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! .
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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