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

1 Answer
MeneerNask
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]}

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