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Basics of the Equation

The diagram on the right shows a basic equation. This equation is similar to problems which you may have done in ordinary mathematics such as:

__ + 16 = 30

You could easily guess that __ equals 14 or do 30 - 16 to find that __ equals 14.

In this problem __ stood for an unknown number; in an equation we use variables, or any letter in the alphabet.

When written algebraically the problem would be:
x + 16 = 30

and the answer should be written:
x = 14

Solving Equations

These equations can be solved relatively easy and without any formal method. But, as you use equations to solve more complex problems, you will want an easier way to solve them.

Pretend you have a scale like the one shown. On the right side there are 45 pennies and on the left side are 23 pennies and an unknown amount of pennies. The scale is balanced, therefore, we know that there must be an equal amount of weight on each side.

As long as the same operation (addition, subtraction, multiplication, etc.) is done to both sides of the scale, it will remain balanced. To find the unknown amount of pennies of the left side, remove 23 pennies from each side of the scale. This action keeps the scale balanced and isolates the unknown amount. Since the weight(amount of pennies) on both sides of the scale are still equal and the unknown amount is alone, we now know that the unknown amount of pennies on the left side is the same as the remaining amount (22 pennies) on the right side.


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