Question 705583
What you really want to ask about is the adjusted inequality.


{{{(3-x)/(x-4)>=2}}}


If x-4 is positive, then {{{(3-x)>=2(x-4)}}}
3-x>=2x-8
3+8>=3x
11>=3x
11/3>=x


If x-4 is negative, then {{{(3-x)>=2(4-x)}}}.  Check that carefully to understand before continuing.
3-x>=8-2x
3-8-x>=-2x
3-8>=-2x+x
-5>=-x
5<=x  [(watch what that says carefully].


{{{x<=11/3}}} OR {{{x>=5}}}