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 is the midpoint of , the segments and must be equal in length. The problem states that:
Since (because is the midpoint), we can set up the following equation:
Solving for
- Subtract from both sides:
- Add to both sides:
- Divide by to isolate :
Finding
Now that we have , substitute this value back into the expression for :
Thus, , which is already in its simplest form as a proper fraction.
Final Answer
Would you like more details on any part of this solution, or do you have any questions?
Related Questions
- What if wasn’t the midpoint? How would that affect the answer?
- Can you convert into a mixed number?
- How would you solve this if and had different units?
- What happens if we use decimals instead of fractions in this problem?
- How could we verify that 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