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Section 1.7 Linear Inequalities and Absolute Value Inequalities

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Interval Notation

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Example Express the interval in set builder notation and graph:

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Intersections and Unions of Intervals

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Example Find the set:

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Example Find the set:

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Solving Linear Inequalities in One Variable

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

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Checking the solution of a linear inequality on a Graphing Calculator Y1=2x+1 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. 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.

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Inequalities with Unusual Solution Sets

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Example Solve each inequality:

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Solving Compound Inequalities

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

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Solving Inequalities with Absolute Value

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

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

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Applications

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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?

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

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

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