Note that `(a)/(b)gt0 " when "(agt0 andbgt0)or (alt0 and blt0)`.
either `(x+4gt0 and x-2gt) or (x+4lt0 and x-2lt0)`.
Case I When `x+4gt0 and x-2gt0`.
In this case, `x+4gt0 and x-2 gt0`
`rArrxgt-4 and x gt2`
`rArrxgt2`
`rArrx in(2,oo)`
Case II When `x+4 lt0 and x-2 lt0`.
In this case, `x+4lt 0 and x-2lt0`
`rArr xlt-4 and xlt2`
`rArr xlt-4`
`rArrx in(-oo,-4)`
`therefore`"solution set" `=(-oo,-4)uu(2,oo)`
The graph of the solution set is given below.
