Answer
$x =\dfrac{ac + d}{ab}$ or $x =\dfrac{ac – d}{ab}$
Work Step by Step
First, isolate the absolute value by dividing both sides by $a$:
$|bx – c| = \dfrac{d}{a}$
Separate the equation into its positive and negative cases (since $|x|=a \longrightarrow x=a \text{ or } x =-a$):
$bx – c = \dfrac{d}{a}$ or $bx – c = –\dfrac{d}{a}$
Solve each equation for $x$ separately:
$bx – c = \dfrac{d}{a}$
$bx = c + \dfrac{d}{a}$
$x =\dfrac{c + \frac{d}{a}}{b}$
or
$bx – c = –\dfrac{d}{a}$
$bx = c – \dfrac{d}{a}$
$x =\dfrac{c – \frac{d}{a}}{b}$
So our answer is
$x =\dfrac{c + \frac{d}{a}}{b}$ or $x =\dfrac{c – \frac{d}{a}}{b}$
We could also simplify these by multiplying numerator and denominator by a, then we’d have:
$x =\dfrac{ac + d}{ab}$ or $x =\dfrac{ac – d}{ab}$
