Solve the inequality.
-$$( a + 4 ) ( a - 4 ) ( a - 5 ) 0$$
A) $( - \infty , 4 )$
B) $( 5 , \infty )$
C) $( - \infty , - 4 )$ or $( 4,5 )$
D) $( - 4,4 )$ or $( 5 , \infty )$

Question

Solve the inequality.
-$$( a + 4 ) ( a - 4 ) ( a - 5 ) > 0$$
A) $( - \infty , 4 )$
B) $( 5 , \infty )$
C) $( - \infty , - 4 )$ or $( 4,5 )$
D) $( - 4,4 )$ or $( 5 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $(a + 4)(a - 4)(a - 5) > 0$, we find the roots of the equation $(a + 4)(a - 4)(a - 5) = 0$, which are $a = -4$, $a = 4$, and $a = 5$. These roots divide the real number line into four intervals: $(-\infty, -4)$, $(-4, 4)$, $(4, 5)$, and $(5, \infty)$. Testing values from each interval in the inequality, we find that the inequality holds for intervals $(-4, 4)$ and $(5, \infty)$.

Solve the Inequality (a+4)(a−4)(a−5)>0( a + 4 ) ( a - 4 ) ( a - 5 ) > 0(a+4)(a−4)(a−5)>0

Solve the Inequality $( a + 4 ) ( a - 4 ) ( a - 5 ) > 0$