Download lesson 6.2

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
v9
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.