I know this is painfully basic for some of you, but please do help me, proof writing is very new to me. thanks
We start with $ax+b=c.$
We obtain $ax=c-b$ by subtracting $b$ from both sizes of the equation.
Then, we get the following solution to the equation. $x=(c-b)/a$
Now we must prove that $x=(c-b)/a$ is a unique solution.
let $z$ be a solution to our equation.
We have $az+b=c$.
Because $ax+b=c$ and $az+b=c$ we get $ax+b=az+b$
Now we obtain $ax=az$ by subtracting $b$ from both sides.
Then, we divide by $a$ and obtain $x=z$.
Therefore, $x=(c-b)/a$ is a unique solution to our equation.