#### Answer

$|x+3|\lt4$

#### Work Step by Step

$|u|\lt a~↔~-a\lt u\lt a$
$|u|\leq a~↔~-a\leq u\leq a$
$|u|\gt a~↔~u\lt-a~or~u\gt a$
$|u|\geq a~↔~u\leq-a~or~u\geq a$
The numbers must be greater than -7 and less than 1:
$-7\lt x\lt1$
$-7+3\lt x+3\lt1+3$
$-4\lt x+3\lt4$
$|x+3|\lt4$