1. Creating and Solving Compound Inequalities
Section 2.5
Creating and Solving Compound Inequalities

2. Objective By following instructions students will be able to:
Solve a compound inequality and graph the solution set.

3. Def: compound statement is formed by combining two or more simple statements. A compound statement can be true or false.
AND= both statements are true.
OR= when either one statement is true or both.

4. Explore A: P Q P (T/F) Q (T/F) P and Q (T/F) A dog is a mammal.
Red is a color.
Red is not a color.
A dog is a fish.
P AND Q is true when ____________.

5. Explore B: P Q P (T/F) Q (T/F) P OR Q (T/F) 1 is an odd number.
2 is an even number.
2 is an odd number.
1 is an even number.
P OR Q is true when ____________.

6. Def: A compound inequality consists of two separate inequalities joined by an “and” or “or.” “And” – two inequalities whose graphs intersect. “Or” – two inequalities whose graphs point in opposite directions.

7. Def: A compound inequality consists of two separate inequalities joined by an “and” or “or.”
“And” – two inequalities whose graphs intersect.
“Or” – two inequalities whose graphs point in opposite directions.

8. Explain 1A
Solve and graph.

9. Explain 1B
Solve and graph.

10. Your-Turn #1
Solve and graph. a) b)

11. Explain 2A
Solve and graph.

12. Explain 2B
Solve and graph.

13. Reflect #1
What kind of compound inequality has no solution?
Your-Turn #2
Solve and graph. a) b)

14. Explain 3A
Write the compound inequality shown by each graph.

15. Explain 3B
Write the compound inequality shown by each graph.

16. Your-Turn #3
Write the compound inequality shown by each graph. a) b)

17. Explain 4A
Write a compound inequality to represent the indicated quality-control level, and graph the solutions.
The recommended pH level for swimming pool water is between 7.2 and 7.6, inclusive. Let p be the pH level of swimming pool water.

18. Explain 4B
Write a compound inequality to represent the indicated quality-control level, and graph the solutions.
The recommended free chlorine level for swimming pool water is between 2.0 and 3.0 parts per million, inclusive.
Let c be the free chlorine level in the pool.

19. Your-Turn #4
Write a compound inequality to represent the indicated quality-control level, and graph the solutions. The recommended alkalinity level for swimming pool water is between 80 and 120 parts per million, inclusive.

20. Revisit Objective Did we…
Solve a compound inequality and graph the solution set?

21. Homework
HW:
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