Find all $x \in \mathbb R$ for which $$ \lfloor 2x\rfloor +\lfloor 3x\rfloor =1$$ where $\lfloor x \rfloor $ is the greatest integer less than or equal to $x$.
What is the way to approach these type of question? I have tried to use the fact that $\lfloor x+k \rfloor =\lfloor x \rfloor +k$ to answer the question but I am not able to simplify. This is in my 12th grade math textbook.
EDIT: i tried to solve it graphically and the answer came out to be [$\frac{1}{3}$,$\frac{1}{2}$)