How to Solve Linear Equations (Combined Methods)

Change Sides, Change Sign

I’m sure you remember that equations always have to be balanced. When you do something to one side, you have to do the same thing to the other side. With change sides, change sign, this happens behind the scenes, so don’t worry if it doesn’t look exactly like you’re used to at first.

Plus Change Sides, Change Sign, to Minus

$$\begin{array}{llll}\hfill x+3& =5& \hfill & \\ \hfill x& =5-3& \hfill & \\ \hfill x& =2& \hfill & \end{array}$$ We move $+3$ to the RS of the equation. Then we change the sign so that $+3$ becomes $-3$.

Minus Change Sides, Change Sign, to Plus

$$\begin{array}{llll}\hfill x-4& =9& \hfill & \\ \hfill x& =9+4& \hfill & \\ \hfill x& =13& \hfill & \end{array}$$ We move $-4$ to the RS of the equation. We change the sign so that $-4$ becomes $+4$.

To Get Rid of the Number In Front of $x$

It’s important to remember that multiplying and dividing are inverse arithmetic operations. What multiplying can do, dividing can undo, and vice versa.

Here are some more complicated examples: