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Worksheets

Absolute Value Equations and Inequalities

Total questions: 10

Worksheet time: 8mins

Name
Class
Date
1.

Which of the following statements is TRUE?

I. The absolute value of a number is its distance from 0 on the number line.

II. Absolute values are always greater than or equal to zero.

III. For any algebraic expression X, and any positive real number a, if |X| = a, then X = a or X = -a.

a)

I and II only.

b)

I and III only.

c)

II and III only.

d)

I, II, and III.

2.

Which of the following is the solution set of the AVE |x + 2| = 7?

a)

{-9, 5}

b)

{-5, 9}

c)

[-9,5]

d)

(-5,9)

3.

Which of the following mathematical sentences is represented by the given graph?

a)

x ≥ 2

b)

|x| = 2

c)

|x| > 2

d)

|x| = ±2

4.

What is the sum of the solutions of the AVE |x - 7| + 1 = 3?

a)

10

b)

12

c)

14

d)

16

5.

Which of the following absolute-value inequality corresponds to –2 < x < 4?

a)

|x| < 4

b)

|x| > -2

c)

|x| < 2

d)

|x - 1| < 3

6.

For any algebraic expression χ, and any positive real number a, which of the following is NOT TRUE?

a)

If |χ| < α, then, -α < χ < α

b)

If |χ| ≤ α, then, -α ≤ χ ≤ α

c)

If |χ| α, then, -α ≥ χ ≥ α

d)

If |χ| > α, then, χ > α or χ <

7.

Which of the following compound inequalities represents the AVI | 2x – 3 | > 5, when split into compound inequalities?

a)

-5 < 2x - 3 < 5

b)

-5 > 2x - 3 > 5

c)

2x - 3 > 5 or 2x - 3 < -5

d)

2x - 3 > ± 5

8.

What is the solution set of the AVI | x – 3 | < 0?

a)

(−∞,∞)

b)

{ }

c)

{3}

d)

(−∞,3) ∪ (3,∞)

9.

For any algebraic expression X, which of the following statements is NOT TRUE?

a)

The solution set of |x| > -1 is (−∞, ∞).

b)

The solution set of |x| < -1 is { }.

c)

The solution set of |x| ≤ 0 is { 0 }.

d)

The solution set of |x| > 0 is (−∞, ∞).

10.

What is the solution set of the AVI | x – 5 | > -8?

a)

(−∞,∞)

b)

{ }

c)

{-3, 13}

d)

(−∞,-3) ∪ (13,∞)