I will continue, starting from the point where you stop.


So, we should solve this inequality

    0 <  < 


Thus, we have, actually, two inequalities

    (a)  0 <    and   (b)   < .


From (a), we have that 2x-4 is positive

    2x - 4 > 0,

which implies  2x > 4;  hence,  x > 2  (after diving both sides by 2 in the previous inequality).



From (b), we have 2 < 2x-4  (after cross-multiplying of (b)).

It implies  2+4 < 2x,  or  6 < 2x;  hence,  x > 3.



Of two inequalities,  x > 2  and  x > 3,  their solution is  x > 3.


ANSWER.  The solution to given compound inequality is the interval (3,oo),  or  {x |  x > 3}.