(9x+1)/(x-1)≤11.
If we assume x-1>0:
9x+1≤11(x-1),
9x+1≤11x-11,
12≤2x, 6≤x, so x≥6. This is acceptable since x>1 as per assumption.
If we assume x-1<0:
9x+1≥11x-11, 12≥2x, 6≥x, x≤6, so x<1 because of the assumption.
Therefore x<1 or x≥6.
CHECK
x=6: 55/5=11 OK
x=7: 64/6<11 OK
x=0: -1<11 OK
x=0.5: 5.5/(-0.5)=-11<11 OK
x=-1: -8/(-2)=4<11 OK