Question

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

Answer 1

`x = 2`

Explanation:

`|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`