Variables are used in almost every part of mathematics.  While important, variables are not difficult to understand.

They are just a substitue.  They only take the place of a number or value.

Variable can be a letter (A), or a symbol (q).

Types of mathematical statements

Equations are just mathematic statements that have an equal sign within them.

EX: 4=2a

2+2=4

An Inequality is a mathematical statement that has a less than (<), greater than (>), less than or equal to (£), greater than or equal to (³), or approximately (@).

EX: 2@1.5

5³4

Solving algebraic equations.

Now that you know what equations are we will learn how to solve them.  The main idea to keep in mind is what you do to one side you must do to the other.  This simple concept is key.  When solving equations the main idea is to get the variable by itself on one side of the equal sign.

Addition and subtraction in algebraic equations:

x+3=5

In order to solve this we will first subtract 3 from both sides.

x+3-3=5-3

x+0=2

Result

x=2

We have just found the value that x is equal to.  To make sure we have done this correctly, we will replace the variable (x) with the value (2).

2+3=5

Subtraction is very similar to the addition process.

x-2=3

We will again get x by itself on one side of the equal sign.

x-2+2=3+2

x-0=5

x=5

This time we had to add the 2, not subract because that gave us the x-0 we were searching for.

HINT!!!

Multiplication and division are done the same way.

2x=5

Again the key is to get x by itself.  To do this divide x by 2.

2x/2=5/2

x*1=2.5

x=2.5

Division is the same way.

x/2=20

x/2*2=20*2

x/1=40

x=40

HINT!!!

2-x =5

Subtract 2 from both sides

2-2-x=5-2

-x=3

Now what?

divide by a negative 1 (-1)

-x/-1=3/-1

x=-3

These are the basics of algebraic equations.  Test your skills with this next problem:

5(2x-3)=45

Hint!!!

The answer is 6.  If you did this correctly give yourself a hand and lets move on to inequalities.

Inequalities are solved the same way as equations with one exception.  When dividing by a negative number (-2) and the symbol is less than (<), greater than (>), less than or equal to (£), greater than or equal to (³), you must flip the symbol in the other direction.

EX:

-2x³6

divide by -2

(-2)x/(-2)£6/(-2)

x£-3

Double check it.  It does work out.