#### Answer

$n=-\dfrac{5}{2}$

#### Work Step by Step

Using the properties of equality and combining like terms, the value of the variable that satisfies the given equation, $
-2n+1-3n+n-4=7
,$ is
\begin{array}{l}\require{cancel}
-2n-3n+n=7-1+4
\\\\
-4n=10
\\\\
n=\dfrac{10}{-4}
\\\\
n=\dfrac{\cancel{2}\cdot5}{\cancel{2}\cdot(-2)}
\\\\
n=\dfrac{5}{-2}
\\\\
n=-\dfrac{5}{2}
.\end{array}