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Chapter 4: Q56. (page 181)

Write an absolute value inequality for each graph.

Short Answer

Expert verified

Absolute value inequality is x+1>2

Step by step solution

01

- Definition of absolute value inequality

For real numbers aandb with b>0

Absolute value inequality is a<b when -b<aanda<b, and

Absolute value inequality is a>b when a<-bora>b

02

- Observation from image

From image, solution is all real less than-3 or greater than 1

03

- Write absolute value inequality

Let the real number be x

As x<-3orx>1

Since, adding same number on both sides does not change the sign of inequality

Add 1 on both sides

x+1<鈭�3+1orx+1>1+1x+1<鈭�2orx+1>2

So from definition, absolute value inequality is

x+1>2

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