question stringlengths 16 86 | problem stringclasses 8
values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve: |-2x + -12| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -13 ≤ x ≤ 1 |
If each item costs 3 dollars and the total cost is 54, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 18 |
Solve: 2x + -13 < -43 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -15 |
Solve for x: 1x + -30 = -42 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -12 |
Solve: |7x + -10| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
Solve: |-2x + 13| = 20 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |5x + 15| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: 2x + -2x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7y |
Solve for x: 4(x + 0) = -16 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -4 |
If each item costs -10 dollars and the total cost is 130, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -13 |
What is -4% of 0? | Compute the percent value (integer-safe). | Compute -4/100 × 0. | 0 |
If each item costs 7 dollars and the total cost is -112, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -16 |
Solve: |-1x + -19| ≤ 18 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -37 ≤ x ≤ -1 |
What is -37% of 700? | Compute the percent value (integer-safe). | Compute -37/100 × 700. | -259 |
If each item costs 4 dollars and the total cost is -24, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -6 |
Solve: |-1x + -14| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -18 ≤ x ≤ -10 |
Solve: |-2x + -3| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -1 |
Solve: |3x + -14| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 3 |
Solve: |4x + 18| ≤ 20 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -9 ≤ x ≤ 0 |
Solve for x: -8x + -4 = -108 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 13 |
Solve for x: 8x + -27 = -187 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -20 |
Solve: |-4x + -9| ≤ 0 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
Solve: |-6x + -10| ≤ 3 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -2 |
Solve: |4x + -10| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is 95% of 120? | Compute the percent value (integer-safe). | Compute 95/100 × 120. | 114 |
Solve for x: -5x + -17 = 43 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -12 |
Solve for x: 3(x + 10) = 63 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 11 |
Solve: |4x + -13| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 6 |
What is 64% of 225? | Compute the percent value (integer-safe). | Compute 64/100 × 225. | 144 |
Solve for x: -7x + -18 = 38 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -8 |
Solve for x: 5x + 4 = 79 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 15 |
Solve for x: -12x + 26 = -58 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 7 |
Solve: |-6x + -1| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 12x + -13 = -133 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -10 |
Solve for x: -1(x + 14) = -29 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 15 |
Solve for x: 3x + 2 = -49 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -17 |
Simplify: 7x + 3x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 10x + 8y |
Solve: |3x + 1| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ 5 |
What is -49% of 900? | Compute the percent value (integer-safe). | Compute -49/100 × 900. | -441 |
What is 97% of 100? | Compute the percent value (integer-safe). | Compute 97/100 × 100. | 97 |
Solve: |3x + -14| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-3x + -5| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ 2 |
Simplify: 1x + 4x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 5x - 4y |
Solve: |-3x + 12| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 8 |
What is -24% of 200? | Compute the percent value (integer-safe). | Compute -24/100 × 200. | -48 |
Solve for x: -4(x + -14) = 80 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
Solve: |-1x + 5| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -12, 22 |
Solve: |3x + 14| = 1 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -5 |
Solve: |5x + -11| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |5x + -4| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 2 |
Solve: |-2x + 12| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -3, 15 |
Solve: |-5x + -2| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 2 |
Solve: |1x + -18| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 4 ≤ x ≤ 32 |
Simplify: 8x + 3x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 11x + 2y |
Solve: |1x + 19| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -21 ≤ x ≤ -17 |
Solve for x: 5(x + 5) = -45 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -14 |
Simplify: 6x + -4x + 5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x + 5y |
Solve: |-6x + 1| = 14 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs 8 dollars and the total cost is 168, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 21 |
Solve: |3x + -7| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 7 |
Solve: |-7x + -16| ≤ 5 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -2 |
Solve: |-2x + 13| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 5, 8 |
Simplify: 0x + 3x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 3x + 8y |
Solve: -3x + 8 < 20 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -4 |
Solve: |7x + -15| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 9x + 7 = 97 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 10 |
If each item costs 1 dollars and the total cost is 4, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 4 |
Solve for x: 7(x + -4) = 42 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 10 |
Simplify: -3x + 5x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x - 4y |
Solve for x: 10x + 30 = -30 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -6 |
Solve: -4x + 1 ≥ -39 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 10 |
Solve for x: 4(x + -3) = -56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -11 |
Solve: |-3x + -16| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ -4 |
If each item costs -10 dollars and the total cost is 200, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -20 |
What is 67% of 1000? | Compute the percent value (integer-safe). | Compute 67/100 × 1000. | 670 |
What is 100% of 1? | Compute the percent value (integer-safe). | Compute 100/100 × 1. | 1 |
What is 9% of 200? | Compute the percent value (integer-safe). | Compute 9/100 × 200. | 18 |
Solve: |-3x + -5| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: -8x + -8x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -16x - 8y |
What is 75% of 32? | Compute the percent value (integer-safe). | Compute 75/100 × 32. | 24 |
If each item costs 10 dollars and the total cost is 60, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 6 |
Solve for x: -12x + -18 = 66 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -7 |
Solve: |-6x + 11| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 3 |
Simplify: 2x + -2x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4y |
What is 61% of 800? | Compute the percent value (integer-safe). | Compute 61/100 × 800. | 488 |
Solve: |7x + 12| = 14 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: -11x + -3 = -124 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
Solve for x: 4x + -13 = -89 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -19 |
Simplify: -5x + 0x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -5x - 1y |
If each item costs -9 dollars and the total cost is -72, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 8 |
Solve for x: 12x + 7 = -29 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -3 |
Solve for x: 8(x + -6) = 16 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 8 |
Solve: |-2x + -3| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -10, 7 |
Solve: |-6x + 20| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 5 |
If each item costs 19 dollars and the total cost is 228, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 12 |
Solve: |6x + -9| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
What is 72% of 175? | Compute the percent value (integer-safe). | Compute 72/100 × 175. | 126 |
Solve: |-8x + 8| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |4x + 11| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: 5x + -5x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 8y |
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