Question:
Solve the given inequality for real $x: 3(x-1) \leq 2(x-3)$
Solution:
$3(x-1) \leq 2(x-3)$
$\Rightarrow 3 x-3 \leq 2 x-6$
$\Rightarrow 3 x-3+3 \leq 2 x-6+3$
$\Rightarrow 3 x \leq 2 x-3$
$\Rightarrow 3 x-2 x \leq 2 x-3-2 x$
$\Rightarrow x \leq-3$
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 $(-\infty,-3]$.