Chapter 2 - Equations, Inequalities, and Problem Solving - 2.1 Solving Equations - 2.1 Exercise Set - Page 87: 61

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

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}