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Exploring Compound Inequalities: Solve and Graph with Precision

Learn to solve and graph compound inequalities, understanding the intersection and opposite directions of graphs. Apply skills to quality control levels for pool water pH, free chlorine, and alkalinity. Homework included.

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Exploring Compound Inequalities: Solve and Graph with Precision

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  1. Section 2.5 Creating and Solving Compound Inequalities

  2. Objective By following instructions students will be able to: Solve a compound inequality and graph the solution set.

  3. Def: compound statement is formed by combining two or more simple statements. A compound statement can be true or false. AND= both statements are true. OR= when either one statement is true or both.

  4. Explore A: P AND Q is true when ____________.

  5. Explore B: P OR Q is true when ____________.

  6. Def: A compound inequality consists of two separate inequalities joined by an “and” or “or.” “And” – two inequalities whose graphs intersect. “Or” – two inequalities whose graphs point in opposite directions.

  7. Def: A compound inequality consists of two separate inequalities joined by an “and” or “or.” “And” – two inequalities whose graphs intersect. “Or” – two inequalities whose graphs point in opposite directions.

  8. Explain 1A Solve and graph.

  9. Explain 1B Solve and graph.

  10. Your-Turn #1 Solve and graph. a) b)

  11. Explain 2A Solve and graph.

  12. Explain 2B Solve and graph.

  13. Reflect #1 Solve and graph. a) b) What kind of compound inequality has no solution? Your-Turn #2

  14. Explain 3A Write the compound inequality shown by each graph.

  15. Explain 3B Write the compound inequality shown by each graph.

  16. Your-Turn #3 Write the compound inequality shown by each graph. a) b)

  17. Explain 4A Write a compound inequality to represent the indicated quality-control level, and graph the solutions. The recommended pH level for swimming pool water is between 7.2 and 7.6, inclusive. Let p be the pH level of swimming pool water.

  18. Explain 4B Write a compound inequality to represent the indicated quality-control level, and graph the solutions. The recommended free chlorine level for swimming pool water is between 2.0 and 3.0 parts per million, inclusive. Let c be the free chlorine level in the pool.

  19. Your-Turn #4 Write a compound inequality to represent the indicated quality-control level, and graph the solutions. The recommended alkalinity level for swimming pool water is between 80 and 120 parts per million, inclusive.

  20. Revisit Objective Did we… Solve a compound inequality and graph the solution set?

  21. Homework HW: Page 73 #s 1-23, 26

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