Answer
$$[12, \infty)$$
Work Step by Step
Solve the inequality as follows:
$\frac{x}{3}\ge 2+\frac{x}{6}$
$\frac{x}{3}-\frac{x}{6}\ge 2$
$\frac{2x}{6}-\frac{x}{6}\ge 2$
$\frac{x}{6}\ge 2$
$x\ge 12$
Therefore, the solution in interval notation is $[12, \infty)$.
The solution can be graphed as follows:
