This document discusses using sign charts to solve non-linear inequalities. Sign charts are used to determine the signs of expressions over intervals of x to identify possible solutions. Examples shown include using sign charts to solve inequalities like (3)1 0x x− + ≥, 2 3( 4) 0x x− < + 1, and 5 3 0x x+ < + − 3 1. Homework problems listed are from page 265 problems 33 through 54.

1. Homework QuestionsHomework Questions

2. Section 2.9Section 2.9
Sign ChartsSign Charts
Solving Non-LinearSolving Non-Linear
InequalitiesInequalities

3. Using sign charts:Using sign charts:

2 1
( 3)( 1)
x
x x
+
+ −

4. Using sign charts:Using sign charts:
 ( 3) 1 0x x− + ≥

5. Using sign charts:Using sign charts:

2
0
3
x
x
−
≤
+

6. Using sign charts:Using sign charts:

3
2
0
1
x x
x
−
≤
+

7. Using sign charts:Using sign charts:

2 3
( 4)
0
1
x x
x
−
<
+

8. Using sign charts:Using sign charts:

2
0
3
x
x
−
≤
+

9. Using sign charts:
 3 2
2 7 10 24 0x x x− − + >

10. Using sign charts:
 2 2
( 7)( 1) 0x x+ + <

11. Using sign charts:
 5 3
0
3 1x x
+ <
+ −

12. HomeworkHomework
 P. 265 (33-54)P. 265 (33-54)