Free Printable Absolute Value Inequalities

1.

Solve.

|x + 4| < 5

a)

x < -9 or x > 1

b)

-9 < x < 1

c)

x < 9 or x > -1

d)

-1 < x < 9

2.

Solve.
|y - 4| ≥ 8

a)

y ≤ -4 or y ≥ 12

b)

-4 ≤ y ≤ -12

c)

y ≤ 4 or y ≥ -12

d)

-12 ≤ x ≤ 4

3.

Solve.
|y - 1| ≤ 6

a)

-7 ≤ y ≤ 5

b)

y ≤ -7 or y ≥ 5

c)

-5 ≤ y ≤ 7

d)

y ≤ -5 or y ≥ 7

4.

Solve.
|3c - 4| < 12

a)

-2 2/3 < c < 5 1/3

b)

c < -5 1/3 or c > 2 2/3

c)

c < 5 1/3 or c > -2 2/3

d)

-5 1/3 < c < 2 2/3

5.

Solve.
|3c - 4| < 12

a)

-2 2/3 < c < 5 1/3

b)

c < -5 1/3 or c > 2 2/3

c)

c < 5 1/3 or c > -2 2/3

d)

-5 1/3 < c < 2 2/3

6.

Solve.

3|d - 4| ≥ 12

a)

d = -8 or d = 0

b)

no solution

c)

d ≥ 8 or d ≤ 0

d)

d = 40 or d = 32

7.

Solve.

|d + ⅔| + ¾ < 0

a)

no solution

b)

d > -9 and d < ½

c)

d > -¾ and d < 9

d)

d < -1/12 and d > -7/12

8.

Solve.
|5x + 7| < 22

a)

x < -5 ⅘ or x > 3

b)

-5 ⅘ < x < 3

c)

-3 < x < 5 ⅘

d)

x < -3 or x > 5 ⅘

9.

Solve.

|4v + 12| ≥ 6

a)

v ≤ -4.5 or v ≥ -1.5

b)

-4.5 ≤ v ≤ -1.4

c)

-1.5 ≤ v ≤ 4.5

d)

v ≤ -1.5 or v ≥ 4.5

10.

Solve.

3|2d + 9| + 13 > 10

a)

d > 5 or d < -1

b)

d < -4 or d > 5

c)

No Solution

d)

All real numbers

11.

Which interval notation is represented by the graph?

a)

$\left(-20,\ -10\right)$

b)

$\left[-20,\ -10\right]$

c)

$\left(-20,\ -10\right]$

d)

$\left[-20,\ -10\right)$

12.

Which interval notation is represented by the graph?

a)

$\left(-16,\ 2\right)$

b)

$\left[-16,\ 4\right]$

c)

$\left(-\infty,-16\right)\cup\left(2,\ \infty\right)$

d)

( $-\infty,-16$ ] , [ $2,\infty$ )

13.

Identify the absolute value inequality that would generate the given graph.

a)

$\left|x+12\right|>5$

b)

$\left|x+12\right|\ge5$

c)

$\left|x+12\right|<5$

d)

$\left|x+12\right|\le5$

14.

Identify each value that is a solution to the indicated inequality. $\left|x\right|-2\le0$

a)

$-4$

b)

$-2$

c)

$0$

d)

$1$

e)

$4$

Absolute Value Inequalities

Total questions: 14

Worksheet time: 52mins

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