Solve the given inequality for real x:

$\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}$

$\Rightarrow 9(x-2) \leq 25(2-x)$

$\Rightarrow 9 x-18 \leq 50-25 x$

$\Rightarrow 9 x-18+25 x \leq 50$

$\Rightarrow 34 x-18 \leq 50$

$\Rightarrow 34 x \leq 50+18$

$\Rightarrow 34 x \leq 68$

$\Rightarrow \frac{34 x}{34} \leq \frac{68}{34}$

$\Rightarrow x \leq 2$

Thus, all real numbers $x$, which are less than or equal to 2, are the solutions of the given inequality.

Hence, the solution set of the given inequality is $(-\infty, 2]$.