C H A P T E R 2 Polynomial and Rational Functions
C H A P T E R 2 Polynomial and Rational Functions
C H A P T E R 2 Polynomial and Rational Functions
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39.<br />
−2 −1 0 1 2 3 4 5<br />
x<br />
Section 2.7 Nonlinear Inequalities 229<br />
x 6<br />
2 < 0<br />
x 1<br />
40.<br />
x 12<br />
3 ≥ 0<br />
x 2<br />
x 6 2x 1<br />
< 0<br />
x 1<br />
x 12 3x 2<br />
≥ 0<br />
x 2<br />
4 x<br />
< 0<br />
x 1<br />
6 2x<br />
≥ 0<br />
x 2<br />
Critical numbers: x 1, x 4<br />
Critical numbers: x 2, x 3<br />
Test intervals: , 1, 1, 4, 4, <br />
Test intervals: , 2 ⇒<br />
4 x<br />
Test: Is < 0?<br />
x 1<br />
6 2x<br />
2, 3 ⇒<br />
x 2<br />
By testing an x-value in each test interval in the inequality,<br />
we see that the solution set is: , 1 4, <br />
3, ⇒<br />
3 6 9<br />
12 15 18<br />
Solution interval: 2, 3<br />
−2 −1 0 1 2 3<br />
−2 −1<br />
−<br />
1<br />
2<br />
0 1 2<br />
x<br />
x<br />
6 2x<br />
x 2<br />
6 2x<br />
x 2<br />
41.<br />
3x 5<br />
> 4<br />
x 5<br />
42.<br />
3x 5<br />
4 > 0<br />
x 5<br />
3x 5 4x 5<br />
> 0<br />
x 5<br />
15 x<br />
> 0<br />
x 5<br />
Critical numbers:<br />
Critical numbers: x 5, x 15<br />
Test intervals: , 5, 5, 15, 15, <br />
Test intervals:<br />
15 x<br />
Test: Is > 0?<br />
x 5<br />
By testing an x-value in each test interval in the inequality,<br />
we see that the solution set is: 5, 15<br />
5<br />
x<br />
Solution intervals: , 1<br />
2 1, <br />
1 1 x<br />
, 1 ⇒ > 0<br />
2 1 2x<br />
1 x<br />
1, ⇒ < 0<br />
1 2x<br />
<br />
, 1<br />
x <br />
1 x<br />
⇒ < 0<br />
2 1 2x 1<br />
5 7x<br />
< 4<br />
1 2x<br />
5 7x 41 2x<br />
< 0<br />
1 2x<br />
1 x<br />
< 0<br />
1 2x<br />
, x 1<br />
2<br />
> 0<br />
< 0<br />
< 0