Chapter 2 - Equations, Inequalities, and Problem Solving - 2.1 Solving Equations - 2.1 Exercise Set - Page 86: 37

$z=-\dfrac{1}{20}$

Adding $ \dfrac{1}{5} $ to both sides of the given equation, $ -\dfrac{1}{5}+z=-\dfrac{1}{4} $, then, \begin{array}{l} -\dfrac{1}{5}+z+\dfrac{1}{5}=-\dfrac{1}{4}+\dfrac{1}{5} \\\\ z=-\dfrac{1}{4}+\dfrac{1}{5} \\\\ z=-\dfrac{5}{20}+\dfrac{4}{20} \\\\ z=-\dfrac{1}{20} .\end{array}