https://file.aiquickdraw.com/mathbot/file/1727227267884na55k93k.jpg

The image shows a geometry problem where three points \( J \), \( K \), and \( L \) are collinear, and the lengths of segments \( JL \), \( KL \), and \( JK \) are given in terms of a variable \( x \). Here is what we know:

- \( JL = 26 \)
- \( KL = 3x + 7 \)
- \( JK = 8x + 8 \)

Since the points \( J \), \( K \), and \( L \) are collinear, the sum of the lengths of \( JK \) and \( KL \) must equal \( JL \). This gives the equation:

\[
JK + KL = JL
\]

Substituting the given expressions:

\[
(8x + 8) + (3x + 7) = 26
\]

Now, let's solve this equation.

### Simplifying:

\[
8x + 3x + 8 + 7 = 26
\]
\[
11x + 15 = 26
\]

### Solving for \( x \):

\[
11x = 26 - 15
\]
\[
11x = 11
\]
\[
x = 1
\]

Now, substitute \( x = 1 \) into the expression for \( KL \):

\[
KL = 3(1) + 7 = 3 + 7 = 10
\]

Thus, the length of \( KL \) is \( \boxed{10} \).

---

Would you like more details on any step or further clarification?

Here are 5 related questions to expand your understanding:
1. How would the solution change if \( KL \) were expressed differently?
2. Can you find the length of \( JK \) after solving for \( x \)?
3. What method would you use if this problem involved angles instead of distances?
4. How would you approach solving if \( JL \) was not given as a specific number?
5. How does solving this problem help in understanding segment addition postulate?

**Tip:** Always check if the variables in a geometry problem represent direct lengths, angles, or other quantities to apply the correct equations.

If JL = 26, KL = 3x + 7, and JK = 8x + 8, find KL.

Learn how to find the length of KL using algebraic expressions and the Segment Addition Postulate. The problem involves solving the equation 8x + 8 + 3x + 7 = 26. Suitable for students in Grades 8-10.

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