Answer:
The value of [tex]x[/tex] is 5.
Step-by-step explanation:
Firstly, we'll name as P the point of intersection between the internal line of the triangle (that comes from the point A) with the side BC.
By the Angle Bisector Theorem, we can write the following relation
[tex]\dfrac{AB}{BP}=\dfrac{AC}{PC}\\\\\dfrac{9}{2x-1}=\dfrac{15}{3x}\\\\\dfrac{9}{2x-1}=\dfrac{5}{x}\\\\9x = (2x-1)\cdot5\\\\9x = 10x - 5\\\\\boxed{x=5}[/tex]
