Question

solve for x and graph the solution.
(x + 1)^3 < 0
plot the endpoints. select an endpoint to change it from closed to a segment, ray, or line to delete it.

Explanation:

Step1: Take cube - root on both sides

Since $y = \sqrt[3]{x}$ is a monotonically increasing function, taking the cube - root of both sides of the inequality $(x + 1)^3<0$ gives $\sqrt[3]{(x + 1)^3}<\sqrt[3]{0}$.
$x + 1<0$

Step2: Solve for x

Subtract 1 from both sides of the inequality $x + 1<0$.
$x<-1$

Answer:

The solution of the inequality is $x\in(-\infty,-1)$. On the number - line, we plot an open circle at $x=-1$ and draw a ray to the left of $x = - 1$.