The given sides are 3 and 2 and the third side is x.

The triangular equality says essentially, if you were walking along the sides
of a triangle ABC, 

1. If you walk from A to B and then to C, you will have walked farther than if
you had just walked straight from A to C.

So AB + BC > AC

2. If you walk from A to C and then to B, you will have walked farther than if
you had just walked straight from A to B.

So AC + CB > AB

3. If you walk from B to C and then to A, you will have walked farther than if
you had just walked straight from B to A.

So BC + CA > BA

-------------------------

The sides are 3, 2 and x.  So by the very obvious triangular inequality:

1.  3 + 2 > x
2.  3 + x > 2
3.  x + 2 > 3

Simplifying:

1. 5 > x
2. x > -1
3. x > 1

Ignore the second one because the lengths of every side of every triangle is
greater than a negative number.  So we only need consider the other two:

5 > x and x > 1

You can write that together as  5 > x > 1, or if you prefer, 1 < x < 5.

Since they are whole numbers, the set of integers that satisfy 1 < x < 5,
are {2, 3, 4}.  The smallest whole number length for the third side in 2.

Edwin