Solve the inequality.
-$$\frac { x - 2 } { x + 5 }

Question

Solve the inequality.
-$$\frac { x - 2 } { x + 5 } < 0$$
A) $( - \infty , - 5 )$
B) $( - \infty , - 5 )$ or $( 2 , \infty )$
C) $( - 5,2 )$
D) $( 2 , \infty )$

Quizplus · Accepted Answer

The inequality $\frac{x - 2}{x + 5} < 0$ is satisfied when the numerator and denominator have opposite signs. This occurs when $x < -5$ (denominator is negative, numerator is positive) or when $-5 < x < 2$ (denominator is positive, numerator is negative). However, the solution $x < -5$ does not satisfy the inequality because it makes the fraction positive. Therefore, the correct interval is $(-5, 2)$, where the numerator is negative and the denominator is positive, making the fraction negative.

Solve the Inequality x−2x+5<0\frac { x - 2 } { x + 5 } < 0x+5x−2​<0

Solve the Inequality $\frac { x - 2 } { x + 5 } < 0$