#### Answer

$n=\dfrac{31}{2}$

#### Work Step by Step

Using the properties of equality, the value of the variable that satisfies the given equation, $
-5(n-2)=-3(n+7)
,$ is
\begin{array}{l}\require{cancel}
-5n+10=-3n-21
\\\\
-5n+3n=-21-10
\\\\
-2n=-31
\\\\
n=\dfrac{-31}{-2}
\\\\
n=\dfrac{31}{2}
.\end{array}