Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } - 6 x + 16

Question

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } - 6 x + 16 < 0$$
A) $( - \infty , \infty )$
B) $( - 8,2 ) \cup ( 2 , \infty )$
C) $( - \infty , - 8 ) \cup ( 2 , \infty )$
D) $( - \infty , - 2 ) \cup ( 8 , \infty )$

Quizplus · Accepted Answer

First, rearrange the inequality to standard form: $-x^2 - 6x + 16 < 0$. Factoring or using the quadratic formula, we find the roots of the corresponding equation $-x^2 - 6x + 16 = 0$ to be $x = -8$ and $x = 2$. Since the coefficient of $x^2$ is negative, the parabola opens downwards, meaning the expression is less than 0 between the roots. Thus, the solution set in interval notation is $(- \infty , - 8 ) \cup ( 2 , \infty )$.

Solve the Inequality −x2−6x+16<0- x ^ { 2 } - 6 x + 16 < 0−x2−6x+16<0

Solve the Inequality $- x ^ { 2 } - 6 x + 16 < 0$