lesson 6-4 solving compound inequalities. transparency 4 click the mouse button or press the space...
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Lesson 6-4
Solving Compound Inequalities
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Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
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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
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.
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Example 2
Then graph the solution set.
First express using and. Then solve each inequality.
and
Answer: The solution set is
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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.
Inequality Cost pernight
is atmost $89 or
thecost
is atleast $109.
c 89 109cor
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Example 3 contNow graph the solution set.
Graph
Graph
Find the union.
Answer:
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Example 4
Then graph the solution set.
or
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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
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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