1. Chapter 4: Solving Inequalities
4.5
Compound Inequalities

2. X > 5 and x < 7 written as 5 < x < 7
Compound Inequality
Two inequalities joined by the word “and” or the word “or”
“And” compound inequalities are sometimes written all together:
X > 5 and x < 7 written as 5 < x < 7

3. Example 1
Write a compound inequality to represent the situation and graph the solution:
All real numbers that are at least -2 and at most 4

4. Example 1a
Write a compound inequality to represent the situation and graph the solution:
Today’s temperatures will be above 32⁰F but not as high as 40⁰F

5. Example 1c
Write a compound inequality to represent the situation and graph the solution:
All real numbers greater than -2 but less than 9

6. Example 1d
Write a compound inequality to represent the situation and graph the solution:
The books were priced between $3.50 and $6.00, inclusive

7. Example 2
Solve -4 < r – 5 ≤ -1 and graph the solution

8. Example 2a
Solve -6 ≤ 3x < 15 and graph the solution

9. Example 2b
Solve -3 < 2x – 1 < 7 and graph the solution

10. Example 2c
Solve 7 < -3n + 1 ≤ 13 and graph the solution

11. Example 3
The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8, inclusive. The first two readings for a swimming pool are 7.4 and What possible values for the third reading p will make the average pH normal?

12. Example 3a
Suppose the first two readings for the acidity of water in a swimming pool are 7.0 and What possible values for the third reading will make the average pH normal?

13. Example 4
Write a compound inequality that represents the situation and graph the solution:
All real numbers that are less than -3 or greater than 7.

14. Example 4a
Write a compound inequality that represents the situation and graph the solution:
Discounted fares are available to children 12 and under or to adults at least 60 years of age.

15. Example 4b
Write a compound inequality that represents the situation and graph the solution:
All real numbers that are at most -5 or at least 3.

16. Example 5
Solve 4v + 3 < -5 or -2v + 7 < 1 and graph the solution.

17. Example 5a
Solve -2x + 7 > 3 or 3x – 4 ≥ 5 and graph the solution

18. Homework
P. 230
6-38 even, 54