Question

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

Answer 1

x = 3 or x = 4.

Explanation:

We are given the following inequality:

`(x - 2)(x - 5) < 0`

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

First case:

`x - 2 > 0 \rightarrow x > 2`

And

`x - 5 < 0 \rightarrow x < 5`

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

Second case:

`x - 2 < 0 \rightarrow x < 2`

And

`x - 5 > 0 \rightarrow x > 5`

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.