1. Solving Equations with Variables
on Both Sides

2. 4. Four times a number plus two is the same as a negative 14.
Solve each equation. Click the box to reveal the answer.
1. x + 8 = -3
x = -11
2. 2p -5 = -11
p = -3
3. 36 = 6 - 5n
n = -6
Reviewing 
is a good 
idea!
Translate and solve.
4. Four times a number plus two is the same 
as a negative 14.
x = -4

3. Solving Equations with Variables on Both Sides
Go to 
Example 1
Record the following steps in your notebook.
We will refer to these steps throughout the lesson.
Go to 
Example 2
Pull
Distribute, if necessary.
Step 1
Step 2
Step 3
Step 4
Step 5
Go to 
Example 3
Practice
Pull
Combine like terms on the same side,
if necessary.
Video: Real 
World Problem
HOMEWORK
Pull
Move your variables to the same side
using opposite operations.
Pull
Move your constants to the same side
using opposite operations.
Pull
Solve for your variable.

4. 6x + 3 + 2x = 5x + 12 8x + 3 = 5x + 12 3(2x + 1) + 2x = 5x + 12
Solving Equations with Variables on Both Sides
Watch me
on this first
one?
Example #1:
3(2x + 1) + 2x = 5x + 12
6x x = 5x + 12
8x + 3 = 5x + 12
8x - 5x + 3 = 5x - 5x + 12
3x + 3 = 12
3x =
3x = 9
x = 3
3(2x + 1) + 2x = 5x + 12
pull
Erase the box to reveal
the steps.
Distribute
Pull
Combine like terms
Move variables together.
Simplify
Move constants together
Simplify
Press for
example 2
Back to
steps.
Solve
Teacher Notes
Teacher Notes: Drag the arrows together to see the problem worked out. You may choose 
to work out the problem after revealing each step instead of dragging the arrows together.

5. Solving Equations with Variables on Both Sides
Let's Do
this Together
Example #2: 19x+8-8x = 4(5x+2)+36
19x+8-8x = 4(5x+2) + 36
Answer hidden here!
Bring the magnifying glass over.
Press for
example 3
Back to
steps.
x = -4

6. Solving Equations with Variables on Both Sides
Try this one
by yourself.
Example #3: 4(2p-8)-6p = 20+4(p+6)
Work this problem in the blue box.
Move the problem to the gray box to reveal the solution.
4(2p-8)-6p = 20+4(p+6)
8p-32-6p = 20+4p+24
2p - 32= 4p+ 44
2p-4p-32 = 4p-4p+44
-2p-32 = 44
-2p-32+32=44+32
-2p=76 (divide)
p = -38
Did You 
Get It 
Right?
yes no
Back to
steps.
More Practice

7. Solving Equations with Variables on Both Sides
Homework
Practice. Solve each problem and show
the work that justifies each answer.
1. 4(3x - 10) = 10(x - 3)
2. 7x x = 3x - 17
3. ½(6x + 8) + 3x = 5x + 25
Teacher
Notes
Answers:
1. x = 5
2. x = -11
3. x = 21
4. x = -6
4. 15x = 10x - 30
Back to
steps.

8. Al's Rentals charges $25 per
hour to rent a Windsurfer and a
wet suit. Wendy's charges $20
per hour plus $15 extra for a wet
suit. Find the number of hours
for which the total charges for
both would be the same.

9. You and your friends want to have a
super fun Halloween party, but you
can't decide where to have it. The
neighborhood clubhouse costs $135 to
rent the room plus $10 per hour. Party
Plus charges $150 to rent a room and
$5 per hour. How many hours would
you need to rent the facility to make
the cost the same?

10. A house painting company charges $376 plus
$12 per hour. Another painting company
charges $280 plus $15 per hour. How long is a
job for which both companies will charge the
same amount? What will that cost be?

11. perimeter. What is the value of x?
The triangles shown have the same
perimeter. What is the value of x?
x + 3
2x - 3 x

12. Happy Paws charges a
flat fee of $19.00 plus
$1.50 per hour to keep a
dog during the day. A
rival service, Woof
Watchers, charges a flat
fee of $15.00 plus $2.75
per hour. Find the
number of hours for
which you would pay the
same total fee to both
services.

13. Solving Equations with Variables on Both Sides
Real World Application:
Watch the video to see a real world example of solving 
equations with variables on both sides.
click here to watch video
Teacher Notes
Teacher Notes: You may stop the video after the problem is presented to 
allow the students to work it out
Back to
steps.
Homework

14. Textbook Work:
page 312, 1 and 2
page 313, 1-8
page 314, 11
page 315, 17-22

15. Roll the number cube to create a new equation to solve.
Practice with a Partner
Back to
steps.
Video
Homework

16. Attachments
real world application.wpl