Chapter 2 - Equations, Inequalities, and Problem Solving - Review Exercises: Chapter 2 - Page 150: 64

$a=\dfrac{y-3}{2-b}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ 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}

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