#### Answer

$x = -\frac{4}{3}$ or $x = \frac{4}{3}$

#### Work Step by Step

First, we subtract $1$ from each side of the equation:
$2|3x| = 8$
Divide each side by $2$:
$|3x| = 4$
Divide each side by $3$:
$|x| = \frac{4}{3}$
Take the absolute value of both sides of the equation:
$x = -\frac{4}{3}$ or $x = \frac{4}{3}$