# the solution of the inequality | x − a | &lt; | x − b | .

### 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 124E
To determine

## To find: the solution of the inequality |x−a|<|x−b| .

Expert Solution

|xa|<|xb| is x<ba .

### Explanation of Solution

Given:

If |ab| is the distance between a and b on the number line.

Calculation:

According to the question,

|x1| and |x1| represents the distance between x and 1, and x and 3 respectively

|x1|<|x3|(x1)2<(x3)2{squaering both sides}x22x+1<x26x+9{factor}2x+1<6x+9{simplify}4x<8x<2x<|31|

If a<b ,then the solution of |xa|<|xb| is x<ba

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