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**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.