Lesson 6-4 Solving Compound Inequalities

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Objectives Solve compound inequalities containing the word ‘and’ and graph their solution sets Solve compound inequalities containing the word ‘or’ and graph their solution sets

Vocabulary Compound inequality – two or more inequalities that are connected by the words ‘and’ or ‘or’ Intersection – the graph of a compound inequality containing ‘and’; the solution is the set of elements common to both inequalities Union – the graph of a compound inequality containing ‘or’; the solution is a solution of either inequality, not necessarily both

Working Backwards Start with the answer “Undo” the operation that got you to the answer Keep “undoing” until you get back to the beginning

Example 1 Graph the solution set of Find the intersection. Graph Answer:The solution set isNote that the graph ofincludes the point 5. The graph ofdoes not include 12.

Example 2 Then graph the solution set. First express using and. Then solve each inequality. and Answer: The solution set is

Example 3 Travel A ski resort has several types of hotel rooms and several types of cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount that a quest would pay per night at the resort. WordsThe hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. VariablesLet c be the cost of staying at the resort per night. Inequality Cost per night is at most $89 or the cost is at least $109. c c or

Example 3 cont Now graph the solution set. Graph Find the union. Answer:

Example 4 Then graph the solution set. or

Example 4 cont Graph Answer: Notice that the graph ofcontains every point in the graph ofSo, the union is the graph of The solution set is

Summary & Homework Summary: –The solution of a compound inequality containing and is the intersection of the graphs of the two inequalities –The solution of a compound inequality containing or is the union of the graphs of the two inequalities Homework: –Pg even