Math Practice Problems - Single Variable Inequalities

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:

Answers

Complexity=5, Mode=1

Solve. Sample answers: v>5, v>=6, z<=-3

#	Problem	Correct Answer	Your Answer
1	k + 3 < 6	Answer:
Solution k + 3 - 3 < 6 - 3 k < 3

#	Problem	Correct Answer	Your Answer
2	w + 4 > 10	Answer:
Solution w + 4 - 4 > 10 - 4 w > 6

Complexity=5, Mode=2

Solve. Sample answers: v>5, v>=6, z<=-3

Problem

Correct Answer

Your Answer

4g + 5 < ^-7

Answer:

Solution
4g + 5 - 5 < ^-7 - 5
4g < ^-12

Divide by 4

g < ^-3

Problem

Correct Answer

Your Answer

^-2e + 1 < 1

Answer:

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

Problem

Correct Answer

Your Answer

9j + 2 < ^-25

Answer:

Solution
9j + 2 - 2 < ^-25 - 2
9j < ^-27

Divide by 9

j < ^-3

Problem

Correct Answer

Your Answer

9c + 8 > 62

Answer:

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

Problem

Correct Answer

Your Answer

5(^-2j + 2) ≥ 100

Answer:

Solution
^-10j + 10 - 10 ≥ 100 - 10
^-10j ≥ 90

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

j ≤ ^-9

Problem

Correct Answer

Your Answer

4(4r - 4) ≥ 128

Answer:

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

Problem

Correct Answer

Your Answer

2(3w + 4) < 8

Answer:

Solution
6w + 8 - 8 < 8 - 8
6w < 0

Divide by 6

w < 0

Problem

Correct Answer

Your Answer

5(5q + 3) ≤ ^-135

Answer:

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

Problem

Correct Answer

Your Answer

5(3m + 2) > ^-65

Answer:

Solution
15m + 10 - 10 > ^-65 - 10
15m > ^-75

Divide by 15

m > ^-5

Problem

Correct Answer

Your Answer

3(3w - 3) < ^-63

Answer:

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

Problem

Correct Answer

Your Answer

4 > ^-4h + 40

Answer:

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

Problem

Correct Answer

Your Answer

^-6s + 2 < ^-2s - 30

Answer:

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

Problem

Correct Answer

Your Answer

^-3r - 4 ≥ ^-6r - 19

Answer:

Solution
^-3r - 4 + 4 ≥ ^-6r - 19 + 4
^-3r ≥ ^-6r - 15

^-3r + 6r ≥ ^-6r - 15 + 6r
3r ≥ ^-15

Divide by 3

r ≥ ^-5

Problem

Correct Answer

Your Answer

-k + 2 ≤ 2k - 19

Answer:

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

Problem

Correct Answer

Your Answer

^-10n + 4 ≤ ^-7n + 28

Answer:

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

Problem

Correct Answer

Your Answer

2z + 6 > 5z + 3

Answer:

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

Problem

Correct Answer

Your Answer

9c - 4 ≤ 5c + 8

Answer:

Solution
9c - 4 + 4 ≤ 5c + 8 + 4
9c ≤ 5c + 12

9c - 5c ≤ 5c + 12 - 5c
4c ≤ 12

Divide by 4

c ≤ 3

Problem

Correct Answer

Your Answer

15k + 3 ≥ 9k + 51

Answer:

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

Problem

Correct Answer

Your Answer

^-16q + 11 > ^-10q + 53

Answer:

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

Problem

Correct Answer

Your Answer

13q - 2 > 2q + 42

Answer:

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

Problem

Correct Answer

Your Answer

q + 14 < 8q + 28

Answer:

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

Problem

Correct Answer

Your Answer

^-10t + 4 ≤ ^-13t - 2

Answer:

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

^-10t + 13t ≤ ^-13t - 6 + 13t
3t ≤ ^-6

Divide by 3

t ≤ ^-2

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