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Chapter 1: Q4. (page 43)

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers are between -8 and 8.

Short Answer

Expert verified

The absolute value inequality for all numbers between -8 and 8 is x<8

Step by step solution

01

-Write the inequalities 

Let the numbers are denoted by xbetween -8 and 8.

The inequalities for the numbers between -8 and 8 are as follows:

x>鈭�8

and

x<8

Therefore, the compound inequality will be -8<x<8.

02

– The absolute value inequality

The absolute inequality is defined as x<a for -a<x<a.

Therefore, the absolute value inequality for the numbers between -8 and 8 is as follows:

x>鈭�8

and

x<8

|x|<8

03

– Graph of the solution set 

The graph for the absolute inequality x<8 is as shown below

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