Question

solve for x and graph the solution.
(x + 6)^3 < 0
plot the endpoints. select an endpoint to change it from closed to open, a segment, ray, or line to delete it.

Explanation:

Step1: Take cube - root of both sides

If \((x + 6)^{3}<0\), then taking the cube - root of both sides (since the cube - root function \(y = \sqrt[3]{u}\) is a one - to - one function and preserves the inequality sign for all real numbers), we get \(x+6<\sqrt[3]{0}\).

Step2: Simplify the right - hand side and solve for x

Since \(\sqrt[3]{0}=0\), the inequality becomes \(x + 6<0\). Subtracting 6 from both sides gives \(x<-6\).

Answer:

The solution of the inequality \((x + 6)^{3}<0\) is \(x<-6\). On the number line, we use an open circle at \(x=-6\) and draw a ray to the left of \(x = - 6\).