[tex]u-1< [u]\leq u\quad (\text{inegalitatea partii intregi)}\\ \\ \\ u = \dfrac{x+1}{3},\quad [u] = \dfrac{x-1}{2} \\ \\ \\\dfrac{x+1}{3}-1 <\dfrac{x-1}{2}\leq \dfrac{x+1}{3} \Big|\cdot 6 \\ \\ 2x+2-6 < 3x-3\leq 2x+2 \\ \\ 2x-4 < 3x-3 \leq 2x+2 \Big|-2x \\ \\ -4 < x-3\leq 2 \Big|+3 \\ \\ -1<x\leq 5 \\ \\ \Rightarrow x \in (-1,5]\\ \\\\ \text{Dar }\dfrac{x-1}{2}\in \mathbb{Z} \Rightarrow \boxed{x \in \Big\{1,3,5\Big\}}[/tex]
