Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)

$3(x-1) \leq 2(x-3)$

$\Rightarrow 3 x-3 \leq 2 x-6$

$\Rightarrow 3 x-3+3 \leq 2 x-6+3$

$\Rightarrow 3 x \leq 2 x-3$

$\Rightarrow 3 x-2 x \leq 2 x-3-2 x$

$\Rightarrow x \leq-3$

Thus, all real numbers $x$, which are less than or equal to $-3$, are the solutions of the given inequality.

Hence, the solution set of the given inequality is $(-\infty,-3]$.