1. Warm Up # 70

2. Solving Two-Step Equations CCSS Aligned
My mom
warned me that if
I hold sneezes in, my head might grow abnormally
large!
Only those with single-step equation experience dare proceed!
©Mike’s Math Mall

3. Equation Solving
When we solve equations, our goal is to find the value of the variable; the solution to the equation.
𝟏𝟒𝒙−𝟑𝟕=𝟏𝟕𝟑
I’m afraid we’ll need a time machine and travel back to around 210 AD in order to do that, Sparky!
My goal
is to find the
person responsible
for mixing letters in
with math!
I’ll
pack my
bags!

4. Equation Solving
To find the solution to an equation, we isolate the variable by mathematically undoing the equation.
If you can name a two-step equation, you will automatically know how to undo or solve it.
Check this out! →

5. Two-Step Equations 𝟏𝟒𝒙−𝟑𝟕=𝟏𝟕𝟑
There are four types of two-step equations:
Multiplication/Addition
Division/Addition
Multiplication/Subtraction
Division/Subtraction
What type of an equation is this?
𝟏𝟒𝒙−𝟑𝟕=𝟏𝟕𝟑
If you said multiplication/subtraction, you’re correct!

6. Name that Equation! 1) 𝒙 𝟗 +𝟓=𝟏𝟎 2) 𝟕=𝟔𝒚−𝟏𝟏 3) 𝟒𝒏+𝟖=𝟐𝟒 4) 𝟑= 𝒓 𝟐 −𝟏𝟕
Name the following equations.
1) 𝒙 𝟗 +𝟓=𝟏𝟎
Division/Addition
2) 𝟕=𝟔𝒚−𝟏𝟏
Multiplication/Subtraction
3) 𝟒𝒏+𝟖=𝟐𝟒
Multiplication/Addition
4) 𝟑= 𝒓 𝟐 −𝟏𝟕
Division/Subtraction

7. Two-Step Equations
Because we use inverse operations to solve equations, we just use the opposite of an equation’s name to solve it.
Great question, Sparticus!
You MUST undo the addition or subtraction part first!
With just one catch!
Great
Caesar's ghost!
Why does there ALWAYS have to be
a catch?
How does
naming equations
help you solve
them?
Must…
find…happy
place…now!
Calm down and I’ll show you what I’m talking about!

8. Solving Two-Step Equations
Let’s start with this equation:
𝟕𝒏+𝟒=𝟓𝟑
Step 1: Name the equation.
Multiplication/Addition
Step 2: Name the inverse.
Division/Subtraction
Continued →

9. Solving Two-Step Equations
Step 3: Undo the addition part first (with subtraction)
𝟕𝒏+𝟒=𝟓𝟑
− 𝟒 −𝟒
𝟕𝒏=𝟒𝟗
Step 4: Undo multiplication part next (with division)
𝟕𝒏=𝟒𝟗
𝒏=𝟕 𝟕 𝟕

10. Don’t Forget to  the Solution
𝒏=𝟕
𝟕𝒏+𝟒=𝟓𝟑
𝟕(𝟕)+𝟒=𝟓𝟑
𝟒𝟗+𝟒=𝟓𝟑 

11. Solving Two-Step Equations
Let’s try another one:
𝒙 𝟖 −𝟔=𝟓
Step 1: Name the equation.
Division/Subtraction
Step 2: Name the inverse.
Multiplication/Addition
Continued →

12. Solving Two-Step Equations
Step 3: Undo the subtraction part first (with addition)
𝒙 𝟖 −𝟔=𝟓
+ 𝟔 +𝟔
𝒙 𝟖 =𝟏𝟏
Step 4: Undo the division part next (with multiplication)
𝟖 𝟏
𝒙 𝟖 =𝟏𝟏 ∙ ∙ 𝟖
𝒙=𝟖𝟖

13. Don’t Forget to  the Solution
𝒙=𝟖𝟖
To be honest, that’s not what I’m finding a little weird right now!
𝒙 𝟖 −𝟔=𝟓
Is it a
little weird that
I’m actually starting to understand this
stuff?
I don’t
get it! Why
is everyone laughing?
𝟖𝟖 𝟖 −𝟔=𝟓
𝟏𝟏−𝟔=𝟓 

14. Let’s Try a Couple More! 𝟏𝟎𝒚−𝟏𝟏=𝟔𝟗 𝟏𝟎𝒚−𝟏𝟏=𝟔𝟗 𝟏𝟎𝒚=𝟖𝟎 + 𝟏𝟏 + 𝟏𝟏
Step 1: Name it!
Multiplication/Subtraction
Step 2: Think inverse!
Division/Addition
Step 3: Undo Subtraction first!
𝟏𝟎𝒚−𝟏𝟏=𝟔𝟗
+ 𝟏𝟏
+ 𝟏𝟏
𝟏𝟎𝒚=𝟖𝟎
Continued →

15. Let’s Try a Couple More! 𝒚=𝟖 𝟏𝟎𝒚=𝟖𝟎 𝟏𝟎𝒚−𝟏𝟏=𝟔𝟗 𝟏𝟎(𝟖)−𝟏𝟏=𝟔𝟗 𝟖𝟎−𝟏𝟏=𝟔𝟗 
Step 4: Undo Multiplication!
𝟏𝟎𝒚=𝟖𝟎 𝟏𝟎 𝟏𝟎
𝒚=𝟖
Check it!
𝟏𝟎𝒚−𝟏𝟏=𝟔𝟗
𝟏𝟎(𝟖)−𝟏𝟏=𝟔𝟗
𝟖𝟎−𝟏𝟏=𝟔𝟗 

16. Last One! 𝟏𝟖= 𝒏 𝟕 +𝟗 𝟏𝟖= 𝒏 𝟕 +𝟗 𝟗= 𝒏 𝟕 −𝟗 −𝟗 Continued →
Step 1: Name it!
Division/Addition
Step 2: Think inverse!
Multiplication/Subtraction
Step 3: Undo Addition first!
𝟏𝟖= 𝒏 𝟕 +𝟗 −𝟗 −𝟗
𝟗= 𝒏 𝟕
Continued →

17. Last One! ∙ ∙ 𝟗= 𝒏 𝟕 𝟕 𝟏 𝟕 or 𝟔𝟑=𝒏 𝒏=𝟔𝟑 𝟏𝟖= 𝒏 𝟕 +𝟗 𝟏𝟖= 𝟔𝟑 𝟕 +𝟗
Step 4: Undo Division!
𝟗= 𝒏 𝟕
𝟕 𝟏 𝟕 ∙ ∙
𝟔𝟑=𝒏 or
𝒏=𝟔𝟑
Check it!
𝟏𝟖= 𝒏 𝟕 +𝟗
𝟏𝟖= 𝟔𝟑 𝟕 +𝟗
𝟏𝟖=𝟗+𝟗 

18. It’s Time to Show Your Stuff!
Solve the following equations. Be sure to include the variable with your answer.
2) 𝒎 𝟐 +𝟕=𝟏𝟗
1) 𝟑𝒙−𝟗=𝟏𝟖
𝒙=𝟗
𝒎=𝟐𝟒
3) 𝒏 𝟓 −𝟐𝟎=𝟓
4) 𝟔𝒓+𝟏𝟒=𝟖𝟔
𝒏=𝟏𝟐𝟓
𝒓=𝟏𝟐
6) 𝟐𝟐= 𝒚 𝟏𝟓 +𝟏𝟕
5) 𝟏𝟎𝟒=𝟖𝒙−𝟖
𝒙=𝟏𝟒
𝒚=𝟕𝟓

19. Let’s Try it with some Integers!
Solve the following equations. Be sure to include the variable with your answer.
2) 𝒚 𝟔 −𝟏=−𝟖
1) −𝟒𝒙+𝟏𝟏=−𝟐𝟏
𝒙=𝟖
𝒚=−𝟒𝟐
3) − 𝒄 𝟓 +𝟏𝟐=𝟕
4) 𝟓𝒋−𝟐𝟏=−𝟓𝟔
𝒄=𝟐𝟓
𝒋=−𝟕
6) −𝟏𝟒=− 𝒂 𝟖 +𝟗
5) 𝟏𝟐𝟐=−𝟔𝒃+𝟐𝟔
𝒃=−𝟏𝟔
𝒂=𝟏𝟖𝟒

20. Equations and Word Problems!
The perimeter of a rectangle is 54 inches. Its length is 22 inches. Write and solve an equation to determine its width?
Perimeter = 54 inches
width
22 in
Start by defining a variable!
Let 𝒘 = width
2 times the width + 2 times the length = perimeter
𝟐𝒘+𝟒𝟒=𝟓𝟒
𝟐𝒘=𝟏𝟎
−𝟒𝟒
−𝟒𝟒
𝒘=𝟓 𝒊𝒏 𝟐 𝟐
𝟐𝒘=𝟏𝟎

21. Equations and Word Problems!
Katie wants to buy a motor scooter that costs $518. She has already saved $188 and will earn $22 each week from babysitting jobs. Write and solve an equation to
see how many weeks it will take Katie to save
enough money to buy the motor scooter.
Define a variable!
Let 𝒘 = number of weeks
amount saved each week + amount already saved = total cost
𝟐𝟐𝒘=𝟑𝟑𝟎
𝟐𝟐𝒘+𝟏𝟖𝟖=𝟓𝟏𝟖
−𝟏𝟖𝟖
−𝟏𝟖𝟖 𝟐𝟐 𝟐𝟐
𝟐𝟐𝒘=𝟑𝟑𝟎
𝒘=𝟏𝟓 𝒘𝒆𝒆𝒌𝒔

22. Equations and Word Problems! Let 𝒂 = weekly allowance
Ashley spent half of her weekly allowance at the movies. To earn extra money, her parents let her clean the house windows for $8. What is Ashley’s weekly allowance if she ended up with $14?
Define a variable!
Let 𝒂 = weekly allowance
amount of allowance spent at the movies + amount earned washing windows = ending amount of money
𝒂 𝟐 +𝟖=𝟏𝟒
𝒂 𝟐 =𝟔 𝟐 ∙ ∙
To find “half”
of something,
divide by 2. 𝟐 −𝟖 −𝟖
𝒂 𝟐 =𝟔
𝒂=$𝟏𝟐

23. Solving Two-Step Equations
We could start by getting you out of that baby swing!
Then it looks like my work here is done!
So, how did you do on the practice problems, Sparky?
I’m glad I could help!
Now is there
any chance you can
give me some pointers
on how to impress
the ladies?
I did great with
your help, sir! Knowing
multiplication and division facts also made things easier.
Baby swing?
This is a loves seat
built just for me and
that special “Mrs. Sparkles!”
©Mike’s Math Mall
On your way
out, tell the DJ to put on a slow one, will ya?