question
stringlengths 16
86
| problem
stringclasses 8
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stringlengths 18
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stringlengths 1
20
|
|---|---|---|---|
If each item costs 1 dollars and the total cost is 20, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
20
|
Solve: |1x + -14| ≤ 19
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-5 ≤ x ≤ 33
|
Solve for x: 10x + -26 = -216
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-19
|
Solve: |-3x + 1| = 13
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-4
|
Solve: |2x + 1| ≤ 7
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-4 ≤ x ≤ 3
|
Simplify: -8x + 4x + 7y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-4x + 7y
|
Solve for x: -8(x + 2) = -32
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
2
|
If each item costs 10 dollars and the total cost is 290, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
29
|
Solve: -6x + 16 ≥ 112
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ -16
|
Solve for x: -1x + 2 = -7
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
9
|
Solve: 4x + 0 > 48
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > 12
|
Simplify: 8x + 2x + -2y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
10x - 2y
|
Solve for x: 3(x + -4) = -30
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-6
|
What is -30% of 70?
|
Compute the percent value (integer-safe).
|
Compute -30/100 × 70.
|
-21
|
Solve: 3x + 16 > -29
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -15
|
Solve for x: -2(x + -9) = 44
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-13
|
What is -27% of 600?
|
Compute the percent value (integer-safe).
|
Compute -27/100 × 600.
|
-162
|
If each item costs 2 dollars and the total cost is 16, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
8
|
Solve: |1x + 14| ≤ 5
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-19 ≤ x ≤ -9
|
What is -33% of 500?
|
Compute the percent value (integer-safe).
|
Compute -33/100 × 500.
|
-165
|
Simplify: -6x + -5x + -2y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-11x - 2y
|
Solve: -3x + -17 < 37
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x < -18
|
Simplify: 8x + -6x + 6y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
2x + 6y
|
What is 6% of 350?
|
Compute the percent value (integer-safe).
|
Compute 6/100 × 350.
|
21
|
Solve for x: -3x + -3 = -9
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
2
|
Solve: |-5x + -15| ≤ 20
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-7 ≤ x ≤ 1
|
Solve for x: 4(x + 14) = 104
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
12
|
What is -22% of 200?
|
Compute the percent value (integer-safe).
|
Compute -22/100 × 200.
|
-44
|
Solve for x: 4(x + 11) = 52
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
2
|
Solve for x: 1(x + -7) = -3
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
4
|
Solve for x: -12x + -16 = 128
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-12
|
Solve: |-1x + 1| = 7
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-6, 8
|
Simplify: -8x + -4x + -4y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-12x - 4y
|
Solve: |4x + 9| ≤ 0
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
no integer solutions
|
Solve: -6x + -8 > 4
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -2
|
Solve for x: 5(x + 13) = 15
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-10
|
Simplify: -4x + -3x + -6y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-7x - 6y
|
What is 119% of 1000?
|
Compute the percent value (integer-safe).
|
Compute 119/100 × 1000.
|
1190
|
Simplify: 8x + -3x + 8y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
5x + 8y
|
Solve: |3x + -17| ≤ 14
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
1 ≤ x ≤ 10
|
If each item costs 12 dollars and the total cost is -192, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-16
|
Solve for x: 6x + -14 = 46
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
10
|
Solve for x: 8x + -17 = -49
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-4
|
Solve for x: 8(x + -12) = -192
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-12
|
If each item costs 19 dollars and the total cost is 114, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
6
|
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 for x: -3x + -25 = -25
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
0
|
If each item costs 12 dollars and the total cost is -120, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-10
|
If each item costs 3 dollars and the total cost is 51, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
17
|
If each item costs 19 dollars and the total cost is -361, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-19
|
Solve: |-5x + 10| ≤ 4
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
2 ≤ x ≤ 2
|
Solve: |-7x + 20| ≤ 13
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
1 ≤ x ≤ 4
|
Solve for x: 1(x + -12) = -17
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-5
|
Solve: |-8x + 5| ≤ 17
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-1 ≤ x ≤ 2
|
Solve: -9x + -19 ≤ -172
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ 17
|
Solve: |-2x + 13| ≤ 9
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
2 ≤ x ≤ 11
|
Solve: |8x + -6| = 18
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
3
|
Solve: |-3x + 3| ≤ 14
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-3 ≤ x ≤ 5
|
Solve: |3x + -2| = 10
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
4
|
Solve for x: 6(x + 10) = 102
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
7
|
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 for x: -5(x + -11) = 50
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
1
|
If each item costs 1 dollars and the total cost is -9, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-9
|
Solve: |4x + -14| = 15
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
no integer solutions
|
Solve: -6x + 12 > 18
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -1
|
Solve for x: -1(x + -5) = -9
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
14
|
If each item costs 8 dollars and the total cost is 0, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
0
|
Simplify: -3x + -3x + 5y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-6x + 5y
|
Solve for x: 2(x + -4) = -4
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
2
|
If each item costs 15 dollars and the total cost is 240, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
16
|
Solve for x: -3x + -14 = -50
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
12
|
If each item costs 12 dollars and the total cost is -84, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-7
|
Solve: |-8x + -9| ≤ 2
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-1 ≤ x ≤ -1
|
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
|
Simplify: -6x + -5x + -4y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-11x - 4y
|
Solve for x: -12x + -5 = -77
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
6
|
Solve for x: -8(x + 1) = 80
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-11
|
Solve: |5x + 2| = 18
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-4
|
Simplify: -3x + -3x + -2y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-6x - 2y
|
Simplify: -8x + -3x + 6y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-11x + 6y
|
If each item costs 2 dollars and the total cost is -36, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-18
|
Solve: |1x + 0| ≤ 12
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-12 ≤ x ≤ 12
|
Solve: |-8x + -12| ≤ 7
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-2 ≤ x ≤ -1
|
Solve: 5x + -11 > -1
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > 2
|
Simplify: -7x + -1x + 0y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-8x
|
What is 67% of 800?
|
Compute the percent value (integer-safe).
|
Compute 67/100 × 800.
|
536
|
Simplify: 7x + 5x + 0y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
12x
|
What is 26% of 250?
|
Compute the percent value (integer-safe).
|
Compute 26/100 × 250.
|
65
|
Solve: -6x + -4 > -64
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > 10
|
Simplify: 6x + -1x + 2y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
5x + 2y
|
Solve for x: 5x + 30 = 85
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
11
|
Solve for x: -11x + 11 = 55
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-4
|
Solve: |-1x + -9| ≤ 4
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-13 ≤ x ≤ -5
|
Solve: |5x + -12| ≤ 19
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-1 ≤ x ≤ 6
|
Solve for x: -2(x + -10) = 4
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
8
|
If each item costs 2 dollars and the total cost is 12, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
6
|
Solve: |7x + 10| ≤ 0
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
no integer solutions
|
Solve: |3x + 11| ≤ 11
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-7 ≤ x ≤ 0
|
Solve: -8x + -2 ≥ 14
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ -2
|
Solve: -9x + -20 ≥ 61
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ -9
|
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