Example 1 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}.

Example 1 Graph z ≤ 9. Find the intersection. Graph 5 5. Answer: Solve and Graph an Intersection

A.A B.B C.C D.D Example 1 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}

Example 2 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.

Example 2 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 Example 2 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

Example 3 Solve and Graph a Union Solve 4k – 7 ≤ 25 or 12 – 9k ≥ 30. Graph the solution set.

Example 3 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 ofk ≤ –2. So, the union is the graph of k ≤ 8. The solution set is {k | k ≤ 8}. Find the union.

A.A B.B C.C D.D Example 3 Solve –2x Then graph the solution set. A.{x | x > 1} B.{x | x < –5} C.{x | x > –5} D.{x | x < 1}

Example 3 Graph x > -2 or x < 1