SOLUTION: If 3 < x < 7 and 4 < y < 7, which of the following best describes the range of values of x- y ? (A) –4 < x - y < 3 (B) 0 < x – y < 4 (C) 3 < x- y < 4 (D) 3 < x - y <

3 < x < 7 and 4 < y < 7

There is a rule of ADDING inequalities in the same order, that is

if A < B < C and D < E < F, then A+D < B+E < C+F

But there is NO rule for subtracting them!

But all is not lost, for we can change the second inequality 
to involve -y instead of +y and then we can use the addition rule.

4 < y < 7

Multiply through by -1. This will change the direction of the
inequalities:

-4 > -y > -7

But then that can be written equivantly as:

-7 < -y < -4.

Now we can use the rule for adding inequalities in the same order:

  3 <  x  <  7
 -7 < -y  < -4 
----------------
 -4 < x-y <  3

This is choice A

Edwin