Solve the inequality and write the solution set in interval notation. $x ^ { 8 } ( x - 2 ) \leq 0$
A) $( - \infty , 2 ]$
B) $( - \infty , - 2 ) ]$
C) $( - \infty , 2 )$
D) $( - 2,2 ]$

Question

Solve the inequality and write the solution set in interval notation.​ $x ^ { 8 } ( x - 2 ) \leq 0$ ​ ​
A) $( - \infty , 2 ]$
B) $( - \infty , - 2 ) ]$
C) $( - \infty , 2 )$
D) $( - 2,2 ]$

Quizplus · Accepted Answer

The inequality $x^8(x - 2) \leq 0$ is satisfied when $x - 2 \leq 0$, because $x^8$ is always non-negative for all real x (since any even power of a real number is non-negative). This gives $x \leq 2$. Therefore, the solution set includes all x less than or equal to 2, which is $(-\infty, 2]$.

Solve the Inequality and Write the Solution Set in Interval x8(x−2)≤0x ^ { 8 } ( x - 2 ) \leq 0x8(x−2)≤0

Solve the Inequality and Write the Solution Set in Interval $x ^ { 8 } ( x - 2 ) \leq 0$