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

1 Answer
May 29, 2016

Answer:

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#