Answer
$x=\frac{c}{a-1}$
Work Step by Step
We are trying to isolate the variable $x$ in the equation $ax-x=c$.
To do this, first we will factor out the $x$ using the distributive property: $x(a-1)=c$
Then, we will divide by $a-1$ to isolate $x$: $x=\frac{c}{a-1}$