Go through Lesson 3.5 to figure out this puzzle. Then come back to it and try it by

setting up an equation.

Josh and Amber and arguing about how a number trick they heard goes. Amber tells Nick to think of a number, multiply it by five and subtract three from the result. Then Josh tells Nick to think of a number, add five and multiply the result by three. Nick says that whichever way he does the trick he gets the same answer. What was Nick’s number?

Lesson 3.5 Solving Equations with Variables on Both Sides

When solving equations with variables on both sides, you need to cancel one of the terms with x on one side.

3x = -6x – 10

*Remember, you can’t combine them because the x’s are on different sides of the equal sign!

Solving Equations with Variables on both sides

How would you solve this?

3x = 5x + 8Get the variables on one side of the equal sign!

Cancel out one of the x terms.

-5x-5x

-2x = 8-2 -2

x = -4

Example 1: 6x + 8 = 4x – 10 -4x-4x

2x + 8 = -10

cancel 4x

subtract 4x

subtract 8-8 -8

2x = -18divide 22 2

x = - 9Will the answer be the same if you cancel the 6x instead?

Try it and find out!

Example 2: -6x – 7 = x

Which side should we cancel the x?

+6x +6x add 6x

-7 = 7x7 7

divide 7

-1 = x

Three types of answers you can get…

One solution: x equals any real number

x = 3

No Solution: x cancels and you get

5 = -36

Infinite solutions or an Identity: x cancels and you get 5 = 5

Practice:1. 2x – 5 = 15 + 5x 2. 20x + 16 = 2x

3. 2(4x – 4) = 8x – 6 4. 3(6 + 5y) = 2(-5 + 4y)

Try the puzzle now!