The set of real values of x satisfying the inequality |x^2+x-6 | < 6,…

We have,

$|x^2 + x −6] < 6$

$⇒-6<x^2+x-6<6$

$⇒-6 <x^2+x-6$ and $x^2 + x-6<6$

$⇒x^2 + x > 0$ and $x^2+x-12 <0$

$⇒x (x + 1) > 0$ and $(x + 4) (x-3) <0$

$⇒x∈(-∞,-1)∪(0, ∞)$ and $-4 <x<3$

$⇒x∈(-4, -1)∪(0,3)$