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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.
The solution set is {z | 5 < z ≤ 9}.
Graph z ≤ 9.
Find the intersection.
Graph 5 < z or z > 5.
Answer:
Solve and Graph an Intersection
A. A
B. B
C. C
D. D
Solve –3 < x – 2 < 5. Then graph the solution set.
A. {x | –1 < x < 7}
B. {x | –5 < x < 3}
C. {x | x < 7}
D. {x | –1 < x < 3}
Write and Graph a Compound Inequality
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.
Write and Graph a Compound Inequality
Graph n ≤ 89.
Find the union.
Graph n ≥ 109.
Answer: {n | n ≤ 89 or n ≥ 109}
Now graph the solution set.
A. A
B. B
C. C
D. 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.
A. c ≤ 65 or c ≥ 80
B. c ≥ 65 or c ≤ 80
C. c ≥ 65 or c ≥ 80
D. c ≤ 65 or c ≤ 80
Solve and Graph a Union
Solve 4k – 7 ≤ 25 or 12 – 9k ≥ 30. Graph the solution set.
Solve and Graph a Union
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}.
Find theunion.
A. A
B. B
C. C
D. D
Solve –2x + 5 < 15 or 5x + 15 > 20. Then graph the solution set.
A. {x | x > 1}
B. {x | x < –5}
C. {x | x > –5}
D. {x | x < 1}
