How do you solve #|x + 6| = 2x# and find any extraneous solutions?

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Answer 1 · 2016-06-16T19:34:26

#x=-2# if #x<-6#
#x=6# if#x>=-6#

Knowing the property of absolute value that says:

if#|x|=a# then
#x=-a , x<0#

#x=a,x>=0#

Applying the above property we have:

#x+6=-2x,x+6<0#. Eq(1)

#x+6=2x,x+6>=0#. Eq(2)

Solving the above equations we have:

Eq(1): if #x+6<0# that is #x<-6#
#x+2x=-6#
#3x=-6#
#x=-6/3=-2#
So,
#x=-2,x<-6#

Eq(2): if #x+6>=0# that is #x>=-6#

#x+6=2x#
#x-2x=-6#
#-x=-6#
#x=6# whenever #x>=-6#