question stringlengths 12 86 | problem stringclasses 31
values | how_to_solve stringlengths 8 96 | answer stringlengths 1 24 |
|---|---|---|---|
Solve for x: log base 2 of x = 0 | Compute x from the log equation (integer-safe). | x = 2^0. | 1 |
Solve for x: -7(x + -4) = -49 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 11 |
What is 60% of 10? | Compute the percent value (integer-safe). | Compute 60/100 × 10. | 6 |
Solve for x: 2x^2 + 4x - 96 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | -8, 6 |
Solve for x: -12x + -28 = -244 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 18 |
Solve the system:
-3x + 4y = -15
2x + -1y = 5 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=1, y=-3 |
Solve for x: (-8/1)x + 3 = 3 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 0 |
If each item costs 12 dollars and the total cost is -144, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -12 |
Solve: |4x + 8| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ 2 |
Simplify -49/7 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | -7 |
Simplify: 2x + -3x + 3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x + 3y |
Solve for x: 4^x = 256 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 4 yields 256. | 4 |
Solve: 2x + 13 ≥ -17 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -15 |
What is -170 mod 28 (remainder after division)? | Compute remainder when a is divided by b. | Divide -170 by 28 and take the integer remainder 0..27. | 26 |
What is 136 - 223? | Subtract the second number from the first. | Subtract 223 from 136. | -87 |
What is 40 ÷ -5? | Divide evenly (negative allowed). | Divide 40 by -5. | -8 |
Solve: |-8x + -5| = 2 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |6x + 14| = 8 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -1 |
Simplify: 3x + -6x + -2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x - 2y |
What is -18 ÷ -3? | Divide evenly. | Divide -18 by -3. | 6 |
Solve for x: -6(x + 4) = 6 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
Solve for x: 1x^3 + -1x^2 + -10x + -8 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | -1, 4, -2 |
Solve for x: (-1x + 45)/(6x + 5) = -1 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | -10 |
Solve for x: (-5x + 135)/(6x + -9) = 2 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | 9 |
What is 0 ÷ 25? | Divide evenly (negative allowed). | Divide 0 by 25. | 0 |
Solve for x: 1x^3 + 8x^2 + 15x + 0 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | 0, -5, -3 |
Solve for x: log base 4 of x = 1 | Compute x from the log equation (integer-safe). | x = 4^1. | 4 |
Simplify: 3x + -7x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x + 8y |
What is -5^5? | Evaluate the integer exponent. | Multiply -5 by itself 5 times (0th power = 1). | -3125 |
Solve: |-3x + 6| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 6 |
Solve for x: 3x^2 + 0x + -192 = 0 | Quadratic with integer roots and non-unit leading coefficient. | Factor or use quadratic formula; roots are integers. | -8, 8 |
Solve: 2x + -12 < 22 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 17 |
Solve for x: (-6x + 189)/(-4x + -9) = -3 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | 9 |
Solve for x: sqrt(-5x + 71) = 11 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | -10 |
Solve for x: 4^x = 64 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 4 yields 64. | 3 |
What is 31 × 23? | Multiply the numbers. | Multiply 31 by 23. | 713 |
What is 18 × -2? | Multiply the numbers. | Multiply 18 by -2. | -36 |
What is 185 mod 17 (remainder after division)? | Compute remainder when a is divided by b. | Divide 185 by 17 and take the integer remainder 0..16. | 15 |
What is 4^3? | Evaluate the integer exponent. | Multiply 4 by itself 3 times (0th power = 1). | 64 |
What is 8 mod 22 (remainder after division)? | Compute remainder when a is divided by b. | Divide 8 by 22 and take the integer remainder 0..21. | 8 |
Solve for x: 1x^3 + -6x^2 + 8x + 0 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | 0, 2, 4 |
Solve for x: 3x^2 + 18x - 21 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 1, -7 |
Solve for x: 8(x + -1) = -40 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -4 |
What is -90 ÷ -6? | Divide evenly. | Divide -90 by -6. | 15 |
Solve for x: -3(x + 6) = -57 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 13 |
Solve the system:
3x + 4y + -1z = 20
-3x + -3y + 0z = -15
3x + 3y + -1z = 20 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=5, y=0, z=-5 |
Solve for x: -3(x + 13) = -21 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
Simplify -8/8 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | -1 |
Solve for x: 1x^3 + 0x^2 + -16x + 0 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | -4, 0, 4 |
Solve for x: (5x + -39)/(4x + -6) = 3 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | -3 |
Find one integer solution to 10x + 11y = 13 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=-2, y=3 |
Solve for x: 5^x = 3125 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 5 yields 3125. | 5 |
Solve for x: 2x^2 + 4x + -16 = 0 | Quadratic with integer roots and non-unit leading coefficient. | Factor or use quadratic formula; roots are integers. | 2, -4 |
What is 79% of 800? | Compute the percent value (integer-safe). | Compute 79/100 × 800. | 632 |
Solve for x: sqrt(5x + 146) = 11 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | -5 |
Find one integer solution to 8x + 4y = 56 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=8, y=-2 |
What is 1^1? | Evaluate the integer exponent. | Multiply 1 by itself 1 times (0th power = 1). | 1 |
Solve for x: (-7x + -44)/(-2x + 0) = -2 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | -4 |
Find one integer solution to 7x + 8y = -68 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=-4, y=-5 |
Solve for x: -3x^2 + 18x + 0 = 0 | Quadratic with integer roots and non-unit leading coefficient. | Factor or use quadratic formula; roots are integers. | 0, 6 |
Solve for x: (-4x + -9)/(-2x + 3) = 5 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | 4 |
Solve for x: (-9/7)x + 20 = -16 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 28 |
What is -114 ÷ -6? | Divide evenly. | Divide -114 by -6. | 19 |
Solve for x: 3(x + 1) = -24 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -9 |
Simplify -84/12 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | -7 |
Solve for x: 1x^2 + 4x - 5 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 1, -5 |
Solve for x: 1x^3 + 3x^2 + -10x + -24 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | -2, 3, -4 |
Solve for x: (4x + -1)/(-7x + 10) = -1 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | 3 |
Simplify: -1x + 5x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x + 2y |
Solve for x: 5^x = 15625 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 5 yields 15625. | 6 |
Solve: |-7x + 11| ≤ 19 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 4 |
Solve the system:
-2x + -2y = 18
-2x + 2y = -2 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=-4, y=-5 |
What is -220 ÷ 20? | Divide evenly. | Divide -220 by 20. | -11 |
Solve: |3x + 10| = 20 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -10 |
Solve for x: 5x + -7 = 58 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 13 |
What is 45 ÷ -9? | Divide evenly (negative allowed). | Divide 45 by -9. | -5 |
What is -150 ÷ 15? | Divide evenly. | Divide -150 by 15. | -10 |
Find one integer solution to 1x + 5y = 53 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=3, y=10 |
What is 176 - 110? | Subtract the second number from the first. | Subtract 110 from 176. | 66 |
What is -12 ÷ -4? | Divide evenly. | Divide -12 by -4. | 3 |
Solve the system:
5x + -5y = 20
-4x + -5y = 11 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=1, y=-3 |
Solve for x: -3x^2 + 0x + 3 = 0 | Quadratic with integer roots and non-unit leading coefficient. | Factor or use quadratic formula; roots are integers. | 1, -1 |
Find smallest non-negative x such that 8x ≡ 7 (mod 19) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 8 |
What is 420 ÷ -21? | Divide evenly (negative allowed). | Divide 420 by -21. | -20 |
Solve: -2x + 12 > 38 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -13 |
Solve for x: sqrt(-5x + 5) = 5 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | -4 |
Solve for x: 1x^3 + -4x^2 + -1x + 4 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | 4, 1, -1 |
What is 20 + 224? | Add the two numbers. | Add 20 and 224. | 244 |
Find smallest non-negative x such that 18x ≡ 0 (mod 6) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 0 |
Solve for x: 3(x + 13) = 18 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -7 |
Convert the improper fraction 1/9 to a mixed number. | Convert to mixed number and simplify the fractional part. | Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator. | 1/9 |
If each item costs 10 dollars and the total cost is 90, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 9 |
Solve for x: -1x^2 + 1x + 42 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 7, -6 |
Find one integer solution to 4x + 8y = 88 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=4, y=9 |
What is 28 ÷ -4? | Divide evenly. | Divide 28 by -4. | -7 |
Find smallest non-negative x such that -14x ≡ 11 (mod 13) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 2 |
What is 5^4? | Evaluate the integer exponent. | Multiply 5 by itself 4 times (0th power = 1). | 625 |
What is -24% of 150? | Compute the percent value (integer-safe). | Compute -24/100 × 150. | -36 |
Solve for x: 1x^2 - 10x + 25 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 5, 5 |
Convert the improper fraction 91/10 to a mixed number. | Convert to mixed number and simplify the fractional part. | Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator. | 9 1/10 |
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