https://file.aiquickdraw.com/mathbot/file/17298711260162dw1wixs.jpg

To solve this, we need to use the information given in the problem. 

1. The total length of \( KM \) is 5.
2. The segments are given as:
   - \( KL = 3x - 4 \)
   - \( LM = x + 1 \)

Since \( KL + LM = KM \), we can set up the equation:

\[
(3x - 4) + (x + 1) = 5
\]

### Step-by-step solution:
1. Combine like terms on the left-hand side:
\[
4x - 3 = 5
\]

2. Add 3 to both sides:
\[
4x = 8
\]

3. Divide by 4 to solve for \( x \):
\[
x = 2
\]

### Now, substitute \( x = 2 \) into the expression for \( KL \):
\[
KL = 3x - 4 = 3(2) - 4 = 6 - 4 = 2
\]

So, \( KL = 2 \).

Would you like more details or have any questions? 

Here are 5 related questions to explore:
1. If \( LM \) were doubled, how would that affect \( KL \)?
2. What would \( KL \) be if \( KM \) were increased to 7?
3. How does solving for \( x \) affect the rest of the segment lengths?
4. Can you explain how to verify your answer by adding \( KL \) and \( LM \) values?
5. What would happen if one segment was unknown but \( KM \) was still given?

**Tip:** When solving for variables in geometry problems, always check if the total distance is consistent with the sum of the parts.

If KL = 3x - 4, LM = x + 1, and KM = 5, what is KL?

Learn how to find the length of KL using algebra and the Segment Addition Postulate. Given KL = 3x - 4, LM = x + 1, and KM = 5, solve for x and determine the segment length. This problem is ideal for students in Grades 7-9 working on linear equations and geometry concepts.

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