#### Answer

$z=-\dfrac{5}{9}$

#### Work Step by Step

Multiplying both sides by $
-5
$, then the solution to the given equation, $
\dfrac{1}{9}=\dfrac{z}{-5}
$, is
\begin{array}{l}\require{cancel}
-5\cdot\dfrac{1}{9}=\dfrac{z}{-5}\cdot(-5)
\\\\
-\dfrac{5}{9}=\dfrac{-5z}{-5}
\\\\
-\dfrac{5}{9}=z
\\\\
z=-\dfrac{5}{9}
.\end{array}