Solve the inequality.
-$$\frac { x - 1 } { x + 4 } 0$$
A) $( - \infty , - 4 )$
B) $( - 4,1 )$
C) $( 1 , \infty )$
D) $( - \infty , - 4 )$ or $( 1 , \infty )$

Question

Solve the inequality.
-$$\frac { x - 1 } { x + 4 } > 0$$
A) $( - \infty , - 4 )$
B) $( - 4,1 )$
C) $( 1 , \infty )$
D) $( - \infty , - 4 )$ or $( 1 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $\frac { x - 1 } { x + 4 } > 0$, we find the critical points by setting the numerator and denominator equal to zero separately. The critical points are $x = 1$ and $x = -4$. These points divide the number line into three intervals: $(-\infty, -4)$, $(-4, 1)$, and $(1, \infty)$. Testing values from each interval in the inequality, we find that the inequality holds for $x$ in $(-\infty, -4)$ and $(1, \infty)$.

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