Vì ( 2n + 7 ) chia hết cho ( n + 1 )
\(\Rightarrow\)\(\left[2n+7-2\left(n+1\right)\right]⋮\left(n+1\right)\)
\(\Rightarrow\)5 chia hết cho n + 1
\(\Leftrightarrow\)\(\orbr{\begin{cases}n+1=1\\n+1=5\end{cases}\Leftrightarrow\orbr{\begin{cases}n=0\\n=4\end{cases}}}\)
Vậy \(n\in\left\{0;4\right\}\)