How do you solve #- 5| x + 1| = -10 #?
Firstly we can simplify this to:
Then there's two ways of doing it:
Case analysis (the generally most preferred method for simple ones like this):
(We take the negative of the left side since we want it to be positive and we've assumed it to already be negative, and two negatives make a positive, which is necessary for the absolute symbols since they always give a positive value by definition).
An alternative method, my personal favourite since it's more rigid:
We can square both sides, since the left side will definitely be positive after it has been squared (by definition of real numbers):