + 2y = -22
Subtract equations
54y = -324
y = -324/54
y = -6
Substitute y
1x + 7(-6) = -173/4
1x = -5/4
x = -5/4/1
x = -5/4 |
Solve quickly: x^2 + 5/2x - 6 = 0 | x^2 + 5/2x - 6 = 0
(x - 3/2)(x - -4) = 0
x - 3/2 = 0 or x - -4 = 0
x = 3/2
x = -4 |
Find x in x^3 + 269/126x^2 + 101/189x + 13/378 = 0 | x^3 + 269/126x^2 + 101/189x + 13/378 = 0
(x - -1/9)(x - -1/6)(x - -13/7) = 0
x - -1/9 = 0
x - -1/6 = 0
x - -13/7 = 0
x = -1/9
x = -1/6
x = -13/7 |
Compute the solution of 2x - 3/4 = 0 | 2x - 3/4 = 0
2x = 3/4
x = 3/4 / 2
x = 3/8 |
What value of x satisfies x^2 + 31/2x + 21 = 0 | x^2 + 31/2x + 21 = 0
(x - -3/2)(x - -14) = 0
x - -3/2 = 0 or x - -14 = 0
x = -3/2
x = -14 |
Compute the solution of x^2 + 15/2x + 9 = 0 | x^2 + 15/2x + 9 = 0
(x - -3/2)(x - -6) = 0
x - -3/2 = 0 or x - -6 = 0
x = -3/2
x = -6 |
What value of x satisfies x^3 - 21/4x - 5/2 = 0 | x^3 - 21/4x - 5/2 = 0
(x - 5/2)(x - -1/2)(x - -2) = 0
x - 5/2 = 0
x - -1/2 = 0
x - -2 = 0
x = 5/2
x = -1/2
x = -2 |
Find x for x^3 - 81/35x^2 - 871/175x + 153/35 = 0 | x^3 - 81/35x^2 - 871/175x + 153/35 = 0
(x - -9/5)(x - 17/5)(x - 5/7) = 0
x - -9/5 = 0
x - 17/5 = 0
x - 5/7 = 0
x = -9/5
x = 17/5
x = 5/7 |
Determine x in 9x + 8 = 0 | 9x + 8 = 0
9x = -8
x = -8 / 9
x = -8/9 |
Solve simultaneously:
5x + 2y = 9/2
6x + 3y = 15/4 | 5x + 2y = 9/2
6x + 3y = 15/4
Using elimination
6*(5x + 2y = 9/2)
5*(6x + 3y = 15/4)
30x + 12y = 27
30x + 15y = 75/4
Subtract equations
-3y = 33/4
y = 33/4/-3
y = -11/4
Substitute y
5x + 2(-11/4) = 9/2
5x = 10
x = 10/5
x = 2 |
Solve simultaneously:
5x + 4y = 87/2
8x + 6y = 277/4 | 5x + 4y = 87/2
8x + 6y = 277/4
Using elimination
8*(5x + 4y = 87/2)
5*(8x + 6y = 277/4)
40x + 32y = 348
40x + 30y = 1385/4
Subtract equations
2y = 7/4
y = 7/4/2
y = 7/8
Substitute y
5x + 4(7/8) = 87/2
5x = 40
x = 40/5
x = 8 |
Find the solution to x^3 - 361/70x^2 + 181/35x + 4 = 0 | x^3 - 361/70x^2 + 181/35x + 4 = 0
(x - 14/5)(x - -1/2)(x - 20/7) = 0
x - 14/5 = 0
x - -1/2 = 0
x - 20/7 = 0
x = 14/5
x = -1/2
x = 20/7 |
Find x and y such that
6x + 10y = -56/3
4x + 10y = -148/9 | 6x + 10y = -56/3
4x + 10y = -148/9
Using elimination
4*(6x + 10y = -56/3)
6*(4x + 10y = -148/9)
24x + 40y = -224/3
24x + 60y = -296/3
Subtract equations
-20y = 24
y = 24/-20
y = -6/5
Substitute y
6x + 10(-6/5) = -56/3
6x = -20/3
x = -20/3/6
x = -10/9 |
Determine x in x^3 + 38/3x^2 - 485/3x - 300 = 0 | x^3 + 38/3x^2 - 485/3x - 300 = 0
(x - 9)(x - -20)(x - -5/3) = 0
x - 9 = 0
x - -20 = 0
x - -5/3 = 0
x = 9
x = -20
x = -5/3 |
Find x for x^2 + 11/6x - 13/18 = 0 | x^2 + 11/6x - 13/18 = 0
(x - 1/3)(x - -13/6) = 0
x - 1/3 = 0 or x - -13/6 = 0
x = 1/3
x = -13/6 |
Find x and y such that
6x + 9y = 48
9x + 4y = 53 | 6x + 9y = 48
9x + 4y = 53
Using elimination
9*(6x + 9y = 48)
6*(9x + 4y = 53)
54x + 81y = 432
54x + 24y = 318
Subtract equations
57y = 114
y = 114/57
y = 2
Substitute y
6x + 9(2) = 48
6x = 30
x = 30/6
x = 5 |
Determine x in 8x + 80/3 = 0 | 8x + 80/3 = 0
8x = -80/3
x = -80/3 / 8
x = -10/3 |
Solve simultaneously:
7x + 3y = -235/6
7x + 10y = -733/18 | 7x + 3y = -235/6
7x + 10y = -733/18
Using elimination
7*(7x + 3y = -235/6)
7*(7x + 10y = -733/18)
49x + 21y = -1645/6
49x + 70y = -5131/18
Subtract equations
-49y = 98/9
y = 98/9/-49
y = -2/9
Substitute y
7x + 3(-2/9) = -235/6
7x = -77/2
x = -77/2/7
x = -11/2 |
Solve x^3 + 1/3x^2 - 301/81x - 247/81 = 0 | x^3 + 1/3x^2 - 301/81x - 247/81 = 0
(x - -1)(x - -13/9)(x - 19/9) = 0
x - -1 = 0
x - -13/9 = 0
x - 19/9 = 0
x = -1
x = -13/9
x = 19/9 |
Determine x in x^3 - 136/35x^2 + 689/175x - 16/25 = 0 | x^3 - 136/35x^2 + 689/175x - 16/25 = 0
(x - 7/5)(x - 16/7)(x - 1/5) = 0
x - 7/5 = 0
x - 16/7 = 0
x - 1/5 = 0
x = 7/5
x = 16/7
x = 1/5 |
Find the solution to x^2 + 80/63x - 16/21 = 0 | x^2 + 80/63x - 16/21 = 0
(x - 4/9)(x - -12/7) = 0
x - 4/9 = 0 or x - -12/7 = 0
x = 4/9
x = -12/7 |
Compute the solution of x^2 - 127/7x + 240/7 = 0 | x^2 - 127/7x + 240/7 = 0
(x - 16)(x - 15/7) = 0
x - 16 = 0 or x - 15/7 = 0
x = 16
x = 15/7 |
Compute the solution of x^3 + 1/14x^2 - 793/175x - 187/50 = 0 | x^3 + 1/14x^2 - 793/175x - 187/50 = 0
(x - -7/5)(x - 17/7)(x - -11/10) = 0
x - -7/5 = 0
x - 17/7 = 0
x - -11/10 = 0
x = -7/5
x = 17/7
x = -11/10 |
Solve quickly: 5x + 35/2 = 0 | 5x + 35/2 = 0
5x = -35/2
x = -35/2 / 5
x = -7/2 |
What value of x satisfies x^3 + 515/168x^2 - 19/21x - 30/7 = 0 | x^3 + 515/168x^2 - 19/21x - 30/7 = 0
(x - -20/7)(x - -4/3)(x - 9/8) = 0
x - -20/7 = 0
x - -4/3 = 0
x - 9/8 = 0
x = -20/7
x = -4/3
x = 9/8 |
Find x for 3x - 3 = 0 | 3x - 3 = 0
3x = 3
x = 3 / 3
x = 1 |
Solve simultaneously:
6x + 10y = -78/35
7x + 3y = -351/35 | 6x + 10y = -78/35
7x + 3y = -351/35
Using elimination
7*(6x + 10y = -78/35)
6*(7x + 3y = -351/35)
42x + 70y = -78/5
42x + 18y = -2106/35
Subtract equations
52y = 312/7
y = 312/7/52
y = 6/7
Substitute y
6x + 10(6/7) = -78/35
6x = -54/5
x = -54/5/6
x = -9/5 |
Compute the solution of x^3 + 10x^2 + 433/49x - 72/49 = 0 | x^3 + 10x^2 + 433/49x - 72/49 = 0
(x - 1/7)(x - -8/7)(x - -9) = 0
x - 1/7 = 0
x - -8/7 = 0
x - -9 = 0
x = 1/7
x = -8/7
x = -9 |
Find x and y such that
1x + 5y = -53/4
9x + 4y = -909/20 | 1x + 5y = -53/4
9x + 4y = -909/20
Using elimination
9*(1x + 5y = -53/4)
1*(9x + 4y = -909/20)
9x + 45y = -477/4
9x + 4y = -909/20
Subtract equations
41y = -369/5
y = -369/5/41
y = -9/5
Substitute y
1x + 5(-9/5) = -53/4
1x = -17/4
x = -17/4/1
x = -17/4 |
What value of x satisfies x^3 - 55/4x^2 + 397/8x - 85/2 = 0 | x^3 - 55/4x^2 + 397/8x - 85/2 = 0
(x - 17/2)(x - 4)(x - 5/4) = 0
x - 17/2 = 0
x - 4 = 0
x - 5/4 = 0
x = 17/2
x = 4
x = 5/4 |
Find x for x^2 + 19/5x + 84/25 = 0 | x^2 + 19/5x + 84/25 = 0
(x - -7/5)(x - -12/5) = 0
x - -7/5 = 0 or x - -12/5 = 0
x = -7/5
x = -12/5 |
Solve the equations:
10x + 7y = 109/14
1x + 2y = 10/7 | 10x + 7y = 109/14
1x + 2y = 10/7
Using elimination
1*(10x + 7y = 109/14)
10*(1x + 2y = 10/7)
10x + 7y = 109/14
10x + 20y = 100/7
Subtract equations
-13y = -13/2
y = -13/2/-13
y = 1/2
Substitute y
10x + 7(1/2) = 109/14
10x = 30/7
x = 30/7/10
x = 3/7 |
Determine x in x^3 + 4/5x^2 - 1/25x - 4/125 = 0 | x^3 + 4/5x^2 - 1/25x - 4/125 = 0
(x - -4/5)(x - 1/5)(x - -1/5) = 0
x - -4/5 = 0
x - 1/5 = 0
x - -1/5 = 0
x = -4/5
x = 1/5
x = -1/5 |
Solve simultaneously:
10x + 1y = 83/4
1x + 4y = 64/5 | 10x + 1y = 83/4
1x + 4y = 64/5
Using elimination
1*(10x + 1y = 83/4)
10*(1x + 4y = 64/5)
10x + 1y = 83/4
10x + 40y = 128
Subtract equations
-39y = -429/4
y = -429/4/-39
y = 11/4
Substitute y
10x + 1(11/4) = 83/4
10x = 18
x = 18/10
x = 9/5 |
Find the solution to x^3 + 117/35x^2 - 72/5x + 324/35 = 0 | x^3 + 117/35x^2 - 72/5x + 324/35 = 0
(x - 6/7)(x - -6)(x - 9/5) = 0
x - 6/7 = 0
x - -6 = 0
x - 9/5 = 0
x = 6/7
x = -6
x = 9/5 |
Solve x^3 - 239/30x^2 + 103/5x - 171/10 = 0 | x^3 - 239/30x^2 + 103/5x - 171/10 = 0
(x - 3)(x - 19/6)(x - 9/5) = 0
x - 3 = 0
x - 19/6 = 0
x - 9/5 = 0
x = 3
x = 19/6
x = 9/5 |
End of preview. Expand in Data Studio
Algebra Equations Dataset
Overview
This dataset contains automatically generated algebra problems with step-by-step solutions. It is intended for training or testing models that solve equations and show intermediate reasoning steps.
The dataset is stored in JSON Lines (.jsonl) format, where each line represents one problem and its solution.
File
equations_dataset.jsonl
Each line contains:
{
"input": "<problem>",
"output": "<step-by-step solution>"
}
Equation Types
The dataset contains randomly generated:
- Linear equations
- Quadratic equations
- Cubic equations
- Systems of two linear equations
Example
{
"input": "Solve 3x - 6 = 0",
"output": "3x - 6 = 0
3x = 6
x = 6 / 3
x = 2"
}
Loading the Dataset
Example Python code:
import json
with open("equations_dataset.jsonl") as f:
for line in f:
data = json.loads(line)
print(data["input"])
print(data["output"])
Notes
- Problems are randomly generated.
- Solutions include clear algebraic steps.
- Fractional values may appear.
- Downloads last month
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