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

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

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

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

$\Rightarrow 6-x \geq 2$

$\Rightarrow 6-x-6 \geq 2-6$

$\Rightarrow-x \geq-4$

$\Rightarrow x \leq 4$

Thus, all real numbers $x$, which are less than or equal to 4 , are the solutions of the given inequality.

Hence, the solution set of the given inequality is $(-\infty, 4]$.