Math Problem Statement
Solution
To solve this problem, we need to use the information given about the segment , which is divided into two parts, and .
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Given Information:
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Setting Up the Equation: Since is the entire length of the segment from to , we can write: Substituting the values we have:
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Solving for : Combine like terms on the left side: Add 3 to both sides to isolate the term with : Divide by 9:
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Finding : Now that we know , substitute it back into the expression for :
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Answer: The length of is .
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:
- How would the solution change if had a different length?
- What if were defined by a different expression, such as ?
- Can you explain how the equation for was set up from the initial problem?
- What does it mean for an answer to be a proper fraction, mixed number, or integer?
- 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