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

Graph

Answer: The solution set is Note that the graph of includes the point 5. The graphof does 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.

Words The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night.

Variables Let c be the cost of staying at the resort per night.

Inequality Cost pernight

is atmost $89 or

thecost

is atleast $109.

c 89 109cor

Example 3 contNow graph the solution set.

Graph

Graph

Find the union.

Answer:

Example 4

Then graph the solution set.

or

Example 4 cont

Graph

Graph

Answer:

Notice that the graph of contains every point in the graph of So, the union is the graph ofThe 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 342 14-44 even