Answer
$w=\dfrac{7}{z-3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
z=\dfrac{3w+7}{w}
,$ for $
w
,$ put all expressions with $
w
$ on one side and all other expressions on the other side. Then use the properties of equality to isolate and solve for the variable.
$\bf{\text{Solution Details:}}$
By cross-multiplication, the given equation is equivalent to
\begin{array}{l}\require{cancel}
zw=3w+7
.\end{array}
Putting all variables with $
w
$ on the left side, the equation above is equivalent to
\begin{array}{l}\require{cancel}
zw-3w=7
.\end{array}
Factoring $
w
$ on the left side and using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
w(z-3)=7
\\\\
\dfrac{w(z-3)}{(z-3)}=\dfrac{7}{(z-3)}
\\\\
w=\dfrac{7}{z-3}
.\end{array}