Answer
$(\frac{16}{3}, +\infty)$
Refer to the image below for the graph.
Work Step by Step
Solving the inequality will be easier of there are no fractions involved.
To get rid of the denominators, multiply the LCD of $6$ on both sides of the inequality to obtain:
$6(\frac{1}{2}x-\frac{2}{3}) \gt 2(6)
\\\frac{6}{2}x-\frac{12}{3|} \gt 12
\\3x - 4 \gt 12$
Add $4$ on both side of the inequality to obtain:
$3x \gt 16$
Divide $3$ on both sides to obtain:
$x \gt \dfrac{16}{3}$
The solution set includes all real numbers greater than $\dfrac{16}{3}$.
In interval notation, the solution set is:
$(\frac{16}{3}, +\infty)$
To graph the solution set, plot a hole (or hollow dot) at $x=\frac{16}{3}$ then shade the region to its right.
(refer to the attached image in the answer portion above)
