Answer
$(-\infty, \frac{1}{3}]$
Refer to the attached image below for the graph.
Work Step by Step
For easier work, get rid of the fractions by multiplying the LCD of 6 to both sides to have:
$\\6(\frac{2}{3}-\frac{1}{2}x) \ge 6(\frac{1}{6}+x)
\\4-3x \ge 1+6x$
Add $3x$ to both sides to have:
$\\4-3x+3x \ge 1+6x+3x
\\4 \ge 1+9x$
Subtract 1 to both sides to have:
$\\4-1 \ge 1+9x-1
\\3 \ge 9x$
Divide 9 to both sides to have:
$\frac{3}{9} \ge x
\\\frac{1}{3} \ge x
\\x \le \frac{1}{3}$
