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

$a=\dfrac{y-3}{2-b}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $y=2a-ab+3$ for $a ,$ 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} y=2a-ab+3 \\\\= y=a(2-b)+3 .\end{array} Using the properties of equality to isolate the variable, the equation above is equivalent to \begin{array}{l}\require{cancel} y=a(2-b)+3 \\\\ y-3=a(2-b) \\\\ \dfrac{y-3}{2-b}=\dfrac{a(2-b)}{2-b} \\\\ \dfrac{y-3}{2-b}=a \\\\ a=\dfrac{y-3}{2-b} .\end{array}