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In this problem, line \( m \) is a **perpendicular bisector**. A perpendicular bisector has two key properties:
1. It intersects the segment it bisects at a right angle.
2. It divides the segment into two equal parts.

In the triangle shown, line \( m \) bisects the segment between points \( A \) and \( B \). We know that segment \( AB \) is divided into two equal parts by line \( m \), which implies the following relationship between the two sides that are bisected:

\[
7x - 6 = 29
\]

Now, let's solve for \( x \):

\[
7x - 6 = 29
\]

Add 6 to both sides:

\[
7x = 35
\]

Now divide by 7:

\[
x = 5
\]

Thus, the value of \( x \) is \( 5 \).

### Would you like more details or further explanations?

Here are 5 related questions for further exploration:
1. What are the properties of perpendicular bisectors in triangles?
2. How does the perpendicular bisector theorem apply to isosceles triangles?
3. How do you determine the midpoint of a segment in coordinate geometry?
4. What is the significance of the perpendicular bisector in the circumcenter of a triangle?
5. How would this problem change if line \( m \) were not a perpendicular bisector?

**Tip:** Always check if the line in question is a perpendicular bisector to apply the concept of equal segments properly!

If line m is a perpendicular bisector, what is x? Given that one side is 29 and the other is 7x - 6.

Learn how to solve for x in a geometric problem where line m is a perpendicular bisector. This problem explores the application of algebra and the perpendicular bisector theorem in geometry, suitable for students in Grades 8-10.

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