#### Answer

$n=-11$

#### Work Step by Step

Using the properties of equality and combining like terms, the value of the variable that satisfies the given equation, $
5n-2-8n=31
,$ is
\begin{array}{l}\require{cancel}
5n-8n=31+2
\\\\
-3n=33
\\\\
n=\dfrac{33}{-3}
\\\\
n=-11
.\end{array}