https://file.aiquickdraw.com/mathbot/file/1725939122510ljv2v73f.jpg

The problem in the image asks you to find the value of segment \( AD \) in a parallelogram, where the length of side \( AD \) is given as \( x + 6 \), and the length of side \( BC \) is given as \( 8x - 386 \).

### Step-by-Step Solution:

Since this is a parallelogram, opposite sides are equal. Therefore, the length of segment \( AD \) is equal to the length of segment \( BC \).

1. Set \( AD = BC \):
\[
x + 6 = 8x - 386
\]

2. Solve for \( x \):

\[
x + 6 = 8x - 386
\]

Subtract \( x \) from both sides:

\[
6 = 7x - 386
\]

Add 386 to both sides:

\[
6 + 386 = 7x
\]

\[
392 = 7x
\]

Divide both sides by 7:

\[
x = 56
\]

3. Find the length of segment \( AD \):

Substitute \( x = 56 \) into \( AD = x + 6 \):

\[
AD = 56 + 6 = 62
\]

Thus, the value of the segment \( AD \) is 62 units.

Let me know if you'd like further details or have any other questions!

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### Related Questions:
1. How do you find the area of a parallelogram?
2. What properties of a parallelogram help solve problems like this?
3. How can you verify if a quadrilateral is a parallelogram using algebra?
4. What are the conditions for the diagonals of a parallelogram?
5. How do you solve equations involving multiple variables in geometry?

### Tip:
Always remember that opposite sides of a parallelogram are equal, and opposite angles are congruent. This property helps solve many algebraic problems involving parallelograms.

This is a parallelogram. Find the value of the segment AD.

Learn how to solve for segment AD in a parallelogram where AD = x + 6 and BC = 8x - 386. This problem focuses on algebraic techniques and the properties of parallelograms. Suitable for students in Grades 8-10.

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