C H A P T E R 2 Polynomial and Rational Functions

230 Chapter 2 Polynomial and Rational Functions
43.
45.
Critical numbers:
Test intervals:
Test: Is
By testing an x-value in each test interval in the inequality,
we see that the solution set is: 5, 3
7x 1
> 0?
x 52x 3 3
2 , 1 , 1, , 5, 5, 3 2
,
x 1, x 5, x 3
2
−5
4x 3 9x 3
x 34x 3
Critical numbers:
Test intervals:
30 5x
Test: Is
≤ 0?
x 34x 3
By testing an x-value in each test interval in the inequality,
we see that the solution set is:
−4
1
x 3
9
≤ 0
4x 3
30 5x
≤ 0
x 34x 3
−2
−4
− 3
4
0
−3
2
−2
3
−
3
2
4
x 5 >
4
x 5
1
> 0
2x 3
42x 3 x 5
x 52x 3
−1
0
1
x 3 ≤
, 3
4 , 3
4 , 3 , 3, 6, 6,
4 6 8
> 0
7x 7
> 0
x 52x 3
≤ 0
9
4x 3
x 3, x 3
, x 6
4
x
1
2x 3
x
2 1,
3
4 , 3 6,
44.
46.
Critical numbers:
Test intervals:
Solution intervals: 14, 2 6,
−14
−2
−15 −10 −5 0 5
1
x ≥
1x 3 1x
≥ 0
xx 3
3
≥ 0
xx 3
Critical numbers:
5
x 6 >
5x 2 3x 6
> 0
x 6x 2
2x 28
> 0
x 6x 2
2, 6 ⇒
6, ⇒
1
x 3
Test intervals: , 3 ⇒
3, 0 ⇒
0, ⇒
Solution intervals: , 3 0,
−4 −3 −2 −1 0 1
6
10
3
x 2
x 14, x 2, x 6
, 14 ⇒
14, 2 ⇒
x
x 3, x 0
x
2x 28
< 0
x 6x 2
2x 28
> 0
x 6x 2
2x 28
< 0
x 6x 2
2x 28
> 0
x 6x 2
3
> 0
xx 3
3
< 0
xx 3
3
> 0
xx 3