1. College Algebra Chapter 1 Equations and Inequalities
Section 1.7
Linear, Compound, and Absolute Value Inequalities

2. 1. Solve Linear Inequalities in One Variable
2. Solve Compound Linear Inequalities
3. Solve Absolute Value Inequalities
4. Solve Applications of Inequalities

3. Solve Linear Inequalities in One Variable
Properties of Inequality
Let a, b, and c represent real numbers.
These statements are also true expressed with the symbols , >, and .

4. Example 1:
Solve the inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

5. Example 2:
Solve the inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

7. Example 3:
Solve the inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

8. Example 4:
Solve the inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

10. Example 5:
Solve the inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

11. Example 6:
Solve the inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

12. 1. Solve Linear Inequalities in One Variable
2. Solve Compound Linear Inequalities
3. Solve Absolute Value Inequalities
4. Solve Applications of Inequalities

13. Solve Compound Linear Inequalities
“and” means intersection
“or” means union

14. Example 7:
Solve the compound inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

16. Example 8:
Solve the compound inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

18. Example 9:
Solve the compound inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

19. Example 10:
Solve the compound inequality. Graph the solution set, and write the solution in set-builder notation and interval notation.

20. Solve Compound Linear Inequalities
Three-part compound inequality (x is between two values): the goal is to isolate x in the middle region

21. Example 11:

22. Example 12:

23. Example 13:

24. Solve Compound Linear Inequalities
Note: A three-part inequality is used to imply that x is between two values.
Yes No

26. 1. Solve Linear Inequalities in One Variable
2. Solve Compound Linear Inequalities
3. Solve Absolute Value Inequalities
4. Solve Applications of Inequalities

27. Solve Absolute Value Inequalities
Example:

28. Example 14:
Solve

29. Example 15:
Solve

31. Solve Absolute Value Inequalities
Example:

32. Example 16:
Solve

33. Example 17:
Solve

35. Example 18:
Solve

36. Example 19:
Solve

38. 1. Solve Linear Inequalities in One Variable
2. Solve Compound Linear Inequalities
3. Solve Absolute Value Inequalities
4. Solve Applications of Inequalities

39. Example 20:
The pH of the water in a public swimming pool should be maintained at a safe swimming value of 7.4. Slight variations in the tested value of the pH levels are acceptable but should differ from the ideal pH level by no more than 0.2.
a. If x represents the exact pH value tested, write an absolute value inequality that represents a safe interval for x.

40. Example 20 continued:
b. Solve the inequality and interpret the answer.

41. Example 21:
One cell phone service charges a flat rate of $35 a month plus1¢ per text. Another company offers a flat monthly fee of $50 with unlimited texting. How many texts would you need to send for the first company to charge you more per month than the second company?

42. Example 21 continued: