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