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The inequality presented is:

\[
x \leq -6 \quad \text{or} \quad x > 9
\]

This is a compound inequality. We are looking for solutions that satisfy either \( x \leq -6 \) **or** \( x > 9 \). The solutions for this inequality are all values of \( x \) that are either less than or equal to -6, or greater than 9.

Looking at the answer options provided, the correct answer is:

- **\( x \leq -6 \quad \text{or} \quad x > 9 \)**

This is the first option in the list.

Would you like more details or have any questions? Here are some related questions for further practice:

1. How do you solve compound inequalities involving "and"?
2. What is the difference between "and" and "or" in inequalities?
3. How do you represent the solution of inequalities on a number line?
4. What happens if there are no solutions to a compound inequality?
5. Can compound inequalities have overlapping solutions?

**Tip:** Remember that "or" in inequalities means that you are looking for values that satisfy at least one of the conditions. This is different from "and," which requires both conditions to be satisfied simultaneously.

Learn how to solve the compound inequality x ≤ -6 or x > 9, which involves understanding inequalities and the use of 'or' in compound inequalities. Suitable for students in Grades 9-11.

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