# How do you solve 2abs(y-3)+6 < 0?

Jun 4, 2018

$y \in \emptyset$

#### Explanation:

$2 | y + 3 | + 6 < 0$
$| y + 3 | + 3 < 0$
$| y + 3 | < - 3$
So:
If $y < - 3$
$- \left(y + 3\right) < - 3$
$- y - 3 < - 3$
$y + 3 > 3$
$\cancel{y > 0}$ because of our domain.
If $y > - 3$,
$y + 3 < - 3$
$\cancel{y < - 6}$ because of our domain.
So : $y \in \emptyset$