How do you solve for x in ax-c=b?

Apr 26, 2017

See the solution process below:

Explanation:

First, add $\textcolor{red}{c}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$a x - c + \textcolor{red}{c} = b + \textcolor{red}{c}$

$a x - 0 = b + c$

$a x = b + c$

Now, divide each side of the equation by $\textcolor{red}{a}$ to solve for $x$ while keeping the equation balanced:

$\frac{a x}{\textcolor{red}{a}} = \frac{b + c}{\textcolor{red}{a}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{a}}} x}{\cancel{\textcolor{red}{a}}} = \frac{b + c}{a}$

$x = \frac{b + c}{a}$

Or

$x = \frac{b}{a} + \frac{c}{a}$

Apr 26, 2017

$\frac{b + c}{a}$

Explanation:

Add 'c' in both sides, we get ax - c + c = b + c

$\Rightarrow a x = b + c$ [now divide by 'a' in both sides]

$\Rightarrow \frac{a x}{a} = \frac{b + c}{a}$

$\Rightarrow x = \frac{b + c}{a}$