Download Warm-Up Exercises Solve an inequality using

LAB: Inequalities with Negative Coefficients
p.304
Q U E ST ION: How do you solve an inequality with a
negative coefficient?
5.2 Solve Inequalities Using
Multiplication and Division
• You will solve inequalities
using multiplication and
division.
Essential Question:
• How do you solve
inequalities using
multiplication and division?
You will learn how
to answer this question by
applying multiplication and
division properties of inequality
and by learning when to reverse
the direction of the inequality
symbol.
EXAMPLE
Warm-Up1Exercises
Solve an inequality using multiplication
Solve
x
< 5 . Graph your solution.
4
x
<5
4
4 x <4 5
4
x < 20
Write original 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.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
Solve the inequality. Graph your solution.
x
1.
>8
3
ANSWER
x > 24
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
Solve the inequality. Graph your solution.
m
2.
 –2
8
ANSWER
m  –16
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
Solve the inequality. Graph your solution.
y
3. 2.5  –4
ANSWER
y  –10
EXAMPLE
Warm-Up2Exercises
Solve an inequality using multiplication
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.
EXAMPLE
Warm-Up2Exercises
Solve an inequality using multiplication
CHECK
x
–6
<7
?
0
<7
–6
0<7
Write original inequality.
Substitute 0 for x.
Solution checks
EXAMPLE
Warm-Up3Exercises
Solve an inequality using division
Solve –3x > 24.
–3x > 24
–3x
< 24
–3
–3
x < –8
Write original inequality.
Divide each side by –3. Reverse
inequality symbol.
Simplify.
• If you graph x < 28, would you use an open or a closed circle?
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
Solve the inequality. Graph your solution.
x
4.
> 12
–4
ANSWER
x < –48
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
Solve the inequality. Graph your solution.
5.
m
< 1.6
–7
ANSWER
m > –11.2
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
Solve the inequality. Graph your solution.
6.
5v  45
ANSWER
v9
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
Solve the inequality. Graph your solution.
7. –6n < 24
ANSWER
n > –4
EXAMPLE
Warm-Up4Exercises
Standardized Test Practice
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.
EXAMPLE
Warm-Up4Exercises
Standardized Test Practice
80
r
<
–
6000
ANSWER
The correct answer is B. A
B
C
D
EXAMPLE
Warm-Up5Exercises
Solve a real-world problem
PILOTING
In Example 4, what are the possible hourly rates that
the student can afford to pay for training?
EXAMPLE
Warm-Up5Exercises
Solve a real-world problem
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.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 4 and 5
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
• You will solve inequalities
using multiplication and
division.
• The multiplication and
division properties of
inequality can be used to
produce equivalent
inequalities.
• Reverse the direction of the
inequality symbol when
multiplying or dividing by a
negative number.
Essential Question:
• How do you solve
inequalities using
multiplication and division?
Multiply or divide each side of
the inequality by the same
number to isolate the variable
and produce an equivalent
inequality. Reverse the direction
of the inequality symbol if you
multiply or divide by a negative
number.
Daily
Homework
Quiz
Warm-Up
Exercises
Solve the inequality. Graph your solution.
1. –72 < 8p
ANSWER
2.
p > –9
w > –5
–
–6
ANSWER
w  30
Daily
Homework
Quiz
Warm-Up
Exercises
3.
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.