Algebra 1B Section 5-2

SECTION 5-2Solving 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 1Matt 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.

34

t = time to get there




34


34

t ≥ 6




34


34

t ≥ 6

43•

34

t ≥ 6•43




34


34

t ≥ 6

43•

34

t ≥ 6•43

t ≥ 8




34


34

t ≥ 6

43•

34

t ≥ 6•43

t ≥ 8

It will take Matt at least 8 hours to walk to Lake Shecky.


Example 2Solve the inequality and graph the solution.

a. −

35

x ≥ 6



a. −

35

x ≥ 6

−

53

⎛

⎝⎜

⎞

⎠⎟ −

35

x⎛

⎝⎜

⎞

⎠⎟ ≥ 6( ) − 5

3

⎛

⎝⎜

⎞

⎠⎟



a. −

35

x ≥ 6

−

53

⎛

⎝⎜

⎞

⎠⎟ −

35

x⎛

⎝⎜

⎞

⎠⎟ ≥ 6( ) − 5

3

⎛

⎝⎜

⎞

⎠⎟

x ≤ −10



a. −

35

x ≥ 6

−

53

⎛

⎝⎜

⎞

⎠⎟ −

35

x⎛

⎝⎜

⎞

⎠⎟ ≥ 6( ) − 5

3

⎛

⎝⎜

⎞

⎠⎟

x ≤ −10

x | x ≤ −10{ }



a. −

35

x ≥ 6

−

53

⎛

⎝⎜

⎞

⎠⎟ −

35

x⎛

⎝⎜

⎞

⎠⎟ ≥ 6( ) − 5

3

⎛

⎝⎜

⎞

⎠⎟

x ≤ −10

x | x ≤ −10{ }

-10 -9 -8 -7 -6-11-12-13-14



b. 12k ≥ 60



b. 12k ≥ 60

12k

12≥

6012



b. 12k ≥ 60

12k

12≥

6012

k ≤ 5



b. 12k ≥ 60

12k

12≥

6012

k ≤ 5

k | k ≤ 5{ }



b. 12k ≥ 60

12k

12≥

6012

k ≤ 5

k | k ≤ 5{ }

5 6 7 8 94321



c. − 8q <136



c. − 8q <136

−8q

−8<

136−8



c. − 8q <136

−8q

−8<

136−8

q > −17



c. − 8q <136

−8q

−8<

136−8

q > −17

q | q > −17{ }



c. − 8q <136

−8q

−8<

136−8

q > −17

q | q > −17{ }

-17 -16 -15 -14 -13-18-19-20-21



d. −

23

m ≤ −10



d. −

23

m ≤ −10

−

32

⎛

⎝⎜

⎞

⎠⎟ −

23

m⎛

⎝⎜

⎞

⎠⎟ ≤ −10( ) − 3

2

⎛

⎝⎜

⎞

⎠⎟



d. −

23

m ≤ −10

−

32

⎛

⎝⎜

⎞

⎠⎟ −

23

m⎛

⎝⎜

⎞

⎠⎟ ≤ −10( ) − 3

2

⎛

⎝⎜

⎞

⎠⎟

m ≥15



d. −

23

m ≤ −10

−

32

⎛

⎝⎜

⎞

⎠⎟ −

23

m⎛

⎝⎜

⎞

⎠⎟ ≤ −10( ) − 3

2

⎛

⎝⎜

⎞

⎠⎟

m ≥15

m | m ≥15{ }



d. −

23

m ≤ −10

−

32

⎛

⎝⎜

⎞

⎠⎟ −

23

m⎛

⎝⎜

⎞

⎠⎟ ≤ −10( ) − 3

2

⎛

⎝⎜

⎞

⎠⎟

m ≥15

m | m ≥15{ }

15 16 17 18 1914131211


Example 3Maggie 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.




c = cost of pizza




c = cost of pizza

216

c ≤ 2.8




c = cost of pizza

216

c ≤ 2.8

18

c ≤ 2.8




c = cost of pizza

216

c ≤ 2.8

18

c ≤ 2.8

8

18

c⎛

⎝⎜

⎞

⎠⎟ ≤ 2.8( )8




c = cost of pizza

216

c ≤ 2.8

18

c ≤ 2.8

8

18

c⎛

⎝⎜

⎞

⎠⎟ ≤ 2.8( )8

c ≤ 22.4




c = cost of pizza

216

c ≤ 2.8

18

c ≤ 2.8

8

18

c⎛

⎝⎜

⎞

⎠⎟ ≤ 2.8( )8

c ≤ 22.4

c | c ≤ 22.4{ }




c = cost of pizza

216

c ≤ 2.8

18

c ≤ 2.8

8

18

c⎛

⎝⎜

⎞

⎠⎟ ≤ 2.8( )8

c ≤ 22.4The 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

Education

Transcript of Algebra 1B Section 5-2