Answer
$2,\frac{-10}{3}$
Work Step by Step
$|\frac{3n+2}{8}| = |-1|$
Absolute value of a negative number is positive number. So,
$|\frac{3n+2}{8}| = 1$
This is equivalent to
$\frac{3n+2}{8} = 1$ or $\frac{3n+2}{8} = -1$
$3n+2 = 8 $ or $3n+2 = -8$
$3n = 8-2 $ or $3n = -8-2$
$3n = 6 $ or $3n = -10$
$n =2 $ or $n = \frac{-10}{3}$
Solutions are $2,\frac{-10}{3}$