Correct Answer - `(2,4)uu(4,6)`
Using `|x| gta iff x lt -a or x gt a`, we get
`(2)/(x-4)lt-1 or (2)/(x-4)gt1`
`rArr(2)/(x-4)lt-1 or (2)/(x-4)-1gt0`
`rArr(x-2)/(x-4)lt0 or (6-x)/(x-4)gt0`.
Case I When `(x-2)/(x-4)lt0`
Then, `(x-2lt 0 and x -4 gt 0) or(x-2 gt 0 and x -4 lt 0)`
`rArr (x lt2 and xgt 4) or(xgt2 and xlt4)`
`rArr (2ltxlt4rArr x in(2,4)`.
Case II When `(6-x)/(x-4)gt0`.
Then, `(6-xlt0 ad x-4lt0) or(6-xgt0 and x-4 gt0)`
`rArr (x lt6 and xlt4) or (xlt6 and x lt4)`
`rArr 4ltxlt6 rArr x in(4,6)`.
`therefore " solution set " =(2,4)uu(4,6)`.
