question stringlengths 16 86 | problem stringclasses 8 values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve: |3x + -10| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 0 |
What is -22% of 150? | Compute the percent value (integer-safe). | Compute -22/100 × 150. | -33 |
Solve: |5x + 16| ≤ 11 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ -1 |
What is -28% of 50? | Compute the percent value (integer-safe). | Compute -28/100 × 50. | -14 |
Solve: |4x + -13| = 11 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 6 |
What is 105% of 180? | Compute the percent value (integer-safe). | Compute 105/100 × 180. | 189 |
What is 46% of 350? | Compute the percent value (integer-safe). | Compute 46/100 × 350. | 161 |
Solve for x: 6(x + 12) = -12 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -14 |
Solve for x: -5(x + -11) = 65 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -2 |
Solve: |8x + -15| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |1x + -4| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 16, -8 |
Solve: |-1x + -4| ≤ 11 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -15 ≤ x ≤ 7 |
Solve: |8x + -14| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: -1x + 4 < 24 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -20 |
Solve for x: 10x + -15 = -85 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -7 |
Simplify: -2x + -1x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x - 6y |
Solve: -4x + 14 ≥ -62 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 19 |
Solve for x: -5x + 2 = -38 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 8 |
Solve: |-7x + -4| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -1 |
Solve for x: 3(x + 11) = 45 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 4 |
Solve for x: -2(x + 15) = -58 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 14 |
Solve for x: 2(x + 3) = 8 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 1 |
Solve for x: 2(x + -2) = -14 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
Solve: |-1x + -7| = 13 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -20, 6 |
Solve for x: -11x + -12 = -133 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
Solve: |6x + 7| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ -1 |
Solve for x: 4x + -29 = -49 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -5 |
If each item costs 7 dollars and the total cost is 119, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 17 |
Solve: |-3x + -14| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -3 |
If each item costs 7 dollars and the total cost is -98, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -14 |
If each item costs 5 dollars and the total cost is 65, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 13 |
Solve: |-7x + 13| = 15 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 4 |
Solve: |-8x + 4| ≤ 19 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 2 |
What is 52% of 200? | Compute the percent value (integer-safe). | Compute 52/100 × 200. | 104 |
Solve for x: 7(x + -1) = 98 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 15 |
If each item costs -4 dollars and the total cost is 40, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -10 |
Solve: |1x + -15| = 20 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 35, -5 |
Solve: |5x + 19| ≤ 2 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ -4 |
Solve for x: -7(x + 14) = -56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
What is 133% of 1000? | Compute the percent value (integer-safe). | Compute 133/100 × 1000. | 1330 |
Solve for x: 2(x + 7) = 20 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 3 |
Solve for x: -10x + 20 = 120 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -10 |
What is 31% of 600? | Compute the percent value (integer-safe). | Compute 31/100 × 600. | 186 |
Simplify: 8x + 1x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 9x - 6y |
Solve: |3x + -14| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 10 |
What is 11% of 0? | Compute the percent value (integer-safe). | Compute 11/100 × 0. | 0 |
If each item costs -5 dollars and the total cost is -145, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 29 |
Solve for x: 9x + -29 = -146 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -13 |
What is -1% of 400? | Compute the percent value (integer-safe). | Compute -1/100 × 400. | -4 |
Solve for x: -8(x + -14) = 96 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 2 |
Solve: -5x + 19 ≥ -6 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 5 |
If each item costs 7 dollars and the total cost is -28, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -4 |
Solve for x: -5(x + -5) = -20 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 9 |
If each item costs 5 dollars and the total cost is 20, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 4 |
What is -28% of 150? | Compute the percent value (integer-safe). | Compute -28/100 × 150. | -42 |
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: |-2x + 8| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -2, 10 |
Solve for x: 4(x + -10) = -64 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
What is 143% of 100? | Compute the percent value (integer-safe). | Compute 143/100 × 100. | 143 |
Solve for x: -1(x + -8) = 8 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 0 |
Simplify: 1x + -6x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -5x + 4y |
Solve for x: -7x + -13 = -41 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 4 |
Solve: |7x + -12| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 2 |
Solve for x: 1(x + 13) = 7 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -6 |
Solve for x: -4(x + -11) = 84 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -10 |
If each item costs -2 dollars and the total cost is -30, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 15 |
Solve for x: 6(x + 2) = -66 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -13 |
Solve for x: -8(x + 2) = -128 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 14 |
If each item costs 15 dollars and the total cost is 420, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 28 |
Solve: |-3x + 19| ≤ 9 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 4 ≤ x ≤ 9 |
Solve: |5x + 8| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -1 |
Solve: |-7x + -12| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: 4x + 2x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 6x + 2y |
Solve for x: -9x + -3 = 141 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -16 |
Solve: 6x + 6 < 66 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 10 |
Solve: |-2x + 18| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 3 ≤ x ≤ 15 |
Simplify: -7x + 5x + 5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -2x + 5y |
If each item costs -5 dollars and the total cost is 15, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -3 |
What is -45% of 40? | Compute the percent value (integer-safe). | Compute -45/100 × 40. | -18 |
Solve: |6x + -12| = 13 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: 5x + -2x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 3x - 6y |
Solve: |3x + 14| ≤ 11 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -8 ≤ x ≤ -1 |
Solve: |-7x + -4| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-5x + -15| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ -2 |
Solve: |-5x + -13| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -2 |
Simplify: 7x + 0x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7x + 1y |
What is -18% of 400? | Compute the percent value (integer-safe). | Compute -18/100 × 400. | -72 |
Simplify: 1x + -5x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x + 7y |
Simplify: 5x + -2x + 3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 3x + 3y |
Solve for x: 3(x + 7) = 57 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 12 |
If each item costs -5 dollars and the total cost is -35, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 7 |
Solve: 3x + 8 < 11 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 1 |
Solve: -9x + -12 > -102 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 10 |
Solve: |-1x + -2| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -19, 15 |
Solve: |-3x + -14| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -5 ≤ x ≤ -5 |
Solve: |8x + 18| ≤ 8 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -2 |
Solve: |1x + -19| ≤ 3 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 16 ≤ x ≤ 22 |
Solve: -1x + -18 > 2 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -20 |
If each item costs 16 dollars and the total cost is 448, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 28 |
Solve for x: -4(x + -3) = -36 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 12 |
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