Solve Equations with
Variables on Both Sides
CW GRADE_______________
65
Name___________________________
Date ______________________________
Subject _________________________________
Homeroom_____________________________
Partners
OBJECTIVE: I will be able to solve equations with variables on both sides.
WHAT ARE YOU BEING ASKED TO DO TODAY?
STOP AND JOT
Solve 16x – 5 = 10x + 19 using two different “first steps”
HARVARD
Solve for the variable. Remember to follow the steps from your guided notes!
1) A student solved the equation below on the board. The first step is shown.
To continue solving, what advantage does adding, –2x to each side of the equation
have over adding –5x?
____________________________________________________________________
2) To solve 10t + 5 = –4t + 7, what can you add to both sides so t is on only one side
the equation? _______________ or ___________________
3) An equation is solved below. Fill in the blanks to explain the steps of the solution.
a.
x – 4 = −3x – 7
Add _________to each side.
b.
4x – 4 = −7
Add _________to each side.
c.
4x = −3
________each side by _________
d.
x 
3
4
Simplify.
4) A dog breeder raises two kinds of dogs. At birth, the average puppy of breed A weighs
14.8 ounces and gains weight at a rate of 0.5 ounce per week. Breed B puppies are
smaller at birth, weighing about 11.6 ounces. But they gain weight faster, at 0.9 ounce
per week. How many weeks will it be before the puppies are the same weight?
PRINCETON
1. HELP ISABELLA! 
Isabella tried to solve an equation. In which step did she make a mistake? Circle that step.
3
5
Step 1:
10 − 𝑥 = 0
Step 2:
− 5 𝑥 = −10
Step 3:
(− 5)(− 5 𝑥) = (−10)(− 5)
Step 4:
𝑥=6
3
3
3
3
2. Ms. Rallo had a bank account with $500 in it. She withdrew an equal amount of money from her account each
week for 6 weeks. At the end of 6 weeks, she had $350 left in her account.
PART A: Write an equation that can be used to solve for the amount of money she withdrew each week.
Equation:__________________________________________________________________________________
PART B: Solve your equation. What is the meaning of your answer?
STANFORD
1) Below, the perimeter of the triangle is equal to the perimeter of the square.
Using an equation, find the perimeter of both figures.
SAMPLE TEST QUESTION
Solve:
7 – (x + 5) = 4(x +11).
Solve Equations with
Variables on Both Sides
ET GRADE_______________
65
Name___________________________
Date ______________________________
Subject _________________________________
Homeroom_____________________________
Variables on both exit ticket 2 Partners
12(3x + 4) = 6(7x + 2)
Solve Equations with
Variables on Both Sides
ET GRADE_______________
3x - 25 = 11x - 5 + 2x
¾x - 12 = ½x -6
65
Name___________________________
Date ______________________________
Subject _________________________________
Homeroom_____________________________
Variables on both exit ticket 2 Partners
12(3x + 4) = 6(7x + 2)
3x - 25 = 11x - 5 + 2x
¾x - 12 = ½x -6
Solve Equations with
Variables on Both Sides
HW GRADE_______________
65
Name___________________________
Date ______________________________
Subject _________________________________
Homeroom_____________________________
Partners
Solve Equations with
Variables on Both Sides
Do Now GRADE_______________
42
Name___________________________
Date ______________________________
Subject _________________________________
Homeroom_____________________________
Partners
1. Simplify the expression (-4 - 3x) -7
2. Solve for y: 10y – 9 = 12y + 5
3. Solve for w: 7 + 2w = 10w - 17
4. Simplify the expression - (-4 + 3x) -7
5. Simplify the expression 36x + 19 – 17x