Question

$\frac{8x^2 + 16 x - 51}{(2x - 3)(x+4)} > 3 $, if $x$ satisfies

• A. $x < -4$
• B. $ -3 < x < 3/2 $
• C. $x > 5/2$
• D. all the above

Answer 1

Answer: (D)

Consider $\frac{8x^2 + 16 x - 51}{(2x - 3)(x+4)} - 3 > 0 $
$\Rightarrow \: \frac{2x^2 + x - 15}{2x^2 + 5x - 12} > 0$
$\frac{(2x - 5)(x+3) }{(2x - 3)(x+4)}$
Hence both Nr and Dr are positive if x < - 4 or x > 5/2 and both negative if -3 < x < 3/2
Hence all the statements are true.