you have to solve for x of a triangle, the sides are 55, 54 and x+74. what is the answer?

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In a triangle, any 2 sides must be less than the sum of the third side and more than the difference.

The 2 sides given have a sum of 109 and a difference of 1.

Therefore, `1 < x+7 < 109`

To solve: `1 lt x + 7` or  `x +...

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In a triangle, any 2 sides must be less than the sum of the third side and more than the difference.

The 2 sides given have a sum of 109 and a difference of 1.

Therefore, `1 < x+7 < 109`

To solve: `1 lt x + 7` or  `x + 7 lt 109`

`-6 < x` or `x < 102`

The solution is x can be any value between -6 and 107 or `-6<x<107.`

Approved by eNotes Editorial Team