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

59.
61.
x
x
x
≥ 0
x 5x 7
Critical numbers: x 0, x 5, x 7
Test intervals: , 5, 5, 0, 0, 7, 7,
x
Test: Is
≥ 0?
x 5x 7
By testing an x-value in each test interval in the inequality,
we see that the domain set is: 5, 0 7,
2 ≥ 0
60.
2x 35
0.4x 2 5.26 < 10.2 62.
0.4x 2 4.94 < 0
0.4x 2 12.35 < 0
Critical numbers: x ±3.51
Test intervals: , 3.51, 3.51, 3.51, 3.51,
By testing an x-value in each test interval in the inequality,
we see that the solution set is: 3.51, 3.51
Section 2.7 Nonlinear Inequalities 233
x
x2 ≥ 0
9
x
≥ 0
x 3x 3
Critical numbers:
Test intervals: , 3 ⇒
3, 0 ⇒
0, 3 ⇒
3, ⇒
Domain: 3, 0 3,
1.3x 2 3.78 > 2.12
1.3x 2 1.66 > 0
x 3, x 0, x 3
x
< 0
x 3x 3
x
> 0
x 3x 3
x
< 0
x 3x 3
x
> 0
x 3x 3
Critical numbers: ±1.13
Test intervals: , 1.13, 1.13, 1.13, 1.13,
Solution set: 1.13, 1.13
63.
The zeros are x
Critical numbers: x 0.13,
x 25.13
Test intervals: , 0.13, 0.13, 25.13, 25.13,
By testing an x-value in each test interval in the inequality,
we see that the solution set is: 0.13, 25.13
12.5 ± 12.52 0.5x
40.51.6
.
20.5
2 12.5x 1.6 > 0 64.
1.2x
Critical numbers: 4.42, 0.42
Test intervals: , 4.42, 4.42, 0.42, 0.42,
Solution set: 4.42, 0.42
2 1.2x
4.8x 2.2 < 0
2 4.8x 3.1 < 5.3
65.
1
> 3.4 66.
2.3x 5.2
1
3.4 > 0
2.3x 5.2
1 3.42.3x 5.2
> 0
2.3x 5.2
7.82x 18.68
> 0
2.3x 5.2
Critical numbers: x 2.39, x 2.26
Test intervals: , 2.26, 2.26, 2.39, 2.39,
By testing an x-value in each test interval in the inequality,
we see that the solution set is: 2.26, 2.39
Critical numbers:
2
> 5.8
3.1x 3.7
2 5.83.1x 3.7
> 0
3.1x 3.7
23.46 17.98x
> 0
3.1x 3.7
x 1.19, x 1.30
Test intervals: , 1.19 ⇒
1.19, 1.30 ⇒
1.30, ⇒
Solution interval: 1.19, 1.30
23.46 17.98x
3.1x 3.7
23.46 17.98x
3.1x 3.7
23.46 17.98x
3.1x 3.7
> 0
< 0
< 0