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

VocabularyEdit

Variable - a letter ($a$-$z$) that takes the place of a number.

Equation - an example would be like $8y - 3 = 1 + 10y$ (The answer is $y=-2$ )

LessonEdit

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: $x=20$ or $20=x$.

Example ProblemsEdit

A simple problem:

$2(x+5)=5(x-10)$<---Problem

$2x+10=5x-50$<---Distributive Prop.

$2x+10-2x=5x-2x-50$<---Subtract the variables with numbers next to them.

$10=3x-50$<---This is what you're left with.

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

$60=3x$<---This is what you're left with.

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

$20=x$<---This is your answer.

Practice GamesEdit

Put links here to games that reinforce these skills

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

Practice ProblemsEdit

(Note: put answer in parentheses after each problem you write)

Practice Problem #1:

$3x - 2 = x + 16$

Answer: $x = 9$

Practice Problem #2:

$2y = 15 - y$

Answer :$y = 5$

Practice Problem #3:

$\frac{z - 5}{-3} = 9 + 3.4z$

Amswer: $z = -1\frac{27}{28}$