# 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 85E
To determine

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

Expert Solution

x(6.001,5.999) .

### Explanation of Solution

Given:

The given inequality is |x+6|<0.001 .

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 inequality is expressed as

0.001<x+6<0.0010.0016<x<0.0016{subtract 6 on both the sides}6.001<x<5.999i.ex(6.001,5.999) .

Hence, the solution set is x(6.001,5.999) .

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

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