Warm Up Lesson Presentation Lesson Quiz Solve Inequalities Using Multiplication and Division Warm Up Lesson Presentation Lesson Quiz

Warm-Up Check whether the given number is a solution of the inequality. 1. x 3  7; 20 ANSWER yes 2. 4m > –23; –6 ANSWER no 3. How long will it take a diver to ascend 36 feet if the average rate of ascent is 30 feet per minute? ANSWER 1.2 min or 1 min and 12 sec

Example 1 x Solve < . Graph your solution. 5 4 x < 5 4 x < 5 Write original inequality. x 4 < 5 Use multiplication property of inequality: Multiply each side by 4. x < 20 Simplify. ANSWER The solutions are all real numbers less than 20. Check by substituting a number less than 20 in the original inequality.

Guided Practice Solve the inequality. Graph your solution. 1. > 8 x 3 x > 24 ANSWER 2.  –2 m 8 ANSWER m  –16 3.  –4 y 2.5 ANSWER y  –10

< 7. Graph your solution. x –6 Solve Example 2 < 7. Graph your solution. x –6 Solve < 7 x –6 Write original inequality. x –6 > –6 7 Multiply each side by –6. Reverse inequality symbol. x > –42 Simplify. ANSWER The solutions are all real numbers greater than –42. Check by substituting a number greater than –42 in the original inequality.

Example 2 CHECK x < 7 –6 ? < 7 –6 0 < 7 Write original inequality. –6 < 7 ? Substitute 0 for x. 0 < 7 Solution checks

Guided Practice Solve the inequality. Graph your solution. 4. > 12 x –4 x < –48 ANSWER 5. < 1.6 m –7 m > –11.2 ANSWER

Example 3 Solve –3x > 24. –3x > 24 –3x 24 < –3 x < –8 Write original inequality. –3x –3 < 24 Use division property of inequality: Divide each side by –3. Reverse inequality symbol. x < –8 Simplify.

Guided Practice Solve the inequality. Graph your solution. 6. 5v  45 v  9 ANSWER 7. –6n < 24 n > –4 ANSWER

Example 4 A student pilot plans to spend 80 hours on flight training to earn a private license. The student has saved $6000 for training. Which inequality can you use to find the possible hourly rates r that the student can afford to pay for training? 80r  6000 A 80r  6000 B 6000r  80 C 6000r  80 D SOLUTION The total cost of training can be at most the amount of money that the student has saved. Write a verbal model for the situation. Then write an inequality.

Example 4 80 r < – 6000 ANSWER The correct answer is B. A D C B

The student can afford to pay at most $75 per hour for training. Example 5 PILOTING In Example 4, what are the possible hourly rates that the student can afford to pay for training? SOLUTION 80 r ≤ 6000 Write inequality. 80r 80 ≤ 6000 Divide each side by 80. r ≤ 75 Simplify. ANSWER The student can afford to pay at most $75 per hour for training.

Guided Practice 8. WHAT IF? In Example 5, suppose the student plans to spend 90 hours on flight training and has saved $6300. Write and solve an inequality to find the possible hourly rates that the student can afford to pay for training. 90r  6300, r  $70/h ANSWER

Lesson Quiz Solve the inequality. Graph your solution. 1. –72 < 8p ANSWER p > –9 2. w – 6 – > –5 ANSWER w  30

Lesson Quiz A fitness walking group walks 4 days each week with a goal of at least 12 miles per week. Write and solve an inequality to find the average number of possible miles m the group should walk each day to meet its goal. 3. ANSWER 4m  12; an average of at least 3 miles per day.