Answer
$\left( \infty,7 \right]$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{1}{2}+\dfrac{2}{3}\ge\dfrac{x}{6}
$ simplifies to
\begin{array}{l}
6\left( \dfrac{1}{2}+\dfrac{2}{3}\right)\ge \left( \dfrac{x}{6} \right) 6
\\\\
3(1)+2(2)\ge x
\\
3+4\ge x
\\
7\ge x
\\
x\le 7
.\end{array}
In interval notation, the solution set is $
\left( \infty,7 \right]
$.