Find all solutions of |||Q| – 7| + Q| = Q ?

I've never seen real GMAT question involving triple modulus. Though the above question is not very hard.


\(|||q|-7|+q|=q\)

Now, absolute value is always non-negative \(|some \ expression|\geq{0}\), so as LHS (left hand side) above is an absolute value it must be non-negative then RHS must also be non-negative --> \(q\geq{0}\), so \(|q|=q\), so \(|||q|-7|+q|=q\) becomes: \(||q-7|+q|=q\).

\(||q-7|+q|=q\):
If \(q\leq{7}\) then \(|q-7|\) becomes \(-(q-7)\) so \(|-q+7+q|=q\) --> \(q=|7|=7\);
If \(q>{7}\) then \(|q-7|\) becomes \(q-7\) so \(|q-7+q|=q\) --> \(|2q-7|=q\) --> as \(q>{7}\) then \(|2q-7|=2q-7\) so \(2q-7=q\) --> \(q=7\).

So, only one solution \(q=7\).