Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 47

$n\gt\dfrac{33}{5}$

Multiplying both sides by the $LCD= 6$ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{n+3}{3}+\dfrac{n-7}{2}\gt3 ,$ is \begin{array}{l}\require{cancel} 2(n+3)+3(n-7)\gt6(3) \\\\ 2n+6+3n-21\gt18 \\\\ 2n+3n\gt18-6+21 \\\\ 5n\gt33 \\\\ n\gt\dfrac{33}{5} .\end{array}