The problem provided asks us to solve the inequality $-5x \geq 30$, graph the solution set, and write it in interval notation.

Step-by-Step Solution

1. Solve the Inequality:

   Start by isolating the variable $x$:

   $-5x \geq 30$

   Divide both sides by $-5$. Remember, when dividing by a negative number, we must reverse the inequality sign:

   $x \leq -6$

2. Graph the Solution:

   The solution is all $x$ values less than or equal to $-6$. On a number line, this would be represented by a solid dot at $-6$ (indicating that $-6$ is included) and an arrow extending to the left.

   Among the provided choices, option D matches this description: a graph with a solid dot at $-6$ and an arrow pointing to the left.

3. Interval Notation:

   The interval notation for $x \leq -6$ is:

   $(-\infty, -6]$

4. Answer Choices:

   • The correct choice for the graph is D.
   • The correct answer in interval notation is A: The solution set is $(- \infty, -6]$.

Would you like further details or have any questions?

Related Questions:

1. How do you solve inequalities with variables on both sides?
2. What is interval notation, and why is it useful?
3. How do you graph a compound inequality?
4. What happens when you multiply or divide by a negative number in an inequality?
5. How do you solve quadratic inequalities?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.