Question 1146820
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<pre>
First, solve the "perimeter" equation 


    (2x-2) + (-2x+18) + (7x-27) = 24.


    2x - 2x + 7x + (-2 +18 - 27) = 24


    7x - 11 = 24

    7x      = 24 + 11

    7x      = 35

     x      = 35/7 = 5.


Thus the side lengths are  2x-2   = 2*5-2   = 10-2   = 8;

                          -2x+18  = -2*5+18 = -10+18 = 8;

                           7x-27  = 7*5-27  = 35-27  = 8.


Thus you have an equilateral triangle.


The triangle inequalities are held by an OBVIOUS way.
</pre>


Solved.


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The sequence of actions that @josgarithmetic proposes in his post is WRONG.


You &nbsp;<U>DO &nbsp;NOT &nbsp;NEED</U> &nbsp;check the triangle inequalities &nbsp;BEFORE &nbsp;finding the side lengths.


You need check these inequalities &nbsp;AFTER &nbsp;finding the triangle' side lengths.



So, &nbsp;for your safety, &nbsp;you better &nbsp;IGNORE &nbsp;the post by @josgarithmetic.