Solve the inequality. Write the solution set in interval notation.
-$\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) 0$
A) $( - \infty , - 8 ) \cup ( - 1,1 ) \cup ( 8 , \infty )$
B) $( - \infty , - 8 ] \cup [ - 1,1 ] \cup [ 8 , \infty )$
C) $[ - 8 , - 1 ] \cup [ 1,8 ]$
D) $( - 8 , - 1 ) \cup ( 1,8 )$

Question

Solve the inequality. Write the solution set in interval notation.
-$\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) > 0$
A) $( - \infty , - 8 ) \cup ( - 1,1 ) \cup ( 8 , \infty )$
B) $( - \infty , - 8 ] \cup [ - 1,1 ] \cup [ 8 , \infty )$
C) $[ - 8 , - 1 ] \cup [ 1,8 ]$
D) $( - 8 , - 1 ) \cup ( 1,8 )$

Quizplus · Accepted Answer

The inequality $(x^2 - 64)(x^2 - 1) > 0$ factors into $(x + 8)(x - 8)(x + 1)(x - 1) > 0$. The critical points are $x = -8, -1, 1, 8$. Testing intervals around these points shows that the inequality is satisfied for $x < -8$, $-1 < x < 1$, and $x > 8$, leading to the solution set $(-\infty, -8) \cup (-1, 1) \cup (8, \infty)$.

Solve the Inequality (x2−64)(x2−1)>0\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) > 0(x2−64)(x2−1)>0

Solve the Inequality $\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 1 \right) > 0$