Let's solve the problem step by step.

Problem Description

We are given:

• $UW = 9x - 39$
• $VW = 40 - 4x$

From the diagram, it is clear that $U, V, W$ lie on a straight line, and $UW = UV + VW$. Therefore, we can write the equation:

$UV + VW = UW$

Step 1: Solve for $UV$

From the diagram, $UV$ is the segment from $U$ to $V$, and since $UW = UV + VW$, we can rewrite $UV$ as:

$UV = UW - VW$

Substitute the expressions for $UW$ and $VW$:

$UV = (9x - 39) - (40 - 4x)$

Simplify:

$UV = 9x - 39 - 40 + 4x$ $UV = 13x - 79$

Step 2: Solve for $x$

Now, the problem may also involve solving for $x$. Let’s check if the diagram implies equality or specific conditions on the segments. Would you like me to elaborate further based! Setting eqlationLet's continue by solving for $x$ based on the given problem.

Step 2: Combine the Information

From the problem and diagram, we know that: $UW = VW$ because it seems to imply equal segments based on the text. So:

$9x - 39 = 40 - 4x$

Step 3: Solve for $x$

Rearrange the equation: $9x + 4x = 40 + 39$ $13x = 79$

Solve for $x$: $x = \frac{79}{13} = 6.08 \text{ (approximately)}.$

Final Answer:

$x \approx 6.08$

Would you like me to clarify the steps, or verify further? 😊

Here are 5 related questions for practice:

1. What is the length of $VW$ if $x = 6.08$?
2. What is the total length of $UW$ in this scenario?
3. If $UV = 13x - 79$, what is $UV$'s value when $x = 6.08$?
4. How would the equation change if $UV + VW = 2UW$?
5. What happens if $VW$ is shorter than $UV$ by 5 units?

Tip: Always double-check how segment relationships are defined in problems to set up the equation correctly!