Math Practice Problems - Single Variable Inequalities

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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=2

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

Complexity=10, Mode=2

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

Complexity=5, Mode=3

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

Complexity=6, Mode=3

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

Complexity=7, Mode=3

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

Complexity=5, Mode=4

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

Complexity=6, Mode=4

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

Complexity=7, Mode=4

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

Complexity=9, Mode=4

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

Complexity=12, Mode=4

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

Complexity=15, Mode=4

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

Answers

Complexity=5, Mode=1

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

Problem

Correct Answer

Your Answer

2p > ^-6

Answer:

Solution
Divide by 2

p > ^-3

Problem

Correct Answer

Your Answer

5w > 5

Answer:

Solution
Divide by 5

w > 1

Complexity=5, Mode=2

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

Problem

Correct Answer

Your Answer

^-2j + 4 < 6

Answer:

Solution
^-2j + 4 - 4 < 6 - 4
^-2j < 2

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

j > ^-1

Problem

Correct Answer

Your Answer

^-3r + 4 > 13

Answer:

Solution
^-3r + 4 - 4 > 13 - 4
^-3r > 9

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

r < ^-3

Complexity=10, Mode=2

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

Problem

Correct Answer

Your Answer

10g + 10 ≤ 60

Answer:

Solution
10g + 10 - 10 ≤ 60 - 10
10g ≤ 50

Divide by 10

g ≤ 5

Problem

Correct Answer

Your Answer

9c + 10 ≥ 10

Answer:

Solution
9c + 10 - 10 ≥ 10 - 10
9c ≥ 0

Divide by 9

c ≥ 0

Complexity=5, Mode=3

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

Problem

Correct Answer

Your Answer

3(^-3r + 2) ≤ 15

Answer:

Solution
^-9r + 6 - 6 ≤ 15 - 6
^-9r ≤ 9

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

r ≥ ^-1

Problem

Correct Answer

Your Answer

4(4q - 3) ≤ ^-60

Answer:

Solution
16q - 12 + 12 ≤ ^-60 + 12
16q ≤ ^-48

Divide by 16

q ≤ ^-3

Complexity=6, Mode=3

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

Problem

Correct Answer

Your Answer

2(^-2a + 3) < 34

Answer:

Solution
^-4a + 6 - 6 < 34 - 6
^-4a < 28

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

a > ^-7

Problem

Correct Answer

Your Answer

6(^-6x + 4) > 348

Answer:

Solution
^-36x + 24 - 24 > 348 - 24
^-36x > 324

Divide by ^-36
Reverse the inequality because we are dividing by a negative value.

x < ^-9

Complexity=7, Mode=3

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

Problem

Correct Answer

Your Answer

5(3a + 2) < ^-80

Answer:

Solution
15a + 10 - 10 < ^-80 - 10
15a < ^-90

Divide by 15

a < ^-6

Problem

Correct Answer

Your Answer

6(^-2k + 3) ≤ ^-54

Answer:

Solution
^-12k + 18 - 18 ≤ ^-54 - 18
^-12k ≤ ^-72

Divide by ^-12
Reverse the inequality because we are dividing by a negative value.

k ≥ 6

Complexity=5, Mode=4

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

Problem

Correct Answer

Your Answer

2h - 3 > ^-3h - 13

Answer:

Solution
2h - 3 + 3 > ^-3h - 13 + 3
2h > ^-3h - 10

2h + 3h > ^-3h - 10 + 3h
5h > ^-10

Divide by 5

h > ^-2

Problem

Correct Answer

Your Answer

4b - 4 > b + 8

Answer:

Solution
4b - 4 + 4 > b + 8 + 4
4b > b + 12

4b - b > b + 12 - b
3b > 12

Divide by 3

b > 4

Complexity=6, Mode=4

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

Problem

Correct Answer

Your Answer

5n - 5 < -n + 49

Answer:

Solution
5n - 5 + 5 < -n + 49 + 5
5n < -n + 54

5n + n < -n + 54 + n
6n < 54

Divide by 6

n < 9

Problem

Correct Answer

Your Answer

^-8d + 4 > ^-4d + 28

Answer:

Solution
^-8d + 4 - 4 > ^-4d + 28 - 4
^-8d > ^-4d + 24

^-8d + 4d > ^-4d + 24 + 4d
^-4d > 24

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

d < ^-6

Complexity=7, Mode=4

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

Problem

Correct Answer

Your Answer

3y + 3 > -y + 11

Answer:

Solution
3y + 3 - 3 > -y + 11 - 3
3y > -y + 8

3y + y > -y + 8 + y
4y > 8

Divide by 4

y > 2

Problem

Correct Answer

Your Answer

^-2t + 7 ≤ 4t - 29

Answer:

Solution
^-2t + 7 - 7 ≤ 4t - 29 - 7
^-2t ≤ 4t - 36

^-2t - 4t ≤ 4t - 36 - 4t
^-6t ≤ ^-36

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

t ≥ 6

Complexity=9, Mode=4

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

Problem

Correct Answer

Your Answer

^-11x + 7 ≥ ^-3x + 39

Answer:

Solution
^-11x + 7 - 7 ≥ ^-3x + 39 - 7
^-11x ≥ ^-3x + 32

^-11x + 3x ≥ ^-3x + 32 + 3x
^-8x ≥ 32

Divide by ^-8
Reverse the inequality because we are dividing by a negative value.

x ≤ ^-4

Problem

Correct Answer

Your Answer

^-14n + 1 ≥ ^-9n + 31

Answer:

Solution
^-14n + 1 - 1 ≥ ^-9n + 31 - 1
^-14n ≥ ^-9n + 30

^-14n + 9n ≥ ^-9n + 30 + 9n
^-5n ≥ 30

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

n ≤ ^-6

Complexity=12, Mode=4

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

Problem

Correct Answer

Your Answer

^-4d - 12 > ^-12d - 84

Answer:

Solution
^-4d - 12 + 12 > ^-12d - 84 + 12
^-4d > ^-12d - 72

^-4d + 12d > ^-12d - 72 + 12d
8d > ^-72

Divide by 8

d > ^-9

Problem

Correct Answer

Your Answer

20q + 4 > 10q + 54

Answer:

Solution
20q + 4 - 4 > 10q + 54 - 4
20q > 10q + 50

20q - 10q > 10q + 50 - 10q
10q > 50

Divide by 10

q > 5

Complexity=15, Mode=4

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

Problem

Correct Answer

Your Answer

16j + 14 ≥ 14j + 12

Answer:

Solution
16j + 14 - 14 ≥ 14j + 12 - 14
16j ≥ 14j - 2

16j - 14j ≥ 14j - 2 - 14j
2j ≥ ^-2

Divide by 2

j ≥ ^-1

Problem

Correct Answer

Your Answer

d + 12 < 8d - 2

Answer:

Solution
d + 12 - 12 < 8d - 2 - 12
d < 8d - 14

d - 8d < 8d - 14 - 8d
^-7d < ^-14

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

d > 2

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