question stringlengths 12 86 | problem stringclasses 31
values | how_to_solve stringlengths 8 96 | answer stringlengths 1 24 |
|---|---|---|---|
What is -90 ÷ 30? | Divide evenly (negative allowed). | Divide -90 by 30. | -3 |
Simplify: -4x + 5x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 1x - 7y |
Solve: |-3x + 6| ≤ 20 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 8 |
Solve for x: (-8/9)x + -14 = -22 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 9 |
Solve for x: 10x + 6 = 46 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 4 |
Solve for x: 2^x = 4 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 2 yields 4. | 2 |
What is 44% of 225? | Compute the percent value (integer-safe). | Compute 44/100 × 225. | 99 |
Convert the improper fraction 13/9 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 4/9 |
What is -84 - -29? | Subtract the second number from the first. | Subtract -29 from -84. | -55 |
Solve: 3x + 17 < 50 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 11 |
Solve for x: (5/2)x + 5 = 55 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 20 |
Solve for x: 1x^3 + -1x^2 + -6x + 0 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | 0, 3, -2 |
What is -2 × -40? | Multiply the numbers. | Multiply -2 by -40. | 80 |
What is -494 ÷ -26? | Divide evenly (negative allowed). | Divide -494 by -26. | 19 |
Solve for x: sqrt(-1x + 123) = 11 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | 2 |
Solve the system:
-3x + 3y = -36
4x + -1y = 27 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=5, y=-7 |
What is 280 ÷ -14? | Divide evenly (negative allowed). | Divide 280 by -14. | -20 |
Solve for x: sqrt(-6x + -14) = 2 | Radical equation; return integer solution if it exists. | Square both sides to get ax + b = c^2, then solve. | -3 |
Solve for x: log base 3 of x = 1 | Compute x from the log equation (integer-safe). | x = 3^1. | 3 |
Solve: 4x + 12 ≥ 12 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 0 |
What is 25% of 12? | Compute the percent value (integer-safe). | Compute 25/100 × 12. | 3 |
Solve for x: 3^x = 243 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 3 yields 243. | 5 |
Solve for x: 2^x = 16 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 2 yields 16. | 4 |
Solve: |7x + 11| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is 213 - 32? | Subtract the second number from the first. | Subtract 32 from 213. | 181 |
What is 148 mod 3 (remainder after division)? | Compute remainder when a is divided by b. | Divide 148 by 3 and take the integer remainder 0..2. | 1 |
Solve for x: -1x + -4 = -16 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 12 |
If each item costs 20 dollars and the total cost is 20, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 1 |
Solve for x: -10x + -7 = -27 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 2 |
Solve: 2x + 20 < 16 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -2 |
What is 245 - 118? | Subtract the second number from the first. | Subtract 118 from 245. | 127 |
Factor the polynomial: x^3 - 0x^2 + -13x - 12 | Factor cubic into linear integer factors if possible. | Find integer roots and factor as (x - r1)(x - r2)(x - r3). | (x - -3)(x - -1)(x - 4) |
Solve the system:
5x + -1y = 15
1x + -3y = 31 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=1, y=-10 |
Solve for x: log base 2 of x = 4 | Compute x from the log equation (integer-safe). | x = 2^4. | 16 |
Solve for x: 4^x = 4 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 4 yields 4. | 1 |
Simplify 192/16 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | 12 |
What is 32 × 1? | Multiply the numbers. | Multiply 32 by 1. | 32 |
What is 18 × -14? | Multiply the numbers. | Multiply 18 by -14. | -252 |
Solve for x: (10/6)x + -18 = 132 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 90 |
Solve for x: (10/9)x + 13 = -77 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | -81 |
What is -203 - 93? | Subtract the second number from the first. | Subtract 93 from -203. | -296 |
What is -55 + -37? | Add the two numbers. | Add -55 and -37. | -92 |
What is -93 + 87? | Add the two numbers. | Add -93 and 87. | -6 |
Solve for x: 5x + -23 = 32 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
What is 4^3? | Evaluate the integer exponent. | Multiply 4 by itself 3 times (0th power = 1). | 64 |
Solve for x: 1x^3 + -2x^2 + -3x + 0 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | 3, -1, 0 |
Solve for x: -1(x + 3) = 11 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -14 |
Simplify -48/12 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | -4 |
If each item costs 15 dollars and the total cost is -225, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -15 |
What is -128 + -271? | Add the two numbers. | Add -128 and -271. | -399 |
Find one integer solution to 1x + 6y = -39 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=3, y=-7 |
Solve the system:
-2x + -5y = 28
-3x + -5y = 37 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=-9, y=-2 |
Simplify: 6x + 0x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 6x - 4y |
Solve: |-6x + 16| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 3 ≤ x ≤ 3 |
Solve the system:
2x + -3y + -4z = -10
3x + -1y + -3z = -10
-4x + 2y + 3z = 19 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=-5, y=4, z=-3 |
Solve the system:
-4x + 4y = -44
2x + -4y = 26 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=9, y=-2 |
What is 134 mod 4 (remainder after division)? | Compute remainder when a is divided by b. | Divide 134 by 4 and take the integer remainder 0..3. | 2 |
Solve for x: -7(x + 2) = 56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -10 |
Solve the system:
1x + 0y + 2z = -14
-2x + -3y + -2z = 29
-4x + 3y + -1z = 19 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=-6, y=-3, z=-4 |
Solve: |5x + -12| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 4^x = 4 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 4 yields 4. | 1 |
Solve for x: 3^x = 27 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 3 yields 27. | 3 |
Solve: |1x + -10| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 8 ≤ x ≤ 12 |
Solve the system:
-1x + 0y + -1z = 7
-4x + -2y + 3z = -4
2x + -3y + 2z = 1 | Find integer x,y,z satisfying the linear system. | Use elimination or Cramer's rule (matrix is invertible). | x=-1, y=-5, z=-6 |
Solve for x: (-6/5)x + -16 = -76 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 50 |
Find one integer solution to 1x + 8y = -41 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=7, y=-6 |
Solve: |-4x + 17| ≤ 19 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 9 |
What is -24 + 204? | Add the two numbers. | Add -24 and 204. | 180 |
What is 95 mod 28 (remainder after division)? | Compute remainder when a is divided by b. | Divide 95 by 28 and take the integer remainder 0..27. | 11 |
Solve for x: 6(x + 4) = 90 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 11 |
What is -38 + 268? | Add the two numbers. | Add -38 and 268. | 230 |
Solve: |6x + -3| ≤ 0 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
Solve for x: (6/9)x + -8 = 4 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | 18 |
What is 125 mod 14 (remainder after division)? | Compute remainder when a is divided by b. | Divide 125 by 14 and take the integer remainder 0..13. | 13 |
Solve for x: 1x^3 + -15x^2 + 75x + -125 = 0 | Cubic polynomial factorable to (x - r1)(x - r2)(x - r3). | Find integer root by rational root theorem then factor. | 5, 5, 5 |
Solve the system:
2x + -1y = 7
-4x + -5y = -49 | Find integer x and y that satisfy both equations. | Use substitution or elimination. | x=6, y=5 |
What is 51 × -6? | Multiply the numbers. | Multiply 51 by -6. | -306 |
Solve for x: 1x^3 + -2x^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 |
What is 45% of 40? | Compute the percent value (integer-safe). | Compute 45/100 × 40. | 18 |
Solve for x: 5^x = 1 | Solve the exponential equation for integer x. | Find x such that repeated multiplication of 5 yields 1. | 0 |
What is 52 ÷ -26? | Divide evenly (negative allowed). | Divide 52 by -26. | -2 |
Solve for x: (-7/8)x + -2 = 89 | Linear equation with fractional coefficient. | Subtract c then multiply by b/a (watch sign). | -104 |
Solve for x: -12x + 19 = -161 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 15 |
What is 144 ÷ 8? | Divide evenly. | Divide 144 by 8. | 18 |
What is 20 × 13? | Multiply the numbers. | Multiply 20 by 13. | 260 |
What is -6^1? | Evaluate the integer exponent. | Multiply -6 by itself 1 times (0th power = 1). | -6 |
Find one integer solution to 10x + 7y = 28 | Linear Diophantine equation (return one integer pair). | Find any particular solution (here constructed). | x=7, y=-6 |
Simplify 42/14 | Reduce the fraction to simplest form. | Divide numerator and denominator by their GCD and normalize sign. | 3 |
Convert the improper fraction 49/4 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 1/4 |
What is 0 ÷ -29? | Divide evenly (negative allowed). | Divide 0 by -29. | 0 |
Solve for x: 7(x + 4) = 14 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -2 |
What is -5^3? | Evaluate the integer exponent. | Multiply -5 by itself 3 times (0th power = 1). | -125 |
Solve: 4x + 12 ≤ 52 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 10 |
What is -143 mod 29 (remainder after division)? | Compute remainder when a is divided by b. | Divide -143 by 29 and take the integer remainder 0..28. | 2 |
Solve for x: log base 4 of x = 3 | Compute x from the log equation (integer-safe). | x = 4^3. | 64 |
Find smallest non-negative x such that -7x ≡ 1 (mod 3) | Solve linear congruence. | Use gcd and modular inverse on reduced modulus (if solution exists). | 2 |
What is 208 + -192? | Add the two numbers. | Add 208 and -192. | 16 |
Solve for x: (2x + 46)/(-3x + 8) = 4 | 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: 4x + 0 = -60 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -15 |
Solve: |-7x + -10| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
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