Question

solve for x and graph the solution. -(x - 2)^5 ≤ 0 plot the endpoints. select an endpoint to change it from closed a segment, ray, or line to delete it.

Explanation:

Step1: Multiply both sides by -1

When we multiply the inequality $-(x - 2)^{5}\leq0$ by - 1, the direction of the inequality sign changes. We get $(x - 2)^{5}\geq0$.

Step2: Take the fifth - root of both sides

Since the fifth - root function $y = \sqrt[5]{u}$ is a one - to - one function, taking the fifth - root of both sides of the inequality $(x - 2)^{5}\geq0$ gives $x-2\geq\sqrt[5]{0}$.

Step3: Solve for x

Adding 2 to both sides of the inequality $x - 2\geq0$, we get $x\geq2$.

Answer:

The solution of the inequality is $x\geq2$. On the number - line, we plot a closed circle at $x = 2$ (because the inequality includes equality, $\geq$) and draw a ray to the right of $x = 2$.