If JK = 10, KL = 6x, and JL = 11x, what is KL?

To solve for \( KL \), we can use the Triangle Inequality Theorem. According to this problem, points \( J \), \( K \), and \( L \) form a straight line, meaning \( JK + KL = JL \).

Given:
- \( JK = 10 \),
- \( KL = 6x \),
- \( JL = 11x \).

Using the equation \( JK + KL = JL \), we substitute the values:

\[
10 + 6x = 11x
\]

Now, solve for \( x \):

\[
10 = 11x - 6x
\]
\[
10 = 5x
\]
\[
x = 2
\]

Now that we have \( x = 2 \), substitute it back into \( KL = 6x \):

\[
KL = 6(2) = 12
\]

Thus, \( KL = 12 \).

Would you like more details on this solution? Here are five related questions to expand your understanding:

1. What is the Triangle Inequality Theorem and when is it used?
2. If \( JL \) was given as \( 15x \), how would that change the problem?
3. What would happen if \( KL = 7x \) instead of \( 6x \)?
4. How do we determine if the points form a straight line versus a triangle?
5. What are the properties of a straight line in geometry?

**Tip**: Always double-check the relationships between the line segments to confirm whether they form a straight line or a triangle.

Learn how to solve for KL in a line segment problem where JK = 10, KL = 6x, and JL = 11x. This problem demonstrates the use of the Triangle Inequality Theorem and basic algebraic manipulation to find the value of KL. Suitable for students in Grades 6-8.

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