Answer
$(2.5, 5.5]$
Refer to the image below for the graph.
Work Step by Step
Multiply $12$ to each part of the inequality to eliminate the fractions:
$\begin{array}{ccccc}
&12\left(\dfrac{2}{3}\right) &\ge &12\left(\dfrac{2x-3}{12}\right) &\gt &12\left(\dfrac{1}{6}\right)
\\&8 &\ge &2x-3 &\gt &2
\end{array}$
Add $3$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&8+3 &\ge &2x-3+3 & \gt &2+3
\\&11 &\ge &2x &\gt &5
\end{array}$
Divide each part by $2$ to obtain:
$\begin{array}{ccccc}
&\dfrac{11}{2} &\ge &\dfrac{2x}{2} &\gt &\dfrac{5}{2}
\\&5.5 &\ge &x &\gt &2.5
\end{array}$
This inequality is equivalent to:
$2.5 \lt x \le 5.5$
Thus, the solution set is $\bf(2.5 , 5.5]$.
To graph this solution set, a hole (hollow dot) at $2.5$ and a solid dot at $5.5$ then shade the region in between.
(refer to the attached image in the answer part above for the graph)
