Solve for x : x^2 - 5x + 6 =

To solve the inequality above, first we have to calculate
the roots of the equation x^2 - 5x + 6 = 0.

After finding
the roots of the equation, we could write the expression in a factored form
as:

1*(x-x1)(x-x2) =<
0

So, let's apply the quadratic formula to calculate the
roots:

x1 =
[5+sqrt(25-24)]/2

x1 =
(5+1)/2

x1 =
6/2

x1 =
3

x2 =
(5-1)/2

x2 =
4/2

x2 =
2

The inequality will be written
as:

(x - 3)(x - 2) =<
0

Now, we'll discuss the
inequality:

- the product is  negative if one factor is
positive and the other is negative:

x -
3>=0

We'll add 3 both
sides:

x >
=3

and

x - 2 =<
0

x =< 2

The common
solution is the empty set.

Now, we'll consider the other
alternative:

x - 3 =<
0

x =<
3

and

x - 2 >=
0

x >= 2

So, x belongs
to the interval [2 , 3].

Finally, the
solution of the inequality is the inetrval identified above:
[2 , 3].