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.

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