The problem states:

• $UV = 6$
• $UW = 5x$
• $VW = 4x - 1$

You are tasked with finding the numerical length of $VW$.

Since $V$ is on the line segment $UW$, the following equation must hold:

$UV + VW = UW$

Substitute the given values:

$6 + (4x - 1) = 5x$

Simplify this equation:

$6 + 4x - 1 = 5x$ $5 + 4x = 5x$

Now, solve for $x$:

$5 = 5x - 4x$ $5 = x$

Now that we know $x = 5$, substitute this value back into the expression for $VW$:

$VW = 4x - 1 = 4(5) - 1 = 20 - 1 = 19$

So, the numerical length of $VW$ is 19.

Would you like more details or further clarifications? Here are some related questions:

1. How do you solve for $x$ in an algebraic equation?
2. Can you explain why we add $UV$ and $VW$ to get $UW$?
3. What would change if the values of $UV$, $VW$, or $UW$ were different?
4. How can we verify the solution for $x$?
5. What is the significance of $V$ being a point on line segment $UW$?

Tip: Always check if the given variables are consistent with the problem conditions after solving.