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6.2 Solve Inequalities Using Multiplication and Division Warm Up Lesson Presentation Lesson Quiz 6.2 Warm-Up Check whether the given number is a solution of the inequality. 1. x 7; 20 3 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 6.2 Example 1 Solve x < 5 . Graph your solution. 4 x <5 4 4 x <4 5 4 x < 20 Write original inequality. Use multiplication property of inequality: Multiply each side by 4. Simplify. ANSWER The solutions are all real numbers less than 20. Check by substituting a number less than 20 in the original inequality. 6.2 Guided Practice Solve the inequality. Graph your solution. x 1. >8 3 ANSWER 2. x > 24 m –2 8 ANSWER y 3. 2.5 m –16 –4 ANSWER y –10 6.2 Example 2 x < 7. Graph your solution. Solve –6 x Write original inequality. <7 –6 Multiply each side by –6. Reverse –6 x > –6 7 inequality symbol. –6 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. 6.2 Example 2 CHECK x –6 <7 ? 0 <7 –6 0<7 Write original inequality. Substitute 0 for x. Solution checks 6.2 Guided Practice Solve the inequality. Graph your solution. x 4. > 12 –4 ANSWER 5. x < –48 m < 1.6 –7 ANSWER m > –11.2 6.2 Example 3 Solve –3x > 24. –3x > 24 –3x < 24 –3 –3 x < –8 Write original inequality. Use division property of inequality: Divide each side by –3. Reverse inequality symbol. Simplify. 6.2 Guided Practice Solve the inequality. Graph your solution. 6. 5v 45 ANSWER v9 7. –6n < 24 ANSWER n > –4 6.2 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? A 80r 6000 B 80r 6000 C 6000r 80 D 6000r 80 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. 6.2 Example 4 80 r < – 6000 ANSWER The correct answer is B. A B C D 6.2 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 80r ≤ 6000 80 80 r ≤ 75 Write inequality. Divide each side by 80. Simplify. ANSWER The student can afford to pay at most $75 per hour for training. 6.2 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. ANSWER 90r 6300, r $70/h 6.2 Lesson Quiz Solve the inequality. Graph your solution. 1. –72 < 8p ANSWER 2. p > –9 w > –5 – –6 ANSWER w 30 6.2 3. 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. ANSWER 4m 12; an average of at least 3 miles per day.