Question

What is the value of x? Please show the steps

Answer 1

Let D be the endpoint of the angle bisector opposite A on lying on side BC. The angle bisector theorem states that the ratio of BD to CD is equal to the ratio of AB to AC. In this case, you have

$\dfrac{2x-1}{3x}=\dfrac9{15}$

(This is the same equation that you have, it's just rearranged.)

Multiply both sides by $3x$ and 15.

$15\times3x\times\dfrac{2x-1}{3x}=15\times3x\times\dfrac9{15}$
$15(2x-1)=3x\times9$

Now you can solve for $x$.

$30x-15=27x$
$3x=15$
$x=5$