Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 34

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

Multiplying both sides by the $LCD= 12 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{2}{3}n-\dfrac{1}{2}n\gt\dfrac{1}{4} ,$ is \begin{array}{l}\require{cancel} 4(2n)-6(1n)\gt3(1) \\\\ 8n-6n\gt3 \\\\ 2n\gt3 \\\\ n\gt\dfrac{3}{2} .\end{array}