#### Answer

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

#### Work Step by Step

$|-5x+7|-4\lt-6$
Take $4$ to the right side of the inequality:
$|-5x+7|\lt-6+4$
$|-5x+7|\lt-2$
This inequality has no solution, because an absolute value expression will never be less than a negative number.