Sorry I am confused. The rule is that any two sides of a triangle is greater than the third side.
This will actually give us 3 inequalities, and not just one inequality.
If x, y, z are the lengths of each side of a triangle. So we can actually write three equations.
a) x + y > z
b) y + z > x
c) z + x > y
If we applied statement 2, y=3, and z=6
a) x + 3 > 6
b) 3 + 6 > x
c) 6 + x > 3
since we know that for a triangle a side cannot be negative, a) tells us x has to greater than 3. But b), c) tells us that 9 > x > 0. My question is that how did you know to use x + y > z instead of the other two equally valid equations? When I was solving this question I picked equation B) because that was the most convenient for me.
I think to properly solve this problem, you have to actually work through all three inequalities, to find the minimum. And cannot just randomly pick one of the three inequalities, and hope to get lucky.