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The given compound inequality is:

\[
x \leq -3 \quad \text{or} \quad x > 0
\]

We are asked to determine whether \( x = 1 \) is part of the solution set.

### Checking the conditions:
- For \( x = 1 \), check the first inequality \( x \leq -3 \). Clearly, \( 1 \) is not less than or equal to \( -3 \), so this inequality is **false**.
- Next, check the second inequality \( x > 0 \). Since \( 1 > 0 \), this inequality is **true**.

### Conclusion:
- Since at least one of the inequalities in the compound statement is true (specifically, \( x > 0 \)), \( x = 1 \) **is** in the solution set.

The correct answer is **Yes**.

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

1. What is the solution set of the inequality \( x \leq -3 \) or \( x > 0 \)?
2. Can you graph the solution of the compound inequality on a number line?
3. What would happen if the inequalities were connected by "and" instead of "or"?
4. How do you solve a compound inequality involving "and" instead of "or"?
5. What other values of \( x \) would satisfy both inequalities?

**Tip:** In a compound inequality with "or," only one of the conditions needs to be true for a value to be part of the solution set.

Determine whether 1 is in the solution set of the compound inequality below: x <= -3 or x > 0.

Learn how to determine if 1 is part of the solution set for the compound inequality x <= -3 or x > 0. This problem involves understanding inequalities and compound 'or' inequalities. Suitable for students in Grades 7-10.

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