Solve the inequality. Write the solution set in interval notation.
-$$x ( x + 6 ) ( x - 5 ) 0$$
A) $( - \infty , - 6 ) \cup ( 0,5 )$
B) $[ - 6,0 ] \cup [ 5 , \infty )$
C) $( - \infty , - 6 ] \cup [ 0,5 ]$
D) $( - 6,0 ) \cup ( 5 , \infty )$

Question

Solve the inequality. Write the solution set in interval notation.
-$$x ( x + 6 ) ( x - 5 ) > 0$$
A) $( - \infty , - 6 ) \cup ( 0,5 )$
B) $[ - 6,0 ] \cup [ 5 , \infty )$
C) $( - \infty , - 6 ] \cup [ 0,5 ]$
D) $( - 6,0 ) \cup ( 5 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $x(x+6)(x-5) > 0$, we find the roots of the equation $x(x+6)(x-5) = 0$, which are $x = 0$, $x = -6$, and $x = 5$. These roots divide the real number line into four intervals: $(-\infty, -6)$, $(-6, 0)$, $(0, 5)$, and $(5, \infty)$. Testing values from each interval in the inequality, we find that the expression is positive in the intervals $(-6, 0)$ and $(5, \infty)$. Therefore, the solution set in interval notation is $(-6, 0) \cup (5, \infty)$.

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