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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.

Solve the following inequality: -5x ≥ 30. Graph the solution set and then write it in interval notation.

Learn how to solve the inequality -5x ≥ 30 with a detailed step-by-step solution, graph the result, and write the solution in interval notation. This lesson covers key algebraic concepts, suitable for Grades 8-10.

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