# Section 1.7 Linear Inequalities and Absolute Value Inequalities

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Section 1.7 Linear Inequalities and Absolute Value Inequalities

Interval Notation

Example Express the interval in set builder notation and graph:

Intersections and Unions of Intervals

Example Find the set:

Example Find the set:

Solving Linear Inequalities in One Variable

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

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

Inequalities with Unusual Solution Sets

Example Solve each inequality:

Solving Compound Inequalities

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

Solving Inequalities with Absolute Value

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

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

Applications

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?

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

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