1. Inequality
1

2. Rational Inequality
x ­ 1
Example < 0
(x ­ 2)(x + 3)
1. Simplify the rational expression so that zero is on one side
and the expression involving x is on the other side
2. Factor any quadratic expressions
3. Place critical numbers on a number line
Critical Numbers: the zeros, and the values that make
the inequality undefined(non­permissible values)
4. Test points within each interval between the critical values, to
determine if the expression as a whole is positive or negative
5. State the intervals that qualify as solutions to the
inequality
2

3. Solve the inequality
x ­ 1
< 0
(x ­ 2)(x + 3)
­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10
3

4. x ­ 1
The graph of y = (x ­ 2)(x + 3)
< 0
4

5. Solve:
x2 ­ 2x ­ 8
> 0
_
x ­ 1
­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10
5

6. Graph of y = x2 ­ 2x ­ 8
x ­ 1
6

7. Solve
x 1
>
x ­ 3 x + 2
­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10
7

8. 8

9. Absolute Value Inequality
Graph y = x Graph y = x
9

10. Graph y = x + 5 What will graph of
y = x + 5 look like?
10

11. 11

12. 12

13. 13

14. Solve graphically x ­ 2 <
_ 5
14

15. Solve algebraically x ­ 2 <
_ 5
15

16. x
+ 1 _
< 3
2
16

17. x
Solve algebraically + 1 _
< 3
2
17

18. Exercise 28
questions 6 ­ 12
18