Solve the rational inequality. Write the answer in interval notation. $$\frac { x + 15 } { x } \geq 0$$
A) $( - \infty , - 15 ]$
B) $( - \infty , - 15 ] \cup ( 0 , \infty )$
C) $( - \infty , \infty )$
D) $( 0,15 ]$

Question

Quizplus · Accepted Answer

The inequality $\frac{x + 15}{x} \geq 0$ is solved by finding the zeros and undefined points of the rational expression. The numerator $x + 15 = 0$ gives $x = -15$, and the denominator $x = 0$ is where the expression is undefined. Plotting these points on a number line divides it into three intervals: $(-\infty, -15)$, $(-15, 0)$, and $(0, \infty)$. Testing values from each interval in the inequality shows that the expression is non-negative in the intervals $(-\infty, -15]$ and $(0, \infty)$, hence the correct answer is $(-\infty, -15] \cup (0, \infty)$.

Solve the Rational Inequality x+15x≥0\frac { x + 15 } { x } \geq 0xx+15​≥0

Solve the Rational Inequality $\frac { x + 15 } { x } \geq 0$