1. Compound Inequalities
2.5
Creating and Solving
Compound Inequalities
LEARNING TARGETS:
I will be able to…
Write an graph compound inequalities.
Solve a compound inequality with and.
Solve a compound inequality with or.

2. Consists of two separate inequalities joined by AND or OR
Compound Inequality
Consists of two separate inequalities joined by
AND or OR

3. A tautology is a logic statement.
A compound statement using AND is true when both of the simple statements are true.
A compound statement using OR is true when one of the simple statements is true.

4. P Q P or Q P and Q True False P: Mrs. Dushek has brown hair.
Example
P: Mrs. Dushek has brown hair.
Q: Mrs. Dushek has hazel eyes.
∴ P and Q: Mrs. Dushek has brown hair and hazel eyes. P Q
P or Q
P and Q
True
False

5. (graph everything that is true)
OR means union
(graph everything that is true)
x < -2
x > 5
x<-2 or x>5
FINAL ANSWER: x < -2 or x > 5

6. (graph everything that is true)
OR means union
(graph everything that is true)
x < 7
x < 2
x<7 or x<2
FINAL ANSWER: x < 7

7. (graph the overlap where both graphs are true)
AND means intersection
(graph the overlap where both graphs are true)
x > -2
x < 7
x > -2 and x < 7
FINAL ANSWER: -2 < x < 7
HELPFUL HINT: Graph the solution to each inequality vertically. Easy to see overlap

8. AND means intersection
(look for the overlap)
x < 6
x < 1
x < 6 and x < 1
FINAL ANSWER: x < 1

9. AND means intersection
(look for the overlap)
x < -3
x > 2
x < -3 and x > 2
FINAL ANSWER: { }
Called the Empty Set (Nothing overlaps)

10. Write an inequality to describe each graph.

11. Translate into an inequality.
All real numbers that are greater than or equal to -4 and less than 4.
All real numbers that are less than -1 or greater than 2.
-4 < x < 4
x < -1 or x > 2

12. Solve and graph the solution.
-1 < x + 1 < 7

13. Solve and graph the solution.
3x – 2 > -11 or 2x + 8 > 16

14. Solve and graph the solution.
1 < -2x + 3 < 19

15. At an auction, the lowest bid for an autographed trading card is $20
At an auction, the lowest bid for an autographed trading card is $20. The highest bid is $54. Write and graph a compound inequality that describes the possible bids.

16. The perimeter of the rectangle must be between 20 and 50
The perimeter of the rectangle must be between 20 and 50. What are the possible values of x ?
x + 4 2x

17. Let’s see what you learned. Open the link below.

18. Homework
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