Question

solve for x and graph the solution.
$(x + 6)^3 \leq 0$
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, \\(y\\), 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: Find critical point

Set $x+6=0$, so $x=-6$.

Step2: Analyze sign of the cube

A cube preserves the sign of its base. For $(x+6)^3 \leq 0$, we need $x+6 \leq 0$.

Step3: Solve the linear inequality

Subtract 6 from both sides:
$x+6-6 \leq 0-6$
$x \leq -6$

Step4: Graph setup

On the number line, place a closed endpoint at $x=-6$ (since the inequality includes equality), then draw a line extending left from this point to represent all values less than -6.

Answer:

The solution is $x \leq -6$.
For the graph:

1. Mark a closed (filled) dot at $x=-6$ on the number line.
2. Draw a solid line with an arrow pointing left from this dot, covering all values less than -6.