Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 19

$z=-7$

Using the properties of equality, the solution to the given equation, $ 8z+2=-54 $, is \begin{array}{l} 8z+2-2=-54-2 \\\\ 8z=-56 \\\\ \dfrac{8z}{8}=\dfrac{-56}{8} \\\\ z=-7 .\end{array} Checking: \begin{array}{l} 8(-7)+2=-54 \\\\ -56+2=-54 \\\\ -54=-54 \text{ (TRUE)} .\end{array} Hence, the solution is $ z=-7 .$