How do you solve |x+2|=5?

1 Answer
Mar 20, 2016

There are usually two answers, depending on the function inside the absolute brackets being positive or negative.

Explanation:

(1) x>= -2->x+2>=0 the equation is unchanged

->x+2=5->x=3

(2) x<-2->x+2<0 then the signs are 'flipped' to make the function as a whole positive:

->-(x+2)=-x-2=5->-x=7->x=-7
graph{|x+2| [-8.17, 11.83, -2.16, 7.84]}