Solve the inequality and give the solution in interval notation.
-$$\frac { x - 6 } { ( x + 5 ) ( x - 2 ) } 0$$
A) $$( - 5,2 ) \cup ( 6 , \infty )$$
B) $$( - 6 , - 2 ) \cup ( 5 , \infty )$$
C) $$( - 2,5 ) \cup ( 6 , \infty )$$
D) $$( - 5 , - 6 ) \cup ( 5 , \infty )$$

Question

Solve the inequality and give the solution in interval notation.
-$$\frac { x - 6 } { ( x + 5 ) ( x - 2 ) } > 0$$
A) $$( - 5,2 ) \cup ( 6 , \infty )$$
B) $$( - 6 , - 2 ) \cup ( 5 , \infty )$$
C) $$( - 2,5 ) \cup ( 6 , \infty )$$
D) $$( - 5 , - 6 ) \cup ( 5 , \infty )$$

Quizplus · Accepted Answer

To solve the inequality $\frac { x - 6 } { ( x + 5 ) ( x - 2 ) } > 0$, we find the zeros of the numerator and denominator: $x = 6$, $x = -5$, and $x = 2$. These values divide the real number line into intervals. Testing values from each interval in the inequality, we find that the inequality is satisfied for $x \in ( - 5,2 ) \cup ( 6 , \infty )$.

Solve the Inequality and Give the Solution in Interval Notation x−6(x+5)(x−2)>0\frac { x - 6 } { ( x + 5 ) ( x - 2 ) } > 0(x+5)(x−2)x−6​>0

Solve the Inequality and Give the Solution in Interval Notation $\frac { x - 6 } { ( x + 5 ) ( x - 2 ) } > 0$