Lesson 4 Menu : Lesson 4 Menu Five-Minute Check (over Lesson 6-3)
Main Ideas and Vocabulary
California Standards
Example 1: Graph an Intersection
Example 2: Solve and Graph an Intersection
Example 3: Write and Graph a Compound Inequality
Example 4: Solve and Graph a Union
Lesson 4 MI/Vocab : Lesson 4 MI/Vocab compound inequality intersection
union Solve compound inequalities containing the word and and graph their solution sets. Solve compound inequalities containing the word or and graph their solution sets.
Lesson 4 CA : Lesson 4 CA Standard 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x – 5) + 4(x – 2) = 12. (Key, CAHSEE)
Standard 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. (Key, CAHSEE)
Lesson 4 Ex1 : Lesson 4 Ex1 Graph an Intersection Graph the solution set of y ≥ 5 and y < 12. Graph y ≥ 5. Find the intersection. Graph y < 12.
Lesson 4 Ex1 : Lesson 4 Ex1 Graph an Intersection Answer: The solution set is {y | 5 ≤ y < 12}. Note that the graph of y ≥ 5 includes the point 5. The graph of y < 12 does not include 12.
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D Graph the solution set of y > 6 and y ≤ 10.
Lesson 4 Ex2 : Lesson 4 Ex2 Solve and Graph an Intersection Solve 7 < z + 2 ≤ 11. Graph the solution set. First express 7 < z + 2 ≤ 11 using and. Then solve each inequality. 7 < z + 2 and z + 2 ≤ 11 Write the inequalities.
7 – 2 < z + 2 – 2 z – 2 + 2 ≤ 11 – 2 Subtract 2 from each side.
5 < z z ≤ 9 Simplify. The solution set is {z | 5 < z ≤ 9}.
Lesson 4 Ex2 : Lesson 4 Ex2 Solve and Graph an Intersection Graph z ≤ 9. Find the intersection. Graph 5 < z or z > 5. Answer:
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D Solve –3 < x – 2 < 5. Then graph the solution set.
Lesson 4 Ex3 : Lesson 4 Ex3 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. Write and Graph a Compound Inequality Words Cost per night is at most $89 or the cost is at least $109. Variable Let n be the cost of staying at the resort per night. Equation n ≤ 89 or n ≥ 109
Lesson 4 Ex3 : Lesson 4 Ex3 Now graph the solution set. Graph n ≤ 89. Find the union. Write and Graph a Compound Inequality Graph n ≥ 109. Answer: {n | n ≤ 89 or n ≥ 109}
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D 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.
Lesson 4 Ex4 : Lesson 4 Ex4 Solve 4k – 7 ≤ 25 or 12 – 9k ≥ 30. Graph the solution set. or Solve and Graph a Union Animation: Solve and Graph a Union
Lesson 4 Ex4 : Lesson 4 Ex4 Graph k ≤ 8. Graph k ≤ –2. Answer:
Notice that the graph of k ≤ 8 contains every point in the graph of k ≤ –2. So, the union is the graph of k ≤ 8. The solution set is {k | k ≤ 8}. Solve and Graph a Union
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D Solve –2x + 5 < 15 or 5x + 15 > 20. Then graph the solution set.
End of Lesson 3 : End of Lesson 3