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The expression presented is:

\[
x \leq -1 \quad \text{or} \quad x > 3
\]

This is a compound inequality, meaning the solution includes all values of \(x\) that satisfy either of the two conditions:

1. \( x \leq -1 \) means that \(x\) can be any number less than or equal to \(-1\).
2. \( x > 3 \) means that \(x\) can be any number greater than 3.

Since these conditions are connected by "or", the solution is the union of the two sets of values. So, the solution to this inequality can be written as:

\[
(-\infty, -1] \cup (3, \infty)
\]

This represents all real numbers that are either less than or equal to \(-1\) or greater than 3.

Would you like more details or have any specific questions?

Here are 5 related questions:
1. How would the solution set change if the "or" was replaced with "and"?
2. What is the difference between a union and an intersection of intervals?
3. How can this solution be represented on a number line?
4. How would this inequality change if both inequalities were strict (i.e., \(x < -1\) and \(x > 3\))?
5. Can you think of a real-world example where this type of compound inequality might be used?

**Tip:** When dealing with "or" in compound inequalities, remember that it expands the solution set, including all values that satisfy either condition.

Learn how to solve the compound inequality x ≤ -1 or x > 3. This problem involves key mathematical concepts such as inequalities and the union of sets. Suitable for students in Grades 8-10, it explains how to represent the solution using interval notation.

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