Solve the inequation 8> x^2 – 4 > 4?

4 < x^2 - 4 <
8

Add 4 to both
sides.

==> 8 < x^2 <
12

Now let us separate and solve each
side.

==> 8 < x^2    and  x^2 <
12

Let us solve 8 <
x^2

Take the square root of both
sides.

==> sqrt8 < x and  sqrt8 <
-x

==> 2sqrt2 < x   and 
-2sqrt2 > x

==>
x = ( 2sqrt2,inf) U ( -inf, -2sqrt2)

Now the
other side.

==> x^2 <
12

==> x < sqrt12   OR    -x
< sqrt12

==> x < 2sqrt3   OR    x
> -2sqrt3

==> x = ( 2sqrt3,
inf) U ( -inf, -2sqrt3)