# Easy as 1, 2, 3?

Algebra Level 4

$\Large { \left \lceil x \right \rceil } + 2 \times {\left \lfloor x \right \rfloor } + 3 \times {\left \{ x \right \} } = 6$

How many different values of $x$ satisfy the equation above?


Notations:

• $\left \lceil x \right \rceil$ is the ceiling of $x.$
• $\left \lfloor x \right \rfloor$ is the floor of $x.$
• $\left \{ x \right \}$ is the fractional part of $x.$
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