Solve `(1/3)^((|x+2|)/(2-|x|))> 9.`

Explanation

`(1/3) ^(|1+2|/(2-|x|))gt9`
`or 3 ^(|x+2|/(2-|x|)) gt 3^2`
or `(-|x+2|)/(2-|x|) gt 2`
or `(-|x+2|)/(2-|x|) lt -2`
Case (i) : `x lt -2`
`rArr -((x+2))/(2+x) lt -2`
`rArr -1lt-2` which is not true
Case (ii): `-2 lt x lt 0`
`rArr (x+2)/(2+x) lt -2`
`rArr 1 lt -2 ` which is not true
Case : (iii) `(x +2)/(2-x) lt -2`
or` (x+2)/(2-x)+2 lt 0`
`or (6-x)/(2-x) lt 0`
`rArr 2 lt x lr 6`
Hence solution is (2,6)