Answer
$(7.5, 10.5]$
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 (which is 12) to each part to have:
$\\12(\frac{1}{6}) \lt 12 \cdot \frac{2x-13}{12} \le 12(\frac{2}{3})
\\2 \lt 2x-13 \le 8$
Add 13 to each part to have:
$\\2+13 \lt 2x-13+13 \le 8+13
\\15 \lt 2x \le 21$
Divide 2 to each part to have:
$\\7.5 \lt x \le 10.5$
Thus, the solution is $(7.5, 10.5]$.
