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How can inequalities be related to and solve problems with triangles?

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If the side lengths of a triangle are a, b, and c, and a > b > 0, a > c > 0 (i.e., a is the longest side);
then the following must be true to make a triangle: b + c > a.
Otherwise the ends either wouldn't meet or the segments would be collinear.
Which of the following sets would make triangles and why?
(a, b, c):