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

(Note to contributors: Please use the ^ symbol to designate exponents when you enter them in the wikibook. I will format them on the student-user interface.--HSTutorials 00:42, 17 July 2006 (UTC)

## Vocabulary

Variable - a letter (A-Z) that takes the place of a number.

Equation - an example would be: 8y - 3 = 1 + 10y (The answer is -2 [negative two] = y)

## Lesson

NOTE: WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER! 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: x=20 or 20=x

## Example Problems

A simple problem:

$\displaystyle 10+50=3x-50+50$ <---get rid of the 50 by subtracting

$\displaystyle 60=3x$ <---This is what your left with.

$\displaystyle 60/3=3x/3$ <---Get rid of the three by dividing by three

$\displaystyle 20=x$ <---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: put answer in parentheses after each problem you write)

Practice Problem #1:

3v - 2 = v + 16 {v = 9}

Practice Problem #2:

2x = 15 - x {x = 5}

Practice Problem #3:

([z - 5] / -3) = 9 + 3.4z {z = _?_}

Note: Help with Problems 2 & 3. No answer!