Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x - 7 } { x + 8 } \leq 0$$
A) $( - 7,8 ]$
B) $[ - 8,7 ]$
C) $[ - 7,8 ]$
D) $( - 8,7 ]$

Question

Quizplus · Accepted Answer

The inequality $\frac{x - 7}{x + 8} \leq 0$ is satisfied when the numerator and denominator have opposite signs or when the numerator is 0 (making the whole expression equal to 0). The critical points are $x = 7$ (where the numerator is 0) and $x = -8$ (where the denominator is 0 and the expression is undefined). Testing intervals around these points, we find that the inequality holds for $x \in (-8, 7]$, including $x = 7$ but excluding $x = -8$ because the expression is undefined there.

Solve the Rational Inequality x−7x+8≤0\frac { x - 7 } { x + 8 } \leq 0x+8x−7​≤0

Solve the Rational Inequality $\frac { x - 7 } { x + 8 } \leq 0$