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Section 1.7 Linear Inequalities and Absolute Value Inequalities Slide 2 Interval Notation Slide 3 Slide 4 Slide 5 Slide 6 Example Express the interval in set builder notation and graph: Slide 7 Intersections and Unions of Intervals Slide 8 Slide 9 Slide 10 Example Find the set: Slide 11 Example Find the set: Slide 12 Solving Linear Inequalities in One Variable Slide 13 Slide 14 Slide 15 Slide 16 Example Solve and graph the solution set on a number line: Slide 17 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. Slide 18 Inequalities with Unusual Solution Sets Slide 19 Slide 20 Example Solve each inequality: Slide 21 Solving Compound Inequalities Slide 22 Slide 23 Example Solve and graph the solution set on a number line. Slide 24 Solving Inequalities with Absolute Value Slide 25 Slide 26 Example Solve and graph the solution set on a number line. Slide 27 Example Solve and graph the solution set on a number line. Slide 28 Applications Slide 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? Slide 30 (a) (b) (c) (d) Solve the absolute value inequality. Slide 31 (a) (b) (c) (d) Solve the linear inequality.