question stringlengths 16 86 | problem stringclasses 8 values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
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. | 18 |
Solve: -2x + 20 ≤ 4 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 8 |
Solve: 7x + -4 < -4 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 0 |
Solve for x: 2x + -28 = -46 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -9 |
Solve for x: -2(x + 15) = -2 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -14 |
Simplify: -1x + -6x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -7x + 8y |
Solve: 9x + 9 > 63 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 6 |
Solve: |2x + -15| ≤ 16 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 15 |
If each item costs -4 dollars and the total cost is -116, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 29 |
Solve for x: -12x + -23 = 193 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -18 |
Solve: |4x + 4| ≤ 10 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 1 |
Solve: |-5x + 2| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 4 |
Solve: |-1x + -1| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 0 |
Simplify: -7x + 3x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x - 5y |
Solve for x: 4(x + -3) = 44 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 14 |
Solve: |-6x + -5| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 1 |
Solve for x: 6(x + -6) = 24 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 10 |
Solve: |4x + 15| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs 7 dollars and the total cost is 14, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 2 |
Solve: |2x + 15| = 14 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: -2x + 4x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x - 8y |
Solve: |4x + -6| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs 6 dollars and the total cost is -60, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -10 |
Solve: 8x + 10 ≤ -62 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -9 |
Solve for x: -8(x + 6) = 32 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -10 |
Solve: |1x + 14| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -14 |
Solve: 10x + -15 ≤ -25 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -1 |
If each item costs 13 dollars and the total cost is -247, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -19 |
What is 63% of 600? | Compute the percent value (integer-safe). | Compute 63/100 × 600. | 378 |
Solve: |1x + 15| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -6, -24 |
If each item costs 15 dollars and the total cost is -105, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -7 |
Solve: |-3x + 11| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 9 |
What is -23% of 400? | Compute the percent value (integer-safe). | Compute -23/100 × 400. | -92 |
Solve: |-8x + 16| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 3 |
Solve for x: -6(x + 2) = 78 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
Solve: |-8x + -14| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
If each item costs 6 dollars and the total cost is -90, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -15 |
Simplify: 5x + 8x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 13x - 8y |
Solve: |2x + -9| ≤ 8 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 8 |
If each item costs -4 dollars and the total cost is -8, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 2 |
Solve: -2x + 4 > -12 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 8 |
Simplify: -6x + 3x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x - 7y |
If each item costs -3 dollars and the total cost is -9, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 3 |
Solve for x: -7(x + 2) = -70 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 8 |
What is 142% of 250? | Compute the percent value (integer-safe). | Compute 142/100 × 250. | 355 |
Solve: -9x + 0 < -153 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 17 |
Simplify: -6x + -8x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -14x - 4y |
Solve for x: -7(x + 15) = -14 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -13 |
If each item costs -5 dollars and the total cost is 85, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -17 |
Solve: 2x + 13 ≤ 49 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 18 |
Solve: 10x + 13 ≥ -147 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -16 |
Solve for x: 9x + 27 = 45 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 2 |
Simplify: -3x + 7x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x + 7y |
Solve: |-6x + -20| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ -1 |
Solve: |2x + 0| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ 6 |
What is -41% of 800? | Compute the percent value (integer-safe). | Compute -41/100 × 800. | -328 |
Solve: |6x + -8| = 15 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: -3x + 0 ≥ -15 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 5 |
Solve for x: 2(x + 6) = 22 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 5 |
Solve for x: -1(x + -7) = 19 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -12 |
Solve for x: -1x + 21 = 16 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 5 |
Solve: 2x + -11 > 21 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 16 |
Solve: |-2x + 8| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is -21% of 300? | Compute the percent value (integer-safe). | Compute -21/100 × 300. | -63 |
Solve: |1x + 18| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -35 ≤ x ≤ -1 |
Solve: 8x + 16 ≥ -112 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -16 |
What is 39% of 700? | Compute the percent value (integer-safe). | Compute 39/100 × 700. | 273 |
Solve: |-1x + 3| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 5 |
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: 8x + 4 ≥ 76 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 9 |
Solve: |2x + 11| = 6 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-3x + -12| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -8, 0 |
Solve for x: 2x + 17 = -13 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -15 |
Simplify: 5x + -2x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 3x - 6y |
Solve: |7x + -15| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 3 |
Solve: |7x + -15| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 3 |
Solve: |1x + -9| = 19 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 28, -10 |
What is -10% of 70? | Compute the percent value (integer-safe). | Compute -10/100 × 70. | -7 |
If each item costs 11 dollars and the total cost is 154, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 14 |
Solve for x: -10x + 12 = -158 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 17 |
Solve: 9x + 2 ≤ -160 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -18 |
Solve for x: 4x + -16 = -60 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -11 |
Solve: |4x + -2| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 2 |
Solve for x: 4(x + -4) = 0 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 4 |
Solve for x: -2x + -26 = -30 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 2 |
If each item costs 10 dollars and the total cost is -50, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -5 |
Simplify: -3x + -7x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -10x - 5y |
Solve for x: 7(x + 2) = -49 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -9 |
If each item costs 2 dollars and the total cost is -18, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -9 |
Solve for x: 1x + 29 = 48 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 19 |
Solve: -8x + 6 ≥ 38 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -4 |
Solve: -2x + -4 ≤ 36 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -20 |
What is -19% of 400? | Compute the percent value (integer-safe). | Compute -19/100 × 400. | -76 |
What is -32% of 175? | Compute the percent value (integer-safe). | Compute -32/100 × 175. | -56 |
Solve for x: -6x + 14 = -4 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 3 |
What is 33% of 500? | Compute the percent value (integer-safe). | Compute 33/100 × 500. | 165 |
If each item costs 4 dollars and the total cost is 76, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 19 |
Solve for x: -4(x + 8) = -20 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -3 |
Solve: |-6x + -12| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -5, 1 |
What is -5% of 100? | Compute the percent value (integer-safe). | Compute -5/100 × 100. | -5 |
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