This document discusses linear inequalities and their properties. A linear inequality is any relationship of the form ax + b, where a is not equal to 0. The key points covered include: - Linear inequalities can use the symbols <, >, ≤, or ≥ to represent relationships. - When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol flips. - Graphing linear inequalities results in solutions represented by regions on a number line. - Compound inequalities involving AND or OR statements can be solved by evaluating each inequality separately and combining the solutions appropriately.

1. Linear Inequalities
Section 3.9

2. What is a linear inequality?
A linear inequality is defined as any relationship
of the following form:
0
0
0




bax
bax
bax
bax
Where 0a

3. The Theory
Start with 4<6
Do the following: New Inequality Is it True?
Add 20 to both sides
Add -10 to both sides
Multiply both sides by -1
Divide both sides by -2
What do you do when you multiply or divide by
a negative number?

4. Homework Slide 2
Let’s look at:
1)
2)
3)
6352  pp
18.82.73.16  p
kk 31364 

5. Graphing Linear Inequalities

6. Group Work
AND and OR Statments

7. Solving Compound
Inequalities
1. Solve each inequality separately.
2. Choose OR or AND.
3. Graph both solutions on the same number
line.
4. Express final solution in interval notation or
set builder notation.

8. Homework Slide 4
Let’s look at:
1) AND
2) OR
3) OR
27 x
1035 x
912 x
27 x 912 x
51x

9. Homework
Exercises page 287
# 18, 21-24, 38-44, 53, 54, 55, 61, 64, 65, 66
No My Math Lab for the rest of the semester!