Find x values if (x^2 -3x -4)

Given the inequality:

(x^2 -
3x -4) < 0

First we will factor
.

==> (x-4)(x+1) <
0

Since the product is negative, then the terms should have
different signs.

==> Then we have two
cases:

(x-4) < 0   and   (x+1) >
0

==> x < 4   and   x >
-1

==> -1 < x <
4

==> x = (-1,
4)

OR:

(x-4) > 0   and 
x+1 < 0

==> x > 4    and  x <
-1   ( no solution).

Then the solution is
that x belongs to the interval ( -1, 4).