Section 1.7Linear InequalitiesandAbsolute Value Inequalities

Interval Notation

ExampleExpress the interval in set builder notation and graph:

Intersections andUnions of Intervals

ExampleFind the set:

ExampleFind the set:

Solving Linear Inequalitiesin One Variable

ExampleSolve and graph the solution set on a number line:

Checking the solution of a linear inequality on a Graphing CalculatorThe region on the graph of the red box is where y1 is greater than y2. This is when x is greater than 1.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.Separate the inequality into two equations.

Inequalities withUnusual Solution Sets

ExampleSolve each inequality:

Solving Compound Inequalities

ExampleSolve and graph the solution set on a number line.

Solving Inequalitieswith Absolute Value

ExampleSolve and graph the solution set on a number line.

ExampleSolve and graph the solution set on a number line.

Applications

ExampleA 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?

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

(a)

(b)

(c)(d)Solve the linear inequality.