1. Solve Multiple Step Algebraic Equations with Variables on Both Sides
MS Algebra A-REI-1 – Ch. 3.4 Multi-step Problems & Variables on Both Sides
Mr. Deyo
Solve Multiple Step Algebraic Equations with Variables on Both Sides

2. Title: 3.4 Multi-Step Problems With Variables on Both Sides
Date:
Learning Target
By the end of the period, I will solve multi-step equations that have variables on both sides of the equal sign.
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 3.4 Pg ) Section ______
TxtBk. Prob. #23-31 Odd,50-54 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
A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225.
Find the number of hours she spent surfing.

6. Daily Warm-Up Exercises
For use with pages xxx–xxx
A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225.
Find the number of hours she spent surfing.
ANSWER
4 hours

7. Vocabulary Simplest Form Equation Inverse Operations Reciprocal
Distributive Property

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. Whole Class
Multiple Choice Practice 1
The equation is solved below. 6x – 5 = (
16x + 60 ) 4
STEP 1 – 4x = 5 6x + 15
STEP 2 – 15 = 5
10x
STEP 3 20 =
10x
STEP 4 2 = x
Which is the first incorrect step in the solution?
Step 1
Step 2
Step 3
Step 4

10. Whole Class
Multiple Choice Practice
SOLUTION 1
The equation is solved below. 6x – 5 = (
16x + 60 ) 4
STEP 1 – 4x = 5 6x + 15
ANSWER
STEP 2 – 15 = 5
10x
STEP 3 20 =
10x
The correct answer is B.
STEP 4 2 = x
Which is the first incorrect step in the solution?
Step 1
Step 2
Step 3
Step 4
In Step 2, 4x should have been subtracted from the left side of the equation instead of being added.

11. – 4x = 8x 7 17 Solve for the value of x. Problem A
Solve an equation with variables on both sides
Solve for the value of x. – 4x = 8x 7 17

12. x = 2 – 4x = 8x 7 17 Solve for the value of x. – 4x = 8x 7 17 – 4x =
Problem A
Solve an equation with variables on both sides
Solve for the value of x. – 4x = 8x 7 17 – 4x = 8x 7 17
Write original equation. – 4x = 8x 7 17 +
Add 8x to each side.
12x = – 17 7
Simplify each side.
12x = 24
Add 17 to each side. x = 2
Divide each side by 12.
ANSWER

13. Problem B
Solve the equation.
3 – 4a = 5(a – 3)

14. a = 2 3 – 4a = 5(a – 3) 3 – 4a = 5a – 15 3 = 9a – 15 18 = 9a 2 = a
Problem B
Solve the equation.
3 – 4a = 5(a – 3)
3 – 4a = 5a – 15
3 = 9a – 15
18 = 9a
2 = a
ANSWER
a = 2

15. CAR SALES
Problem A
Solve a real-world problem
The annual sales report for a car dealership is shown. If these trends continue, in how many years will the number of new cars sold be twice the number of used cars sold?
(-) =2

16. 78 + 6x = ) ( 2 4x – 67 SOLUTION Problem A ANSWER
Solve a real-world problem
Let x represent the number of years from now. Then 6x represents the increase in the number of new cars sold over x years, and - 4x represents the decrease in the number of used cars sold over x years. Write a verbal model. 78 + 6x = ) ( 2 4x – 67
78 + 6x = 2 (67 – 4x) Write equation.
78 + 6x = 134 – 8x Distributive property
x = Add 8x to each side.
14x = 56 Subtract 78 from each side.
x = 4 Divide each side by 14.
ANSWER
The number of new cars sold will be twice the number of used cars sold in 4 years.

17. Problem B
WHAT IF?
Suppose the car dealership sold 50 new cars this year. In how many years will the number of new cars sold be twice the number of used cars sold?
(-) =2 50

18. 6 years =2 50 WHAT IF? Problem B
Suppose the car dealership sold 50 new cars this year. In how many years will the number of new cars sold be twice the number of used cars sold?
(-) =2 50
ANSWER
6 years

19. Storm Check (Think, Write, Discuss, Report)
How do you take the words of a word problem and create an equation to solve (3-4 sentences)? When I read a word problem in math, I ___________ ___________________________________________ __________________________________________.

20. Vocabulary Simplest Form Equation Inverse Operations Reciprocal
Distributive Property

21. Title: 3.4 Multi-Step Problems With Variables on Both Sides
Date:
Learning Target
By the end of the period, I will solve multi-step equations that have variables on both sides of the equal sign.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

22. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 3.4 Pg ) Section ______
TxtBk. Prob. #23-31 Odd,50-54 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

23. Rock Climbing Ticket OUT.
For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. After how many visits is the total cost for a member and a nonmember the same?
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.

24. V represents the number of visits
Solution - Rock Climbing
Ticket OUT.
For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. After how many visits is the total cost for a member and a nonmember the same?
V represents the number of visits
V = 10V + 6V
V = 16V
360 = 12V
30 = V
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.