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The question asks to identify the segment bisector of segment \( JK \), where \( J \), \( M \), and \( K \) are points on a line segment. It also provides the following information:

- The distance from \( J \) to \( M \) is \( 7x + 5 \)
- The distance from \( M \) to \( K \) is \( 8x \)

Since a segment bisector divides a segment into two equal parts, we can set the two distances equal to each other:

\[
7x + 5 = 8x
\]

Let's solve this equation to find \( x \):

\[
7x + 5 = 8x
\]

Subtract \( 7x \) from both sides:

\[
5 = x
\]

Now that we know \( x = 5 \), we can calculate the lengths of \( JM \) and \( MK \):

1. \( JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40 \)
2. \( MK = 8x = 8(5) = 40 \)

Since both lengths are equal, point \( M \) is the midpoint of \( JK \), and it bisects the segment.

Thus, the correct answer is:

- **\( M \) is the segment bisector of \( JK \)**.

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

1. If \( JM = 3x + 10 \) and \( MK = 5x \), find the value of \( x \) for which \( M \) bisects \( JK \).
2. How do you determine if a point is the midpoint of a line segment?
3. What is the formula for calculating the midpoint between two points on a coordinate plane?
4. If the total length of segment \( JK \) is 60, what is the length of each bisected part if \( M \) is the midpoint?
5. In a triangle, how can you determine if a median also serves as the segment bisector?

**Tip:** A segment bisector always cuts a segment into two equal parts. The midpoint formula on a coordinate plane is a useful tool for verifying this division.

Identify the segment bisector of JK. The distances are JM = 7x + 5 and MK = 8x. The task is to find the point that bisects segment JK.

Learn how to solve for the segment bisector of segment JK with JM = 7x + 5 and MK = 8x. This problem involves solving linear equations and understanding the Segment Bisector Theorem. Ideal for students in Grades 6-8.

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