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# Absolute value inequality problem

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Two sides of a triangle measure 39cm and 15cm. Write and solve an absolute value inequality stating the possible lengths of the third side. State the solution set and graph.

minniedo  Sep 23, 2018
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legs of a triangle a, b, c

the triangle inequality states

$$|a|+|b| >|c| \\ \text{with strict inequality else we'd just have a line segment, not a triangle.}$$

$$|c| < |39|+|15| = 54 \Rightarrow c < 54 \\ \text{we also must have }\\ |c|+|15| > 39 \Rightarrow c > 24 \text{ thus}\\ 24 < c < 54$$

Rom  Sep 23, 2018