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3.6 Solving Compound Inequalities

3.6 Solving Compound Inequalities. Algebra 5.0 Solve compound inequalities in one variable. Graph solution sets of compound inequalities in on variable. Vocabulary. Compound inequality -when two simple inequalities are combined into one statement by words AND or OR.

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3.6 Solving Compound Inequalities

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  1. 3.6 Solving Compound Inequalities Algebra 5.0 Solve compound inequalities in one variable. Graph solution sets of compound inequalities in on variable.

  2. Vocabulary Compound inequality-when two simple inequalities are combined into one statement by words AND or OR. Intersection- this is the overlapping region of two numbers lines and shows the numbers that are solutions to both inequalities. (AND) Union- this is the combined regions and show the numbers that are solutions of either inequality. (OR)

  3. Intersection AND inequalities are segments

  4. Example-Intersections (AND) Solve using AND and the other by inverse operations. Graph solutions.

  5. Intersections (AND) Every solution of a compound inequality involving AND must be a solution of both parts of the compound inequality. If no numbers are solutions of both simple inequalities, then the compound inequality has no solutions.

  6. Practice Solve a using AND and b using inverse operations. Graph solutions.

  7. Union OR inequalities are opposite rays

  8. Example- Union (OR) Solve and graph solutions. OR inequalities typically have OR in them

  9. Example- Union (OR) The solutions of a compound inequality involving OR are not always two separate sets of numbers. This is rare, but not impossible. Some numbers may be solutions of both parts of the compound inequality.

  10. Practice Solve and graph solutions.

  11. Example-Writing Compound Inequalities from Graph • Use the shaded region as the key. • If the shaded portion is: • Between two values  AND (2 ways to write them) • Not between two values  OR

  12. Practice • Write the compound inequality shown by each graph. Write the AND two ways.

  13. Review • Which compound inequality is an intersection and which is a union? • What does the AND inequality and OR inequality look like? • What are the two ways you can write an AND inequality solution?

  14. Review • Solve and graph the inequalities.

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