[tex]\displaystyle\\
\left[\frac{3x+2}{3}\right] =3\{x\}\\\\
\left[\frac{3x+2}{3}\right] \in Z\\\\
\Longrightarrow~~3\{x\} \in Z\\\\
\text{Avem 2 solutii:}\\
S_1:~~x = 0~\Longrightarrow~ 3\{x\}=3\cdot 0 = 0\in Z \\\\
\text{Verificam solutia in partea stanga a egalului.}\\\\
\left[\frac{3x+2}{3}\right]=\left[\frac{3\cdot 0+2}{3}\right]=\left[\frac{2}{3}\right]=0\\\\
\Longrightarrow~~\boxed{\bf x_1 = 0}
[/tex]
[tex]\displaystyle\\
S_2: x= \frac{1}{3} ~\Longrightarrow~ 3\{x\}=3\cdot \frac{1}{3} = 1\in Z \\\\
\text{Verificam solutia in partea stanga a egalului.}\\\\
\left[\frac{3x+2}{3}\right]=\left[\frac{3\cdot \dfrac{1}{3}+2}{3}\right]=\left[\frac{1+2}{3}\right]=\left[\frac{3}{3}\right]=1\\\\
\Longrightarrow~~\boxed{x_2 = \frac{1}{3}}\\\\[/tex]
