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Chapter 4: Q57. (page 181)

Write an absolute value inequality for each graph

57.

Short Answer

Expert verified

Absolute value inequality is x-1<1

Step by step solution

01

- Definition of absolute value inequality

For real numbers aandb with 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 0 and less than 2

03

- Write absolute value inequality

Let the real number be x

As x>0andx<2

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

Subtract 1 on both sides

x−1>0−1andx−1<2−1x−1>−1andx−1<1

So from definition, absolute value inequality is

x-1<1

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Most popular questions from this chapter

For exercises 30 and 31, use the costs for an overnight stay at a hotel that are given below.

Single room: \(60 weekday; \)79 weekend

Double room: \(70weekday; \)89weekend

Suite: \(75 weekday; \)95 weekend

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3x-3y=6-6y=-305z-2x=6

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