#### Answer

$(-\infty, \frac{1}{3}]$
Refer to the image below for the graph.

#### Work Step by Step

Multiply the LCD of $12$ to both sides of the inequality to eliminate the fractions:
$\begin{array}{ccc}
&6\left(\dfrac{2}{3} - \dfrac{1}{2}x\right) &\ge &6\left(\dfrac{1}{6} +x\right)
\\&6\left(\dfrac{2}{3}\right) - 6\left(\dfrac{1}{2}x\right) &\ge &6\left(\dfrac{1}{6}\right)+6(x)
\\&4 - 3x &\ge &1+6x
\end{array}$
Add $3x$ and subtract $1$to both sides of the inequality to obtain:
$\begin{array}{ccc}
&4-3x+3x -1&\ge & 1+6x+3x - 1
\\&3 &\ge &9x
\end{array}$
Divide $9$ to both sides of the inequality to obtain:
$\begin{array}{ccc}
\\&\dfrac{3}{9} &\ge & \dfrac{9x}{9}
\\&\dfrac{1}{3} &\ge &x
\\&x &\le &\dfrac{1}{3}
\end{array}$
Thus, the solution set is $(-\infty, \frac{1}{3}]$.
To graph this solution set, plot a solid dot at $\dfrac{1}{3}$ then shade the region to its left.
(refer to the attached image in the answer part above for the graph)