What is value of x?

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x =

The bisector divides the line BC in the following ratio.

(x + 8) / 10 = (2x - 5) / 14      Cross Multiply

14(x + 8) = 10(2x - 5)            Remove the brackets.

14x + 112 = 20x  - 50           Subtract 14x from both sides . Add                                                                                                                             50 to both sides

112 + 50 = 20x - 14x             Collect like terms

162 = 6x                               Divide by 6  

x = 27