Answer
Solutions are $5, \frac{-17}{3}$
Work Step by Step
$|\frac{1+3n}{4}| = 4$
This is equivalent to
$\frac{1+3n}{4} = 4$ or $\frac{1+3n}{4} = -4$
$1+3n = 16$ or $1+3n = -16$
$3n = 15$ or $3n = -16-1$
$n= 5 $ or $ 3n = -17$
$n= 5 $ or $ n= \frac{-17}{3}$
Solutions are $5, \frac{-17}{3}$