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Compound Inequalities. Vocabulary. Compound Inequality – two inequalities joined by the words “and” or “or”. Investigation. Stand if the following condition applies. You have a birthday between January and June. Investigation. Stand if the following condition applies.
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Vocabulary • Compound Inequality – two inequalities joined by the words “and” or “or”
Investigation Stand if the following condition applies • You have a birthday between January and June
Investigation Stand if the following condition applies • You have a birthday between the first and the tenth of the month
Investigation Stand if the following condition applies • You have a birthday between January and June, AND you have a birthday between the first and the tenth of the month
Investigation Stand if the following condition applies • You have a birthday between January and June, OR you have a birthday between the first and the tenth of the month
Investigation What other words might you use instead of “and” & “or” ?
Conditional Inequalities • Any graph of an equation, represents all possible solutions to the equation • When two equations are connected with AND, the solution set includes only the points that satisfy BOTH equations • When two equations are connected with OR, the solutions set includes only the points that satisfy EITHER equation
Graph the solution set of Graph Graph Example 4-1a Find the intersection.
Answer: The solutionset is Note that the graph of includes the point 5. The graph of does not include 12. Example 4-1a Compound Inequalities with AND can be written on one line like above 5 ≤ y ≤ 12 Inequalities with OR must be written separately
Graph the solution set of and Example 4-1b
Then graph the solution set. First express using and. Then solve each inequality. Example 4-2a and
Graph Graph Example 4-2a The solution set is the intersection of the two graphs. Find the intersection.
Answer: The solution set is Example 4-2a
Then graph the solution set. Answer: Example 4-2b
Inequality Cost pernight is atmost thecost is atleast $89 $109. or 89 or c c 109 Example 4-3a 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 guest 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 pernight.
Graph Graph Example 4-3a Now graph the solution set. Find the union.
Answer: Example 4-3a
Answer: where c is the cost per seat Example 4-3b Ticket Sales A professional hockey arena has seats available in the Lower Bowl level that cost at most $65 per seat. The arena also has seats available at the Club Level and above that cost at least $80 per seat. Write and graph a compound inequality that describes the amount a spectator would pay for a seat at the hockey game.
Example 4-4a Then graph the solution set. or
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 4-4a Answer:
Answer: Example 4-4b Then graph the solution set.
Compound Summary • There are exactly six different combinations that can occur with two number lines using AND and OR • Handout
Homework – Write in your planner • 6-4 Compound Inequalities Two pages All Problems
