Solve the inequality and write the solution set in interval notation.
$x ^ { 5 } ( x - 4 ) \leq 0$
A) $( \infty , 4 ]$
B) $( - \infty , - 4 ]$
C) $( \infty , 4 )$
D) $( - 4,4 ]$
E) $( - \infty , 4 ]$

Question

Solve the inequality and write the solution set in interval notation. 
$x ^ { 5 } ( x - 4 ) \leq 0$ 
A) $( \infty , 4 ]$
B) $( - \infty , - 4 ]$
C) $( \infty , 4 )$
D) $( - 4,4 ]$
E) $( - \infty , 4 ]$

Quizplus · Accepted Answer

The inequality $x^5(x - 4) \leq 0$ is satisfied when $x = 0$ or $x = 4$, or when $x$ is between these values. Since $x^5$ is negative for $x < 0$ and positive for $x > 0$, and $x - 4$ is negative for $x < 4$ and positive for $x > 4$, the solution set includes all $x$ less than or equal to 4, hence $(- \infty , 4 ]$.

Solve the Inequality and Write the Solution Set in Interval x5(x−4)≤0x ^ { 5 } ( x - 4 ) \leq 0x5(x−4)≤0

Solve the Inequality and Write the Solution Set in Interval $x ^ { 5 } ( x - 4 ) \leq 0$