Solve the inequality and give the solution in interval notation.
-$$( a + 5 ) ( a - 3 ) ( a - 6 ) 0$$
A) $$( - 5,3 ) \cup ( 6 , \infty )$$
B) $$( - \infty , 3 )$$
C) $$( - \infty , - 5 ) \cup ( 3,6 )$$
D) $$( 6 , \infty )$$

Question

Solve the inequality and give the solution in interval notation.
-$$( a + 5 ) ( a - 3 ) ( a - 6 ) > 0$$
A) $$( - 5,3 ) \cup ( 6 , \infty )$$
B) $$( - \infty , 3 )$$
C) $$( - \infty , - 5 ) \cup ( 3,6 )$$
D) $$( 6 , \infty )$$

Quizplus · Accepted Answer

To solve the inequality $(a + 5)(a - 3)(a - 6) > 0$, we find the zeros of the function, which are $a = -5$, $a = 3$, and $a = 6$. These divide the number line into four intervals: $(-\infty, -5)$, $(-5, 3)$, $(3, 6)$, and $(6, \infty)$. Testing values from each interval in the inequality shows that the function is positive in the intervals $(-5, 3)$ and $(6, \infty)$, leading to the solution in interval notation as $(-5, 3) \cup (6, \infty)$.

Solve the Inequality and Give the Solution in Interval Notation (a+5)(a−3)(a−6)>0( a + 5 ) ( a - 3 ) ( a - 6 ) > 0(a+5)(a−3)(a−6)>0

Solve the Inequality and Give the Solution in Interval Notation $( a + 5 ) ( a - 3 ) ( a - 6 ) > 0$