(a) If (x - 2)(x-5) <0 and x e N then find x.​

x = 3 or x = 4.

Step-by-step explanation:

We are given the following inequality:

It is a product, and a product is negative when one term is positive and the other is negative.

First case:

And

Thus, in the natural set: x = 3 and x = 4.

Second case:

And

Empty set.

Union of the cases:

Second case is the empty set, so we only count the first case. Thus x = 3 or x = 4.