# the absolute value inequality. Express the solution using interval notation and graph the solution set.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.7, Problem 83E
To determine

## To solve: the absolute value inequality. Express the solution using interval notation and graph the solution set.

Expert Solution

x(4,8) .

### Explanation of Solution

Given:

The given inequality is |x23|<2 .

Concept used:

Properties of absolute value inequalities:

 Inequality Equivalent form Graph |x|c x<−c or c

Calculation:

According to the properties of absolute value inequalities, the given inequalityis expressed as

2<x23<26<x2<6{mutiply 3 on both the sides}4<x<8{add 2 on both the sides}i.ex(4,8) .

Hence,the solution set is x(4,8) .

The solution set of the inequality graphed on the number line.

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