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20
Solve: |-2x + -12| ≤ 14
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-13 ≤ x ≤ 1
If each item costs 3 dollars and the total cost is 54, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
18
Solve: 2x + -13 < -43
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x < -15
Solve for x: 1x + -30 = -42
Solve the linear equation.
Subtract b from both sides, then divide by a.
-12
Solve: |7x + -10| ≤ 2
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
no integer solutions
Solve: |-2x + 13| = 20
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve: |5x + 15| = 18
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Simplify: 2x + -2x + 7y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
7y
Solve for x: 4(x + 0) = -16
Solve a two-step equation.
Divide both sides by a, then subtract b.
-4
If each item costs -10 dollars and the total cost is 130, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-13
What is -4% of 0?
Compute the percent value (integer-safe).
Compute -4/100 × 0.
0
If each item costs 7 dollars and the total cost is -112, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-16
Solve: |-1x + -19| ≤ 18
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-37 ≤ x ≤ -1
What is -37% of 700?
Compute the percent value (integer-safe).
Compute -37/100 × 700.
-259
If each item costs 4 dollars and the total cost is -24, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-6
Solve: |-1x + -14| ≤ 4
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-18 ≤ x ≤ -10
Solve: |-2x + -3| ≤ 2
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-2 ≤ x ≤ -1
Solve: |3x + -14| = 5
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
3
Solve: |4x + 18| ≤ 20
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-9 ≤ x ≤ 0
Solve for x: -8x + -4 = -108
Solve the linear equation.
Subtract b from both sides, then divide by a.
13
Solve for x: 8x + -27 = -187
Solve the linear equation.
Subtract b from both sides, then divide by a.
-20
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 + -10| ≤ 3
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-2 ≤ x ≤ -2
Solve: |4x + -10| = 7
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
What is 95% of 120?
Compute the percent value (integer-safe).
Compute 95/100 × 120.
114
Solve for x: -5x + -17 = 43
Solve the linear equation.
Subtract b from both sides, then divide by a.
-12
Solve for x: 3(x + 10) = 63
Solve a two-step equation.
Divide both sides by a, then subtract b.
11
Solve: |4x + -13| ≤ 14
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
0 ≤ x ≤ 6
What is 64% of 225?
Compute the percent value (integer-safe).
Compute 64/100 × 225.
144
Solve for x: -7x + -18 = 38
Solve the linear equation.
Subtract b from both sides, then divide by a.
-8
Solve for x: 5x + 4 = 79
Solve the linear equation.
Subtract b from both sides, then divide by a.
15
Solve for x: -12x + 26 = -58
Solve the linear equation.
Subtract b from both sides, then divide by a.
7
Solve: |-6x + -1| = 10
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: 12x + -13 = -133
Solve the linear equation.
Subtract b from both sides, then divide by a.
-10
Solve for x: -1(x + 14) = -29
Solve a two-step equation.
Divide both sides by a, then subtract b.
15
Solve for x: 3x + 2 = -49
Solve the linear equation.
Subtract b from both sides, then divide by a.
-17
Simplify: 7x + 3x + 8y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
10x + 8y
Solve: |3x + 1| ≤ 17
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-6 ≤ x ≤ 5
What is -49% of 900?
Compute the percent value (integer-safe).
Compute -49/100 × 900.
-441
What is 97% of 100?
Compute the percent value (integer-safe).
Compute 97/100 × 100.
97
Solve: |3x + -14| = 9
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve: |-3x + -5| ≤ 12
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-5 ≤ x ≤ 2
Simplify: 1x + 4x + -4y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
5x - 4y
Solve: |-3x + 12| ≤ 13
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
0 ≤ x ≤ 8
What is -24% of 200?
Compute the percent value (integer-safe).
Compute -24/100 × 200.
-48
Solve for x: -4(x + -14) = 80
Solve a two-step equation.
Divide both sides by a, then subtract b.
-6
Solve: |-1x + 5| = 17
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-12, 22
Solve: |3x + 14| = 1
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-5
Solve: |5x + -11| = 3
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve: |5x + -4| ≤ 6
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
0 ≤ x ≤ 2
Solve: |-2x + 12| = 18
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-3, 15
Solve: |-5x + -2| = 12
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
2
Solve: |1x + -18| ≤ 14
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
4 ≤ x ≤ 32
Simplify: 8x + 3x + 2y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
11x + 2y
Solve: |1x + 19| ≤ 2
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-21 ≤ x ≤ -17
Solve for x: 5(x + 5) = -45
Solve a two-step equation.
Divide both sides by a, then subtract b.
-14
Simplify: 6x + -4x + 5y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
2x + 5y
Solve: |-6x + 1| = 14
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
If each item costs 8 dollars and the total cost is 168, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
21
Solve: |3x + -7| ≤ 14
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-2 ≤ x ≤ 7
Solve: |-7x + -16| ≤ 5
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-3 ≤ x ≤ -2
Solve: |-2x + 13| = 3
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
5, 8
Simplify: 0x + 3x + 8y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
3x + 8y
Solve: -3x + 8 < 20
Solve the inequality.
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
x < -4
Solve: |7x + -15| = 9
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: 9x + 7 = 97
Solve the linear equation.
Subtract b from both sides, then divide by a.
10
If each item costs 1 dollars and the total cost is 4, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
4
Solve for x: 7(x + -4) = 42
Solve a two-step equation.
Divide both sides by a, then subtract b.
10
Simplify: -3x + 5x + -4y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
2x - 4y
Solve for x: 10x + 30 = -30
Solve the linear equation.
Subtract b from both sides, then divide by a.
-6
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 for x: 4(x + -3) = -56
Solve a two-step equation.
Divide both sides by a, then subtract b.
-11
Solve: |-3x + -16| ≤ 4
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
-6 ≤ x ≤ -4
If each item costs -10 dollars and the total cost is 200, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
-20
What is 67% of 1000?
Compute the percent value (integer-safe).
Compute 67/100 × 1000.
670
What is 100% of 1?
Compute the percent value (integer-safe).
Compute 100/100 × 1.
1
What is 9% of 200?
Compute the percent value (integer-safe).
Compute 9/100 × 200.
18
Solve: |-3x + -5| = 12
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Simplify: -8x + -8x + -8y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-16x - 8y
What is 75% of 32?
Compute the percent value (integer-safe).
Compute 75/100 × 32.
24
If each item costs 10 dollars and the total cost is 60, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
6
Solve for x: -12x + -18 = 66
Solve the linear equation.
Subtract b from both sides, then divide by a.
-7
Solve: |-6x + 11| = 7
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
3
Simplify: 2x + -2x + -4y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-4y
What is 61% of 800?
Compute the percent value (integer-safe).
Compute 61/100 × 800.
488
Solve: |7x + 12| = 14
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve for x: -11x + -3 = -124
Solve the linear equation.
Subtract b from both sides, then divide by a.
11
Solve for x: 4x + -13 = -89
Solve the linear equation.
Subtract b from both sides, then divide by a.
-19
Simplify: -5x + 0x + -1y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
-5x - 1y
If each item costs -9 dollars and the total cost is -72, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
8
Solve for x: 12x + 7 = -29
Solve the linear equation.
Subtract b from both sides, then divide by a.
-3
Solve for x: 8(x + -6) = 16
Solve a two-step equation.
Divide both sides by a, then subtract b.
8
Solve: |-2x + -3| = 17
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
-10, 7
Solve: |-6x + 20| ≤ 12
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
2 ≤ x ≤ 5
If each item costs 19 dollars and the total cost is 228, how many items were bought?
Solve using algebra.
Divide total cost by price per item.
12
Solve: |6x + -9| ≤ 2
Find integer range of x satisfying the absolute inequality.
Isolate and produce interval then take integer bounds.
no integer solutions
What is 72% of 175?
Compute the percent value (integer-safe).
Compute 72/100 × 175.
126
Solve: |-8x + 8| = 10
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Solve: |4x + 11| = 16
Find integer solutions x, if any.
Set inside equal to ±c and solve both linear equations.
no integer solutions
Simplify: 5x + -5x + 8y
Combine like terms.
Add coefficients of like terms (x with x, y with y).
8y