Question

solve for x and graph the solution. (x - 5)^3 >= 0 plot the endpoints. select an endpoint to change it from a segment, ray, or line to delete it.

Explanation:

Step1: Take cube - root on both sides

If \((x - 5)^3\geq0\), then \(\sqrt[3]{(x - 5)^3}\geq\sqrt[3]{0}\). Since \(\sqrt[3]{a^3}=a\) for any real number \(a\), we have \(x - 5\geq0\).

Step2: Solve for \(x\)

Add 5 to both sides of the inequality \(x - 5\geq0\). We get \(x\geq5\).

To graph the solution on the number - line:

1. Locate the point \(x = 5\) on the number - line.
2. Since the inequality is \(x\geq5\), we use a closed circle at \(x = 5\) (because \(x\) can equal 5) and draw a ray to the right of \(x = 5\) to represent all the values of \(x\) that satisfy the inequality.

Answer:

The solution of the inequality \((x - 5)^3\geq0\) is \(x\geq5\). On the number - line, we have a closed circle at \(x = 5\) and a ray extending to the right.