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The problem asks to express the following inequalities in interval notation:

\[
-8 < x \leq 9 \quad \text{or} \quad x > 15
\]

### 1. Interval for \(-8 < x \leq 9\):
This inequality means \(x\) is greater than \(-8\) but less than or equal to 9. In interval notation, this is written as:

\[
(-8, 9]
\]

### 2. Interval for \(x > 15\):
This means \(x\) is greater than 15, which corresponds to:

\[
(15, \infty)
\]

### 3. Combine the intervals:
Since the conditions are connected by "or", the solution is the union of these intervals:

\[
(-8, 9] \cup (15, \infty)
\]

Thus, the interval equivalent is:

\[
(-8, 9] \cup (15, \infty)
\]

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Would you like more details on how this was derived or have any other questions?

### Related Questions:
1. How do we represent a range with "and" instead of "or" in interval notation?
2. What is the difference between open and closed intervals in math?
3. How would the interval change if we had \(-8 \leq x < 9\)?
4. How can we graph these intervals on a number line?
5. What are other types of unions and intersections in set theory?

**Tip**: Remember that parentheses \(( \)) denote values that are not included, while brackets \([ ]\) denote values that are included.

Enter the interval equivalent to -8 < x ≤ 9 or x > 15.

Understand how to express the inequality -8 < x ≤ 9 or x > 15 in interval notation. This problem explores key algebraic concepts and interval representation, perfect for students in Grades 9-10.

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