The problem in the image asks to solve the inequality and then graph the solution set, writing the solution in interval notation. The inequality is given as:

$-3x \geq 9$

Step 1: Solve the inequality

To solve for $x$, divide both sides of the inequality by $-3$. Remember, when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign.

$x \leq \frac{9}{-3}$

This simplifies to:

$x \leq -3$

Step 2: Graph the solution

The solution $x \leq -3$ means all values of $x$ that are less than or equal to $-3$. On a number line, this would be represented by a solid circle at $-3$ with an arrow pointing to the left (since it's less than or equal to).

Step 3: Write the interval notation

In interval notation, $x \leq -3$ is written as:

$(-\infty, -3]$

The square bracket on $-3$ indicates that $-3$ is included in the solution.

Answer:

• Graph: A solid circle at $-3$ with an arrow extending to the left.
• Interval notation: $(-\infty, -3]$

Among the provided options, choose the graph that shows a solid point at $-3$ with the line extending to the left.

Do you need further clarification or additional details?

Related questions:

1. What happens to an inequality if you multiply both sides by a negative number?
2. How do you graph inequalities that use "less than" and "greater than" on a number line?
3. Can inequalities have solutions that extend to both positive and negative infinity?
4. How do you convert inequalities with absolute values into interval notation?
5. What is the difference between strict inequalities and non-strict inequalities in interval notation?

Tip: When solving inequalities, always remember to flip the inequality sign if you multiply or divide by a negative number!