`(1-5x)/(x-1)>=1`
`<=>(1-5x)/(x-1)-1>=0`
`<=>(1-5x-x+1)/(x-1)>=0`
`<=>(2-6x)/(x-1)>=0(x ne 1)`
`<=>(6x-2)/(x-1)<=0`
`<=>(x-2/6)/(x-1)<=0`
`TH1:x-2/6>=0,x-1<0`
`<=>2/6<=x<1(TM)`
`TH2:x-2/6<=0,x-1>0`
`<=>1<x<=2/6`(vô lý)
Vậy `2/6<=x<1`
Ta có: \(\dfrac{1-5x}{x-1}\ge1\)
\(\Leftrightarrow\dfrac{1-5x-x+1}{x-1}\ge0\)
\(\Leftrightarrow\dfrac{-6x+2}{x-1}\ge0\)
Trường hợp 1: \(\dfrac{-6x+2}{x-1}=0\)
\(\Leftrightarrow-6x+2=0\)
\(\Leftrightarrow-6x=-2\)
hay \(x=\dfrac{1}{3}\)
Trường hợp 2: \(\dfrac{-6x+2}{x-1}>0\)
\(\Leftrightarrow\dfrac{1}{3}< x< 1\)
Vậy: \(\dfrac{1}{3}\le x< 1\)
