Chatting on Slack brings inspiration!

Algebra Level 4

Find the number of real values $x$ that satisfy the equation

$\lfloor x \rfloor + |x| + \lceil x \rceil =1000.$

Notations:

$| \cdot |$ denotes the absolute value function.
$\lfloor \cdot \rfloor$ denotes the floor function.
$\lceil \cdot \rceil$ denotes the ceiling function.

Special thanks to Jason Chrysoprase for inspiring this question.

More than 6 1 0 6 4 2 3 5