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.