Answer:
x = 5
Step-by-step explanation:
For better explanation of the solution, see the attached diagram of the problem :
The triangle angle bisector theorem states that the line which bisects an angle of a triangle divides the opposite two sides of the triangle in two equal segment which are proportional to the other two sides of the triangle.
Now, from the diagram : AD is the angle bisector angle B
[tex]\implies\frac{AB}{AC}=\frac{BD}{CD}\\\\\implies \frac{9}{15} = \frac{(2x-1)}{(3x)}[/tex]
On Cross multiplication :
⇒ 9 × 3x = 15 × (2x - 1)
Using the distributive property,
⇒ 27x = 15×2x - 15×1
⇒ 27x = 30x - 15
Subtract 30x from each side:
⇒ 27x - 30x = 30x - 15 - 30x
⇒ -3x = -15
⇒ x = 5
