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

1 Answer
May 29, 2016

See below.

Explanation:

Firstly we can simplify this to:
|x+1|=2

Then there's two ways of doing it:

Case analysis (the generally most preferred method for simple ones like this):

Consider if x+1 is positive:
Then: x+1=2 so x=1
Consider if x+1 is negative:
Then: -(x+1)=2 so x=-3
(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:
|x+1|=2
We can square both sides, since the left side will definitely be positive after it has been squared (by definition of real numbers):
(x+1)^2=4
x^2+2x+1=4
x^2+2x-3=0
(x+3)(x-1)=0
x=1 or -3