Questions: Find KI.

Transcript text: Find $K I$.

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the length of segment $ KZ $ given the positions of points $ J $, $ K $, and $ L $ on a number line. The coordinates are given as follows:

$ J = x + 3 $
$ K = x $
$ L = x + 8 $ The total length from $ J $ to $ L $ is 7 units.

Step 2: Set Up the Equation

The distance from $ J $ to $ L $ is given by the absolute difference between their coordinates: \[ |(x + 8) - (x + 3)| = 7 \]

Step 3: Simplify the Equation

Simplify the expression inside the absolute value: \[ |(x + 8) - (x + 3)| = |8 - 3| = 5 \]

Step 4: Verify the Given Information

The given information states that the total length from $ J $ to $ L $ is 7 units, but our calculation shows 5 units. This suggests there might be an error in the problem setup or interpretation. Let's re-evaluate the problem.

Step 5: Re-evaluate the Problem

Given the coordinates:

$ J = x + 3 $
$ K = x $
$ L = x + 8 $

The distance from $ J $ to $ L $ should be: \[ |(x + 8) - (x + 3)| = |5| = 5 \]

Step 6: Correct the Interpretation

Since the problem states the total length from $ J $ to $ L $ is 7 units, we need to find the correct interpretation. Let's assume the problem meant to find the length of $ KZ $ where $ Z $ is another point on the line.

Step 7: Find $ KZ $

If $ Z $ is another point on the line, we need more information to find $ KZ $. Given the current information, we cannot determine $ KZ $ without additional details.

Final Answer

The problem setup seems to have inconsistencies. Based on the given information, the distance from $ J $ to $ L $ is 5 units, not 7. Therefore, we cannot accurately determine $ KZ $ without further clarification.

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