Question

if x²+2x+7/2x+3 <6 then x belongs to​

Answer 1

SOLUTION :

$\sf \frac{{x}^{2} + 2x + 7}{2x + 3} > 6$

$\sf \implies \: \frac{ {x}^{2} + 2x + 7 }{2x + 3} - 6 > 0$

$\sf \implies \: \frac{ {x}^{2} + 2x + 7 - 12x - 18}{2x + 3} > 0$

$\sf \implies \: \frac{ {x}^{2} - 10x - 11}{2x + 3} > 0$

$\sf \implies \: \frac{(x - 11)(x + 1)}{(2x + 3)} > 0$

$\sf \: x \in \: (11, \infty ) \: U( - \infty ,1) \: U( - \infty ,\frac{3}{2} )$

$\sf \: x \in(11 ,\frac{3}{2} )$