Problem Analysis:

The problem involves a line segment divided into two parts:

• $JK = 4x$
• $KL = x + 1$
• The total length $JL = 6$.

The goal is to find $JK$, and the answer must be simplified as a proper fraction, mixed number, or integer.

Step 1: Set Up the Equation

Since $JL = JK + KL$: $4x + (x + 1) = 6$

Step 2: Simplify the Equation

Combine like terms: $4x + x + 1 = 6 \quad \Rightarrow \quad 5x + 1 = 6$

Step 3: Solve for $x$

Subtract 1 from both sides: $5x = 5$

Divide by 5: $x = 1$

Step 4: Find $JK$

Substitute $x = 1$ into $JK = 4x$: $JK = 4(1) = 4$

Final Answer:

$JK = 4$

Let me know if you’d like further explanation or have additional questions!

5 Related Questions:

1. What is the value of $KL$ in this problem?
2. How would the result change if $JL$ were 12 instead of 6?
3. What are the steps to solve for $KL$ after finding $x$?
4. How would you represent $JK$ and $KL$ if $JL$ was given in terms of a variable?
5. What is the significance of verifying your solution in such problems?

Tip:

Always double-check your equation setup to ensure all parts of the line segment are correctly represented.