question stringlengths 12 86 | problem stringclasses 31 values | how_to_solve stringlengths 8 96 | answer stringlengths 1 24 |
|---|---|---|---|
What is 7^3? | Evaluate the integer exponent. | Multiply 7 by itself 3 times (0th power = 1). | 343 |
Find one integer solution to 6x + 12y = 0 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=10, y=-5 |
If each item costs 0 dollars and the total cost is 0, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 17 |
Solve for x: log base 5 of x = 5 | Compute x from the log equation (integer-safe). | x = 5^5. | 3125 |
Convert the improper fraction 39/9 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. | 4 1/3 |
Solve: -2x + -19 < -25 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 3 |
Solve for x: (5x + 9)/(-6x + -10) = -1 | Rational equation that reduces to a linear equation. | Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0). | -1 |
Solve for x: -10x + 29 = 109 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -8 |
What is -50% of 14? | Compute the percent value (integer-safe). | Compute -50/100 × 14. | -7 |
Solve: |7x + 16| ≤ 18 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 0 |
Simplify 8/2 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | 4 |
What is 102% of 0? | Compute the percent value (integer-safe). | Compute 102/100 × 0. | 0 |
Simplify -160/16 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | -10 |
Factor the polynomial: x^3 - 6x^2 + -7x - -60 | Factor cubic into linear integer factors if possible. | Find integer roots and factor as (x - r1)(x - r2)(x - r3). | (x - 4)(x - 5)(x - -3) |
Solve for x: 2x^2 - 14x - 16 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 8, -1 |
Solve for x: -2x^2 + 8x + 64 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 8, -4 |
What is 272 ÷ 16? | Divide evenly. | Divide 272 by 16. | 17 |
What is 11 × 8? | Multiply the numbers. | Multiply 11 by 8. | 88 |
Factor the polynomial: 1x^2 + -1x + -20 | Factor quadratic into integer linear factors. | Find integers r1 and r2 such that polynomial = (x - r1)(x - r2). | (x - 5)(x - -4) |
Simplify: -1x + -1x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -2x + 8y |
Solve the system:
1x + -4y = 7
3x + -5y = 21 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=7, y=0 |
Find smallest non-negative x such that 6x ≡ 7 (mod 11) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 3 |
Solve for x: log base 3 of x = 5 | Compute x from the log equation (integer-safe). | x = 3^5. | 243 |
Solve for x: (9/12)x + 3 = 57 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 72 |
Simplify: 5x + -6x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x - 3y |
Solve for x: 3^x = 9 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 3 yields 9. | 2 |
Solve: 7x + -2 > 110 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 16 |
What is 0 ÷ 15? | Divide evenly. | Divide 0 by 15. | 0 |
Solve for x: 4(x + -7) = -88 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
Solve for x: -3x + -22 = -25 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 1 |
Simplify: 1x + 2x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 3x + 2y |
Solve for x: sqrt(3x + 27) = 6 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | 3 |
Factor the polynomial: 1x^2 + 3x + 0 | Factor quadratic into integer linear factors. | Find integers r1 and r2 such that polynomial = (x - r1)(x - r2). | (x - 0)(x - -3) |
Solve for x: (4/12)x + -5 = -45 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | -120 |
Solve the system:
1x + -1y + 4z = -21
1x + -2y + 0z = 2
0x + 1y + -3z = 19 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=4, y=1, z=-6 |
Solve: -7x + 5 ≥ 82 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -11 |
Find smallest non-negative x such that 9x ≡ 4 (mod 5) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 1 |
What is 136% of 250? | Compute the percent value (integer-safe). | Compute 136/100 × 250. | 340 |
Solve: |4x + 10| ≤ 15 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ 1 |
What is 1^5? | Evaluate the integer exponent. | Multiply 1 by itself 5 times (0th power = 1). | 1 |
Solve: |6x + -13| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 5 |
Solve for x: sqrt(-3x + 76) = 7 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | 9 |
Find smallest non-negative x such that 19x ≡ 18 (mod 25) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 22 |
Solve for x: 1x^3 + 10x^2 + 31x + 30 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | -5, -3, -2 |
What is 3^1? | Evaluate the integer exponent. | Multiply 3 by itself 1 times (0th power = 1). | 3 |
Solve the system:
-5x + 5y = 15
-1x + -1y = 7 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=-5, y=-2 |
What is 36 × 3? | Multiply the numbers. | Multiply 36 by 3. | 108 |
Solve: |-8x + 2| ≤ 10 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 1 |
What is -3 ÷ 3? | Divide evenly. | Divide -3 by 3. | -1 |
Factor the polynomial: 1x^2 + 7x + 6 | Factor quadratic into integer linear factors. | Find integers r1 and r2 such that polynomial = (x - r1)(x - r2). | (x - -6)(x - -1) |
Solve for x: sqrt(-6x + 45) = 9 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | -6 |
Solve for x: -7x + -21 = -35 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 2 |
Solve for x: 12x + -22 = -118 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -8 |
What is -78 - 67? | Subtract the second number from the first. | Subtract 67 from -78. | -145 |
What is -252 ÷ 21? | Divide evenly. | Divide -252 by 21. | -12 |
Solve for x: 3x^2 - 9x + 6 = 0 | Solve the quadratic equation with integer roots. | Factor or use quadratic formula (should factor cleanly). | 1, 2 |
Solve for x: 2^x = 2 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 2 yields 2. | 1 |
Simplify: 6x + -3x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 3x - 7y |
Solve for x: -1x + 20 = 30 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -10 |
Find smallest non-negative x such that 8x ≡ 4 (mod 12) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 2 |
Solve the system:
3x + 1y + 0z = 18
1x + -4y + -4z = -44
1x + 1y + 3z = 28 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=4, y=6, z=6 |
Factor the polynomial: 1x^2 + -6x + 0 | Factor quadratic into integer linear factors. | Find integers r1 and r2 such that polynomial = (x - r1)(x - r2). | (x - 6)(x - 0) |
What is 19% of 900? | Compute the percent value (integer-safe). | Compute 19/100 × 900. | 171 |
Solve for x: -8x + 28 = 52 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -3 |
Solve: |3x + -1| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve the system:
-1x + -3y + 1z = 2
2x + 4y + 4z = -32
-2x + -1y + 0z = 9 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=-4, y=-1, z=-5 |
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 104 ÷ -13? | Divide evenly. | Divide 104 by -13. | -8 |
What is 29% of 500? | Compute the percent value (integer-safe). | Compute 29/100 × 500. | 145 |
What is 166 mod 28 (remainder after division)? | Compute remainder when a is divided by b. | Divide 166 by 28 and take the integer remainder 0..27. | 26 |
Simplify -18/2 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | -9 |
Solve for x: 1x^3 + 13x^2 + 56x + 80 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | -4, -5, -4 |
What is -238 - 34? | Subtract the second number from the first. | Subtract 34 from -238. | -272 |
Solve for x: 1x^3 + 3x^2 + -4x + -12 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | -3, 2, -2 |
Simplify: 5x + -8x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x - 3y |
Convert the improper fraction 112/9 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. | 12 4/9 |
Solve for x: log base 2 of x = 0 | Compute x from the log equation (integer-safe). | x = 2^0. | 1 |
Find one integer solution to 11x + 3y = -4 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=-2, y=6 |
Solve for x: sqrt(-6x + 58) = 4 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | 7 |
Convert the improper fraction -19/2 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 -1/2 |
What is 231 ÷ 21? | Divide evenly. | Divide 231 by 21. | 11 |
Solve for x: (-7/7)x + -13 = -48 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 35 |
What is -13 × 45? | Multiply the numbers. | Multiply -13 by 45. | -585 |
Solve for x: (4/11)x + 9 = 57 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 132 |
Convert the improper fraction 17/8 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. | 2 1/8 |
What is 133 ÷ 7? | Divide evenly (negative allowed). | Divide 133 by 7. | 19 |
Solve for x: sqrt(2x + 46) = 8 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | 9 |
Solve for x: log base 3 of x = 1 | Compute x from the log equation (integer-safe). | x = 3^1. | 3 |
If each item costs 5 dollars and the total cost is 75, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 15 |
Solve for x: 8(x + -8) = -72 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -1 |
What is 195 ÷ -13? | Divide evenly (negative allowed). | Divide 195 by -13. | -15 |
Solve for x: -2x^2 + -2x + 4 = 0 | Quadratic with integer roots and non-unit leading coefficient. | Factor or use quadratic formula; roots are integers. | 1, -2 |
What is 418 ÷ -22? | Divide evenly. | Divide 418 by -22. | -19 |
What is -56 ÷ -8? | Divide evenly. | Divide -56 by -8. | 7 |
Solve for x: 4x^2 + -12x + -72 = 0 | Quadratic with integer roots and non-unit leading coefficient. | Factor or use quadratic formula; roots are integers. | 6, -3 |
What is 240 ÷ 30? | Divide evenly. | Divide 240 by 30. | 8 |
What is 4^5? | Evaluate the integer exponent. | Multiply 4 by itself 5 times (0th power = 1). | 1024 |
Solve for x: -1(x + 12) = -19 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 7 |
Solve: 4x + 2 < 70 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 17 |
What is -35% of 60? | Compute the percent value (integer-safe). | Compute -35/100 × 60. | -21 |
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All Mathematical Reasoning-750000
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Contents
addsubmuldivlinear_eqtwo_step_eqfractionexponentinequalityword_algebraquadraticsystem_2x2abs_eqpercentmodsimplify_exprmixed_fractionneg_divlinear_fraction_eqrational_eqquadratic_nonunitcubic_int_rootsystem_3x3diophantineexponential_eqlog_eqradical_eqcongruence_modabsolute_ineqpolynomial_factor
Synthetic algebra-heavy math reasoning dataset.
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