question stringlengths 16 86 | problem stringclasses 8
values | how_to_solve stringlengths 18 82 | answer stringlengths 1 20 |
|---|---|---|---|
Solve: |-4x + -2| = 1 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |8x + -14| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 2 |
If each item costs 2 dollars and the total cost is 54, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 27 |
If each item costs 14 dollars and the total cost is -56, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -4 |
If each item costs 19 dollars and the total cost is 323, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 17 |
What is 58% of 450? | Compute the percent value (integer-safe). | Compute 58/100 × 450. | 261 |
Simplify: -5x + 7x + 6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x + 6y |
If each item costs 12 dollars and the total cost is 0, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 0 |
Solve: |-6x + -12| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 0 |
What is -44% of 0? | Compute the percent value (integer-safe). | Compute -44/100 × 0. | 0 |
Solve: |7x + -10| ≤ 4 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 2 |
Solve for x: 4x + 4 = -40 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -11 |
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 |
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 |
What is -13% of 200? | Compute the percent value (integer-safe). | Compute -13/100 × 200. | -26 |
If each item costs 15 dollars and the total cost is 390, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 26 |
What is -46% of 350? | Compute the percent value (integer-safe). | Compute -46/100 × 350. | -161 |
Solve for x: -4x + 13 = -31 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
Solve for x: -8(x + -13) = 120 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -2 |
Solve for x: 4(x + -8) = 16 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 12 |
What is -23% of 400? | Compute the percent value (integer-safe). | Compute -23/100 × 400. | -92 |
Simplify: 5x + -8x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x + 7y |
Solve: 10x + -7 < 173 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 18 |
Solve for x: -8(x + -10) = -24 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 13 |
Simplify: 6x + 4x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 10x - 3y |
Solve for x: 7x + -9 = -44 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -5 |
Solve: |-3x + 2| = 2 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 0 |
Solve for x: 9x + -16 = -79 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -7 |
Solve for x: 6(x + 13) = 162 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 14 |
Solve: -7x + -2 ≥ -142 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 20 |
Solve: |5x + 3| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 0 |
What is -7% of 700? | Compute the percent value (integer-safe). | Compute -7/100 × 700. | -49 |
What is 34% of 200? | Compute the percent value (integer-safe). | Compute 34/100 × 200. | 68 |
Solve for x: -12x + 18 = -138 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 13 |
What is 57% of 100? | Compute the percent value (integer-safe). | Compute 57/100 × 100. | 57 |
If each item costs 8 dollars and the total cost is -16, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -2 |
What is 46% of 350? | Compute the percent value (integer-safe). | Compute 46/100 × 350. | 161 |
What is -44% of 250? | Compute the percent value (integer-safe). | Compute -44/100 × 250. | -110 |
Solve for x: -4x + 17 = 61 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -11 |
Solve for x: -2(x + 8) = -24 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 4 |
Solve: |8x + 6| ≤ 5 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -1 ≤ x ≤ -1 |
Solve for x: -7x + 16 = -47 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 9 |
Solve: |-8x + 7| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 3x + -24 = -72 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -16 |
Solve: 6x + 7 < 19 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 2 |
Solve: |2x + -14| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 4 ≤ x ≤ 10 |
If each item costs 10 dollars and the total cost is -150, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -15 |
What is 82% of 250? | Compute the percent value (integer-safe). | Compute 82/100 × 250. | 205 |
If each item costs 7 dollars and the total cost is -7, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -1 |
Solve: |-6x + -14| = 11 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |6x + -8| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: 4x + -9 ≤ -9 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 0 |
Simplify: -1x + 1x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1y |
Simplify: -8x + -1x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -9x + 1y |
Solve for x: 3x + 3 = -54 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -19 |
Solve for x: -7x + 17 = 108 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -13 |
Simplify: 4x + -7x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x + 4y |
Simplify: -4x + 0x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x + 7y |
If each item costs 7 dollars and the total cost is 210, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 30 |
Simplify: 5x + 0x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 5x + 1y |
If each item costs 4 dollars and the total cost is 16, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 4 |
Simplify: 0x + -1x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x + 1y |
Solve for x: 8(x + 11) = 120 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 4 |
Solve: |-7x + 7| = 16 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: -1x + -17 = -26 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 9 |
Solve: |-8x + -8| = 17 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is 29% of 600? | Compute the percent value (integer-safe). | Compute 29/100 × 600. | 174 |
Solve: |-4x + 8| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -1, 5 |
What is 30% of 30? | Compute the percent value (integer-safe). | Compute 30/100 × 30. | 9 |
Solve for x: 6x + -1 = -61 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -10 |
If each item costs -4 dollars and the total cost is 60, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -15 |
Solve for x: 3(x + -14) = -36 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 2 |
Solve for x: 2(x + 12) = 26 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 1 |
Solve for x: -8(x + 6) = -72 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 3 |
Solve: |6x + 0| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: -5x + 4x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x - 1y |
Solve for x: 8x + 4 = 92 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 11 |
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: 8(x + -11) = -128 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -5 |
Solve: -2x + 6 > -2 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 4 |
Solve for x: 5x + 16 = 16 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 0 |
Solve: 8x + 4 < -84 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -11 |
Solve: -10x + 17 < 87 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -7 |
Solve: -7x + 14 ≥ 0 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 2 |
If each item costs -5 dollars and the total cost is -95, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 19 |
Solve: |-4x + 0| ≤ 15 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 3 |
If each item costs 1 dollars and the total cost is -16, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -16 |
Solve: |-7x + 19| ≤ 13 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 4 |
Solve for x: 4(x + 3) = 56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 11 |
Solve: |1x + 19| ≤ 8 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -27 ≤ x ≤ -11 |
Solve for x: -3(x + 7) = -21 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 0 |
Simplify: 1x + -6x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -5x - 5y |
Simplify: 4x + 6x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 10x + 4y |
Simplify: -5x + -4x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -9x + 4y |
If each item costs -6 dollars and the total cost is -162, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 27 |
Solve for x: 3(x + 0) = -45 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
Solve for x: -2(x + -13) = 56 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -15 |
If each item costs 20 dollars and the total cost is 340, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 17 |
Simplify: -8x + 4x + 5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -4x + 5y |
What is 49% of 400? | Compute the percent value (integer-safe). | Compute 49/100 × 400. | 196 |
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