Question 395565
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.