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.