Solve the inequality. Write the solution set in interval notation.
-$$\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 1 \right) 0$$
A) $( - \infty , - 4 ] \cup [ - 1,1 ] \cup [ 4 , \infty )$
B) $[ - 4 , - 1 ] \cup [ 1,4 ]$
C) $( - 4 , - 1 ) \cup ( 1,4 )$
D) $( - \infty , - 4 ) \cup ( - 1,1 ) \cup ( 4 , \infty )$

Question

Solve the inequality. Write the solution set in interval notation.
-$$\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 1 \right) > 0$$
A) $( - \infty , - 4 ] \cup [ - 1,1 ] \cup [ 4 , \infty )$
B) $[ - 4 , - 1 ] \cup [ 1,4 ]$
C) $( - 4 , - 1 ) \cup ( 1,4 )$
D) $( - \infty , - 4 ) \cup ( - 1,1 ) \cup ( 4 , \infty )$

Quizplus · Accepted Answer

The inequality $(x^2 - 16)(x^2 - 1) > 0$ factors into $(x + 4)(x - 4)(x + 1)(x - 1) > 0$. The critical points are $x = -4, -1, 1, 4$. Testing intervals around these points shows that the inequality is satisfied for $x < -4$, $-1 < x < 1$, and $x > 4$, leading to the solution set $(-\infty, -4) \cup (-1, 1) \cup (4, \infty)$.

Solve the Inequality (x2−16)(x2−1)>0\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 1 \right) > 0(x2−16)(x2−1)>0

Solve the Inequality $\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 1 \right) > 0$