question stringlengths 16 86 | problem stringclasses 8
values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve for x: -3x + 29 = 83 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -18 |
Solve: |4x + -8| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 6, -2 |
What is 82% of 350? | Compute the percent value (integer-safe). | Compute 82/100 × 350. | 287 |
Solve for x: -5x + -21 = -41 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 4 |
What is -32% of 0? | Compute the percent value (integer-safe). | Compute -32/100 × 0. | 0 |
Solve: |5x + -1| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 1 |
Solve: |1x + 15| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -8, -22 |
Solve: |1x + 7| ≤ 9 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -16 ≤ x ≤ 2 |
Solve for x: -7(x + 14) = -98 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 0 |
Solve for x: -7(x + -5) = 49 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -2 |
Solve: |5x + 19| ≤ 3 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ -4 |
Solve: |-7x + -14| ≤ 8 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -1 |
If each item costs 10 dollars and the total cost is 100, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 10 |
Simplify: 4x + -8x + 6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x + 6y |
Solve: |-4x + 11| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 6 |
Solve: |7x + -1| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 0 |
What is -34% of 0? | Compute the percent value (integer-safe). | Compute -34/100 × 0. | 0 |
What is 15% of 200? | Compute the percent value (integer-safe). | Compute 15/100 × 200. | 30 |
Solve: -3x + 16 < -14 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 10 |
Solve for x: -10x + 22 = 42 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -2 |
Simplify: -8x + -6x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -14x - 1y |
Simplify: 6x + -1x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 5x + 4y |
Simplify: 1x + 8x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 9x - 8y |
Solve: -7x + -19 ≥ -103 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 12 |
Solve for x: -5(x + 11) = -85 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 6 |
Solve for x: 6x + -12 = -132 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -20 |
Solve: |6x + -4| ≤ 20 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 4 |
Solve: 9x + 6 ≤ -156 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -18 |
Solve: |-7x + -8| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 4(x + 6) = 28 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 1 |
Solve: -1x + 12 ≤ 9 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 3 |
Solve: |6x + 19| ≤ 16 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ -1 |
Solve for x: 3x + 15 = 33 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 6 |
Solve: |-1x + 7| = 4 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 3, 11 |
What is 79% of 500? | Compute the percent value (integer-safe). | Compute 79/100 × 500. | 395 |
Solve: |-2x + 6| ≤ 5 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 5 |
What is 143% of 700? | Compute the percent value (integer-safe). | Compute 143/100 × 700. | 1001 |
What is -25% of 24? | Compute the percent value (integer-safe). | Compute -25/100 × 24. | -6 |
If each item costs 13 dollars and the total cost is 377, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 29 |
Solve: |-5x + -20| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ -4 |
Solve: |6x + 6| = 19 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |5x + -7| = 13 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 4 |
Solve: -7x + -11 ≤ -137 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 18 |
Solve for x: 7(x + -6) = 7 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 7 |
If each item costs 5 dollars and the total cost is 55, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 11 |
Solve: |4x + 13| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -5 |
Solve: 2x + 0 ≥ -14 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -7 |
Solve for x: -8(x + -3) = -56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 10 |
Solve: -2x + -5 ≥ -29 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 12 |
Simplify: 3x + -4x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x + 8y |
Solve: -1x + -4 ≤ 1 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -5 |
Simplify: -4x + 6x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x - 1y |
What is -40% of 5? | Compute the percent value (integer-safe). | Compute -40/100 × 5. | -2 |
What is -10% of 70? | Compute the percent value (integer-safe). | Compute -10/100 × 70. | -7 |
What is 62% of 450? | Compute the percent value (integer-safe). | Compute 62/100 × 450. | 279 |
Simplify: -6x + 4x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -2x - 8y |
Simplify: 4x + 5x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 9x - 6y |
Solve for x: 11x + 2 = 145 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 13 |
Solve: 5x + 13 ≥ -37 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -10 |
If each item costs 19 dollars and the total cost is 95, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 5 |
Solve: |-6x + 5| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 1 |
Solve for x: 1(x + -2) = 0 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 2 |
Solve: |7x + 19| ≤ 5 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -2 |
Solve for x: -9x + 10 = 37 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -3 |
Solve for x: 5(x + -11) = -30 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 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. | -3 |
Solve for x: 5(x + -4) = -95 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
Solve: 1x + 5 ≥ 2 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -3 |
Solve: |2x + -12| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 15, -3 |
Solve for x: 10x + 0 = 110 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
Solve for x: -3x + 0 = 30 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -10 |
Solve for x: 4x + 22 = 90 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 17 |
If each item costs 16 dollars and the total cost is 336, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 21 |
Solve for x: -9x + 17 = -82 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
Solve: |1x + 14| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 3, -31 |
Solve: 5x + 20 ≥ 85 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 13 |
Solve for x: 5x + 17 = -8 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -5 |
Simplify: 1x + 4x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 5x - 8y |
What is -22% of 50? | Compute the percent value (integer-safe). | Compute -22/100 × 50. | -11 |
Solve: |-7x + 6| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is 44% of 75? | Compute the percent value (integer-safe). | Compute 44/100 × 75. | 33 |
Solve: -2x + -18 ≥ -10 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -4 |
Solve: |-8x + 2| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 3(x + 14) = 9 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -11 |
Solve: -2x + -15 ≤ -7 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -4 |
Solve for x: 7x + -24 = -59 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -5 |
Solve: 2x + 0 ≥ 8 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 4 |
Solve: |-1x + -6| ≤ 5 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -11 ≤ x ≤ -1 |
Solve: |3x + -14| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs 19 dollars and the total cost is 247, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 13 |
Simplify: -3x + 4x + 0y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 1x |
What is 141% of 500? | Compute the percent value (integer-safe). | Compute 141/100 × 500. | 705 |
Solve for x: 6x + 1 = -65 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -11 |
Solve: |1x + 15| ≤ 19 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -34 ≤ x ≤ 4 |
Solve: |-4x + 6| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 3 |
What is -41% of 200? | Compute the percent value (integer-safe). | Compute -41/100 × 200. | -82 |
Solve: |6x + 16| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
Solve: |-1x + -12| ≤ 0 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -12 ≤ x ≤ -12 |
Solve: |5x + 12| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ 1 |
Solve: |-2x + 3| = 2 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
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