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
[tex]\dfrac{2x-1}{3x}=\dfrac9{15}[/tex]
(This is the same equation that you have, it's just rearranged.)
Multiply both sides by [tex]3x[/tex] and 15.
[tex]15\times3x\times\dfrac{2x-1}{3x}=15\times3x\times\dfrac9{15}[/tex]
[tex]15(2x-1)=3x\times9[/tex]
Now you can solve for [tex]x[/tex].
[tex]30x-15=27x[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
