1. MS Algebra A-REI-3 – Ch. 4.3 Multi-Step Inequalities
Mr. Deyo
Apply Properties of Inequality to Solve Multi-Step Inequalities

2. Title: 4.3 Multi-Step Inequalities
Date:
Learning Target
By the end of the period, I will apply properties of inequality to solve multi-step inequalities.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 4.3 Pg ) Section ______
TxtBk. Prob. #9-17 Odd,35-39 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

4. Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer:
How are the two images similar?
How are they different?
How can these two images be related to math?
IMAGE 1
IMAGE 2

5. Daily Warm-Up Exercises
For use with pages xxx–xxx
Solve and graph the inequalities.
You estimate you can read at least 8 history text pages per day. What are the possible numbers of days it will take you to read at most 118 pages?
6 ≤ 2x – 4

6. Daily Warm-Up Exercises
For use with pages xxx–xxx
Solve and graph the inequalities.
You estimate you can read at least 8 history text pages per day. What are the possible numbers of days it will take you to read at most 118 pages?
6 ≤ 2x – 4
ANSWER
all real numbers greater than or equal to 5
ANSWER
at most 15 days

7. Vocabulary Addition Property of Inequality (P.O.I.) Subtraction P.O.I.
Multiplication P.O.I.
Division P.O.I. by a Positive(+) Number / by a Negative (-) Number

8. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing

9. Problem A
Solve a multi-step inequality
Solve the inequality and graph your solution.
-6(x – 5) ≤ 150

10. The solutions are all real numbers greater than or equal to -20.
Problem A
Solve a multi-step inequality
SOLUTION
Solve the inequality and graph your solution.
-6(x - 5) ≤ 150
Write original inequality.
-6x + 30 ≤ 150
Distributive property
-6x ≤ 120
Subtract 30 from each side.
x ≥ -20
Divide each side by -6 and
Reverse the inequality symbol.
ANSWER
The solutions are all real numbers greater than or equal to -20.

11. Problem B
Solve a multi-step inequality
Solve the inequality and graph your solution.
6x – 7 > 2x + 17

12. x 6 > 6x – 7 > 2x + 17 6x 24 2x + > 4x 24 >
Problem B
Solve a multi-step inequality
SOLUTION
Solve the inequality and graph your solution.
6x – 7 > 2x + 17
Write original inequality. 6x 24 2x +
>
Add 7 to each side. 4x 24
>
Subtract 2x from each side. x 6
>
Divide each side by 4.
ANSWER
The solutions are all real numbers greater than 6.

13. +c +c −c −c c c −c −c ¿¿ c c −c −c ??
Properties of Inequality (P.O.I.) +c +c −c −c c c −c −c ¿¿ c c −c −c ??

14. -6y + 5 ≤ -3y - 16 Guided Practice
Solve the inequality. Graph your solution.
-6y + 5 ≤ -3y - 16

15. y ≥ 7 -6y + 5 ≤ -3y - 16 -6y ≤ -3y - 21 -3y ≤ - 21 Guided Practice
SOLUTION
Solve the inequality. Graph your solution.
-6y + 5 ≤ -3y - 16
-6y ≤ -3y - 21
-3y ≤ - 21 y ≥ 7
ANSWER

16. Title: 4.3 Multi-Step Inequalities
Date:
Learning Target
By the end of the period, I will apply properties of inequality to solve multi-step inequalities.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

17. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 4.3 Pg ) Section ______
TxtBk. Prob. #9-17 Odd,35-39 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

18. Storm Check (Think, Write, Discuss, Report)
When you use the division property of inequality, what happens when you divide by a negative number? When I divide an inequality by a negative number, ___________________________________________ __________________________________________.

19. Problem A
Solve a multi-step problem
CAR WASH
Gasoline
$3.99/gal. rg. unleaded
$4.19/gal. supreme
Vehicle Wash
$5.99 car
$6.99 SUV
A gas station offers gasoline and car washes at the prices shown. The gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of regular unleaded gasoline that you can buy if you also get a car wash and can spend at most $30?

20. ($3.99 – 0.10) • G + $5.99 ≤ $30.00 Problem A SOLUTION
Solve a multi-step problem
SOLUTION
Gasoline
$3.99/gal. rg. unleaded
$4.19/gal. supreme
Vehicle Wash
$5.99 car
$6.99 SUV
A gas station offers gasoline and car washes at the prices shown. The gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of regular unleaded gasoline that you can buy if you also get a car wash and can spend at most $30?
STEP 1
Write a verbal model. Then write an inequality.
($3.99 – 0.10) • G $ ≤ $30.00

21. G ≤ 6.172236. . . 1 2 3 4 5 6 7 STEP 2 Solve the inequality.
Problem A
Solve a multi-step problem
SOLUTION
STEP 2
Solve the inequality.
3.89G ≤ 30.00
Write inequality.
3.89G ≤ 24.01
Subtract 5.99 from each side.
G ≤
Divide each side by 3.89.
You can buy up to slightly more than 6 gallons of gasoline.
ANSWER
CHECK
You can use a table to check the reasonableness of your answer.
Gasoline
(gal) 1 2 3 4 5 6 7
Total Amount Spent ($)
5.99
9.88
13.77
17.66
21.95
25.84
29.73
33.62

22. Problem B $3.99/gal. rg. unleaded $4.19/gal. supreme $5.99 car
Solve a multi-step problem
Gasoline
$3.99/gal. rg. unleaded
$4.19/gal. supreme
Vehicle Wash
$5.99 car
$6.99 SUV
A gas station offers gasoline and car washes at the prices shown. The gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of supreme gasoline that you can buy if you also get an SUV wash and can spend at most $20?

23. Problem B
Solve a multi-step problem
SOLUTION
4.09G ≤ 20.00
Write inequality.
4.09G ≤ 13.01
Subtract 6.99 from each side.
G ≤
Divide each side by 4.09.
You can buy up to slightly more than 3 gallons of gasoline.
ANSWER
CHECK
You can use a table to check the reasonableness of your answer.
Gasoline
(gal) 1 2 3 4 5 6 7
Total Amount Spent ($)
6.99
11.08
15.17
19.26
27.44
31.53
35.62
39.71

24. Guided Practice
CAMP COSTS
You are saving money for a summer camp that costs $1800. You have saved $500 so far, and you have 14 more weeks to save the total amount. What are the possible average amounts of money that you can save per week in order to have a total of at least $1800 saved?

25. at least $92.86 per week 500 + 14C ≥ 1800 14C ≥ 1300 C ≥ 92.857…
Guided Practice
CAMP COSTS
You are saving money for a summer camp that costs $1800. You have saved $500 so far, and you have 14 more weeks to save the total amount. What are the possible average amounts of money that you can save per week in order to have a total of at least $1800 saved?
C ≥ 1800
14C ≥ 1300
C ≥ …
ANSWER
at least $92.86 per week

26. Vocabulary Addition Property of Inequality (P.O.I.) Subtraction P.O.I.
Multiplication P.O.I.
Division P.O.I. by a Positive(+) Number / by a Negative (-) Number

27. Title: 4.3 Multi-Step Inequalities
Date:
Learning Target
By the end of the period, I will apply properties of inequality to solve multi-step inequalities.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

28. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 4.3 Pg ) Section ______
TxtBk. Prob. #9-17 Odd,35-39 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

29. Ticket OUT.
You spend $108 on supplies to make picture frames and plan to sell the picture frames for $11 each. What are the possible numbers of picture frames that you can sell in order for your profit to be positive?
at least 9
at least 10
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.
at most 10
at most 9

30. Ticket OUT.
You spend $108 on supplies to make picture frames and plan to sell the picture frames for $11 each. What are the possible numbers of picture frames that you can sell in order for your profit to be positive?
at least 9
at least 10
ANSWER B
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.
at most 10
at most 9