Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 33

$n\gt-\dfrac{9}{2}$

Multiplying both sides by the $LCD= 24 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{3}{4}n-\dfrac{5}{6}n\lt\dfrac{3}{8} ,$ is \begin{array}{l}\require{cancel} 6(3n)-4(5n)\lt3(3) \\\\ 18n-20n\lt9 \\\\ -2n\lt9 \\\\ n\gt\dfrac{9}{-2} \\\\ n\gt-\dfrac{9}{2} .\end{array}