# 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 88E
To determine

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

Expert Solution

x>157orx<137 .

### Explanation of Solution

Given:

The given inequality is 7|x+2|+5>4 .

Concept used:

Properties of absolute value inequalities:

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

Calculation:

The given expression is expressed as

7|x+2|>1{subtract 5 from both the sides}|x+2|>17{divide 7 from both the sides}

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

|x+2|>17x+2>17orx+2<(17)x+2>17orx+2<17{subtract 2 on both the sides}x>172orx<172x>157orx<137

Hence,the solution set is x>157orx<137 .

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

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