question
stringlengths
16
86
problem
stringclasses
8 values
how_to_solve
stringlengths
18
82
answer
stringlengths
1
20
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.
27
Simplify: -8x + -7x + 5y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-15x + 5y
Solve: |-6x + -14| = 1
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve: |1x + 11| ≤ 5
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-16 ≤ x ≤ -6
Solve for x: -12x + -15 = -159
Solve the linear equation.
Subtract b from both sides, then divide by a.
12
Solve for x: 7x + -30 = 19
Solve the linear equation.
Subtract b from both sides, then divide by a.
7
Solve: |3x + 11| ≤ 4
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-5 ≤ x ≤ -3
What is -50% of 20?
Compute the percent value (integer-safe).
Compute -50/100 × 20.
-10
Simplify: 8x + -7x + 1y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
1x + 1y
Solve: |-1x + 7| ≤ 6
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
1 ≤ x ≤ 13
Simplify: -4x + 7x + -6y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
3x - 6y
Simplify: 1x + -1x + 2y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
2y
What is -4% of 175?
Compute the percent value (integer-safe).
Compute -4/100 × 175.
-7
If each item costs -8 dollars and the total cost is 152, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-19
Solve: |1x + -16| ≤ 4
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
12 ≤ x ≤ 20
If each item costs -6 dollars and the total cost is 66, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-11
Simplify: 6x + -8x + 3y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-2x + 3y
Solve for x: -7x + -22 = 34
Solve the linear equation.
Subtract b from both sides, then divide by a.
-8
Solve for x: 12x + -8 = 196
Solve the linear equation.
Subtract b from both sides, then divide by a.
17
Solve: 1x + -8 > 1
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x > 9
Solve for x: -2(x + 6) = -28
Solve a two-step equation.
Divide both sides by a, then subtract b.
8
Solve: |-2x + 18| ≤ 13
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
3 ≤ x ≤ 15
Solve: |-3x + 2| = 10
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
4
Solve: |-8x + -2| = 17
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: 4(x + 7) = 72
Solve a two-step equation.
Divide both sides by a, then subtract b.
11
Solve: |4x + 9| = 3
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-3
Solve: -9x + -8 ≥ -17
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x ≥ 1
Solve: 9x + -1 < 125
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x < 14
What is 141% of 400?
Compute the percent value (integer-safe).
Compute 141/100 × 400.
564
Solve for x: -12x + 13 = 205
Solve the linear equation.
Subtract b from both sides, then divide by a.
-16
Solve: |5x + -6| = 20
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Simplify: -4x + 0x + -1y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-4x - 1y
Solve: |6x + -9| = 0
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: -1x + -9 = -23
Solve the linear equation.
Subtract b from both sides, then divide by a.
14
Solve for x: -5x + -1 = 54
Solve the linear equation.
Subtract b from both sides, then divide by a.
-11
If each item costs 18 dollars and the total cost is -90, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-5
Solve: -9x + 10 ≤ 19
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x ≤ -1
Solve for x: -7x + 14 = -105
Solve the linear equation.
Subtract b from both sides, then divide by a.
17
If each item costs 12 dollars and the total cost is -204, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-17
Solve for x: -1(x + -10) = 14
Solve a two-step equation.
Divide both sides by a, then subtract b.
-4
What is 15% of 120?
Compute the percent value (integer-safe).
Compute 15/100 × 120.
18
Simplify: -5x + -4x + -1y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-9x - 1y
If each item costs 11 dollars and the total cost is 0, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
0
Solve for x: 1(x + -1) = -5
Solve a two-step equation.
Divide both sides by a, then subtract b.
-4
Simplify: 5x + -7x + 4y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-2x + 4y
Solve: |-7x + -1| ≤ 5
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
0 ≤ x ≤ 0
What is -42% of 400?
Compute the percent value (integer-safe).
Compute -42/100 × 400.
-168
Solve: |-6x + -3| = 6
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: 7x + -11 = -95
Solve the linear equation.
Subtract b from both sides, then divide by a.
-12
If each item costs 3 dollars and the total cost is 72, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
24
Simplify: 8x + 8x + -7y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
16x - 7y
Solve for x: 7x + 19 = -86
Solve the linear equation.
Subtract b from both sides, then divide by a.
-15
Solve: |1x + -10| = 4
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
14, 6
Simplify: 2x + 8x + -2y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
10x - 2y
Solve for x: 7(x + -2) = -70
Solve a two-step equation.
Divide both sides by a, then subtract b.
-8
Solve for x: 7(x + -14) = -28
Solve a two-step equation.
Divide both sides by a, then subtract b.
10
Simplify: 0x + 4x + -7y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
4x - 7y
Solve: |-7x + 17| ≤ 15
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
1 ≤ x ≤ 4
Solve: 9x + 6 ≤ 69
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x ≤ 7
Solve: -2x + -17 ≤ -37
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x ≤ 10
Simplify: 7x + 3x + -6y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
10x - 6y
Solve: |4x + -10| = 15
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
What is 34% of 100?
Compute the percent value (integer-safe).
Compute 34/100 × 100.
34
Solve for x: -6x + 5 = 101
Solve the linear equation.
Subtract b from both sides, then divide by a.
-16
Simplify: -6x + 6x + -7y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-7y
What is 23% of 400?
Compute the percent value (integer-safe).
Compute 23/100 × 400.
92
Solve: |5x + 0| = 16
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve: |1x + 0| = 6
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
6, -6
Solve for x: 2(x + 2) = -26
Solve a two-step equation.
Divide both sides by a, then subtract b.
-15
Solve: |6x + 15| ≤ 5
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-3 ≤ x ≤ -2
What is 57% of 400?
Compute the percent value (integer-safe).
Compute 57/100 × 400.
228
Simplify: 5x + -7x + -6y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-2x - 6y
What is 2% of 200?
Compute the percent value (integer-safe).
Compute 2/100 × 200.
4
Solve: |7x + -12| ≤ 2
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
2 ≤ x ≤ 2
Simplify: 5x + -1x + 2y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
4x + 2y
Solve for x: 5x + -4 = 36
Solve the linear equation.
Subtract b from both sides, then divide by a.
8
Solve for x: 8x + -14 = -174
Solve the linear equation.
Subtract b from both sides, then divide by a.
-20
If each item costs 15 dollars and the total cost is -60, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-4
Solve: 5x + -7 ≥ -92
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x ≥ -17
If each item costs -10 dollars and the total cost is -300, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
30
Solve: |-6x + 14| ≤ 3
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
2 ≤ x ≤ 2
What is 146% of 100?
Compute the percent value (integer-safe).
Compute 146/100 × 100.
146
What is 46% of 250?
Compute the percent value (integer-safe).
Compute 46/100 × 250.
115
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
Solve for x: 2x + 11 = 27
Solve the linear equation.
Subtract b from both sides, then divide by a.
8
Solve: |-3x + 8| = 17
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-3
Solve: |-3x + -9| = 0
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-3
Simplify: 0x + 4x + -3y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
4x - 3y
Solve: |2x + 12| ≤ 3
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-7 ≤ x ≤ -5
If each item costs 18 dollars and the total cost is 144, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
8
Solve for x: -5x + -20 = -40
Solve the linear equation.
Subtract b from both sides, then divide by a.
4
Solve for x: 1(x + 10) = 25
Solve a two-step equation.
Divide both sides by a, then subtract b.
15
Solve for x: 4x + -17 = 47
Solve the linear equation.
Subtract b from both sides, then divide by a.
16
What is 102% of 50?
Compute the percent value (integer-safe).
Compute 102/100 × 50.
51
Solve for x: 6(x + 14) = 6
Solve a two-step equation.
Divide both sides by a, then subtract b.
-13
Solve: 1x + -6 ≥ 1
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x ≥ 7
Solve: |-6x + 14| = 19
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: -7(x + 3) = 14
Solve a two-step equation.
Divide both sides by a, then subtract b.
-5
Solve: |8x + -8| ≤ 13
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
0 ≤ x ≤ 2
Solve: -1x + -16 > -10
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x > -6