Question

1. solve the rational inequality \\(\frac{-5}{x + 10} < 0\\). express the answer in interval form.\

\\(\bigcirc\\ (10, \infty)\\)\
\\(\bigcirc\\ (-infty, 10)\\)\
\\(\bigcirc\\ (-10, \infty)\\)\
\\(\bigcirc\\ (-infty, -10)\\)

Explanation:

Step1: Identify sign of numerator

The numerator is $-5$, which is negative.

Step2: Analyze inequality condition

For $\frac{-5}{x+10} < 0$, since the numerator is negative, the denominator must be positive (negative divided by positive is negative). So we solve $x+10 > 0$.

Step3: Solve the linear inequality

Subtract 10 from both sides:
$x > -10$

Answer:

C. $(-10, \infty)$