Question

solve for x and graph the solution.
$(x - 1)^3 > 0$
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.
(number line from -6 to 6 with ticks at each integer, and a submit button on the left)

Explanation:

Step1: Isolate the cubic expression

We start with the given inequality:
$$(x - 1)^3 > 0$$

Step2: Take cube root of both sides

Since the cube root preserves inequality direction for all real numbers, we get:
$$\sqrt[3]{(x - 1)^3} > \sqrt[3]{0}$$
Simplifying both sides:
$$x - 1 > 0$$

Step3: Solve for x

Add 1 to both sides to isolate x:
$$x - 1 + 1 > 0 + 1$$
$$x > 1$$

Step4: Describe the graph

For the number line: use an open circle at $x=1$ (since $x=1$ is not included in the solution), and draw a ray extending to the right from this point to represent all values greater than 1.

Answer:

The solution is $x > 1$. To graph this: place an open endpoint at 1 on the number line, then draw a ray pointing to the right (toward increasing values of x) from this open endpoint.