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 \(x\).
\(30x-15=27x\)
\(3x=15\)
\(x=5\)
