(8x2 + 16 x - 51/(2x - 3)(x+4)) 3 , if x satisfies

Question

(8x2 + 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

Tardigrade Admin · Accepted Answer

Consider (8x2 + 16 x - 51/(2x - 3)(x+4)) - 3 > 0 ⇒ : (2x2 + x - 15/2x2 + 5x - 12) > 0 ((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.

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

$x < - 4$

$- 3 < x < 3/2$

$x > 5/2$

all the above

Q. (2x−3)(x+4)8x2+16x−51​>3, if x satisfies

x<−4

−3<x<3/2

x>5/2

all the above

Consider (2x−3)(x+4)8x2+16x−51​−3>0 ⇒2x2+5x−122x2+x−15​>0 (2x−3)(x+4)(2x−5)(x+3)​ 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.

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

$x < - 4$

$- 3 < x < 3/2$

$x > 5/2$