Chapter 4 - Proportions, Percents, and Solving Inequalities - Chapter 4 Review Problem Set - Page 184: 67

$n\le120$

Multiplying both sides by the $LCD= 12 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{3}{4}n-6\le\dfrac{2}{3}n+4 ,$ is \begin{array}{l}\require{cancel} 3(3n)-12(6)\le4(2n)+12(4) \\\\ 9n-72\le8n+48 \\\\ 9n-8n\le48+72 \\\\ n\le120 .\end{array}