Math Problem Statement

K is the midpoint of JL. If JK = 4x and KL = 9x - 6, what is JK?

Solution

To solve this problem, let's analyze the given information.

Since KK is the midpoint of JLJL, the segments JKJK and KLKL must be equal in length. The problem states that:

  • JK=4xJK = 4x
  • KL=9x6KL = 9x - 6

Since JK=KLJK = KL (because KK is the midpoint), we can set up the following equation: 4x=9x64x = 9x - 6

Solving for xx

  1. Subtract 4x4x from both sides: 0=5x60 = 5x - 6
  2. Add 66 to both sides: 6=5x6 = 5x
  3. Divide by 55 to isolate xx: x=65x = \frac{6}{5}

Finding JKJK

Now that we have x=65x = \frac{6}{5}, substitute this value back into the expression for JKJK: JK=4x=4×65=245JK = 4x = 4 \times \frac{6}{5} = \frac{24}{5}

Thus, JK=245JK = \frac{24}{5}, which is already in its simplest form as a proper fraction.

Final Answer

JK=245JK = \frac{24}{5}

Would you like more details on any part of this solution, or do you have any questions?

Related Questions

  1. What if KK wasn’t the midpoint? How would that affect the answer?
  2. Can you convert 245\frac{24}{5} into a mixed number?
  3. How would you solve this if JKJK and KLKL had different units?
  4. What happens if we use decimals instead of fractions in this problem?
  5. How could we verify that KK is indeed the midpoint with this value?

Tip

When you know a point is a midpoint, setting the two segments equal simplifies the setup for finding unknown values.

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Math Problem Analysis

Mathematical Concepts

Algebra
Equations
Midpoint

Formulas

Setting equal lengths for midpoint: JK = KL

Theorems

Midpoint theorem

Suitable Grade Level

Grades 7-8