Answer:
x = 6
Explanation:
You want the value of x in the geometry where an angle bisector has divided a triangle into sides 42 and (6x-1), and corresponding sides 78 and (10x+5).
Proportion
The angle bisector divides the sides of the triangle proportionally:
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . . . . . multiply by 546
78x -13 = 70x +35 . . . . . . . simplify
8x = 48 . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . . . . divide by 8