Given:
[tex]\begin{gathered} m\angle2=2x-5 \\ \\ m\angle\text{FDE}=3x-1 \end{gathered}[/tex]
As PD is a angle bisector, the measure of angle 2 is the half of the measure of angle FDE:
[tex]\begin{gathered} m\angle2=\frac{1}{2}m\angle FDE \\ \\ 2x-5=\frac{1}{2}(3x-1) \end{gathered}[/tex]
Use the equation above to solve x:
[tex]\begin{gathered} 2x-5=\frac{3}{2}x-\frac{1}{2} \\ \\ 2x-\frac{3}{2}x-5=\frac{3}{2}x-\frac{3}{2}x-\frac{1}{2} \\ \\ 2x-\frac{3}{2}x-5+5=-\frac{1}{2}+5 \\ \\ 2x-\frac{3}{2}x=-\frac{1}{2}+5 \\ \\ \frac{4}{2}x-\frac{3}{2}x=-\frac{1}{2}+\frac{10}{2} \\ \\ \frac{1}{2}x=\frac{9}{2} \\ \\ (2)(\frac{1}{2}x)=(2)(\frac{9}{2}) \\ \\ x=9 \end{gathered}[/tex]
Then, the value of x is 9
