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The compound inequality given is:

\[
x \leq 2 \quad \text{or} \quad x \leq 5
\]

Since it is an "or" condition, the solution set will include all \( x \) values that satisfy either one or both of the inequalities. Let's analyze the two conditions:

- \( x \leq 2 \) means all values of \( x \) that are less than or equal to 2.
- \( x \leq 5 \) means all values of \( x \) that are less than or equal to 5.

Since \( x \leq 5 \) already covers \( x \leq 2 \) (because every number less than or equal to 2 is also less than or equal to 5), the overall solution set is just \( x \leq 5 \).

### Interval Notation:
The solution set in interval form is:
\[
(-\infty, 5]
\]

### Graph Form:
On a number line, this would be a shaded region extending from \( -\infty \) to 5, with a closed circle at \( x = 5 \) to indicate that 5 is included in the solution.

So the correct choice is **A**, and the interval form is \((- \infty, 5]\).

Do you need any additional details or clarification? Here are some related questions:

1. How do you graph compound inequalities?
2. What does a closed circle on a number line represent?
3. What are the differences between "and" and "or" conditions in inequalities?
4. How would the solution change if the inequalities were combined with "and" instead of "or"?
5. What is the difference between interval notation and set notation?

**Tip:** In an "or" inequality, the solution set includes all values that satisfy either inequality, so you take the union of both intervals.

For the following compound inequality, give the solution set in both interval and graph forms. x ≤ 2 or x ≤ 5.

Learn how to solve the compound inequality x ≤ 2 or x ≤ 5 and find the solution set in interval notation and graph form. This problem explores inequalities and the union of intervals, suitable for students in Grades 7-9.

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