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!

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.