The problem in the image shows a rectangular shape with segment $DF$, where you are asked to find the length of segment $EF$.

The information provided is:

• $DF = 9x - 39$
• $EF = 3x + 10$
• $D$ is located at 47 on the number line.

I will now solve for the value of $EF$ based on this information.

The complete distance $DF$ can be written as the sum of two parts, namely the segment $DE$ and $EF$. From the image, it appears $DF = 47$, and we have the equations for both segments involving $x$.

So, we can set up the equation: $DF = DE + EF$

Next, let me calculate $EF$.The length of segment $EF$ is $\frac{116}{3}$, or approximately 38.67 units.

Would you like more details or have any questions about this? Here are some related questions to consider:

1. How do you calculate the length of $DF$ given different values of $x$?
2. What happens to $EF$ if the equation for $DF$ changes?
3. Can you solve for the value of $x$ in terms of $DF$ if the total length $DF$ is unknown?
4. How would you approach this problem if the segments were positioned differently in the rectangle?
5. What is the significance of solving such linear equations in geometry?

Tip: In problems involving variables and equations, it's helpful to set up clear relationships between known and unknown quantities first, and then solve step-by-step.