5-4 Compound Inequalities Again! Goals: Write compound inequalities. Model a real-life situation with a compound inequality. Eligible Content: A1.1.3.1.1 / A1.1.3.1.2 / A1.1.3.1.3

Examples Write and graph each compound inequality. x is greater than or equal to 6 and less than 12. 6 ≤ x < 12 x is less than -4 or is greater than 6. x < -4 OR x > 6 x is less than 8 and is greater than 7. 7 < x < 8 x is less than 7 and is at least 0. 0 ≤ x < 7 x is greater than 5 or is less than or equal to 3. x > 5 OR x ≤ 3

Practice Write and graph each compound inequality. x is greater than 4 or less than 2. x is greater than -2 and less than 5. x is less than 6 or greater than or equal to 10. x is at least 5 and less than 8. x is between 2 and 8.

Word Problem #1 In a certain restricted air space, airplanes must fly below 10,000 feet or above 15,000 feet. Write and graph a compound inequality that models this situation. x < 10,000 OR x > 15,000

Word Problem #2 The high temperature on a certain day was 98°F and the low was 78°F. Write a compound inequality that models the range in temperatures. 78 ≤ x ≤ 98

Word Problem #3 On a road in the city of Rochester, the maximum speed is 65 miles per hour and the minimum speed is 30 miles per hour. Write a compound inequality that models this situation. 30 ≤ x ≤ 65

Word Problem #4 Junior tickets to an event are available to teenagers below age eighteen at reduced rates. Write an inequality that models this situation. 13 ≤ x < 18

Word Problem #5 Month Temperature January 98°F February 105°F March 108°F April 118°F May 124°F June 129°F July 134°F August 127°F September 126°F October 116°F November December 100°F The highest temperature in the US for each month are shown in the table. Write a compound inequality that represents the range of record high temperatures. 98 ≤ x ≤ 134

A. c ≤ 65 or c ≥ 80 B. c ≥ 65 or c ≤ 80 C. c ≥ 65 or c ≥ 80 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

Practice Worksheet – “5-4 Compound Inequalities”

One last example  The sum of 2 times a number and 5 is greater than 7 and less than 17. 7 < 2x + 5 < 17 1< x < 6

Homework Page 309 #16, 29-33, 35