Answer
$$x= -\frac{B}{A}y-\frac{C}{A} .$$
Work Step by Step
To solve the given equation for $x$, we keep the term $ Ax$ and move out all other terms to the other side and then we divide by $A$ as follows:
$$ Ax+By+C=0\Longrightarrow Ax=-By-C\Longrightarrow \frac{Ax}{A}=\frac{-By-C}{A} \\ \Longrightarrow x=\frac{-By-C}{A}=-\frac{B}{A}y-\frac{C}{A} .$$
