#### Answer

$n\gt\dfrac{3}{2}$

#### Work Step by Step

Using the properties of inequalities, the solution to the given inequality, $
2(n+3)\gt9
,$ is
\begin{array}{l}\require{cancel}
n+3\gt\dfrac{9}{2}
\\\\
n\gt\dfrac{9}{2}-3
\\\\
n\gt\dfrac{9}{2}-\dfrac{6}{2}
\\\\
n\gt\dfrac{3}{2}
.\end{array}