It must be that x + 9 is the longest side since the longest side of a triangle is opposite the largest angle
So
x + 9 > 3x
9 > 2x
9/2 > x
And x + 9 will always be greater than x + 4
But we also have the restriction (by the Triangle Inequalty) that
3x + (x + 4) > x + 9
4x + 4 > x + 9
3x > 5
x > 5/3
So....the allowable values for x that make x + 9 the longest side are
5/3 < x < 9/2