Question

Solve the rational inequality. Write the solution set in interval notation.
$\frac{1}{x+10}>0$

• A. $(-\infty ,10)$
• B. $(10,-\infty )$
• C. $(-10,\infty )$
• D. $[10,\infty ]$

Answer 1

The correct option is C $(-10,\infty )$

The given inequality is,

$\frac{1}{x+10}>10$

We know that $1>0$

Thus, numerator is greater than 1. For LHS to be positive, denominator must be greater than zero.

$\therefore x+10>0$

$\therefore x>-10$

Thus, Interval of the solution is, $(-10,\infty )$

Thus, Answer is option (C)