Solving Compound Inequalities

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Lesson 6-4

• Solving Compound Inequalities

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display the answers.
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Transparency 4a
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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

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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

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Working Backwards

• Start with the answer
• Undo the operation that got you to the answer
• Keep undoing until you get back to the beginning

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Example 1
Find the intersection.
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Example 2
and
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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.
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Example 3 cont
Now graph the solution set.
Find the union.
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Example 4
Then graph the solution set.
or
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Example 4 cont
Answer
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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