Solve: `(1)/(x-1)le2,x in R`

1.	Solve: `(1)/(x-1)le2,x in R`
Answer» Correct Answer - `(-oo,1)uu[(3)/(2),oo)` `(1)/(x-1)-2le0 rArr(1-2x+2)/(x-1)le0rArr(3-2x)/(x-1)le0` `rArr (3-2x le0 and x-1gt0)or(3-2xge0andx-1lt0)` `rArr(3le2x and xgt1) or(-2xge-3 and x lt1)` `rArr(xge(3)/(2) andxgt1) or (xle(3)/(2) andxlt1)` `rArr (xlt1) or(xge(3)/(2))=x in(-oo,1)uu[(3)/(2),oo)`.

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