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

2. 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

3. 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.

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

5. < 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.

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

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

8. 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.

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

10. 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.

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

12. 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.

13. 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

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

15. 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.