What is ((8x^2+16x-51))/(((2x-3)(x+4)))<3 ?

The solution to ((8x^2+16x-51))/(((2x-3)(x+4)))<3 is -4<x<-3\lor 3/2 <x< 5/2

Popular >

((8x^2+16x-51))/(((2x-3)(x+4)))<3

\frac{( 8 x ^{2} + 16 x - 51 )}{( ( 2 x - 3 ) ( x + 4 ) )} < 3

- 4 < x < - 3 or \frac{3}{2} < x < \frac{5}{2}

Interval Notation

(- 4, - 3) \cup (\frac{3}{2}, \frac{5}{2})

Decimal Notation

- 4 < x < - 3 or 1.5 < x < 2.5

Solution steps

\frac{8 x ^{2} + 16 x - 51}{( 2 x - 3 ) ( x + 4 )} < 3

Rewrite in standard form

\frac{2 x ^{2} + x - 15}{( 2 x - 3 ) ( x + 4 )} < 0

Factor

\frac{2 x ^{2} + x - 15}{( 2 x - 3 ) ( x + 4 )} : \frac{( 2 x - 5 ) ( x + 3 )}{( 2 x - 3 ) ( x + 4 )}

\frac{( 2 x - 5 ) ( x + 3 )}{( 2 x - 3 ) ( x + 4 )} < 0

Identify the intervals

- 4 < x < - 3 or \frac{3}{2} < x < \frac{5}{2}

\frac{1}{( x + 1 )} \geq \frac{2}{( x + 2 )}

\frac{( 2 x - x ^{2} + 11 )}{( x ^{2} + 2 x + 3 )} \geq 1

\frac{( 2 x - 1 )}{( x ^{3} + 2 x + x )} > 0

\frac{( ( n + 5 ) ( n - 9 ) )}{( n - 12 )} \geq 0

(x - 1)^{3} \cdot (x + 1) \cdot (x + 2)^{6} < 0

What is ((8x^2+16x-51))/(((2x-3)(x+4)))<3 ?
The solution to ((8x^2+16x-51))/(((2x-3)(x+4)))<3 is -4<x<-3\lor 3/2 <x< 5/2