#### Answer

$x\leq-6, x\geq24$

#### Work Step by Step

Since we are simplifying an absolute value, first solve for the original inequality, and then flip the sign and make the opposite side negative in the second inequality. For each inequality, make sure to isolate the variable on one side, and flip the sign if multiplying or dividing by a negative on the variable's side.
$4+|3-\frac{x}{3}|\geq9$
$|3-\frac{x}{3}|\geq5$
$3-\frac{x}{3}\geq5$
$-6\geq x$
$x\leq-6$
$3-\frac{x}{3}\leq-5$
$x\geq24$
$x\leq-6, x\geq24$