Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 25

$z=19 $

Using the properties of equality, the solution to the given equation, $ -6z-18=-132 $, is \begin{array}{l} -6z=-132+18 \\\\ -6z=-114 \\\\ z=\dfrac{-144}{-6} \\\\ z=19 .\end{array} Checking: \begin{array}{l} -6(19)-18=-132 \\\\ -114-18=-132 \\\\ -132=-132 \text{ (TRUE)} .\end{array} Hence, the solution is $ z=19 .$