In the figure if DE parallel to BC and AD = 4x - 3 , AE = 8x-7 , BD = 3x - 1 and EC = 5x - 3 . Find the value of x

 Given - Triangle ABC, DE parallel to BC

AD = 4x - 3, AE = 8x - 7, BD = 3x - 1, CE = 5x - 3

To find = value of x

Solution,

In triangle ABC, since DE parallel to BC is given,

AD/DB = AE/EC

----> 4x - 3/3x - 1 = 8x - 7/5x - 3

by cross - multiplication we get

20x² - 15x - 12x + 9 = 24x² - 21x - 8x + 7

20x² - 27x + 9 = 24x² - 29x + 7

rearranging equation

4x² - 2x = 2 ------> 2x² - x = 1

2x² - x - 1 = 0

2x² - 2x + x - 1 = 0

2x (x - 1) + 1 (x - 1) = 0

(2x + 1) (x - 1) = 0

----> x = -1/2, 1

hope this helps!!