Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 315

EXAMPLE
Solve the inequality.

2 x – 7 > 5x + 2

We begin by collecting terms with x in them on the left side of the equa-
tion and terms without x in them on the right side.

2752

77

259

55

39

3

3

9

3

xx

xx

xx

x

x

-> +

++

>+

--

->

<

Thesignnchangedatthisstep.

x<- 3

Solve the inequality.

--^1 +>-

2

() 46 xx 27

-++>- 23 xx 27 Distribute -^1

2

.

• 2 x + 5 > x - 7
  
  
  • x -x
  
  
  
  


• 3 x + 5 > - 7


• 5 - 5


• 3 x > - 12


• 
  


• 
  

<-

3

3

12

3

x The sign changed at this step.

x < 4

Solve the inequality.

2 x + 1 < 5

• 1 - 1

2 x < 4
2
2

4

2

x≤ Because2ispositive,wedonotchangethhesign.

x < 2

EXAMPLE
Solve the inequality.