# 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 76E
To determine

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

Expert Solution

x(,2][2,) .

### Explanation of Solution

Given:

The given inequality is 12|x|1 .

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, thegiven inequalityis expressed as

|x|2{multiply by 2}x>2or2x<2i.ex(,2][2,)

Hence,the solution set is x(,2][2,) .

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

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