Answer:
x = 5
Step-by-step explanation:
Call the point where the unnamed line segment intersects BC point Z. Then angle bisector AZ divides segment BC into the same proportion as the other sides of the triangle:
... CZ/CZ = BZ/BZ
... 3x/15 = (2x -1)/9
... 9x = 5(2x -1) . . . . . . multiply by 45 to eliminate fractions
...9x = 10x -5 . . . . . . . eliminate parentheses
... 0 = x -5 . . . . . . . . . subtract 9x
... 5 = x . . . . . . . . . . . add 5
_____
Comment on this geometry
This value of x makes the side lengths BZ = 9 and CZ = 15. Such a triangle cannot be constructed, as point A and point Z would have to be the same point. The "triangle" would look like a line segment.
(Don't worry, the math is correct.)
