How do you solve # abs( x+5) = 2x+3# and find any extraneous solutions?

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Answer 1 · 2016-07-12T07:39:05

2 and an extraneous solution, #-8/3#.

#|x+5|=2x+3# is the combined equation for the pair

#x+5=2x+3#, when #x>=-5# and

#-(x+5)=2x+3#, when #x<=-5# and

So, we get solutions,

#x=2>-5# and

#x=-8/3# not #<-5#,

respectively.

The second is an extraneous (as it is notnot a) solution.