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

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Answer 1 · 2016-07-12T07:39:05

2 and an extraneous solution, $- \frac{8}{3}$ $-8/3$ .

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

$x + 5 = 2 x + 3$ $x+5=2x+3$ , when $x \geq - 5$ $x>=-5$ and

$- (x + 5) = 2 x + 3$ $-(x+5)=2x+3$ , when $x \leq - 5$ $x<=-5$ and

So, we get solutions,

$x = 2 ≻ 5$ $x=2>-5$ and

$x = - \frac{8}{3}$ $x=-8/3$ not $< - 5$ $<-5$ ,

respectively.

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

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