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Chapter 1: Q37. (page 44)

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

b-4>6

Short Answer

Expert verified

Solution of inequality is b<-2orb>10

Solution set in number line is

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

- Write properties of inequality

Properties of inequalities are written in following table:

03

- Simplify b-4>6

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

b-4<-6orb-4>6

Use addition property of inequality, add with same number does not reverse the sign of inequality as shown below

b鈭�4+4<鈭�6+4orb鈭�4+4>6+4b<鈭�2orb>10

04

- Graph the solution set

For b<-2orb>10, number line starts from -2 to -鈭� and from 10 to 鈭�

Open circle on -2and 10 shows these points are not included in the solution.

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