Page 25 - Math Course 3 (Book 1)

Linear Inequalities: Compound Inequalities

Words Cost per night is at most $89 or the Your Turn!
cost is at least $109.

Write and Graph a Compound Inequality
Variable Let n be the cost of staying at the
resort per night. TICKET SALES
A professional hockey arena has seats available
Equation n ≤ 89 or n ≥ 109 in the Lower Bowl level that cost at most $65 per
seat. The arena also has seats available at the
Now graph the solution set. Club Level and above that cost at least $80 per
seat. Write and graph a compound inequality that
Graph n ≤ 89 describes the amount a spectator would pay for a
seat at the hockey game.

84 90 96 102 108 114 A. c ≤ 65 or c ≥ 80
Graph n ≥ 109
40 50 60 70 80 90
84 90 96 102 108 114
B. c ≥ 65 or c ≤ 80
Find the union.
40 50 60 70 80 90

Answer {n | n ≤ 89 or n ≥ 109} C. c ≥ 65 or c ≥ 80

40 50 60 70 80 90
84 90 96 102 108 114 D. c ≤ 65 or c ≤ 80

40 50 60 70 80 90
Solve and Graph a Union
Answer
Example Solve and Graph a Union

Solve –2x + 5 < 15 or 5x + 15 > 20.
Solve 4k – 7 ≤ 25 or 12 – 9k ≥ 30. Then graph the solution set.
Graph the solution set.
A. {x | x > 1}
4k – 7 ≤ 25 or 12 – 9k ≥ 30
4k – 7 + 7 ≤ 25 + 7 12 – 9k –12 ≥ 30 –12
4k ≤ 32 –9k ≥ 18
4k ≤ 32 –9k ≤ 18 B. {x | x < –5}
4 4 –9 –9
k ≤ 8 k ≤ –2
Graph k ≤ 8 C. {x | x > –5}

–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Graph k ≤ –2 D. {x | x < 1}

–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Answer

–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Notice that the graph of k ≤ 8 contains every point
in the graph of k ≤ –2. So, the union is the graph of Answer
k ≤ 8. The solution set is {k | k ≤ 8}.

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