Point J is on line segment start overline, I, K, end overline*IK*. Given I, K, equals, 5, x, comma*IK*=5*x*, I, J, equals, 4, comma*IJ*=4, and J, K, equals, 4, x, comma*JK*=4*x*, determine the numerical length of start overline, I, K, end overline, .*IK*.

We are given that:

- Point \( J \) is on line segment \( IK \).
- The length of \( IK \) is \( 5x \), i.e., \( IK = 5x \).
- The length of \( IJ \) is 4, i.e., \( IJ = 4 \).
- The length of \( JK \) is \( 4x \), i.e., \( JK = 4x \).

We know that \( IJ + JK = IK \). Substituting the given lengths into this equation:

\[
IJ + JK = IK
\]

\[
4 + 4x = 5x
\]

Now, solve for \( x \):

\[
4 = 5x - 4x
\]

\[
4 = x
\]

So, \( x = 4 \).

Now that we have the value of \( x \), we can determine the numerical length of \( IK \), which is given by \( IK = 5x \):

\[
IK = 5 \times 4 = 20
\]

Thus, the length of \( IK \) is \( 20 \).

### Do you want further details or have any questions?

Here are some related questions:
1. What would be the length of \( IK \) if \( IJ \) were doubled?
2. How would the equation change if \( JK \) were \( 6x \) instead of \( 4x \)?
3. What is the midpoint of \( IK \) if \( x = 4 \)?
4. If \( IJ \) were \( 5 \) and \( JK \) remained \( 4x \), what would \( x \) be?
5. Can we find the coordinates of \( I, J, K \) given \( x \)?

**Tip:** When solving for a variable, always isolate it on one side of the equation to simplify the problem.

Point J is on line segment IK. Given IK = 5x, IJ = 4, and JK = 4x, determine the numerical length of IK.

Learn how to solve for the length of line segment IK, where IK = 5x, IJ = 4, and JK = 4x. This problem involves algebra and the segment addition postulate, suitable for students in Grades 6-8.

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