We are given that point $Q$ is on line segment $PR$, and the following distances:

• $PQ = x$
• $QR = 6$
• $PR = 2x - 10$

Since $Q$ is a point on the segment $PR$, the total length of $PR$ should be equal to the sum of $PQ$ and $QR$. Therefore, we can write the equation:

$PQ + QR = PR$

Substitute the given values into this equation:

$x + 6 = 2x - 10$

Now, solve for $x$:

$6 + 10 = 2x - x$ $16 = x$

So, the length of $PQ$ is $\boxed{16}$.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. If $QR$ was $8$ instead of $6$, what would the new value of $PQ$ be?
2. What is the total length of $PR$ if $PQ = 16$ and $QR = 6$?
3. If $PR = 50$ and $QR = 20$, find $PQ$ using the same method.
4. How would the problem change if $PR$ was given as $3x - 12$ instead of $2x - 10$?
5. What is the relationship between the lengths of segments in any general line segment division?

Tip: When solving geometry problems with line segments, always remember that the total length of a segment is the sum of its parts.