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Like Inequalities Can Be Added

If x < y and w < z, then x + w < y + z

 

Example

If 2 < x < 5 and 3 < y < 5, which one of the following best describes x – y?

A.   –3 < x – y < 2
B.   –3 < x – y < 5
C.   0 < x – y < 2
D.   3 < x – y < 5
E.    2 < x – y < 5

 
Multiplying both sides of 3 < y < 5 by –1 yields –3 > –y > –5. Now, we usually write the smaller number on the left side of the inequality.

 

So –3 > –y > –5 becomes –5 < –y < –3. Add this inequality to the like inequality 2 < x < 5:

 

The answer is (A).
 





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