question stringlengths 16 86 | problem stringclasses 8
values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve: |-4x + -13| = 13 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 0 |
Simplify: 7x + -3x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x - 5y |
Simplify: 5x + 6x + 6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 11x + 6y |
Solve: 4x + -14 ≤ -58 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -11 |
Solve for x: -1x + -19 = -32 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 13 |
If each item costs 10 dollars and the total cost is 40, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 4 |
Solve: |-1x + -1| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -18 ≤ x ≤ 16 |
Solve for x: -4(x + -11) = 80 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -9 |
Solve: |-7x + 3| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -2 |
Solve: |-8x + 18| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 3 |
Solve for x: -1(x + 2) = -5 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 3 |
Simplify: -1x + 0x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x - 3y |
What is 118% of 150? | Compute the percent value (integer-safe). | Compute 118/100 × 150. | 177 |
Solve: |2x + 15| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -8 ≤ x ≤ -7 |
What is 136% of 75? | Compute the percent value (integer-safe). | Compute 136/100 × 75. | 102 |
What is 105% of 0? | Compute the percent value (integer-safe). | Compute 105/100 × 0. | 0 |
Solve: 2x + 4 > 0 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -2 |
Simplify: 5x + 2x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7x - 7y |
Solve: |5x + -19| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 4 ≤ x ≤ 4 |
If each item costs -10 dollars and the total cost is -30, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 3 |
Solve for x: 7(x + 7) = -21 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -10 |
Simplify: -1x + 3x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x + 1y |
What is 26% of 0? | Compute the percent value (integer-safe). | Compute 26/100 × 0. | 0 |
What is -28% of 75? | Compute the percent value (integer-safe). | Compute -28/100 × 75. | -21 |
Solve: |-7x + 1| = 14 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: -12x + -17 = -41 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 2 |
Solve: |-7x + 3| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 1 |
Simplify: -2x + -8x + 6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -10x + 6y |
Solve: -6x + 17 < 107 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -15 |
If each item costs -3 dollars and the total cost is -63, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 21 |
Solve: 7x + -18 > -74 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -8 |
Simplify: -2x + -5x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -7x - 6y |
Simplify: 7x + 4x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 11x + 7y |
Solve: 3x + 2 ≥ 41 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 13 |
Solve: |1x + -7| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 12, 2 |
Solve for x: 1(x + 10) = 5 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
If each item costs 16 dollars and the total cost is -144, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -9 |
What is 31% of 500? | Compute the percent value (integer-safe). | Compute 31/100 × 500. | 155 |
Solve for x: -11x + 17 = 116 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -9 |
Solve: |7x + -14| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 2 |
Simplify: -7x + -1x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -8x - 1y |
Solve for x: 1(x + -5) = -9 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -4 |
Solve for x: 1(x + -11) = -3 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 8 |
Solve for x: -2x + 4 = -20 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 12 |
Simplify: 2x + 2x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 4x - 7y |
Solve: |-7x + 18| ≤ 8 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 3 |
Solve for x: 3(x + -8) = -3 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 7 |
Solve for x: -4(x + 11) = -88 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 11 |
What is 116% of 75? | Compute the percent value (integer-safe). | Compute 116/100 × 75. | 87 |
Solve for x: -8x + 25 = -95 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 15 |
Solve for x: 1(x + -11) = -26 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
Solve: -7x + -13 ≤ 64 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -11 |
Solve: 6x + -12 ≤ -12 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 0 |
Solve for x: 9x + 7 = -47 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -6 |
Solve for x: -1(x + 2) = -12 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 10 |
What is -23% of 0? | Compute the percent value (integer-safe). | Compute -23/100 × 0. | 0 |
Solve for x: -2x + 5 = 25 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -10 |
Solve: 4x + 0 > -24 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > -6 |
If each item costs 4 dollars and the total cost is 0, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 0 |
Solve: |-8x + 1| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-2x + -10| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -11 ≤ x ≤ 1 |
If each item costs 2 dollars and the total cost is -24, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -12 |
Solve for x: 5x + 4 = 79 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 15 |
If each item costs 3 dollars and the total cost is -15, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -5 |
Solve for x: -4(x + -1) = -56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 15 |
Solve: |1x + 1| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 0 |
What is 15% of 140? | Compute the percent value (integer-safe). | Compute 15/100 × 140. | 21 |
Solve: |-1x + 10| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 5, 15 |
What is 79% of 600? | Compute the percent value (integer-safe). | Compute 79/100 × 600. | 474 |
Simplify: -6x + -2x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -8x + 4y |
Solve: -8x + -9 < -57 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 6 |
Solve: 8x + 7 ≤ -9 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -2 |
Solve: |5x + 6| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 1 |
If each item costs 9 dollars and the total cost is 36, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 4 |
Solve: 9x + 16 < -146 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -18 |
Solve: 7x + 7 ≤ -98 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -15 |
Simplify: 7x + 2x + 6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 9x + 6y |
Solve for x: -8(x + -7) = 48 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 1 |
Solve: 4x + -10 < 26 | 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 + 0) = 16 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 2 |
Solve for x: 7x + -1 = -15 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -2 |
If each item costs -8 dollars and the total cost is -88, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 11 |
Solve: |7x + -7| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 2, 0 |
What is -7% of 300? | Compute the percent value (integer-safe). | Compute -7/100 × 300. | -21 |
Solve for x: -1x + -10 = 7 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -17 |
Solve: |-1x + 10| ≤ 9 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 19 |
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 |
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. | 8 |
Solve: |7x + 11| = 11 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 0 |
Solve: |5x + 2| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 10x + -30 = 140 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 17 |
Solve for x: 5x + -22 = 63 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 17 |
Solve: |-7x + 7| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ 3 |
If each item costs -8 dollars and the total cost is -216, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 27 |
If each item costs -4 dollars and the total cost is -36, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 9 |
Solve for x: 7(x + 8) = -42 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -14 |
Solve for x: -1x + 2 = -16 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 18 |
Simplify: 2x + 5x + 2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7x + 2y |
Solve: 8x + -11 ≤ -99 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -11 |
If each item costs 15 dollars and the total cost is 285, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 19 |
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