$$ \left|\left|\left|x-1\right|-2\right|-4\right|=4 $$
What is the number of solutions for this equation? This one was particularly easy to me. If first observed that if this inequality were to hold, then $ | x - 1 | $ should be 9. Because $ | x -1 |$ will always be positive, and once we remove $ | x- 1 |$, the only positive number that can lead to a possible solution is 9. So solving for $ | x - 1 | $ gives me $ 10 $ or $ -8 $, and I'm done. Number of solutions is 2.
But I was curious on what I'd do if I had different numbers. Say:
$$ \left|\left|\left|x-1\right|-2\right|-5\right|=4 $$
Now, Desmos says there are five possible solutions. How should one go about finding the number of solutions (or finding the solutions themselves) for something like this by hand? A general method would be appreciated.