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Section 1.7 Linear Inequalities and Absolute Value Inequalities

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.

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Section 1.7 Linear Inequalities and Absolute Value Inequalities

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  1. Section 1.7Linear InequalitiesandAbsolute Value Inequalities

  2. Interval Notation

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

  4. Intersections and Unions of Intervals

  5. Example Find the set:

  6. Example Find the set:

  7. Solving Linear Inequalities in One Variable

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

  9. Y2=-x+4 Y1=2x+1 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. The region on the graph of the red box is where y1 is greater than y2. This is when x is greater than 1.

  10. Inequalities with Unusual Solution Sets

  11. Example Solve each inequality:

  12. Solving Compound Inequalities

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

  14. Solving Inequalities with Absolute Value

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

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

  17. Applications

  18. 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?

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

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

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