1. 6.4 Solving Compound Inequalities
A compound inequality has more than one part, contains an “and” or an “or” in the statement.
Inequalities containing “and”: True if and only if both inequalities are true.
This is called the intersection.
Graph the solution set of x > 5 and x < 10.
Graph them on the same number line. 5 10 6 4 11 9
Graph x > 5 first in one color.
Graph x < 10 second in another color.
Where they overlap is the answer.
Remember the answer does not include 5 or 10.

2. Another form of an “and” statement. (sandwich)
6 < x + 5 < 15
Break into 2 equations.
6 < x + 5 and x + 5 < 15
1 < x and x < 10
Graph
Try this one.
Graph the solution set of y > 5 and y < 12
The answer DOES include the 5 but not the 12. 5 12 6 4 11 13
Solution {x|1 < x < 10} 1 2 10 9 11

3. Try These Four
p #1, #2, #3, & #6

4. Inequalities containing “or”
These are called unions.
x > 5 or x < 1
Graph both on the same line.
Answer is anything that is shaded.
4k – 7 < 25 or 12 – 9k > 30
4k < k > 18
k < 8 k < -2
Graph on the same line.
Since the answer is anything shaded, you really only need k < 8. 1 2 5 6 -2 -1 8 7 9 4

5. Try These Two
p #4 & #5

6. Homework #42
p odd, 26-31, 33, 38, 51-53