Question

The appoximate percentage of the interval $[-5,15]$ for which the inequality $x>4-\frac{7}{x+4}$ is satisfied, is

• A. $55\%$
• B. $65\%$
• C. $60\%$
• D. $45\%$

Answer 1

Answer: (B)

$(x-4)+\frac{7}{x+4}>0\Rightarrow \frac{\left(x^2-16\right)+7}{x+4}>0\Rightarrow \frac{x^2-9}{x+4}>0$
$\therefore \frac{(x-3)(x+3)}{(x+4)}>0$
$\therefore x\in (-4,-3)\cup x>3$
$\text{ permissible length }=13$
$\therefore \text{ Percentage }=\frac{13}{20}\times 100=65\%$