# Basic Algebra/Solving Equations/Solving Equations with Variables on Both Sides of the Equation

## Vocabulary

Variable
A letter (${\displaystyle a}$ -${\displaystyle z}$ ) that takes the place of a number.
Equation
An example would be like ${\displaystyle 8y-3=1+10y}$  (The answer is ${\displaystyle y=-2}$  )

## Lesson

NOTE: WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER SIDE! NO EXCEPTIONS!

1) do the distributive property.

2) Combine like terms on both sides.

3) add/subtract numbers next to a variable on both sides.

4) divide by the number next to the variable on both sides.

5) The answer should look like: ${\displaystyle x=20}$  or ${\displaystyle 20=x}$ .

## Example Problems

A simple problem:

 ${\displaystyle 2(x+5)=5(x-10)}$ ${\displaystyle 2x+10=5x-50}$  ${\displaystyle 2x+10-2x=5x-2x-50}$  ${\displaystyle 10=3x-50}$  ${\displaystyle 10+50=3x-50+50}$  ${\displaystyle 60=3x}$  ${\displaystyle 60/3=3x/3}$  ${\displaystyle 20=x}$ Problem Distributive Prop. Subtract the variables with numbers next to them. This is what you're left with. get rid of the 50 by subtracting This is what you're left with. Get rid of the three by dividing by three This is your answer.

## Practice Games

Put links here to games that reinforce these skills

Purplemath.com: http://www.purplemath.com/modules/index.htm

## Practice Problems

Note: Use / as the fraction line and put spaces between wholes and fractions!

1 ${\displaystyle 3x-2=x+16}$

2 ${\displaystyle 2y=15-y}$
3 ${\displaystyle {\frac {z-5}{-3}}=9+3.4z}$