What is the solution for the inequation x^2 - x - 6 > 0

x^2- x - 6 > 0

First
we will factor the left side.

==> (x-3)(x+2)
> 0

Now we have a product of two
terms.

In order for the product to be positive, then both
terms should be positive or both terms should be
negative.

Then we will
write:

x-3 > 0   AND    x+2 >
0

==> x > 3  AND  x >
-2

==> x = ( 3, inf ) n (-2, inf) = (3,inf)
..........(1)

Now for the other option, both terms are
negative.

==> x-3 < 0  AND   x+ 2 <
0

==> x < 3  AND   x <
-2

==> x = ( -inf, 3) n ( -inf , -2) = ( -inf,
-2)............(2)

Then, from (1) and (2) we have two
solutions:

==> x = ( -inf , -2) U ( 3,
inf)