Answer
$n\le-\dfrac{180}{13}$
Work Step by Step
Multiplying both sides by the $LCD=
30
$ and then using the properties of inequalities, the solution to the given inequality, $
\dfrac{1}{2}n-\dfrac{1}{3}n-4\ge\dfrac{3}{5}n+2
,$ is
\begin{array}{l}\require{cancel}
15(1n)-10(1n)-30(4)\ge6(3n)+30(2)
\\\\
15n-10n-120\ge18n+60
\\\\
15n-10n-18n\ge60+120
\\\\
-13n\ge180
\\\\
n\le\dfrac{180}{-13}
\\\\
n\le-\dfrac{180}{13}
.\end{array}
