Solve the inequality and give the solution in interval notation.
-$$( b + 6 ) ( b - 4 ) ( b - 5 )

Question

Solve the inequality and give the solution in interval notation.
-$$( b + 6 ) ( b - 4 ) ( b - 5 ) < 0$$
A) $$( - \infty , 4 )$$
B) $$( - \infty , - 6 ) \cup ( 4,5 )$$
C) $$( 5 , \infty )$$
D) $$( - 6,4 ) \cup ( 5 , \infty )$$

Quizplus · Accepted Answer

The given inequality $( b + 6 ) ( b - 4 ) ( b - 5 ) < 0$ has roots at $b = -6$, $b = 4$, and $b = 5$. To solve the inequality, we consider the intervals created by these roots: $(-\infty, -6)$, $(-6, 4)$, $(4, 5)$, and $(5, \infty)$. Testing values from each interval in the inequality, we find that the inequality holds for $b$ values in the intervals $(-\infty, -6)$ and $(4, 5)$. Therefore, the solution in interval notation is $(-\infty, -6) \cup (4, 5)$.

Solve the Inequality and Give the Solution in Interval Notation (b+6)(b−4)(b−5)<0( b + 6 ) ( b - 4 ) ( b - 5 ) < 0(b+6)(b−4)(b−5)<0

Solve the Inequality and Give the Solution in Interval Notation $( b + 6 ) ( b - 4 ) ( b - 5 ) < 0$