Math Problem Statement

If JK = 2x, KL = 7x - 3, and JL = 6, what is JK? Simplify your answer and write it as a proper fraction, mixed number, or integer.

Solution

To solve this problem, we need to use the information given about the segment JLJL, which is divided into two parts, JKJK and KLKL.

  1. Given Information:

    • JK=2xJK = 2x
    • KL=7x3KL = 7x - 3
    • JL=6JL = 6
  2. Setting Up the Equation: Since JLJL is the entire length of the segment from JJ to LL, we can write: JK+KL=JLJK + KL = JL Substituting the values we have: 2x+(7x3)=62x + (7x - 3) = 6

  3. Solving for xx: Combine like terms on the left side: 9x3=69x - 3 = 6 Add 3 to both sides to isolate the term with xx: 9x=99x = 9 Divide by 9: x=1x = 1

  4. Finding JKJK: Now that we know x=1x = 1, substitute it back into the expression for JKJK: JK=2x=2×1=2JK = 2x = 2 \times 1 = 2

  5. Answer: The length of JKJK is 2\boxed{2}.

Would you like a detailed explanation on any of these steps, or do you have any further questions?

Here are some related questions to explore this topic further:

  1. How would the solution change if JLJL had a different length?
  2. What if KLKL were defined by a different expression, such as 5x25x - 2?
  3. Can you explain how the equation for xx was set up from the initial problem?
  4. What does it mean for an answer to be a proper fraction, mixed number, or integer?
  5. How can we verify if our answer is correct?

Tip: When working with line segments in algebra problems, it's useful to set up an equation that represents the total length as a sum of its parts. This helps in organizing and solving for unknown variables.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Sum of segment parts (JK + KL = JL)
Solving linear equations

Theorems

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Suitable Grade Level

Grade 8