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Chapter 1: Q34. (page 44)

Solve each inequality. Graph the solution set on a number line.

2m鈮�8

Short Answer

Expert verified

Solution of inequality is m鈮�-4orm鈮�4

Solution set in number line is

Step by step solution

01

- Definition of absolute value inequality

For real numbers aandb with b>0

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

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

02

- Write properties of inequality

Properties of inequalities are written in following table:

03

- Simplify 2m≥8

From definition of absolute value inequality, given expression is simplified to

2m鈮�-8or2m鈮�8

Use division property of inequality, divide with same positive number does not reverse the sign of inequality as shown below

2m2鈮�鈭�82or2m2鈮�82m鈮�鈭�4orm鈮�4

04

- Graph the solution set

For m鈮�-4orm鈮�4, number line starts from -4 to -鈭� and from 4 to 鈭�

Dot on -4and 4 shows these points are included in the solution.

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