#### Answer

This inequality has no solution, because an absolute value expression will never be less than a negative number.

#### Work Step by Step

$|3x-7|+1\lt-2$
Take $1$ to the right side:
$|3x-7|\lt-2-1$
$|3x-7|\lt-3$
This inequality has no solution, because an absolute value expression will never be less than a negative number.