The question provided is:

Point C is on line segment $BD$. Given $BD = 2x$, $CD = 8$, and $BC = x$, determine the numerical length of $BD$.

Solution:

1. From the problem, we know that:

   • $BD = 2x$
   • $CD = 8$
   • $BC = x$

2. We also know that $BD = BC + CD$. Using the given information:

$BD = BC + CD$ $2x = x + 8$

3. Now solve for $x$:

$2x - x = 8$ $x = 8$

4. Since $BD = 2x$, substitute $x = 8$:

$BD = 2(8) = 16$

Final Answer:

The numerical length of $BD$ is 16 units.

Would you like any further details or clarifications on the steps?

Here are 5 related questions for practice:

1. If $BD = 3x$, $CD = 10$, and $BC = x$, what is the length of $BD$?
2. How would the problem change if $CD$ were given as a variable instead of a constant?
3. Can you express $BD$ as a function of $CD$ and $BC$?
4. If $BC$ and $CD$ were swapped in terms of their lengths, what would the solution be?
5. What happens if the midpoint of $BD$ is also specified?

Tip: In problems involving line segments, always remember that the total length of the segment is the sum of its parts.