Solving Equations with Variables on Both Sides

x = -4

n = -6

p = -3

x = -11

Reviewing is a good idea!

Solve each equation. Click the box to reveal the answer.

1. x + 8 = -3

2. 2p -5 = -11

3. 36 = 6 - 5n

Translate and solve.

4. Four times a number plus two is the same as a negative 14.

PullSolve for your variable.

Pull

Move your constants to the same side using opposite operations.

Pull

Move your variables to the same side using opposite operations.

Pull

Combine like terms on the same side, if necessary.

PullDistribute, if necessary.Step 1

Step 2

Step 3

Step 4

Step 5

Solving Equations with Variables on Both Sides

Record the following steps in your notebook. We will refer to these steps throughout the lesson.

Go to Example 1

Go to Example 2

Go to Example 3

Practice

Video: Real World Problem

HOMEWORK

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.

Move constants together

Watch me on this first

one?

Move variables together.

Combine like terms

Distribute

Solving Equations with Variables on Both Sides

Back to steps.

Example #1: 3(2x + 1) + 2x = 5x + 12

6x + 3 + 2x = 5x + 12

8x + 3 = 5x + 12

8x - 5x + 3 = 5x - 5x + 12

3x + 3 = 12

3x + 3 - 3 = 12 - 3

3x = 9

x = 3

3(2x + 1) + 2x = 5x + 12

pull

Pull

Erase the box to reveal the steps.

Simplify

Solve

SimplifyPress for example 2

Teacher Notes

Solving Equations with Variables on Both Sides

Let's Do this Together

Back to steps.

Press for example 3

Example #2: 19x+8-8x = 4(5x+2)+36

19x+8-8x = 4(5x+2) + 36

Answer hidden here! Bring the magnifying glass over.

x = -4

Solving Equations with Variables on Both Sides

Back to steps.

Try this one by yourself.Example #3: 4(2p-8)-6p = 20+4(p+6)

4(2p-8)-6p = 20+4(p+6)

8p-32-6p = 20+4p+242p - 32= 4p+ 442p-4p-32 = 4p-4p+44-2p-32 = 44-2p-32+32=44+32 -2p=76 (divide) p = -38

Work this problem in the blue box. Move the problem to the gray box to reveal the solution.

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More Practice

Solving Equations with Variables on Both Sides

Homework

Back to steps.

Practice. Solve each problem and showthe work that justifies each answer.

1. 4(3x - 10) = 10(x - 3)

2. 7x + 5 - 2x = 3x - 17

3. ½(6x + 8) + 3x = 5x + 25

4. 15x = 10x - 30

Answers:1. x = 52. x = -113. x = 214. x = -6

Teacher Notes

Al's Rentals charges $25 perhour to rent a Windsurfer and awet suit. Wendy's charges $20per hour plus $15 extra for a wetsuit. Find the number of hoursfor which the total charges forboth would be the same.

You and your friends want to have asuper fun Halloween party, but youcan't decide where to have it. Theneighborhood clubhouse costs $135 torent the room plus $10 per hour. PartyPlus charges $150 to rent a room and$5 per hour. How many hours wouldyou need to rent the facility to makethe cost the same?

A house painting company charges $376 plus$12 per hour. Another painting companycharges $280 plus $15 per hour. How long is ajob for which both companies will charge thesame amount? What will that cost be?

The triangles shown have the sameperimeter. What is the value of x?

x + 3

x + 3

x + 3

x + 3 2x - 3

x

Happy Paws charges aflat fee of $19.00 plus$1.50 per hour to keep adog during the day. Arival service, WoofWatchers, charges a flatfee of $15.00 plus $2.75per hour. Find thenumber of hours forwhich you would pay thesame total fee to bothservices.

Real World Application:

Watch the video to see a real world example of solving equations with variables on both sides.

Solving Equations with Variables on Both Sides

click here to watch video

Teacher Notes: You may stop the video after the problem is presented to allow the students to work it out

Teacher Notes

Back to steps.

Homework

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

Roll the number cube to create a new equation to solve.

Practice with a Partner Back to steps.

Video

Homework

Attachments

real world application.wpl