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Lesson 6-4

Lesson 6-4. Solving Compound Inequalities. Transparency 4. Click the mouse button or press the Space Bar to display the answers. Transparency 4a. Objectives. Solve compound inequalities containing the word ‘ and’ and graph their solution sets

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Lesson 6-4

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  1. Lesson 6-4 Solving Compound Inequalities

  2. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 4a

  4. 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

  5. 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

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

  7. Graph the solution set of Answer: The solutionset is Note that the graph of includes the point 5. The graph of does not include 12. Graph Graph Example 1 Find the intersection.

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

  9. Inequality Cost pernight is atmost thecost is atleast $89 $109. or 89 or c c 109 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 $89per night and the cabins cost at least $109per night. Variables Let c be the cost of staying at the resort pernight.

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

  11. Example 4 Then graph the solution set. or

  12. Graph Graph Notice that the graph of contains every point in the graph of So, the union is the graph ofThe solution set is Example 4 cont Answer:

  13. 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

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