Single Variable Inequalities Sample Problems

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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

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