2021/063) Solve $x+\lfloor 2x\rfloor +\lfloor 3x\rfloor=7$

 Because RHS is integer so LHS is integer

As $\lfloor 2x \rfloor$ and $\lfloor 3x \rfloor$ are integers so x is integer so   $\lfloor 2x \rfloor = 2x$ and  $\lfloor 3x \rfloor = 3x$

so x + 2x + 3x = 6x = 7 so $x = \frac{7}{6}$ which is not integer so NO solution