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In this problem, we are asked to find the length of the segment \( LN \), which is composed of two sub-segments: \( LM \) and \( MN \).

### Given Information:
- The length of segment \( LM \) is \( x + 20 \).
- The length of segment \( MN \) is \( 5x - 4 \).

The total length of segment \( LN \) is the sum of these two parts:
\[
LN = LM + MN = (x + 20) + (5x - 4)
\]

Now, let's simplify the expression:
\[
LN = x + 20 + 5x - 4 = 6x + 16
\]

So, the length of \( LN \) is \( 6x + 16 \).

If more information is provided (like the value of \( x \)), we could calculate the exact value of \( LN \). Do you have the value for \( x \), or would you like further details on how to proceed?

### Additional Questions:
1. How would you solve for \( LN \) if you knew the total length of the line?
2. Can you determine the value of \( x \) if another condition or equation is provided?
3. What happens to the length of \( LN \) if \( x \) increases or decreases?
4. How do you verify that your calculation of \( LN \) is correct?
5. How would you interpret the result in a real-world context if this was a physical distance?

**Tip:** When solving equations involving line segments, always break them into parts and sum them step by step to avoid missing any details.

Find the length of LN, given LM = x + 20 and MN = 5x - 4.

Learn how to solve for LN by summing the lengths of LM and MN, where LM = x + 20 and MN = 5x - 4. This problem covers key algebraic concepts, including linear equations and the segment addition postulate. Suitable for students in Grades 6-8.

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