Solving for an equation for one variable (algebra)

Question

I have to solve for $n$ in this equation $M=a+c(n-6)$. I have already used the distributive property. However, I don’t have any like terms. I have tried different ways to get the answer, but none of them seem to logically make sense. How would you solve this? Again, I’m solving for $n$.

Answer 1

It is $$M-a=cn-6c$$ $$M-a+6c=cn$$so $$n=\frac{M-a+6c}{c}$$ for $$c\neq 0$$

Answer 2

You used the distributive property to get from $M=a+c(n-6)$ to $M=a+cn-6c.$

Since your goal is to solve for $n$,

subtract $a-6c$ from each side to get all the terms not involving $n$ on one side of the equation:

$M-(a-6c)=a+cn-6c-(a-6c)\implies M-a+6c=cn$.

Now simply divide both sides by $c$ to solve for $n$.

(You can do so provided $c\ne0$. If $c=0, $ you could not solve for $n$; $n$ could be anything.)