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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