SOLUTION: If the side lengths for the triangle are x+3, 3x, and 2x+1, how would I use the triangle inequality theorem to find all possible values of x?

Question 395565: If the side lengths for the triangle are x+3, 3x, and 2x+1, how would I use the triangle inequality theorem to find all possible values of x?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
From the length of the 2nd side 3x, we know that x > 0.
From the triangle inequality, x + 3 + 3x > 2x + 1, or 4x + 3 > 2x +1, or 2x > -2, or x > -2. No new information from this because of the 1st statement above.
Also, 3x + 2x + 1 > x +3, ==> 5x + 1 > x +3 ==> 4x > 2, or x > 1/2.
Lastly, x+3 +2x + 1 > 3x, ==> 3x +4 > 3x, or 4 > 0, and again no new information is obtained from this inequality.
Hence as long as x > 1/2, we can form a triangle from the three given sides.
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