Moving Straight Ahead: Linear Relationships
Name: ______________________ Per: _____
Investigation 3: Solving Equations

7.EE.B.4: Use variables to represent quantities in the real world or mathematical
problem, and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
Date
Learning Target/s
Day 1-Wed,
Feb. 1
Solve visual equations
with one variable.
Day 2-Thurs,
Feb. 2
Write and solve
symbolic equations with
one variable.
Solve symbolic
equations with one
variable.
Day 3-Fri.
Feb. 3
Day 4- Mon.
Feb. 6
Solve symbolic
equations with one
variable.
Day 5-Tues.
Feb. 7
Solving inequality
equations with one
variable
Create and solve word
problems involving
inequalities
Day 6-Wed.
Feb 8th
Classwork
Homework
(Check Off
Completed/
Corrected Items)
(Check Off Completed/
Corrected Items)
 MSA 3.2 p. 2-3
Exploring
Equalities:
Coins & Pouches
 MSA 3.3 p. 5-6
Writing Equations
 Complete CW p. 2-3
 MSA Inv 3 Day 1 p. 4
Correct with the
EDpuzzle
 MSA Inv 3 Day 2 p. 7
Correct with the KEY
 MSA 3.4 Pg. 8-9:
Solving Equations
 MSA Inv 3 Day 3 p. 10
Correct with the
EDpuzzle
 Additional practice
Pg. 11-12 Solving
linear equations
 Exit Ticket 2
 Additional practice
p. 13-14 on solving
2 step-inequalities
 MSA 3.5: p. 16
INEQUALITY WORD
PROBLEMS
 MSA Inv 3 Day 4
Complete and correct
the classwork with
the KEY
 MSA Inv 3 Day 5 p. 15
Correct with the KEY
 MSA Inv 3 Day 6
Complete the
classwork and correct
with the KEY
Self-Assess
Your
Understanding
of the
Learning
Target/s
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



I have reviewed with a parent/guardian and I am satisfied with the work produced in this packet.
Student signature: ________________________________________
Parent/Guardian Signature:__________________________________
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Day 1 MSA 3.2: EXPLORING EQUALITY - Mystery Pouches in the Kingdom of Montarek
In the Kingdom of Montarek, money takes the form of $1 gold coins called rubas. Messengers carry money
between the king’s castles in sealed pouches that always hold equal numbers of coins.
One day a messenger arrived at one of the castles with a box containing two sealed pouches and five loose $1
coins. The ruler thanks the messenger for the money, which equaled $11.

Does the following visual equation help in finding the number of coins in each pouch?
Visual Equation
Remember:


Each pouch contains the same
number of $1 gold coins.
The total number of coins on each
side of the equation is the same.
Find the number of gold coins in
each pouch. Write down your
steps so that someone else
could follow your steps to find
the number of coins in a pouch.
Describe how you can check
your answer. That is, how do
you know you have found the
correct number of gold coins in
each pouch?
1.
2.
3.
2
4.
5.
6.
Challenge:
In Visual Equation 2, Nichole thought of the left-hand side of the situation as
having two groups. Each group contained one pouch and two coins. She
visualized the following steps to help her find the number of coins in a pouch.
Is Nichole correct? Explain.
Noah looked at Nichole’s strategy and claimed that she was applying the Distributive Property. Is Noah’s claim
correct? Explain.
Are there other situations in which Nichole’s method might work? Explain.
3
Day 1 Homework: MSA 3.2: Complete and CORRECT with the EDpuzzle.
Visual Equation
Remember:


Each pouch contains the same
number of $1 gold coins.
The total number of coins on each
side of the equation is the same.
Find the number of gold coins in
each pouch. Write down your
steps so that someone else
could follow your steps to find
the number of coins in a pouch.
Describe how you can check
your answer. That is, how do
you know you have found the
correct number of gold coins in
each pouch?
1.
2.
3.
4.
4
Day 2 MSA 3.3: WRITING EQUATIONS
Because the number of gold coins in each pouch is unknown, you can let x
represent the number of coins in one pouch. You can let 1 represent the
value of one gold coin.
You can write the following equation to represent the situation: 2x + 4 = 12
Or, you can use Nichole’s method from Problem 3.2 to write this equation: 2(x+2) = 12
The expressions 2x + 4 and 2(x +2) are _______________________ expressions. Two or more expressions are equivalent if
they have the same value, regardless of what number is substituted for the variable. These two expressions are an example of
the Distributive Property for numbers.
2(x+2) = 2x +4
In this problem, you will revisit situations with pouches and coins, but you will use symbolic equations to represent your
solution process.
A.
Visual Equation
Description of Steps for Finding the
Coins in Each Pouch
Symbolic Equation



Use x to represent the number
of gold coins in each pouch
Use the number 1 to represent
each coin
Remember the Balance Check
1.
2.
3.
5
4.
B. Work backwards from the Symbolic Equation to complete the table
Visual Equation


Each x represents a pouch
Each 1 represents a coin
Description of Steps for Finding the Coins in
Each Pouch
Symbolic Equation

Remember the Balance Check
3x = 12
2x+5=19
4x+5=2x+19
X+12=2x+6
3(x+4)=18
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Inv 3 Day 2 Homework: Complete and CORRECT with the KEY
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Day 3 MSA 3.4: SOLVING EQUATIONS
To maintain the equality of two expressions, you can add, subtract, multiply or divide each side of the equality by
the same number. These are called the properties of equality. In the last problem, you applied properties of
equality and numbers to find a solution to an equation.
So far in the Investigation, all of the situations have involved positive whole numbers.
What strategies do you have for solving an equation like -2x + 10 = 15?
1. For each problem, record each step you take to find your solution and then check your answer.
5x + 10 = 20
5x – 10 = 20
5x + 10 = -20
5x – 10 = -20
Balance Check
10 –x = 20
Balance Check
Balance Check
Balance Check
Balance Check
10 – 5x = -20
How do you solve a symbolic equation?
Balance Check
How do you check to make sure your equation is
balanced?
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2. For each problem, record each step you take to find your solution and then check your answer.
𝑥
¼ x + 6 = 12
3/5 = -x + 15
−(2𝑥 − 15) = 3𝑥
+ 15 = 12
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Balance Check
Balance Check
Balance Check
Balance Check
15 – 4x = 10x + 45
3(x + 1) = 21
2 + 3(x + 1) = 6x
-2(2x – 3) = -2
Balance Check
Balance Check
Balance Check
Balance Check
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Day 3 Homework MSA 3.4: Complete and CORRECT with the EDpuzzle
1. Solve each equation. Check your answers.
2x + 6 = 6x + 2
2x – 6 = -6x + 2
2x + 6 = 6x – 2
-2x – 6 = -6x – 2
Balance Check:
Balance Check:
Balance Check:
Balance Check:
2. Solve each equation. Check your answers. (Remember to use the Distributive Property)
3(x+2) = 12
3(x+2) = x – 18
3(x+2) = 2x
Balance Check:
Balance Check:
Balance Check:
Balance Check:
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Day 4: ADDITIONAL PRACTICE
11
12
Day 5 MSA 3.5: SOLVING INEQUALITIES
Tips to remember graphing inequalities:
1) < and > will have an ______________ dot.
2) ≤ 𝑎𝑛𝑑 ≥ will have a ________________dot.
3) When multiplying or dividing what do you do to the sign?___________________________
Solve the inequality
Graph the inequality
3x+8>2
Test point:
7x-1<20
Test point:
8 − 4𝑥 ≥ −12
Test point:
−5𝑥 − 9 ≥ −4
Test point:
−10 + 2𝑥 ≤ −𝑥 + 11
Test point:
13
𝑥
− 13 < −23
7
Test point:
−𝑥
+ 2 ≤ −12
8
Test point:
−3𝑥 − 7 > 2𝑥 − 23
Test point:
1
3
𝑥 + 13 < − 10
4
4
Test point:
8(2 + 𝑥) ≤ 3𝑥 − 9
Test point:
5(−3𝑥 − 1) + 7 ≤ −𝑥 − 10
Test point:
14
Day 5 Homework MSA 3.5: Complete and CORRECT with the KEY
Multi-step equations and inequality practice
−5 1
2
+ 𝑥=
7
3
7
−𝑥 + 13 = 7
Balance check:
Balance check:
6=
𝑎
+2
4
2(𝑛 + 5) = −2
Balance check:
Balance check:
Solve and graph:
Solve and graph:
1+𝑚
>1
9
−2𝑟 − 2 ≤ 4
Test point:
Test point:
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Day 6 MSA 3.5: INEQUALITY WORD PROBLEMS
At fabulous Fabian’s bakery, the expenses (E) to make n cakes per month is given by the equation
E=825+3.25n. The income (I) for selling n cakes is given by the equation I=8.20n.
A. What does the coefficient next to n in each equation represent?
B. Fabian sells 100 cakes in January.
1. What are his expenses? Show your reasoning
2. What is his income? Show your reasoning.
3. What is his profit? Describe how you found your answer.
4. How many cakes can Fabian make if he wants his expenses to be less than $2,400 a month?
Write an inequality and solve.
5. How many cakes can he make if he wants his income to be greater than $2,400 a month?
Write an inequality and solve.
C. For the following inequalities, find the number of cakes Fabian needs to make in a month.
1) 𝐸 < 1,475
2) 𝐼 > 1,640
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Back in the day (around the time Mrs. Grow was your age and Ms. Pendley was still in diapers) cell phones were
becoming increasingly popular. Different carriers offered different plans to their members and people had to use
mathematical reasoning and inequalities to determine the best plan for their family (I wish I was kidding, but I am
not).
Driftless Region Telephone Company had a plan that charged a monthly rate of $10 and $.03 per text (there was no
such thing as unlimited texting! The horror!). Walby Communications charged $7.50 a month plus $.04 cents a text.
a. Predict: If you were paying for a plan what carrier would you choose and why?
b. Write an equation that represents the scenario using the variable t for texts and d for dollars.
Driftless Region Telephone:
Walby Communications:
c. At about what point is it less expensive to go with Walby Communications? At what point is it better to go
with Driftless Region Telephone? Think about the “break even” point! Justify your reasoning.
d. If you had a maximum of $15 to spend per month, what plan would you chose?
Set up an inequality for both and solve, to determine the best plan.
Driftless Region Telephone:
Walby Communications:
e. If you had a maximum of $25 to spend per month, what plan would you chose? Set up an inequality for
both and solve, to determine the best plan.
Driftless Region telephone:
Walby Communications:
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