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Chapter 1: Q26. (page 44)

Write an absolute value inequality for each graph

26.

Short Answer

Expert verified

Absolute value inequality is x-1鈮�3

Step by step solution

01

- Definition of absolute value inequality

For real numbers aandbwith 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 greater than or equal to -2 and less than or equal to 4

03

- Write absolute value inequality

Let the real number be x

As x鈮�-2andx鈮�4

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

Subtract 1 on both sides

x鈭�1鈮�鈭�2鈭�1andx鈭�1鈮�4鈭�1x鈭�1鈮�鈭�3andx鈭�1鈮�3

So from definition, absolute value inequality is

|x鈭�1|鈮�3

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