point j is on line segment IK. Given JK = 2x, IJ = 5x, and IK = x + 6, determine the numerical length of JK

To find the length of JK, let's analyze the given information:

1. \( J \) is on line segment \( IK \), which means \( IJ + JK = IK \).
2. The given lengths are:
   - \( JK = 2x \)
   - \( IJ = 5x \)
   - \( IK = x + 6 \)

Now, set up the equation according to the segment addition:

\[
IJ + JK = IK
\]

Substituting the given values:

\[
5x + 2x = x + 6
\]

Simplify the equation:

\[
7x = x + 6
\]

Subtract \( x \) from both sides:

\[
6x = 6
\]

Divide by 6:

\[
x = 1
\]

Now, plug the value of \( x \) back into \( JK \):

\[
JK = 2x = 2 \times 1 = 2
\]

Thus, the numerical length of \( JK \) is **2**.

Would you like any further details, or do you have any other questions? Here are some related questions:

1. What is the length of \( IJ \) given the value of \( x \)?
2. How would the solution change if \( IK \) was given as \( 2x + 6 \) instead?
3. How do you find the midpoint of a line segment given its endpoints?
4. How can you determine if a point is exactly at the midpoint of a line segment?
5. What are the properties of line segments in coordinate geometry?

**Tip:** Always double-check your equation setup when dealing with line segments and points on them to ensure accurate results.

Point J is on line segment IK. Given JK = 2x, IJ = 5x, and IK = x + 6, determine the numerical length of JK.

Determine the length of JK on a line segment where JK = 2x, IJ = 5x, and IK = x + 6. This algebra and geometry problem involves segment addition and solving linear equations, suitable for Grades 7-9.

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