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The compound inequality is \( x \leq 2 \) or \( x > 5 \). To interpret this, we need to understand:

1. \( x \leq 2 \) means that the solution includes all values less than or equal to 2, which would be shown with a closed circle at 2 and a line extending to the left.
2. \( x > 5 \) means all values greater than 5, which would be shown with an open circle at 5 and a line extending to the right.

Now let's analyze the options:

- **Option 1**: This shows a line extending left from 2 (with a closed circle at 2) and a line extending right from 5 (with an open circle at 5), which matches the given inequality.
- **Option 2**: This is incorrect because both circles are filled, suggesting \( x \geq 5 \), not \( x > 5 \).
- **Option 3**: This is incorrect because the circle at 5 is closed, which implies \( x \geq 5 \) instead of \( x > 5 \).
- **Option 4**: This is incorrect because it represents the solution for \( 2 \leq x \leq 5 \), which is a different range.
- **Option 5**: This is incorrect because there is no line extending from 5, and it misrepresents the inequality.
- **Option 6**: This is incorrect because both ends have closed circles, which would mean \( x \geq 5 \).

### The correct answer is **Option 1**.

Would you like more details or have any further questions? Here are 5 related questions to explore this further:

1. How do you graph compound inequalities that use "and" instead of "or"?
2. What is the difference between open and closed circles on a number line?
3. How do you write inequalities that include absolute values?
4. What types of problems require compound inequalities?
5. Can you convert compound inequalities into interval notation?

**Tip:** Remember that closed circles on a graph represent values included in the solution, while open circles indicate values that are excluded.

Which graph matches the compound inequality x ≤ 2 or x > 5?

Learn how to graph the compound inequality x ≤ 2 or x > 5. This problem involves graphing two inequalities on a number line, with a closed circle at 2 and an open circle at 5. Suitable for Grades 7-9, this problem reinforces the key concepts of inequalities and number line representations.

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