Q. The appoximate percentage of the interval $[-5,15]$ for which the inequality $x>4-\frac{7}{x+4}$ is satisfied, is
Complex Numbers and Quadratic Equations
Solution:
$(x-4)+\frac{7}{x+4}>0 \Rightarrow \frac{\left(x^2-16\right)+7}{x+4}>0 \Rightarrow \frac{x^2-9}{x+4}>0$
$\therefore \frac{(x-3)(x+3)}{(x+4)}>0 $
$\therefore x \in(-4,-3) \cup x>3 $
$\text { permissible length }=13 $
$\therefore \text { Percentage }=\frac{13}{20} \times 100=65 \%$
