How to Manipulate a Single Variable Equation

In order to solve a single variable equation, we must isolate our variable on one side of the equation. And the way we do this is by shifting the rest of our terms to the other side of the equation.

In order to shift our terms (numbers), we must therefore cancel them out on their original side by performing the opposite function of the term.

 Opposite function pairs are:

·         Addition and subtraction

·         Multiplication and division

So if we have a term on one side that has a plus sign (addition), we must subtract that same amount from both sides.

x+2=6

x+2−2=6−2

x=4

If we have a term that is multiplied, we must divide that same amount from both sides.

And so on.

Whatever you do on one side of the equation, you must do on the other. This cancels out like terms and essentially moves your terms from one side of the equation to the other.

Single variable equations are all about maintaining balance.