# an inequality involving an absolute value that describes the sets.

### 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 98E
To determine

## To find:an inequality involving an absolute value that describes the sets.

Expert Solution

|x+2|>1 .

### Explanation of Solution

Given:

A set of real number is graphed on the number line:

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, theequivalent form of the given set of real number is

x<3 or 1<x{add 2 on both the sides}x+3<0 or 2<x+3|x+2|<1or |x+2|>1|x+2|>1

Therefore, the inequality is |x+2|>1

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