Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 184: 62

$n\gt\dfrac{5}{11}$

Multiplying both sides by the $LCD= 30 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{n+4}{5}+\dfrac{n-3}{6}\gt\dfrac{7}{15} ,$ is \begin{array}{l}\require{cancel} 6(n+4)+5(n-3)\gt2(7) \\\\ 6n+24+5n-15\gt14 \\\\ 6n+5n\gt14-24+15 \\\\ 11n\gt5 \\\\ n\gt\dfrac{5}{11} .\end{array}