question stringlengths 16 86 | problem stringclasses 8 values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve: |-2x + 12| = 15 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: 2x + -17 < -39 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -11 |
Solve: |4x + -4| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 5 |
Solve for x: -5x + 25 = -55 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 16 |
Solve: |7x + -13| ≤ 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 + -11) = -102 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
Solve: |7x + -7| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 2 |
Simplify: 5x + 8x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 13x + 2y |
Simplify: 8x + 2x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 10x - 1y |
Solve for x: 2x + 20 = 16 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -2 |
Solve for x: -5(x + -15) = 25 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 10 |
Solve for x: -6(x + -6) = 12 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 4 |
Simplify: -5x + -6x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -11x + 2y |
Solve: |-4x + -15| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ -3 |
Solve: 9x + -8 > -80 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -8 |
Solve for x: 11x + -2 = 97 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 9 |
Solve for x: 5(x + 8) = 115 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 15 |
Solve: |-2x + 4| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -7, 11 |
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 |
Simplify: -4x + 8x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x + 2y |
Simplify: 1x + 0x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 1x + 8y |
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: |3x + 10| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -5 |
If each item costs 1 dollars and the total cost is 12, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 12 |
Simplify: -8x + 4x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x - 8y |
Solve: |6x + 14| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |8x + 20| ≤ 10 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -2 |
Solve: |4x + -2| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: 4x + 4 ≤ -60 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -16 |
Solve: |-7x + -4| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 7(x + -4) = -126 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -14 |
What is 48% of 200? | Compute the percent value (integer-safe). | Compute 48/100 × 200. | 96 |
What is -11% of 300? | Compute the percent value (integer-safe). | Compute -11/100 × 300. | -33 |
If each item costs 11 dollars and the total cost is -11, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -1 |
Simplify: -1x + 5x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x + 4y |
Solve: 10x + 2 ≥ -58 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -6 |
What is 144% of 25? | Compute the percent value (integer-safe). | Compute 144/100 × 25. | 36 |
Solve: |8x + 9| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 0 |
Solve: |-1x + 2| = 0 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 2 |
Solve for x: 1x + -2 = 11 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 13 |
Solve for x: 2x + 10 = -20 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -15 |
Solve for x: -3(x + -12) = 54 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
What is -31% of 600? | Compute the percent value (integer-safe). | Compute -31/100 × 600. | -186 |
Simplify: 2x + 7x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 9x - 6y |
Solve: |3x + 1| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 2 |
Solve for x: -8(x + -2) = -48 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 8 |
What is 125% of 8? | Compute the percent value (integer-safe). | Compute 125/100 × 8. | 10 |
Solve for x: -4(x + 8) = -60 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 7 |
If each item costs -9 dollars and the total cost is 54, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -6 |
Solve for x: 1x + -3 = -10 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -7 |
If each item costs 19 dollars and the total cost is 57, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 3 |
Simplify: 3x + 5x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 8x + 8y |
Solve: |6x + -10| = 19 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 1x + 3 = 14 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
Solve: |5x + 5| ≤ 11 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 1 |
If each item costs 13 dollars and the total cost is -91, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -7 |
Solve: |-8x + -5| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 0 |
Solve for x: 2x + -12 = 2 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 7 |
What is 104% of 250? | Compute the percent value (integer-safe). | Compute 104/100 × 250. | 260 |
Solve: 3x + -5 ≥ 43 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 16 |
Solve: |-4x + 3| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: -10x + 14 > 114 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -10 |
Solve for x: 7(x + 6) = -49 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -13 |
Solve for x: -8x + -26 = -162 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 17 |
Solve: |-8x + 4| = 19 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-2x + -6| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ 0 |
If each item costs 19 dollars and the total cost is 38, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 2 |
Solve: |4x + 5| = 11 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -4 |
What is 65% of 100? | Compute the percent value (integer-safe). | Compute 65/100 × 100. | 65 |
Solve: |-3x + -8| = 19 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -9 |
If each item costs 13 dollars and the total cost is 169, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 13 |
If each item costs 17 dollars and the total cost is -34, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -2 |
Solve: |-5x + -11| = 20 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: -1x + 2x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 1x + 1y |
Solve for x: -8(x + -14) = 184 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -9 |
Solve: 10x + 15 > -65 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -8 |
Simplify: 4x + -7x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x + 4y |
Solve for x: -1(x + -6) = -8 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 14 |
Solve: |-6x + -12| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -2 |
Solve: -9x + 10 ≤ 100 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -10 |
Solve for x: -6(x + -13) = 138 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -10 |
If each item costs -4 dollars and the total cost is 80, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -20 |
Solve: 5x + 19 ≥ 114 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 19 |
Simplify: -5x + 3x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -2x - 8y |
If each item costs -6 dollars and the total cost is 78, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -13 |
If each item costs -10 dollars and the total cost is 180, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -18 |
Solve: |-4x + -10| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ -1 |
Solve: |3x + 15| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ -5 |
What is 44% of 200? | Compute the percent value (integer-safe). | Compute 44/100 × 200. | 88 |
Solve for x: 2x + -10 = 8 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 9 |
Solve: |5x + -4| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-4x + 19| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 3 ≤ x ≤ 6 |
Solve for x: -6(x + -7) = 36 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 1 |
Simplify: -5x + -4x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -9x - 6y |
Solve for x: 5(x + 13) = 90 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 5 |
Solve for x: 6(x + -5) = -60 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
Solve: 7x + -5 ≥ -33 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ -4 |
Solve for x: 1(x + -12) = 0 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 12 |
Solve for x: 5(x + -13) = -125 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -12 |
Solve: 3x + 14 ≥ 44 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 10 |
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