question stringlengths 16 86 | problem stringclasses 8
values | how_to_solve stringclasses 940
values | answer stringlengths 1 20 |
|---|---|---|---|
Solve: 6x + -14 < 106 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 20 |
Solve: |8x + 0| = 14 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is -3% of 0? | Compute the percent value (integer-safe). | Compute -3/100 × 0. | 0 |
Solve: |8x + -12| = 2 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Simplify: 7x + -6x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 1x - 7y |
Solve: 9x + -1 < -100 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < -11 |
If each item costs 7 dollars and the total cost is -91, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | -13 |
Simplify: -1x + 8x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7x + 4y |
Solve: |7x + -1| ≤ 18 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 2 |
Simplify: 1x + -7x + -5y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -6x - 5y |
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: |-6x + -10| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: -8x + -10 < -130 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 15 |
Simplify: 6x + 7x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 13x + 1y |
Solve for x: -3x + 15 = 33 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -6 |
Solve: |7x + -13| = 7 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-2x + -2| = 3 | 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 -126, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 21 |
Solve: |-4x + -13| = 1 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -3 |
Solve: 10x + 16 ≤ 6 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -1 |
Solve: |-5x + 9| ≤ 9 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 3 |
Simplify: 0x + 8x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 8x + 7y |
Solve: |-6x + 18| ≤ 1 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 3 ≤ x ≤ 3 |
Simplify: 2x + 0x + -8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 2x - 8y |
Solve for x: -8(x + 9) = -8 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -8 |
Solve: |-7x + 9| = 5 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 2 |
Solve: |7x + -3| ≤ 5 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 0 ≤ x ≤ 1 |
Simplify: 7x + -6x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 1x + 7y |
What is 54% of 250? | Compute the percent value (integer-safe). | Compute 54/100 × 250. | 135 |
What is 121% of 100? | Compute the percent value (integer-safe). | Compute 121/100 × 100. | 121 |
Solve: 4x + 11 ≤ 15 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ 1 |
Simplify: -7x + 6x + -6y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -1x - 6y |
What is 14% of 250? | Compute the percent value (integer-safe). | Compute 14/100 × 250. | 35 |
Solve for x: 5(x + 12) = 105 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 9 |
Solve for x: 3x + -4 = 38 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 14 |
Solve for x: 5x + -7 = -47 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -8 |
Solve: |7x + -17| ≤ 6 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 2 ≤ x ≤ 3 |
Solve: |-4x + 14| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |8x + -13| ≤ 0 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | no integer solutions |
If each item costs -5 dollars and the total cost is -125, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 25 |
Solve: |-8x + 2| = 13 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: -5(x + -1) = 45 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -8 |
Solve for x: -4(x + 0) = -20 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 5 |
Solve: |1x + -2| = 15 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | 17, -13 |
Solve: |-1x + 9| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -8 ≤ x ≤ 26 |
Solve: -4x + 18 > 2 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x > 4 |
Solve for x: 6(x + -5) = -72 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -7 |
Solve: |-8x + -6| = 9 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-4x + 8| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -2 ≤ x ≤ 6 |
Solve: |4x + 1| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -4 ≤ x ≤ 4 |
Simplify: 6x + 2x + -2y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 8x - 2y |
If each item costs 2 dollars and the total cost is 32, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 16 |
If each item costs 3 dollars and the total cost is 87, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 29 |
Solve for x: 12x + 0 = 0 | Solve the linear equation. | Subtract b from both sides, then divide by a. | 0 |
Simplify: 4x + -4x + 7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 7y |
Solve for x: 5x + 7 = -53 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -12 |
What is -25% of 28? | Compute the percent value (integer-safe). | Compute -25/100 × 28. | -7 |
Solve for x: 7(x + -15) = -98 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 1 |
Solve: -6x + -16 ≥ -52 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≥ 6 |
Solve: |3x + 4| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve for x: 3(x + 12) = 72 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 12 |
Simplify: 2x + 7x + -7y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 9x - 7y |
Solve for x: 2(x + -8) = -32 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -8 |
Solve for x: -5(x + 9) = -35 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -2 |
Solve for x: -3(x + 7) = -18 | Solve a two-step equation. | Divide both sides by a, then subtract b. | -1 |
Solve: |-8x + -14| = 10 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -3 |
Solve for x: -1x + -7 = -5 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -2 |
Simplify: -4x + -1x + 8y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -5x + 8y |
Simplify: -3x + -3x + -3y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -6x - 3y |
Solve for x: 5(x + 4) = 40 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 4 |
If each item costs 19 dollars and the total cost is 209, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 11 |
Solve: 5x + 20 ≤ -10 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x ≤ -6 |
Solve: |1x + -20| ≤ 14 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 6 ≤ x ≤ 34 |
Solve: |-3x + -13| = 14 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | -9 |
What is 100% of 4? | Compute the percent value (integer-safe). | Compute 100/100 × 4. | 4 |
Simplify: 0x + 6x + 1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | 6x + 1y |
If each item costs 17 dollars and the total cost is 68, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 4 |
Solve: |-5x + -5| ≤ 12 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 1 |
What is 97% of 400? | Compute the percent value (integer-safe). | Compute 97/100 × 400. | 388 |
Solve: |-8x + 11| = 12 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-8x + 3| = 1 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |2x + -6| ≤ 19 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -6 ≤ x ≤ 12 |
What is 6% of 500? | Compute the percent value (integer-safe). | Compute 6/100 × 500. | 30 |
If each item costs -2 dollars and the total cost is -38, how many items were bought? | Solve using algebra. | Divide total cost by price per item. | 19 |
Solve: -7x + 20 < -120 | Solve the inequality. | Isolate x by subtracting b then dividing by a (flip sign if dividing by negative). | x < 20 |
Solve: |7x + -14| = 18 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
What is 137% of 200? | Compute the percent value (integer-safe). | Compute 137/100 × 200. | 274 |
Solve for x: 2(x + -5) = 18 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 14 |
Simplify: -3x + -2x + -4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -5x - 4y |
What is 85% of 160? | Compute the percent value (integer-safe). | Compute 85/100 × 160. | 136 |
Solve: |-3x + -7| = 15 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |3x + 10| = 3 | Find integer solutions x, if any. | Set inside equal to ±c and solve both linear equations. | no integer solutions |
Solve: |-6x + -11| ≤ 7 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ -1 |
Simplify: 3x + -6x + 4y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -3x + 4y |
Solve for x: 6x + -23 = -47 | Solve the linear equation. | Subtract b from both sides, then divide by a. | -4 |
Solve: |4x + -4| ≤ 18 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | -3 ≤ x ≤ 5 |
Simplify: 3x + -5x + -1y | Combine like terms. | Add coefficients of like terms (x with x, y with y). | -2x - 1y |
Solve: |-8x + 19| ≤ 17 | Find integer range of x satisfying the absolute inequality. | Isolate and produce interval then take integer bounds. | 1 ≤ x ≤ 4 |
What is 106% of 150? | Compute the percent value (integer-safe). | Compute 106/100 × 150. | 159 |
Solve for x: 7(x + 14) = 133 | Solve a two-step equation. | Divide both sides by a, then subtract b. | 5 |
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