please find the value of x 9x+1/x-1<11

Question

its acually a less than or equal to symbol

Answer 1

(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