Solve the inequality. Write the solution set in interval notation.
-$$( x + 8 ) ( x + 6 ) ( x - 9 ) 0$$
A) $( - 8 , - 6 ) \cup ( 9 , \infty )$
B) $( 9 , \infty )$
C) $( - \infty , - 8 ) \cup ( - 6,9 )$
D) $( - \infty , - 6 )$

Question

Solve the inequality. Write the solution set in interval notation.
-$$( x + 8 ) ( x + 6 ) ( x - 9 ) > 0$$
A) $( - 8 , - 6 ) \cup ( 9 , \infty )$
B) $( 9 , \infty )$
C) $( - \infty , - 8 ) \cup ( - 6,9 )$
D) $( - \infty , - 6 )$

Quizplus · Accepted Answer

To solve the inequality $( x + 8 ) ( x + 6 ) ( x - 9 ) > 0$, we find the zeros of the function, which are $x = -8$, $x = -6$, and $x = 9$. These divide the number line into four intervals: $(-\infty, -8)$, $(-8, -6)$, $(-6, 9)$, and $(9, \infty)$. Testing values from each interval in the inequality, we find that the function is positive in the intervals $(-8, -6)$ and $(9, \infty)$. Therefore, the solution set in interval notation is $(-8, -6) \cup (9, \infty)$.

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Solve the Inequality $( x + 8 ) ( x + 6 ) ( x - 9 ) > 0$