Given 2 < a < 3 and 5 < b < 6 Find:
a. __ < a-b < __

 5 <  b <  6 

multiplying through by -1 flips inequalities:

-5 > -b > -6 

That is equivalent to

-6 < -b < -5

We add that term by term to 2 < a < 3

 2 < a   <  3 
-6 <  -b < -5
-------------
-4 < a-b < -2





b. __ < a/b < __

 

 
is an interval of all positive numbers,
The interval of reciprocals are in the opposite 
order of inequality:



and that is equivalent to



So we multiply 2 < a < 3 term by term by that:



Edwin