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In this problem, the binary search algorithm is used to search for the number 7 in the list \[1, 3, 4, 6, 7, 10, 11, 15\]. The binary search works by repeatedly dividing the search interval in half and comparing the target value to the middle element of the interval.

The typical variables for binary search are:
- \(i\): the lower index of the search range.
- \(j\): the upper index of the search range.
- \(x\): the middle index, calculated as \(\left\lfloor \frac{i + j}{2} \right\rfloor\).

### Initial values:
1. **Initial value of \(i\)**: The index of the first element in the list, which is \(i = 0\).
2. **Initial value of \(j\)**: The index of the last element in the list, which is \(j = 7\) (since there are 8 elements, and indexing starts at 0).
3. **Initial value of \(x\)**: The middle index of the list, calculated as:

\[
x = \left\lfloor \frac{i + j}{2} \right\rfloor = \left\lfloor \frac{0 + 7}{2} \right\rfloor = \left\lfloor 3.5 \right\rfloor = 3
\]

### Recap:
- Initial value of \(i = 0\)
- Initial value of \(j = 7\)
- Initial value of \(x = 3\)

Let me know if you'd like further details or explanations.

Here are some related questions to expand on this topic:
1. How does binary search improve the search time compared to linear search?
2. What is the time complexity of binary search and how is it derived?
3. What happens if the target value is not in the list? How does binary search terminate?
4. How would binary search behave with an unsorted list?
5. How can binary search be adapted for searching in a descending order list?

**Tip**: Binary search requires the list to be sorted in advance for it to function correctly.

When using the binary search algorithm to search for 7 in the following list: 1, 3, 4, 6, 7, 10, 11, 15; What are the initial values for i, j, and x?

Discover how to find the initial values for i, j, and x when performing a binary search for the number 7 in the sorted list [1, 3, 4, 6, 7, 10, 11, 15]. This problem highlights key concepts in binary search and logarithmic efficiency, suitable for high school students.

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