Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 17

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

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}