7th Grade Math · Unit 4
Solve the inequality. The symbol stays because the coefficient is positive.
The symbol can stay
The inequality symbol stays if you add, subtract, or multiply or divide by a positive number.
Every coefficient on this page is positive.
Undo in the same order
Undo addition or subtraction first. Then multiply or divide.
Do the same move on both sides.
A set of numbers
The solution is many numbers, not just one.
x > 4 means every number greater than 4.
One step. The coefficient is positive, so the symbol stays.
x + 5 > 12
x + 5 − 5 > 12 − 5
x > 7
Answer: x > 7
3x < 12
Divide both sides by 3.
x < 4
Answer: x < 4
2x > 10
Divide both sides by 2.
x > 5
Answer: x > 5
4x ≤ 20
Divide both sides by 4.
x ≤ 5
Answer: x ≤ 5
5x ≥ 15
Divide both sides by 5.
x ≥ 3
Answer: x ≥ 3
6x < 18
Divide both sides by 6.
x < 3
Answer: x < 3
x + 4 > 9
x + 4 − 4 > 9 − 4
x > 5
Answer: x > 5
x + 7 ≤ 10
x + 7 − 7 ≤ 10 − 7
x ≤ 3
Answer: x ≤ 3
x + 2 ≥ 11
x + 2 − 2 ≥ 11 − 2
x ≥ 9
Answer: x ≥ 9
x + 6 < 6
x + 6 − 6 < 6 − 6
x < 0
Answer: x < 0
x + 8 > 20
x + 8 − 8 > 20 − 8
x > 12
Answer: x > 12
Two steps with positive whole numbers. The symbol stays.
5x + 2 ≥ 17
5x + 2 − 2 ≥ 17 − 2
5x ≥ 15
Divide both sides by 5.
x ≥ 3
Answer: x ≥ 3
2x + 3 > 11
2x + 3 − 3 > 11 − 3
2x > 8
Divide both sides by 2.
x > 4
Answer: x > 4
3x + 1 < 13
3x + 1 − 1 < 13 − 1
3x < 12
Divide both sides by 3.
x < 4
Answer: x < 4
4x + 2 ≤ 18
4x + 2 − 2 ≤ 18 − 2
4x ≤ 16
Divide both sides by 4.
x ≤ 4
Answer: x ≤ 4
5x + 5 ≥ 30
5x + 5 − 5 ≥ 30 − 5
5x ≥ 25
Divide both sides by 5.
x ≥ 5
Answer: x ≥ 5
2x + 7 < 15
2x + 7 − 7 < 15 − 7
2x < 8
Divide both sides by 2.
x < 4
Answer: x < 4
3x + 4 > 19
3x + 4 − 4 > 19 − 4
3x > 15
Divide both sides by 3.
x > 5
Answer: x > 5
6x + 3 ≤ 27
6x + 3 − 3 ≤ 27 − 3
6x ≤ 24
Divide both sides by 6.
x ≤ 4
Answer: x ≤ 4
4x + 5 ≥ 25
4x + 5 − 5 ≥ 25 − 5
4x ≥ 20
Divide both sides by 4.
x ≥ 5
Answer: x ≥ 5
2x + 9 > 21
2x + 9 − 9 > 21 − 9
2x > 12
Divide both sides by 2.
x > 6
Answer: x > 6
3x + 6 < 24
3x + 6 − 6 < 24 − 6
3x < 18
Divide both sides by 3.
x < 6
Answer: x < 6
The coefficient is a positive fraction. The symbol still stays.
34x + 1 ≥ 7
34x + 1 − 1 ≥ 7 − 1
34x ≥ 6
Multiply both sides by 43.
x ≥ 8
Answer: x ≥ 8
12x + 3 < 7
12x + 3 − 3 < 7 − 3
12x < 4
Multiply both sides by 2.
x < 8
Answer: x < 8
23x + 1 > 5
23x + 1 − 1 > 5 − 1
23x > 4
Multiply both sides by 32.
x > 6
Answer: x > 6
34x + 2 ≤ 8
34x + 2 − 2 ≤ 8 − 2
34x ≤ 6
Multiply both sides by 43.
x ≤ 8
Answer: x ≤ 8
13x + 4 ≥ 8
13x + 4 − 4 ≥ 8 − 4
13x ≥ 4
Multiply both sides by 3.
x ≥ 12
Answer: x ≥ 12
32x + 3 < 12
32x + 3 − 3 < 12 − 3
32x < 9
Multiply both sides by 23.
x < 6
Answer: x < 6
43x + 2 > 10
43x + 2 − 2 > 10 − 2
43x > 8
Multiply both sides by 34.
x > 6
Answer: x > 6
25x + 1 ≤ 5
25x + 1 − 1 ≤ 5 − 1
25x ≤ 4
Multiply both sides by 52.
x ≤ 10
Answer: x ≤ 10
35x + 2 ≥ 8
35x + 2 − 2 ≥ 8 − 2
35x ≥ 6
Multiply both sides by 53.
x ≥ 10
Answer: x ≥ 10
54x + 1 < 11
54x + 1 − 1 < 11 − 1
54x < 10
Multiply both sides by 45.
x < 8
Answer: x < 8
14x + 5 > 8
14x + 5 − 5 > 8 − 5
14x > 3
Multiply both sides by 4.
x > 12
Answer: x > 12
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