# How do you solve #- 5| x + 1| = -10 #?

##### 1 Answer

See below.

#### Explanation:

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):

Consider if

Then:

Consider if

Then:

(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):