## Single Variable Inequalities - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=5, Mode=1

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   k + 3 < 6 Answer: 2.   w + 4 > 10 Answer:

### Complexity=5, Mode=2

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   4g + 5 < - 7 Answer: 2.   - 2e + 1 < 1 Answer:

### Complexity=10, Mode=2

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   9j + 2 < - 25 Answer: 2.   9c + 8 > 62 Answer:

### Complexity=5, Mode=3

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   5(- 2j + 2) ≥ 100 Answer: 2.   4(4r - 4) ≥ 128 Answer:

### Complexity=6, Mode=3

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   2(3w + 4) < 8 Answer: 2.   5(5q + 3) ≤ - 135 Answer:

### Complexity=7, Mode=3

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   5(3m + 2) > - 65 Answer: 2.   3(3w - 3) < - 63 Answer:

### Complexity=5, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   4 > - 4h + 40 Answer: 2.   - 6s + 2 < - 2s - 30 Answer:

### Complexity=6, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   - 3r - 4 ≥ - 6r - 19 Answer: 2.   -k + 2 ≤ 2k - 19 Answer:

### Complexity=7, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   - 10n + 4 ≤ - 7n + 28 Answer: 2.   2z + 6 > 5z + 3 Answer:

### Complexity=9, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   9c - 4 ≤ 5c + 8 Answer: 2.   15k + 3 ≥ 9k + 51 Answer:

### Complexity=12, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   - 16q + 11 > - 10q + 53 Answer: 2.   13q - 2 > 2q + 42 Answer:

### Complexity=15, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
 1.   q + 14 < 8q + 28 Answer: 2.   - 10t + 4 ≤ - 13t - 2 Answer:

### Complexity=5, Mode=1

Solve. Sample answers: v>5, v>=6, z<=-3
1k + 3 < 6
Solution
k + 3 - 3 < 6 - 3
k < 3

2w + 4 > 10
Solution
w + 4 - 4 > 10 - 4
w > 6

### Complexity=5, Mode=2

Solve. Sample answers: v>5, v>=6, z<=-3
14g + 5 < - 7
Solution
4g + 5 - 5 < - 7 - 5
4g < - 12

Divide by 4

g < - 3

2- 2e + 1 < 1
Solution
- 2e + 1 - 1 < 1 - 1
- 2e < 0

Divide by - 2
Reverse the inequality because we are dividing by a negative value.

e > 0

### Complexity=10, Mode=2

Solve. Sample answers: v>5, v>=6, z<=-3
19j + 2 < - 25
Solution
9j + 2 - 2 < - 25 - 2
9j < - 27

Divide by 9

j < - 3

29c + 8 > 62
Solution
9c + 8 - 8 > 62 - 8
9c > 54

Divide by 9

c > 6

### Complexity=5, Mode=3

Solve. Sample answers: v>5, v>=6, z<=-3
15(- 2j + 2) ≥ 100
Solution
- 10j + 10 - 10 ≥ 100 - 10
- 10j ≥ 90

Divide by - 10
Reverse the inequality because we are dividing by a negative value.

j- 9

24(4r - 4) ≥ 128
Solution
16r - 16 + 16 ≥ 128 + 16
16r ≥ 144

Divide by 16

r ≥ 9

### Complexity=6, Mode=3

Solve. Sample answers: v>5, v>=6, z<=-3
12(3w + 4) < 8
Solution
6w + 8 - 8 < 8 - 8
6w < 0

Divide by 6

w < 0

25(5q + 3) ≤ - 135
Solution
25q + 15 - 15- 135 - 15
25q- 150

Divide by 25

q- 6

### Complexity=7, Mode=3

Solve. Sample answers: v>5, v>=6, z<=-3
15(3m + 2) > - 65
Solution
15m + 10 - 10 > - 65 - 10
15m > - 75

Divide by 15

m > - 5

23(3w - 3) < - 63
Solution
9w - 9 + 9 < - 63 + 9
9w < - 54

Divide by 9

w < - 6

### Complexity=5, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
14 > - 4h + 40
Solution
4 - 40 > - 4h + 40 - 40
- 36 > - 4h

Divide by - 4
Reverse the inequality because we are dividing by a negative value.

9 < h

h > 9

2- 6s + 2 < - 2s - 30
Solution
- 6s + 2 - 2 < - 2s - 30 - 2
- 6s < - 2s - 32

- 6s + 2s < - 2s - 32 + 2s
- 4s < - 32

Divide by - 4
Reverse the inequality because we are dividing by a negative value.

s > 8

### Complexity=6, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
1- 3r - 4 ≥ - 6r - 19
Solution
- 3r - 4 + 4- 6r - 19 + 4
- 3r- 6r - 15

- 3r + 6r- 6r - 15 + 6r
3r- 15

Divide by 3

r- 5

2-k + 2 ≤ 2k - 19
Solution
-k + 2 - 2 ≤ 2k - 19 - 2
-k ≤ 2k - 21

-k - 2k ≤ 2k - 21 - 2k
- 3k- 21

Divide by - 3
Reverse the inequality because we are dividing by a negative value.

k ≥ 7

### Complexity=7, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
1- 10n + 4 ≤ - 7n + 28
Solution
- 10n + 4 - 4- 7n + 28 - 4
- 10n- 7n + 24

- 10n + 7n- 7n + 24 + 7n
- 3n ≤ 24

Divide by - 3
Reverse the inequality because we are dividing by a negative value.

n- 8

22z + 6 > 5z + 3
Solution
2z + 6 - 6 > 5z + 3 - 6
2z > 5z - 3

2z - 5z > 5z - 3 - 5z
- 3z > - 3

Divide by - 3
Reverse the inequality because we are dividing by a negative value.

z < 1

### Complexity=9, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
19c - 4 ≤ 5c + 8
Solution
9c - 4 + 4 ≤ 5c + 8 + 4
9c ≤ 5c + 12

9c - 5c ≤ 5c + 12 - 5c
4c ≤ 12

Divide by 4

c ≤ 3

215k + 3 ≥ 9k + 51
Solution
15k + 3 - 3 ≥ 9k + 51 - 3
15k ≥ 9k + 48

15k - 9k ≥ 9k + 48 - 9k
6k ≥ 48

Divide by 6

k ≥ 8

### Complexity=12, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
1- 16q + 11 > - 10q + 53
Solution
- 16q + 11 - 11 > - 10q + 53 - 11
- 16q > - 10q + 42

- 16q + 10q > - 10q + 42 + 10q
- 6q > 42

Divide by - 6
Reverse the inequality because we are dividing by a negative value.

q < - 7

213q - 2 > 2q + 42
Solution
13q - 2 + 2 > 2q + 42 + 2
13q > 2q + 44

13q - 2q > 2q + 44 - 2q
11q > 44

Divide by 11

q > 4

### Complexity=15, Mode=4

Solve. Sample answers: v>5, v>=6, z<=-3
1q + 14 < 8q + 28
Solution
q + 14 - 14 < 8q + 28 - 14
q < 8q + 14

q - 8q < 8q + 14 - 8q
- 7q < 14

Divide by - 7
Reverse the inequality because we are dividing by a negative value.

q > - 2

2- 10t + 4 ≤ - 13t - 2
Solution
- 10t + 4 - 4- 13t - 2 - 4
- 10t- 13t - 6

- 10t + 13t- 13t - 6 + 13t
3t- 6

Divide by 3

t- 2