SOLUTION: Montrose and Salem are 10 miles apart. Karen lives 12 miles from Salem. What are the possible distances Karen lives from Montrose?

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Question 100079: Montrose and Salem are 10 miles apart. Karen lives 12 miles from Salem. What are the possible distances Karen lives from Montrose?
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Montrose and Salem are 10 miles apart. Karen lives 12 miles from Salem. What are the possible distances Karen lives from Montrose?
 
Let the point M be Montrose and the point S be Salem



Since Karen lives 12 miles from S, we'll draw a circle with center S 
and radius 12 miles:



Karen lives somewhere on that 12 mile radius circle. Let's draw in the 
complete horizontal diameter of that circle, and label its endpoints A
and B:



The closest Karen could live to M is 2 miles if she lives at A.
The farthest Karen could live from M is 22 miles if she lives at B.

Therefore she lives 2 miles or more from Montrose and 22 miles or 
less from Montrose.  So if her home's distance from Melrose is 
represented by the letter D, then the inequality is

      2 < D < 22

Edwin

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