Answer
$a=\dfrac{c}{2b-1}$
Work Step by Step
Using the properties of equality to solve for $a,$ the given equation, $b=\dfrac{a+c}{2a},$ is equivalent to
\begin{align*}\require{cancel}
2a(b)&=\left(\dfrac{a+c}{2a}\right)2a
\\\\
2ab&=a+c
\\
2ab-a&=c
\\
a(2b-1)&=c
&(\text{factor out the }GCF=a)
\\\\
\dfrac{a(\cancel{2b-1})}{\cancel{2b-1}}&=\dfrac{c}{2b-1}
\\\\
a&=\dfrac{c}{2b-1}
.\end{align*}
Hence, in terms of $a,$ the given equation is equivalent to $a=\dfrac{c}{2b-1}$.
