1. Solve Compound Inequalities
Section 6-4
Solve Compound Inequalities

2. Compound Inequality: Two separate inequalities joined by and or or.
• The graph of a compound inequality with and is the intersection of the graphs of the inequalities.
• The graphs go TOWARDS each other.
• The graph of a compound inequality with
or is the union of the graphs of the inequalities.
• The graphs go AWAY from each other.

3. Example 1 Write and graph compound inequalities:
a) All real numbers that are greater than or equal to -4 and less than 4.
-4 ≤ x < 4
Graph:

4. Example 1 Continued Write and graph compound inequalities:
b) All real numbers that are less than -1 or greater than 2.
x < -1 or x > 2
Graph:

5. Example 2 Solve a compound inequality with and: 1 < -2x + 3 < 19
-2 < -2x < 16
1 > x > -8
-8 < x < 1
Graph:
Given
APOI
Simplify
Flip inequalities b/c divided by negative!
MPOI
Simplify

6. Example 3 3x – 2 ≤ -11 or 2x + 8 > 16 +2 +2 - 8 -8 3x ≤ -9
Solve each inequality separately.
Solve a compound inequality with or:
3x – 2 ≤ or 2x + 8 > 16
Graph:
Given
Given
APOI
APOI
Simplify
3x ≤ -9
2x > 8
Simplify
MPOI
MPOI
Simplify
Simplify
x ≤ -3 or
x > 4

7. Homework Section 6-4 Pg. 384 – 387 3 – 5 Solve & Prove: 9 – 19 odd
Follow Directions: 21