#1**+1 **

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

CPhill Jan 29, 2019