Elementary Algebra

$n\lt2$
Multiplying both sides by the $LCD= 20$ and then using the properties of inequalities, the solution to the given inequality, $\dfrac{2n}{5}-\dfrac{n}{4}\lt\dfrac{3}{10} ,$ is \begin{array}{l}\require{cancel} 4(2n)-5(n)\lt2(3) \\\\ 8n-5n\lt6 \\\\ 3n\lt6 \\\\ n\lt\dfrac{6}{3} \\\\ n\lt2 .\end{array}