#### Answer

$x=\frac{2}{3}$
$x=\frac{-20}{3}$

#### Work Step by Step

To solve an absolute value equation, we solve for $x$ using the positive and negative value of the non-absolute value side (after isolating the absolute value expression). In this case, we solve $3x+9=11$ and $3x+9=-11$.
To solve $3x+9=11$, we subtract 9 from both sides to isolate $x$ and its coefficient, and then divide both sides by 3 to fully isolate $x$. $3x=2$ is $x=\frac{2}{3}$
To solve $3x+9=-11$, we subtract 9 from both sides to isolate $x$ and its coefficient and then divide both sides by 3 to fully isolate $x$. $3x=-20$ is $x=\frac{-20}{3}$