question
stringlengths 16
86
| problem
stringclasses 8
values | how_to_solve
stringlengths 18
82
| answer
stringlengths 1
20
|
|---|---|---|---|
Solve for x: 10x + -23 = -113
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-9
|
Solve: -6x + 11 ≤ 17
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ -1
|
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.
|
25
|
Solve for x: -7(x + 15) = -168
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
9
|
What is 3% of 1000?
|
Compute the percent value (integer-safe).
|
Compute 3/100 × 1000.
|
30
|
Solve for x: -1x + 17 = 20
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-3
|
Solve: 4x + 5 ≥ 33
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ 7
|
If each item costs 12 dollars and the total cost is -108, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-9
|
Solve: |-8x + -14| = 14
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
0
|
What is 64% of 200?
|
Compute the percent value (integer-safe).
|
Compute 64/100 × 200.
|
128
|
Solve for x: 6(x + -8) = -102
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-9
|
What is 116% of 75?
|
Compute the percent value (integer-safe).
|
Compute 116/100 × 75.
|
87
|
Solve: |-6x + 12| ≤ 14
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
0 ≤ x ≤ 4
|
Simplify: 6x + 8x + 4y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
14x + 4y
|
Solve for x: 12x + -28 = 56
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
7
|
Solve: |6x + 4| = 13
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
no integer solutions
|
Solve: -2x + 5 < 23
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x < -9
|
Solve for x: -4(x + 1) = 40
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-11
|
If each item costs 6 dollars and the total cost is 90, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
15
|
Simplify: -1x + 1x + -3y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-3y
|
Solve for x: -3(x + -3) = 24
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-5
|
Solve for x: 1(x + -13) = -11
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
2
|
Solve for x: 6(x + -15) = -162
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-12
|
Solve for x: -5(x + 7) = -35
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
0
|
Solve: -4x + 18 > 98
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -20
|
If each item costs 13 dollars and the total cost is 390, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
30
|
Solve: |8x + 7| ≤ 3
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-1 ≤ x ≤ -1
|
Solve for x: 7(x + 13) = 147
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
8
|
Solve: |-3x + 8| = 17
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-3
|
What is 133% of 500?
|
Compute the percent value (integer-safe).
|
Compute 133/100 × 500.
|
665
|
Solve for x: 1(x + 5) = 18
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
13
|
Solve: |-3x + 18| ≤ 14
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
2 ≤ x ≤ 10
|
Solve: -1x + -2 > 3
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -5
|
Solve: |1x + -10| = 14
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
24, -4
|
Solve for x: 5(x + 1) = 35
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
6
|
Solve for x: -2(x + 11) = -8
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-7
|
Solve: |8x + -14| ≤ 20
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
0 ≤ x ≤ 4
|
Solve for x: 2(x + -3) = -18
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-6
|
Solve: |-7x + 13| = 8
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
3
|
Solve for x: -2(x + -7) = -4
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
9
|
Solve: |-4x + -14| ≤ 12
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-6 ≤ x ≤ -1
|
If each item costs -4 dollars and the total cost is -72, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
18
|
What is -31% of 700?
|
Compute the percent value (integer-safe).
|
Compute -31/100 × 700.
|
-217
|
Solve: |-7x + -14| ≤ 9
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-3 ≤ x ≤ -1
|
Solve for x: 12x + -27 = 93
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
10
|
Solve: |-1x + -11| = 4
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-15, -7
|
Simplify: 7x + 0x + 5y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
7x + 5y
|
Solve: 8x + 12 < -4
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x < -2
|
Solve: |6x + 9| ≤ 9
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-3 ≤ x ≤ 0
|
Simplify: -3x + -2x + 8y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-5x + 8y
|
Simplify: 8x + 4x + 4y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
12x + 4y
|
Solve: 10x + 12 ≥ 202
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ 19
|
Solve: |2x + -8| ≤ 13
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-2 ≤ x ≤ 10
|
Solve: |6x + 11| ≤ 14
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-4 ≤ x ≤ 0
|
Solve: |5x + 14| = 17
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
no integer solutions
|
If each item costs 2 dollars and the total cost is 22, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
11
|
Simplify: -7x + 3x + -6y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-4x - 6y
|
If each item costs 13 dollars and the total cost is -143, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-11
|
Solve for x: 9x + 3 = 84
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
9
|
If each item costs -3 dollars and the total cost is -48, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
16
|
If each item costs 11 dollars and the total cost is 77, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
7
|
If each item costs 11 dollars and the total cost is 242, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
22
|
What is -17% of 100?
|
Compute the percent value (integer-safe).
|
Compute -17/100 × 100.
|
-17
|
Solve: |3x + 14| = 8
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-2
|
Simplify: 2x + 7x + 7y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
9x + 7y
|
Solve: 6x + 0 ≥ -96
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ -16
|
Solve for x: 5x + -7 = 83
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
18
|
Solve: 3x + -14 > -38
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -8
|
Solve for x: -5x + 30 = 5
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
5
|
If each item costs 9 dollars and the total cost is 9, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
1
|
What is 95% of 200?
|
Compute the percent value (integer-safe).
|
Compute 95/100 × 200.
|
190
|
Simplify: -1x + -4x + 2y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-5x + 2y
|
Solve for x: -1(x + 5) = -19
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
14
|
Solve: |2x + -15| = 20
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
no integer solutions
|
Solve for x: -8(x + 7) = 0
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-7
|
Solve: 10x + 20 ≤ -50
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ -7
|
If each item costs 19 dollars and the total cost is -342, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-18
|
Solve for x: -8(x + 2) = 16
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-4
|
Solve for x: 5(x + 7) = 15
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-4
|
What is 71% of 200?
|
Compute the percent value (integer-safe).
|
Compute 71/100 × 200.
|
142
|
Solve for x: 6(x + 11) = 156
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
15
|
Simplify: -2x + 3x + 6y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
1x + 6y
|
If each item costs 16 dollars and the total cost is -224, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-14
|
If each item costs 8 dollars and the total cost is -40, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-5
|
Solve: |-7x + -9| = 12
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-3
|
Solve: |-1x + 10| = 1
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
9, 11
|
What is 138% of 100?
|
Compute the percent value (integer-safe).
|
Compute 138/100 × 100.
|
138
|
Solve: |5x + -13| = 18
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-1
|
Solve for x: -4(x + -10) = 56
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-4
|
Solve for x: 3(x + -14) = -72
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-10
|
Solve: -7x + 20 ≤ -22
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ 6
|
Solve: |-4x + -3| = 17
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
-5
|
Solve: |-2x + -7| ≤ 20
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-13 ≤ x ≤ 6
|
Solve for x: -7(x + -4) = -63
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
13
|
Solve: |3x + 17| ≤ 7
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-8 ≤ x ≤ -4
|
Solve for x: -2x + -21 = 3
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-12
|
Solve: |3x + -20| ≤ 2
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
6 ≤ x ≤ 7
|
Solve for x: 8(x + 8) = 104
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
5
|
Solve for x: -2(x + 10) = -46
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
13
|
Solve: |1x + -20| ≤ 0
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
20 ≤ x ≤ 20
|
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