Math Problem Statement
If KL = 10x − 19, LM = 1, and KM = 5x − 8, what is KM?
10x − 19 K 1 L M 5x −
Solution
Given the information, we can use the relationship between the segments KL, LM, and KM to solve for and find the length of KM.
Step 1: Set up the equation
The total length of segment is equal to the sum of the lengths of segments and : We are given the following:
Using the equation :
Step 2: Simplify the equation
Simplify the right-hand side:
Step 3: Solve for
Now, subtract from both sides to get:
Add 18 to both sides:
Divide by 5:
Step 4: Find
Now that we know , substitute it back into the expression for :
So, .
Would you like more details or have any questions?
Related Questions:
- What would the value of be if ?
- How do you solve similar problems involving segment addition postulates?
- Can the values of and change, and how would that affect ?
- What are some real-world applications of segment addition postulates?
- How do you verify your results in problems involving algebraic expressions?
Tip:
Always double-check your algebraic manipulations, especially when combining like terms or moving variables across the equation!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Segment Addition Postulate
Formulas
KM = KL + LM
KL = 10x - 19
LM = 1
KM = 5x - 8
Theorems
Segment Addition Postulate
Suitable Grade Level
Grades 8-10
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