6th Grade (12 Years Old) Mathematics - Triangle Inequality Question My son's math homework has this question which I find to be extremely confusing.  Neither my wife or I can wrap our heads around what they are expecting as an answer:

Two sides of a triangle have lengths $7$ and $9$.  The third side has length $x$.  Tell whether each of the following statements is always, sometimes but not always or never true.
a) $x = 12$
b) $x = 2$
c) $x < 2$
d) $x < 16$
e) $x < 15$

To my mind the answer is sometimes to all of them.  For $x = 12$ and $x = 2$, when considering all the possible values of $x$ it will sometimes be those values.  For $x < 2$, $x < 15$, and $x < 16$, it's sometimes because all values less than those make it true, until you hit $0$ which forms a line and no longer a triangle.
It looks like I've found the the teachers edition of the book (scroll to page 6 in the pdf; question 12), that just confuses me even further!

Think of a "hinge" of two sides with fixed lengths 7 and 9, respectively. You can put it at any opening between $0^\circ$ and $180^\circ$, but not including the extreme values $0^\circ$ and $180^\circ$.
The third side will be given once you fix the degree of opening of your hinge. In the limit where the angle is extremely close to $0^\circ$, the third side tends to $9-7=2$. In the other limit, $180^\circ$, the third side tends to $9+7=16$.
So the third side can have all lengths between 2 and 16, not including those two extreme values.
(Once you guys have thought a bit about this, both you, your wife and your son will understand the triangle inequality well.)
