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

Jul 12, 2016

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

#### Explanation:

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

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

$- \left(x + 5\right) = 2 x + 3$, when $x \le - 5$ and

So, we get solutions,

$x = 2 \succ 5$ and

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

respectively.

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