How do you solve $|x+5| = 2x+3$ and find any extraneous solutions?

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Answer 1 · 2016-06-22T10:50:07

$x = 2$

$|x+5| = 2x+3 = x+5 +x-2$

$1=(x+5)/abs(x+5)+(x-2)/abs(x+5)$

but for $x ne -5->(x+5)/abs(x+5) = pm1$

$1 pm 1 =(x-2)/abs(x+5)$ we have two possibilities

$1)$ $0 = (x-2)/abs(x+5)->x = 2$
$2)$ $2 = (x-2)/abs(x+5)->x = O/$
because for $x>2->(x-2)/abs(x+5) < 1$

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