Solve the inequation: 6

We'll have to solve a system of 2
inequalities:

3x^2 -6 <
 21

and

3x^2 -6 >
6

We'll solve the first
inequality:

3x^2 -6 <
 21

We'll add 6 both
sides:

3x^2 < 27

We'll
divide by 3:

x^2 <
9

We'll calculate the roots of x^2 -
9.

x^2 - 9 = 0

 x1 =
-3

x2 = 3

The expression is
negative over the interval (-3,3).

We'll solve the second
inequality:

3x^2 -6 >
6

We'll add 6 both sides:

3x^2
> 12

We'll divide by
3:

x^2 > 4

We'll
calculate the roots of x^2 - 4.

x^2 - 4 =
0

x1  = -2

x2 =
2

The expression is positive over the intervals
(-inf.,-2)U(2,+inf.).

The common intervals of
values that satisfy both inequalities
are:

(-3 , -2)U(2 ,
3)