If $2x-3(x+2)<5-2x<-x+2$, then find the range/value of $x$.

Let's split this compound inequality into two parts:Part 1:
$$2x-3(x+2)<5-2x$$
$$2x-3x-6<5-2x$$
$$-x-6<5-2x$$
$$-x+2x<5+6$$
$$x<11$$
Part 2:
$$5-2x<-x+2$$
$$5-2<-x+2x$$
$$3<x⟹x>3$$
Combining both parts, the solution range is:
$$3<x<11$$
(Note: The question text asks for a single numerical value among the options that satisfies the set conditions. Out of all options, only $x=10$ lies strictly within this valid interval of $(3,11)$).