Point J is between H and K on line segment HK. Use the given information to solve for x. Also find the length of line segment JK.

HK = 20 HJ = 2x-2 JK = 7x+4

To solve for \( x \) and find the length of line segment \( JK \), we can use the given information:

- \( HK = 20 \)
- \( HJ = 2x - 2 \)
- \( JK = 7x + 4 \)

Since point \( J \) is between \( H \) and \( K \), the lengths of \( HJ \) and \( JK \) should add up to the total length of \( HK \). Therefore, we can write the equation:

\[
HJ + JK = HK
\]

Substituting the given expressions:

\[
(2x - 2) + (7x + 4) = 20
\]

Now, let's solve this equation for \( x \).

Simplify the equation:

\[
2x - 2 + 7x + 4 = 20
\]

Combine like terms:

\[
9x + 2 = 20
\]

Subtract 2 from both sides:

\[
9x = 18
\]

Divide by 9:

\[
x = 2
\]

Now that we have \( x = 2 \), we can find the length of \( JK \):

\[
JK = 7x + 4 = 7(2) + 4 = 14 + 4 = 18
\]

**Therefore, the length of line segment \( JK \) is 18 units.**

Would you like more details or have any questions? Here are some related questions to explore further:

1. What is the length of line segment \( HJ \) with the solved value of \( x \)?
2. If \( J \) were to be exactly halfway between \( H \) and \( K \), how would \( x \) change?
3. Can you find the coordinates of point \( J \) if \( H \) is at the origin?
4. How would the equation change if \( HK \) was not a straight line but a curve?
5. What would the equation be if \( J \) was outside the segment \( HK \)?

**Tip:** Always check your substituted values to verify the solution, ensuring there are no calculation errors.

Point J is between H and K on line segment HK. Use the given information to solve for x. Also find the length of line segment JK.

HK = 20, HJ = 2x-2, JK = 7x+4

Learn how to solve for x and find the length of line segment JK using given values of HK, HJ, and JK. This problem focuses on applying algebraic methods to solve linear equations and understanding the Segment Addition Postulate. Suitable for students in Grades 8-10.

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