Given : In ABC, DE // AB AD = 8x + 9, CD = x + 3, 

BE = 3x + 4, CE = x 

By Basic proportionality theorem, 

If DE // AB then we should have

\(\frac{CD}{DA}=\frac{CE}{EB}\)

\(\frac{x+3}{8x+9}\) = \(\frac{x}{3x+4}\)

⇒ (x + 3) (3x + 4) = x (8x + 9) 

⇒ x (3x + 4) + 3 (3x + 4) – 8x² + 9x 

⇒ 3x² + 4x + 9x + 12 = 8x² + 9x 

⇒ 8x² + 9x – 3x² – 4x – 9x -12 = 0 

⇒ 5x² – 4x – 12 = 0 

⇒ 5x² – 10x + 6x – 12 = 0

⇒ 5x (x – 2) + 6 (x – 2) = 0 

⇒ (5x + 6) (x – 2) = 0 

⇒ 5x + 6 = 0 or x – 2 = 0 

⇒ x =\(\frac{-6}{5}\) or x = 2; 

x cannot be negative. 

∴ The value x = 2 will make DE // AB.