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Chapter 1: Q55. (page 46)

Solve 2x+11>1 for x.

Short Answer

Expert verified

x>-5orx<-6.

Step by step solution

01

– Description of step.

For all real numbers p and q, q>0,

Case1) If p<q then -q<p<q.

Case2) If p>q then p>qorp<-q.

02

– Description of step.

Apply case 2 to 2x+11>1 which implies 2x+11>1or 2x+11<-1.

03

– Description of step.

Solve 2x+11>1. Subtract 11 from each side of 2x+11>1.

2x+11鈭�11>1鈭�112x>鈭�10

04

– Description of step.

Divide each side of the obtained inequality by 2.

2x2>鈭�102x>鈭�5

05

– Description of step.

Solve 2x+11<-1. Subtract 11 from each side of 2x+11<-1.

2x+11鈭�11<鈭�1鈭�112x<鈭�12

06

– Description of step. 

Divide each side of the obtained inequality by 2.

2x2<鈭�122x<鈭�6

Therefore, x>-5orx<-6.

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