Single Variable Inequalities Sample Problems

Math Practice Online > free > lessons > Ohio > 8th grade > Single Variable Inequalities

If your child needs math practice, click here.

These sample problems below for Single Variable Inequalities were generated by the MathScore.com engine.

Sample Problems For Single Variable Inequalities

Complexity=5, Mode=1

Solve.

1. z + 2 > ^-1
Answer:

2. j + 2 > ^-1
Answer:

Complexity=5, Mode=2

Solve.

1. 5m + 1 <= 21
Answer:

2. 4j + 1 > 37
Answer:

Complexity=10, Mode=2

Solve.

1. 8t - 3 >= ^-43
Answer:

2. ^-6s + 10 < ^-8
Answer:

Complexity=5, Mode=3

Solve.

1. 4(5n + 4) < ^-144
Answer:

2. 3(2q + 4) > 24
Answer:

Complexity=6, Mode=3

Solve.

1. 2(6k + 2) >= 100
Answer:

2. 2(5e - 2) >= ^-34
Answer:

Complexity=7, Mode=3

Solve.

1. 6(2h + 5) <= 66
Answer:

2. 5(4y + 2) > ^-170
Answer:

Complexity=5, Mode=4

Solve.

1. -x + 1 >= x + 11
Answer:

2. y - 5 <= ^-2y + 7
Answer:

Complexity=6, Mode=4

Solve.

1. ^-9v + 2 >= ^-3v + 44
Answer:

2. ^-1 >= ^-2p - 3
Answer:

Complexity=7, Mode=4

Solve.

1. ^-2b - 5 < ^-5b + 4
Answer:

2. 14b + 7 < 7b + 56
Answer:

Complexity=9, Mode=4

Solve.

1. ^-9e + 7 < ^-6e + 25
Answer:

2. ^-3k + 3 < 2k + 38
Answer:

Complexity=12, Mode=4

Solve.

1. ^-20w + 3 >= ^-11w + 21
Answer:

2. 8g + 2 > ^-4g + 26
Answer:

Complexity=15, Mode=4

Solve.

1. 29q + 7 < 14q + 22
Answer:

2. ^-3z - 14 < ^-14z - 80
Answer:

Answers

Complexity=5, Mode=1

Solve.

#	Problem	Correct Answer	Your Answer
1	z + 2 > ^-1	Answer:
Solution z + 2 - 2 > ^-1 - 2 z > ^-3

#	Problem	Correct Answer	Your Answer
2	j + 2 > ^-1	Answer:
Solution j + 2 - 2 > ^-1 - 2 j > ^-3

Complexity=5, Mode=2

Solve.

Problem

Correct Answer

Your Answer

5m + 1 <= 21

Answer:

Solution
5m + 1 - 1 <= 21 - 1
5m <= 20

Divide by 5

m <= 4

Problem

Correct Answer

Your Answer

4j + 1 > 37

Answer:

Solution
4j + 1 - 1 > 37 - 1
4j > 36

Divide by 4

j > 9

Complexity=10, Mode=2

Solve.

Problem

Correct Answer

Your Answer

8t - 3 >= ^-43

Answer:

Solution
8t - 3 + 3 >= ^-43 + 3
8t >= ^-40

Divide by 8

t >= ^-5

Problem

Correct Answer

Your Answer

^-6s + 10 < ^-8

Answer:

Solution
^-6s + 10 - 10 < ^-8 - 10
^-6s < ^-18

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

s > 3

Complexity=5, Mode=3

Solve.

Problem

Correct Answer

Your Answer

4(5n + 4) < ^-144

Answer:

Solution
20n + 16 - 16 < ^-144 - 16
20n < ^-160

Divide by 20

n < ^-8

Problem

Correct Answer

Your Answer

3(2q + 4) > 24

Answer:

Solution
6q + 12 - 12 > 24 - 12
6q > 12

Divide by 6

q > 2

Complexity=6, Mode=3

Solve.

Problem

Correct Answer

Your Answer

2(6k + 2) >= 100

Answer:

Solution
12k + 4 - 4 >= 100 - 4
12k >= 96

Divide by 12

k >= 8

Problem

Correct Answer

Your Answer

2(5e - 2) >= ^-34

Answer:

Solution
10e - 4 + 4 >= ^-34 + 4
10e >= ^-30

Divide by 10

e >= ^-3

Complexity=7, Mode=3

Solve.

Problem

Correct Answer

Your Answer

6(2h + 5) <= 66

Answer:

Solution
12h + 30 - 30 <= 66 - 30
12h <= 36

Divide by 12

h <= 3

Problem

Correct Answer

Your Answer

5(4y + 2) > ^-170

Answer:

Solution
20y + 10 - 10 > ^-170 - 10
20y > ^-180

Divide by 20

y > ^-9

Complexity=5, Mode=4

Solve.

Problem

Correct Answer

Your Answer

-x + 1 >= x + 11

Answer:

Solution
-x + 1 - 1 >= x + 11 - 1
-x >= x + 10

-x - x >= x + 10 - x
^-2x >= 10

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

x <= ^-5

Problem

Correct Answer

Your Answer

y - 5 <= ^-2y + 7

Answer:

Solution
y - 5 + 5 <= ^-2y + 7 + 5
y <= ^-2y + 12

y + 2y <= ^-2y + 12 + 2y
3y <= 12

Divide by 3

y <= 4

Complexity=6, Mode=4

Solve.

Problem

Correct Answer

Your Answer

^-9v + 2 >= ^-3v + 44

Answer:

Solution
^-9v + 2 - 2 >= ^-3v + 44 - 2
^-9v >= ^-3v + 42

^-9v + 3v >= ^-3v + 42 + 3v
^-6v >= 42

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

v <= ^-7

Problem

Correct Answer

Your Answer

^-1 >= ^-2p - 3

Answer:

Solution
^-1 + 3 >= ^-2p - 3 + 3
2 >= ^-2p

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

^-1 <= p

p >= ^-1

Complexity=7, Mode=4

Solve.

Problem

Correct Answer

Your Answer

^-2b - 5 < ^-5b + 4

Answer:

Solution
^-2b - 5 + 5 < ^-5b + 4 + 5
^-2b < ^-5b + 9

^-2b + 5b < ^-5b + 9 + 5b
3b < 9

Divide by 3

b < 3

Problem

Correct Answer

Your Answer

14b + 7 < 7b + 56

Answer:

Solution
14b + 7 - 7 < 7b + 56 - 7
14b < 7b + 49

14b - 7b < 7b + 49 - 7b
7b < 49

Divide by 7

b < 7

Complexity=9, Mode=4

Solve.

Problem

Correct Answer

Your Answer

^-9e + 7 < ^-6e + 25

Answer:

Solution
^-9e + 7 - 7 < ^-6e + 25 - 7
^-9e < ^-6e + 18

^-9e + 6e < ^-6e + 18 + 6e
^-3e < 18

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

e > ^-6

Problem

Correct Answer

Your Answer

^-3k + 3 < 2k + 38

Answer:

Solution
^-3k + 3 - 3 < 2k + 38 - 3
^-3k < 2k + 35

^-3k - 2k < 2k + 35 - 2k
^-5k < 35

Divide by ^-5
Reverse the inequality because we are dividing by a negative value.

k > ^-7

Complexity=12, Mode=4

Solve.

Problem

Correct Answer

Your Answer

^-20w + 3 >= ^-11w + 21

Answer:

Solution
^-20w + 3 - 3 >= ^-11w + 21 - 3
^-20w >= ^-11w + 18

^-20w + 11w >= ^-11w + 18 + 11w
^-9w >= 18

Divide by ^-9
Reverse the inequality because we are dividing by a negative value.

w <= ^-2

Problem

Correct Answer

Your Answer

8g + 2 > ^-4g + 26

Answer:

Solution
8g + 2 - 2 > ^-4g + 26 - 2
8g > ^-4g + 24

8g + 4g > ^-4g + 24 + 4g
12g > 24

Divide by 12

g > 2

Complexity=15, Mode=4

Solve.

Problem

Correct Answer

Your Answer

29q + 7 < 14q + 22

Answer:

Solution
29q + 7 - 7 < 14q + 22 - 7
29q < 14q + 15

29q - 14q < 14q + 15 - 14q
15q < 15

Divide by 15

q < 1

Problem

Correct Answer

Your Answer

^-3z - 14 < ^-14z - 80

Answer:

Solution
^-3z - 14 + 14 < ^-14z - 80 + 14
^-3z < ^-14z - 66

^-3z + 14z < ^-14z - 66 + 14z
11z < ^-66

Divide by 11

z < ^-6

MathScore.com