#### Answer

$n\lt\dfrac{2}{11}$

#### Work Step by Step

Using the distributive property and properties of inequalities, the solution to the given inequality, $
-3(n-4)\gt5(n+2)+3n
,$ is
\begin{array}{l}\require{cancel}
-3n+12\gt5n+10+3n
\\\\
-3n-5n-3n\gt10-12
\\\\
-11n\gt-2
\\\\
n\lt\dfrac{-2}{-11}
\\\\
n\lt\dfrac{2}{11}
.\end{array}