Point K is on line segment JL. Given JL = 4x+2, KL = 5x-6, and JK = 3x, determine the numerical length of JK

We are given that point \( K \) is on line segment \( JL \), and the lengths of \( JL \), \( KL \), and \( JK \) are represented by the following expressions:

- \( JL = 4x + 2 \)
- \( KL = 5x - 6 \)
- \( JK = 3x \)

Since point \( K \) is on line segment \( JL \), we know that the total length of \( JL \) is the sum of the lengths of \( JK \) and \( KL \). Therefore, we can set up the equation:

\[
JK + KL = JL
\]

Substitute the given expressions for \( JK \), \( KL \), and \( JL \):

\[
3x + (5x - 6) = 4x + 2
\]

Now, solve for \( x \):

\[
3x + 5x - 6 = 4x + 2
\]
\[
8x - 6 = 4x + 2
\]
\[
8x - 4x = 2 + 6
\]
\[
4x = 8
\]
\[
x = 2
\]

Now that we know \( x = 2 \), we can find the length of \( JK \). Substitute \( x = 2 \) into the expression for \( JK \):

\[
JK = 3x = 3(2) = 6
\]

Thus, the length of \( JK \) is 6 units.

Would you like further clarification or more details?

Here are 5 related questions to expand your understanding:
1. How would the problem change if the length of \( KL \) were negative?
2. What is the total length of \( JL \) when \( x = 2 \)?
3. Can you find the length of \( KL \) with \( x = 2 \)?
4. What would happen if the value of \( x \) were fractional?
5. How can we use geometric concepts to prove that point \( K \) divides \( JL \) into two segments?

**Tip:** Always check the relationship between the parts and the whole in geometry problems involving segments.

Point K is on line segment JL. Given JL = 4x + 2, KL = 5x - 6, and JK = 3x, determine the numerical length of JK.

Learn how to solve a geometry problem involving line segments and algebraic expressions. This step-by-step solution explains how to find the length of JK on line segment JL using the segment addition formula. Suitable for students in Grades 8-10.

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