1. Objective
The learner will solve & graph compound inequalities

2. Compound Inequalities
Lesson 6-4
Compound Inequalities

3. Definitions
Compound inequalities are two inequalities considered together.
Two inequalities that are joined by the word and or the word or form a compound inequality.
The word inclusive is related to the word included.
REMINDER: multiplying or dividing by a negative number changes the direction of the inequality.

4. To solve a compound inequality, first separate it into two inequalities. Determine whether the answer should be a union of sets ("or") or an intersection of sets ("and"). Then, solve both inequalities and graph.

7. Now you try:
Write a compound inequality that represents each situation. Graph your solution.
a. all real numbers greater than -2 but less than 9
b. The books were priced between $3.50 and $6.00, inclusive.

8. Just for thought
A solution of a compound inequality joined by and is any number that makes both inequalities true.
One way you can solve a compound inequality is by writing two inequalities.

10. Now you try:
Write an inequality that represents all real numbers that are at most -5 or at least 3. Graph your solution.

11. Just for thought.
For a compound inequality joined by or, you must solve each of the two inequalities separately.

12. Write an inequality for the situation
All real numbers at most -1 or at least 8.
In town, the maximum speed is 55 mph and the minimum speed is 20 mph

13. Solve the compound inequality:
Now you try:
Solve the compound inequality:
-2x + 7 > 3 or 3x – 4 ≥ 5
Graph your solution.

15. Word Problem
Jenny is saving money for an iphone and needs at least $ She has saved $ so far and is saving $10 a week.
Write an inequality to model the situation.
How many weeks will it be until Jenny has at least $300.00