## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$c=\dfrac{d}{a-b}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $ac-bc=d,$ for $c ,$ use the Distributive Property and the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} ac-bc=d \\\\ c(a-b)=d .\end{array} Using the properties of equality to isolate the variable, the equation above is equivalent to \begin{array}{l}\require{cancel} c(a-b)=d \\\\ \dfrac{c(a-b)}{a-b}=\dfrac{d}{a-b} \\\\ c=\dfrac{d}{a-b} .\end{array}