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!

From your pdf, just use the following:

If a triangle has sides of lengths $x$, $y$, and $z$, the following three inequalities must be true:
  \begin{align}
x+y&>z,\\
x+z&>y,\\
y+z&>x.
\end{align}

Here, $y=7$ and $z=9$.
So, for example, b. and c. can never happen since it would violate the first inequality.
