Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 29

$n\gt-\dfrac{17}{2}$

Using the Distributive Property and the properties of inequalities, the solution to the given inequality, $ 5(n+1)-3(n-1)\gt-9 ,$ is \begin{array}{l}\require{cancel} 5n+5-3n+3\gt-9 \\\\ 5n-3n\gt-9-5-3 \\\\ 2n\gt-17 \\\\ n\gt-\dfrac{17}{2} .\end{array}