How do you solve #abs(x+4)= 3x#?

1 Answer
Mar 27, 2016

Answer:

#x=2#

Explanation:

#abs(x+4)=3x# means
#{: ("either", x+4 = -3x,"or",x+4=+3x), (,rarr 4x+4=0,,rarr-2x+4=0), (,rarr x=-1,,rarr x=2) :}#

but since #abs(x+4)>=0#
#color(white)("XXX")rarr 3x >=0#
#color(white)("XXX")rarr x >= 0#
so the "solution" #x=-1# is extraneous
and only #x=2# is valid