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

1 Answer
Alan P.
Mar 27, 2016

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

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