Question

What is a short method to show the compound inequality x < 2 AND x > 7

Answer 1

These inequalities are not compatible: you are looking for a number that is less than 2, but more than 7. This is impossible, because if a number is less than 2, it can't be more than 7.

Conversely, if a number is more than 7, it can't be less than 2.