[tex]\it [x]=3 \Rightarrow x\in [3,\ \ 4)\\ \\ \ [\it2x]=2 \Rightarrow 2x\in[2,\ 3)|_{:2} \Rightarrow x\in[1;\ 1,5)[/tex]
[tex]\it\Big[ \dfrac{3x+1}{2}\Big] =5 \Rightarrow 5\leq\dfrac{3x+1}{2}<6|_{\cdot2} \Rightarrow 10\leq3x+1<12|_{-1} \Rightarrow \\ \\ \\ \Rightarrow 9\leq3x<11|_{:3} \Rightarrow3\leq x<\dfrac{11}{3} \Rightarrow x\in\Big[3,\ \dfrac{11}{3}\Big)[/tex]
