Solve `|x^2+x-6 |lt 6 `

Answer

`x in (-4,-1) cup (0,3)`

Explanation

`|x^2+x-6|lt 6`
`rArr -6 lt x^2 +x -6 lt 6`
Now `-6 lt x^2 +x -6 `
or `x(x+1) gt 0 `
`rArr x in (-oo, -1)cup(0,oo)`
`x^2+x-6 lt 6`
or `x^2+x-12 lt 0 `
or ` (x+4)(x-3) lt 0 `
`rArr x in (-4,3)`
From (1) and (2) common values are `x in(-4 ,-1 ) cup (0,3)`