Question

The values of $x$ for which $\frac{1-5x}{x^2+1}$ is negative satisfy the inequality:

• A. $x>0$
• B. $x>\frac{1}{5}$
• C. $x<\frac{1}{5}$
• D. $0<x<\frac{1}{5}$
• E. None of the above

Answer 1

The correct option is B $x>\frac{1}{5}$

Given, $\frac{1-5x}{x^2+1}<0$
$\therefore x^2+1$ is always greater than or equal to zero , therefore $1-5x$ must be less than $0$.
We get $1-5x<0$, which implies $x>\frac{1}{5}$