Answer
$\left( \infty,\dfrac{1}{2} \right]$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{3}{4}-\dfrac{2}{3}\ge\dfrac{x}{6}
$ simplifies to
\begin{array}{l}
12\left( \dfrac{3}{4}-\dfrac{2}{3} \right)\ge \left( \dfrac{x}{6} \right) 12
\\\\
3(3)-4(2)\ge 2x
\\
9-8\ge 2x
\\
1\ge 2x
\\
\dfrac{1}{2}\ge x
\\
x\le \dfrac{1}{2}
.\end{array}
In interval notation, the solution set is $
\left( \infty,\dfrac{1}{2} \right]
$.