Because $3$, $5$, and $7$ are pair-wise co-prime, we can apply the CRT. $$\begin{array}{l} 3\times 5\times 7 = 105\\ (5\times 7)^{-1}\equiv 35^{-1} \equiv 2\pmod{3 }\\ (7\times 3)^{-1} \equiv 21^{-1}\equiv 1\pmod{5}\\ (3\times 5)^{-1} \equiv 15^{-1}\equiv 1\pmod{7} \end{array}$$

Therefore the solution is $$x\equiv 1\times 35\times 2 + 2\times 21 \times 1+3 \times 15\times 1\equiv 52\pmod{105} $$