How do you solve for x in a(x + b) = x + 4?

Feb 22, 2016

$x = \frac{4 - a b}{a - 1}$

Explanation:

Expand the left side:
$\textcolor{w h i t e}{\text{XXX}} a x + a b = x + 4$
Subtract $x$ from both sides
$\textcolor{w h i t e}{\text{XXX}} a x + a b - x = 4$
Subtract $a b$ from both sides
$\textcolor{w h i t e}{\text{XXX}} a x - x = 4 - a b$
Factor the $x$ out of the left side
$\textcolor{w h i t e}{\text{XXX}} x \left(a - 1\right) = 4 - a b$
Divide both sides by $\left(a - 1\right)$
$\textcolor{w h i t e}{\text{XXX}} x = \frac{4 - a b}{a - 1}$