Question 31488
SORRY TO NOTE YOUR PLIGHT.THOUGH YOU HAVE PROCEEDED IN A PROPER WAY,I SHALL GIVE YOU AN ALTERNATE ROUTE.SEE IF THAT SUITS YOU.
Problem: (x/x-2)>=5 ..YOU TRANSFERRED 5 TO LHS WHICH IS THE PROPER WAY IN INEQUALITIES`AS YOU DONOT KNOW ABOUT NATURE OF X AND ITS FUNCTIONS.BUT THERE IS ANOTHER WAY TO GO I AM JUST SHOWING IT TO YOU AS AN ILLUSTRTION
WE DONT KNOW NATURE OF X-2...SO....
CASE 1...X-2=0...NOT ALLWED AS THE FUNCTION IS NOT DEFINED THEN.

CASE.2. .....LET X-2 BE POSITIVE OR X>2..THEN
X>5(X-2)
X-5X>-10
-4X>-10
4X<10.....AS MULTIPLICATION WITH NEGATIVE NUMBER WILL REVERSE THE INEQUALITY.
X<10/4=2.5...NOW CHECK WITH OUR ORIGINAL ASSUMPTION THAT X>2..IT IS COMPATABLE...
HENCE FOR THIS CASE THE SOLUTION IS X>2 BUT <2.5...THAT IS X IS BETWEN 2 AND 2.5
CASE.3.....LET X-2 BE NEGATIVE...OR....X<2
X<5(X-2)...AS MULTIPLICATION WITH NEGATIVE NUMBER WILL REVERSE THE INEQUALITY.
X-5X<-10
-4X<-10
4X>10......AS MULTIPLICATION WITH NEGATIVE NUMBER WILL REVERSE THE INEQUALITY.
X>10/4=2.5..NOW CHECK WITH OUR ORIGINAL ASSUMPTION THAT X<2..IT IS NOT COMPATABLE...
HENCE FOR THIS CASE THERE IS NO SOLUTION
HENCE THE TOTAL SOLUTION SET IS 
X LIES BETWEEN 2 AND 2.5
OK GOT IT .IF STILL IN DOUBT OR YOU WANT TO LEARN MORE PLEASE COME BACK.