greater than or equal to 0
x can be any real number, because the absolute value of any number is bigger or equal to 0.
$\displaystyle
|x + 4| \ge 0
$
$\displaystyle \Rightarrow x+4 \ge 0$
$\displaystyle \Rightarrow x\ge -4$ .................................(1)
OR
$\displaystyle |x + 4| \ge 0$
$\displaystyle \Rightarrow -(x+4) \ge 0$
$\displaystyle \Rightarrow -x\ge 4$
$\displaystyle
\Rightarrow x\le -4 ...................................(2)
$
from (1) and (2), x can have all real values. So,
$\displaystyle x\in \mathbb{R}$