Absolute inequality question

Correct me if im wrong... but I'm pretty sure x can be all real numbers?

x-7≥0

x-2≥0

x<5/2 Or 5/2>x or x<13/2 or 13/2>x

All real numbers is correct

|x-2| represents the distance between 2, and |x-7| represents the distance between 7.

The sum of the distance between a number and 2 and a number and 7 is a minimum of 5. 

So x is all real numbers.