## Elementary Algebra

$n\lt\dfrac{68}{7}$
Multiplying both sides by the $LCD= 12$ and then using the properties of inequalities, the solution to the given inequality, $\dfrac{n-4}{4}+\dfrac{n-2}{3}\lt4 ,$ is \begin{array}{l}\require{cancel} 3(n-4)+4(n-2)\lt12(4) \\\\ 3n-12+4n-8\lt48 \\\\ 3n+4n\lt48+12+8 \\\\ 7n\lt68 \\\\ n\lt\dfrac{68}{7} .\end{array}