SOLUTION: if a triangle has sides of length (2x - 1) cm, (3x + 2) cm, and (12 - x) cm, find all the possible values of x .

Question 1093497: if a triangle has sides of length (2x - 1) cm, (3x + 2) cm, and (12 - x) cm, find all the possible values of x .
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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These three inequalities must be held ("the triangle inequalities"):


1.  2x-1 <= (3x+2) + (12-x),  which implies -1 <= 14, which is always TRUE.


2.  3x+2 <= (2x-1) + (12-x),  which implies  x <= 4.5.


3.  12-x <= (2x-1) + (3x+2),  which implies  x <= 1.5.


Answer.  All possible values of x are in this interval  (0,1.5).

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