1. Section 1.7 Linear Inequalities and Absolute Value Inequalities

2. Interval Notation

6. Example
Express the interval in set builder notation and graph:

7. Intersections and Unions of Intervals

10. Example
Find the set:

11. Example
Find the set:

12. Solving Linear Inequalities in One Variable

16. Example
Solve and graph the solution set on a number line:

17. Checking the solution of a linear inequality on a Graphing Calculator
Separate the inequality into two equations.
The intersection of the two lines is at (1,3). You can see this because both y values are the same, – 3.
The region in the red box is where the values of y1 is greater than y2.
Y2=-x+4
The region on the graph of the red box is where y1 is greater than y2. This is when x is greater than 1.
Y1=2x+1

18. Inequalities with Unusual Solution Sets

20. Example
Solve each inequality:

21. Solving Compound Inequalities

23. Example
Solve and graph the solution set on a number line.

24. Solving Inequalities with Absolute Value

26. Example
Solve and graph the solution set on a number line.

27. Example
Solve and graph the solution set on a number line.

28. Applications

29. Example
A national car rental company charges a flat rate of $320 per week for the rental of a 4 passenger sedan. The same car can be rented from a local car rental company which charges $180 plus $ .20 per mile. How many miles must be driven in a week to make the rental cost for the national company a better deal than the local company?

30. Solve the absolute value inequality.
(c)
(d)

31. Solve the linear inequality.
(b)
(c)
(d)