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Chapter 1: Q. 2 TB (page 106)

Find the solution sets of each of the following inequalities.

0<|x+5|<0.1

Short Answer

Expert verified

The solution set of inequality is-5.1,-5∪-5,-4.9.

Step by step solution

01

Step 1. Given information  

Given inequality is0<|x+5|<0.1.

02

Step 2. simplify the first inequality.

Take inequality 0<|x+5|.

0<x+5-5<x

or role="math" localid="1648512971119" 0<-x+50<-x+5-5>x

Sorole="math" localid="1648513556279" x∈-∞,-5∪-5,∞

03

Step 3. simplify the second inequality.

Take inequality |x+5|<0.1.

|x+5|<0.1x+5<0.1x<-4.9

or

role="math" localid="1648513291951" |x+5|<0.1-x+5<0.1-x-5<0.1x>-5.1

sorole="math" localid="1648513589151" -5.1<x<-4.9x∈-5.1,-4.9

04

Step 4. The solution set of the inequality.

Combine both inequalities.

x∈-∞,-5∪-5,∞∩-5.1,-4.9x∈-∞,-5∩-5.1,-4.9∪-5,∞∩-5.1,-4.9x∈-5.1,-5∪-5,-4.9

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