Last one of the day!
need understanding the process

what is the value of x?

thx!

The bisector of the angle at A (call it AQ) divides the segment BC into segments BQ:QC having the ratio AB:AC. Use this fact to find x.

.. 9:15 = (2x -1):3x
.. 15(2x -1) = 9*3x . . . . . the product of the means equals the product of extremes
.. 30x -15 = 27x
.. 3x = 15
.. x = 5

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According to the value of x, the bisector AQ divides the triangle into two isosceles triangles: ABQ, ACQ.