# 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 82E
To determine

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

Expert Solution

x(,158)(98,) .

### Explanation of Solution

Given:

The given inequality is |8x+3|>12 .

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

|8x+3|>128x+3>12or8x+3<12{subtract 3 on both the sides}8x>9or8x+<15{divide both sides by 8}x>98orx<158i.ex(,158)(98,)

Hence,the solution set is x(,158)(98,) .

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

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!