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 = 26 HJ = 7x-2 JK = 3x+8

x =                         JK=

We are given the following information about the line segment \( HK \) with point \( J \) between \( H \) and \( K \):

- \( HK = 26 \)
- \( HJ = 7x - 2 \)
- \( JK = 3x + 8 \)

Since \( J \) is between \( H \) and \( K \), we can express \( HK \) as the sum of the lengths of \( HJ \) and \( JK \):
\[
HK = HJ + JK
\]
Substituting the given expressions:
\[
26 = (7x - 2) + (3x + 8)
\]
Now, combine like terms:
\[
26 = 7x - 2 + 3x + 8
\]
\[
26 = 10x + 6
\]
Next, solve for \( x \):
\[
26 - 6 = 10x
\]
\[
20 = 10x
\]
\[
x = 2
\]

Now that we have \( x = 2 \), we can substitute this value into the expression for \( JK \) to find its length:
\[
JK = 3x + 8 = 3(2) + 8 = 6 + 8 = 14
\]

Thus, the solutions are:
\[
x = 2
\]
\[
JK = 14
\]

Would you like more details on any step or do you have any questions?

Here are 5 related questions to expand on this problem:
1. What if \( JK \) was a different function of \( x \)? How would it affect the solution?
2. How would you solve the problem if \( HJ \) were expressed in terms of a different variable?
3. What is the length of \( HJ \) when \( x = 2 \)?
4. How would the solution change if \( J \) were not exactly between \( H \) and \( K \)?
5. Can you verify that the sum of \( HJ \) and \( JK \) equals \( HK \) with the calculated values?

**Tip:** Always check the sum of the segments after solving for \( x \) to ensure the solution satisfies the original equation!

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 = 26, HJ = 7x - 2, JK = 3x + 8

Learn how to solve for x and find the length of the line segment JK using the given equations: HK = 26, HJ = 7x - 2, and JK = 3x + 8. This problem explores algebraic manipulation and the segment addition postulate, suitable for students in Grades 7-9.

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