## Elementary Algebra

$n=21$
Multiplying both sides by the $LCD= 3$ and then using the properties of equality, the value of the variable that satisfies the given equation, $\dfrac{2n-5}{3}=\dfrac{n+1}{3}+5 ,$ is \begin{array}{l}\require{cancel} 1(2n-5)=1(n+1)+3(5) \\\\ 2n-5=n+1+15 \\\\ 2n-n=1+15+5 \\\\ n=21 .\end{array}