Using the triangle inequality, we have that
x+ 2x+ 1 > x + 4
2x > 3
x > 3/2
And
2x + 1 + x + 4 > x
2x > − 5
x > −5/2
And
x + x + 4 > 2x + 1
2x + 4 > 2x + 1
True for all x
x > 3/2 is the most restrictive interval
So....as long as x >3/2 a triangle is possible
