195. For what values of $x$ will the numbers $\frac{x-3}{7}, \frac{x-2}{5}$, and $\frac{x-4}{3}$ be integers simultaneously?
195. $\left\{\begin{array}{l}\frac{x-3}{7}=y \\ \frac{x-2}{5}=z \\ \frac{x-4}{3}=u\end{array}\right.$ from this $\left\{\begin{array}{l}7 y-5 z=-1 \text { (1) } \\ 5 z-3 u=2\end{array}\right.$

From (1) we find $y=5 t+2, \quad z=7 t+3$; substituting into (2), we get $35 t-3 u=-13$, hence

$$
\left\{\begin{array}{l}
t=3 t_{1}+13 \\
u=35 t_{1}+156
\end{array}\right.
$$

46
therefore, $x=3 u+4=105 t_{1}+472$; without loss of generality, we can replace $t_{1}$ with $t_{1}-4$; then we get $x=105 t_{1}+52$.