Answer
$x=-\frac{2}{3},\frac{2}{3}$
Work Step by Step
The absolute value of multiple terms will change the other side to positive or negative when simplified.
$7|3x|+2=16$
$7|3x|=14$
$|3x|=2$
$3x=2$
$x=\frac{2}{3}$
$3x=-2$
$x=-\frac{2}{3}$
$x=-\frac{2}{3},\frac{2}{3}$