The Foundation

• the goal is to isolate the variable to one side of the equal sign with a coefficient of 1 (Ex: x = 3)

• Undo everything that was done to the variable in reverse order- start with what was done last

• What you do to one side of the equation, you MUST do to the other side also (Ex: if I add 3 to the left side, I must add 3 to the right side too)

Example

5x + 3 = 18

1. Read starting with the variable first: x multiply 5 add 3 equals 18

Let's do it!

Bring down the 5x.

What is 3 + (-3)?

What is 18 + (-3)?

Step 2

What was done before add 3 and how do we undo it

x multiply 5 add 3 equals 18?

Divide by 5 on both sides and simplify

x = 3

Let's try another!

Before we can determine what was done last, we need to perform the distributive property!

Before we start....

• change the subtraction to addition: -6x - 3

• then we can perform the distributive property

Distributive Property

1. -4 * (-6x) = 24x and

2. -4 * (-3) = 12

Now we can use 24x + 12 = 12 to determine what was done last to our variable