Question

Solve the inequality. (Enter your answer using interval notation.)
(x(squared) + 6x − 7)/
(7x(squared) − 46x − 21)
> 0

Answer 1

Solution -

$\frac{(x^2+ 6x-7)}{7x^2-46x-21} >0$

⇒$\frac{x^2+7x-x-7}{7x^2-49x+3x-21} >0$

⇒$\frac{(x-1)(x+7)}{(x-7)(7x+3)} >0$

⇒ (x-1)(x+7) > 0 and (x-7)(7x+3) > 0          (In order to make the whole polynomial +ve, both numerator and denominator have to be +ve )

⇒ (x-1)>0 and (x+7)>0 or  (x-1)<0 and (x+7)<0    

                                 and    (either both of the polynomials are +ve or -ve)

   (x-7)>0 and (7x+3)>0  or  (x-7)<0 and (7x+3)<0

⇒ x > 7 , x < -7 , -3/7 < x < 1

Answer

$x \ \epsilon\ (-\infty , -7) \cup (\frac{-3}{7} , 1) \cup (7 , \infty)$