#### Answer

$z=-7$

#### Work Step by Step

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
.$