# Variables

RECAP: On previous pages, we have learned about equations with positive and negative numbers as well as with several different mystery doors. On this page we are going to learn about variables.

What is a variable? The word variable means something that can differ depending on the circumstances. In math it is much the same. On our previous pages, the mystery door opened on many different numbers depending on what the rest of the equation says - much as an elevator door will open onto different floors depending on what button was pushed in its journey up and down the elevator shaft. .

Since mathematicians try to do things as simply and easily as possible, mystery doors are not used to stand for numbers as they would be more cumbersome to write and type with a computer or calculator. Instead, mathematicians use letters of the alphabet to stand in for the unknown numbers behind the mystery doors. Let's look at an example:

# 2 + 3 = 5

In this case the x is in place of the mystery door. We proceed in the same fashion as with the mystery door equations. The number three is removed from both sides of the equation. The variable x is equal to the number 2. Any letter of the alphabet could have been used instead of x as it is just standing in for the unknown, mystery number.

Here is an equation similar to the one in Equations 6. Notice the mystery doors have been replaced by two letters of the alphabet.

# x + y = 3

Once again, x and y can equal many different numbers. One of the best ways to illustrate this equation is to use the graph to show the endless possibilities.

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