Creating and Solving Compound Inequalities

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Presentation transcript:

Creating and Solving Compound Inequalities Section 2.5 Creating and Solving Compound Inequalities

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

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.

Explore A: P Q P (T/F) Q (T/F) P and Q (T/F) A dog is a mammal. Red is a color. Red is not a color. A dog is a fish. P AND Q is true when ____________.

Explore B: P Q P (T/F) Q (T/F) P OR Q (T/F) 1 is an odd number. 2 is an even number. 2 is an odd number. 1 is an even number. P OR Q is true when ____________.

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.

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.

Explain 1A Solve and graph.

Explain 1B Solve and graph.

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

Explain 2A Solve and graph.

Explain 2B Solve and graph.

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

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

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

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

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.

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.

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.

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

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