Question 168285
How many real numbers satisfies ||||x-1|-2|-3|-2|=1
------------------
|||x-1|-2|-3|-2 = 1 or |||x-1|-2|-3|-2 = -1
A. Looking at the 1st of these you get:

||x-1|-2|-3|-2 = 1 or ||x-1|-2|-3|-2 = -1
B. Now, looking at the 1st of these you get:
|x-1|-2|-3|-2 = 1 or |x-1|-2|-3|-2 = -1
C. And , looking at the 1st of these you get:
}x-1|-2|-3| = 3
Then |x-1|-6 = 3
|x-1| = 9
x-1 = 9 or x-1 = -9
x = 10 or x = -8
-------------------
Now, you would need to look at the 2nd part of B:
|x-1|-2|-3|-2 = -1
}x-1|-6-2 = -1
|x-1|-8=-1
|x-1|= 7
x-1 = 7 or x-1 = -7
x = 8 or x = -6
-----------------------
You would have to keep working thru both part of "A" .
Cheers,
Stan H.