Question

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

Answer 1

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]}