Answer
$x=-\frac{2}{5},\frac{2}{5}$
Work Step by Step
The absolute value of multiple terms will change the other side to positive or negative when simplified.
$7|5x|+2=16$
$7|5x|=14$
$|5x|=2$
$5x=2$
$x=\frac{2}{5}$
$5x=-2$
$x=-\frac{2}{5}$
$x=-\frac{2}{5},\frac{2}{5}$