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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?
  1. –3 < x – y < 2
  2. –3 < x – y < 5
  3. 0 < x – y < 2
  4. 3 < x – y < 5
  5. 2 < xy < 5
Solution
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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