When solving an equation, why is it necessary to perform the same operation on both sides of an equal sign?

In order to keep the equation right, both sides have to balance each other. When you only perform an operation (I'm assuming you're talking about division or multiplication) on one side, it messes up the balance because now one side is larger than the other.

To get the right answer you must perform the same operation on both sides of the equation because the equation will not be correct if it is not. If you subtract something from one side to make it equal you must subtract it from both sides.