The diagram depicts a triangle obtained by linking the points $A(1,2)$, $B(13,2)$ and $C(4,8)$. The equation for line $BC$ is $2x + 3y = 32$.
(a)[2]
Inside triangle $ABC$, the region is described by three inequalities. One of them is $2x + 3y < 32$. State the other two inequalities.
(b)[2]
The point $(k,7)$, with $k$ an integer, is located inside triangle $ABC$. Find the possible values of $k$.
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