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Chapter 1: Q41. (page 44)

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

41. n≥n

Short Answer

Expert verified

Solution of inequality is all real number.

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 n≥n

For a>b, b is always greater than 0

So let n is a positive number

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

n≤-norn≥n

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

n≤−norn≥nnn≤−nnornn≥nn1≤−1(False)or1≥1(True)

04

- Graph the solution set

As solution is all real number, so all points on number line are solution of given inequality.

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