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**Problem:**

Use a graph chart to solve for the inequality. Express the solution set in interval notation.  
Given inequality:  

\[
\frac{x^2 - 9}{x - 3} \leq 0
\]

Options provided:
1. The solution expressed in interval notation: [ ]  
2. The solution expressed in interval notation: [ ]

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To solve this inequality, we should first identify the critical points of the rational expression \(\frac{x^2 - 9}{x - 3}\).

### Step-by-Step Solution:

1. **Factor the numerator:**
   \[
   x^2 - 9 = (x - 3)(x + 3)
   \]
   So, the inequality becomes:
   \[
   \frac{(x - 3)(x + 3)}{x - 3} \leq 0
   \]

2. **Simplify the expression:**
   When simplifying \(\frac{(x - 3)(x + 3)}{x - 3}\), note that \(x \neq 3\) (since dividing by zero is undefined).
   The expression simplifies to:
   \[
   x + 3 \leq 0 \quad \text{for} \; x \neq 3
   \]

3. **Solve the simplified inequality:**
   \[
   x + 3 \leq 0 \implies x \leq -3
   \]

4. **Consider the domain restrictions:**
   The solution \(x \leq -3\) needs to be combined with the restriction \(x \neq 3\). However, since \(x = 3\) is not part of the solution \(x \leq -3\), it does not affect the solution interval.

5. **Write the solution in interval notation:**
   The solution in interval notation is:
   \[
   (-\infty, -3]
   \]

### Conclusion:
- The correct interval notation for the solution set is: **\((- \infty, -3]\)**.

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Would you like a deeper explanation of any of the steps or have any questions?

### Related Questions:
1. How do you find the critical points of a rational expression?
2. What does it mean for a value to be "undefined" in a rational expression?
3. How do you graph rational inequalities on a number line?
4. What is interval notation, and how do you express intervals that include or exclude endpoints?
5. Why do we need to consider the domain of a rational expression when solving inequalities?

### Tip:
When solving rational inequalities, always remember to identify critical points where the expression is either zero or undefined, as these will help determine the correct intervals for the solution.

Use a graph chart to solve for the inequality. Express the solution set in interval notation. Given inequality: (x^2 - 9) / (x - 3) <= 0.

This webpage explains how to solve the rational inequality (x^2 - 9) / (x - 3) <= 0 using graph charts. Learn key concepts in algebra, including factoring, simplification, and interval notation. Suitable for Grades 9-11 students.

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