Algebra 1B Section 5-2

SECTION 5-2
Solving Inequalities by Multiplication and Division
Monday, September 23, 13

Essential Question
How do we solve and graph inequalities with multiplication or
division?

Question
How does the process of solving an inequality compare to the
process of solving an equation?

FLIPPING THE INEQUALITY

FLIPPING THE INEQUALITY
Whenever you multiply or divide each side of an equation by a
negative number, you must ﬂip the inequality sign!

Example 1
Matt Mitarnowski walks at a rate of mile an hour. He knows that
he is at least 6 miles from Lake Shecky. How long will it take him to
get there? Write and solve an inequality to ﬁnd the time.
3
4
t = time to get there

Example 1
3
4
3
4
t ≥ 6

Example 1
3
4
3
4
t ≥ 6
4
3
•
3
4
t ≥ 6•
4
3

Example 1
3
4
3
4
t ≥ 6
4
3
•
3
4
t ≥ 6•
4
3
t ≥ 8

Example 1
3
4
3
4
t ≥ 6
4
3
•
3
4
t ≥ 6•
4
3
t ≥ 8
It will take Matt at least 8 hours to walk to Lake Shecky.

Example 2
Solve the inequality and graph the solution.
a. −
3
5
x ≥ 6

Example 2
a. −
3
5
x ≥ 6
−
5
3
⎛
⎝
⎜
⎞
⎠
⎟ −
3
5
x
⎛
⎝
⎜
⎞
⎠
⎟ ≥ 6( ) −
5
3
⎛
⎝
⎜
⎞
⎠
⎟

Example 2
a. −
3
5
x ≥ 6
−
5
3
⎛
⎝
⎜
⎞
⎠
⎟ −
3
5
x
⎛
⎝
⎜
⎞
⎠
⎟ ≥ 6( ) −
5
3
⎛
⎝
⎜
⎞
⎠
⎟
x ≤ −10

Example 2
a. −
3
5
x ≥ 6
−
5
3
⎛
⎝
⎜
⎞
⎠
⎟ −
3
5
x
⎛
⎝
⎜
⎞
⎠
⎟ ≥ 6( ) −
5
3
⎛
⎝
⎜
⎞
⎠
⎟
x ≤ −10
x | x ≤ −10{ }

Example 2
a. −
3
5
x ≥ 6
−
5
3
⎛
⎝
⎜
⎞
⎠
⎟ −
3
5
x
⎛
⎝
⎜
⎞
⎠
⎟ ≥ 6( ) −
5
3
⎛
⎝
⎜
⎞
⎠
⎟
x ≤ −10
x | x ≤ −10{ }
-10 -9 -8 -7 -6-11-12-13-14

Example 2
b.12k ≥ 60

Example 2
b.12k ≥ 60
12k
12
≥
60
12

Example 2
b.12k ≥ 60
12k
12
≥
60
12
k ≤ 5

Example 2
b.12k ≥ 60
12k
12
≥
60
12
k ≤ 5
k | k ≤ 5{ }

Example 2
b.12k ≥ 60
12k
12
≥
60
12
k ≤ 5
k | k ≤ 5{ }
5 6 7 8 94321

Example 2
c. − 8q <136

Example 2
c. − 8q <136
−8q
−8
<
136
−8

Example 2
c. − 8q <136
−8q
−8
<
136
−8
q > −17

Example 2
c. − 8q <136
−8q
−8
<
136
−8
q > −17
q | q > −17{ }

Example 2
c. − 8q <136
−8q
−8
<
136
−8
q > −17
q | q > −17{ }
-17 -16 -15 -14 -13-18-19-20-21

Example 2
d. −
2
3
m ≤ −10

Example 2
d. −
2
3
m ≤ −10
−
3
2
⎛
⎝
⎜
⎞
⎠
⎟ −
2
3
m
⎛
⎝
⎜
⎞
⎠
⎟ ≤ −10( ) −
3
2
⎛
⎝
⎜
⎞
⎠
⎟

Example 2
d. −
2
3
m ≤ −10
−
3
2
⎛
⎝
⎜
⎞
⎠
⎟ −
2
3
m
⎛
⎝
⎜
⎞
⎠
⎟ ≤ −10( ) −
3
2
⎛
⎝
⎜
⎞
⎠
⎟
m ≥15

Example 2
d. −
2
3
m ≤ −10
−
3
2
⎛
⎝
⎜
⎞
⎠
⎟ −
2
3
m
⎛
⎝
⎜
⎞
⎠
⎟ ≤ −10( ) −
3
2
⎛
⎝
⎜
⎞
⎠
⎟
m ≥15
m | m ≥15{ }

Example 2
d. −
2
3
m ≤ −10
−
3
2
⎛
⎝
⎜
⎞
⎠
⎟ −
2
3
m
⎛
⎝
⎜
⎞
⎠
⎟ ≤ −10( ) −
3
2
⎛
⎝
⎜
⎞
⎠
⎟
m ≥15
m | m ≥15{ }
15 16 17 18 1914131211

Example 3
Maggie Brann and friends order a pizza. Maggie eats 2 of the 16 slices
and pays $2.80 for her share.Assuming that Maggie has paid at least
her fair share, what is the most the pizza cost? Identify a variable, then
set up and solve an inequality. Interpret your solution.

Example 3
c = cost of pizza

Example 3
c = cost of pizza
2
16
c ≤ 2.8

Example 3
c = cost of pizza
2
16
c ≤ 2.8
1
8
c ≤ 2.8

Example 3
c = cost of pizza
2
16
c ≤ 2.8
1
8
c ≤ 2.8
8
1
8
c
⎛
⎝
⎜
⎞
⎠
⎟ ≤ 2.8( )8

Example 3
c = cost of pizza
2
16
c ≤ 2.8
1
8
c ≤ 2.8
8
1
8
c
⎛
⎝
⎜
⎞
⎠
⎟ ≤ 2.8( )8
c ≤ 22.4

Example 3
c = cost of pizza
2
16
c ≤ 2.8
1
8
c ≤ 2.8
8
1
8
c
⎛
⎝
⎜
⎞
⎠
⎟ ≤ 2.8( )8
c ≤ 22.4
c | c ≤ 22.4{ }

Example 3
c = cost of pizza
2
16
c ≤ 2.8
1
8
c ≤ 2.8
8
1
8
c
⎛
⎝
⎜
⎞
⎠
⎟ ≤ 2.8( )8
c ≤ 22.4
The pizza cost at most
$22.40
c | c ≤ 22.4{ }

Summarizer
Using complete sentences, explain when you would switch the sign in
an inequality.What is the reason as to why this occurs?

Problem Sets

Problem Sets
Problem Set 1: p. 293 #1-9
Problem Set 2: p. 293 #12-27 multiplies of 3, 31-33 all, 63-68 all

Problem Sets
Problem Set 1: p. 293 #1-9
Problem Set 2: p. 293 #12-27 multiplies of 3, 31-33 all, 63-68 all
"If you can ﬁnd a path with no obstacles, it probably doesn't lead anywhere."
- Frank A. Clark

Algebra 1B Section 5-2

Recommandé

Recommandé

Contenu connexe

En vedette

En vedette (11)

Plus de Jimbo Lamb

Plus de Jimbo Lamb (20)

Dernier

Dernier (20)

Algebra 1B Section 5-2