\[\large \frac 1{\lfloor x\rfloor}+\frac 1{\lfloor 2x \rfloor}= \{x\}+\frac 13\]

Find the number of real solutions to the equation above.

**Notations**:

- \(\lfloor \cdot \rfloor\) denotes the floor function.
- \(\{ \cdot \}\) denotes the fractional part function.

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