If KL = 10x − 19, LM = 1, and KM = 5x − 8, what is KM?

10x − 19
K
1
L
M
5x − 

Given the information, we can use the relationship between the segments KL, LM, and KM to solve for \( x \) and find the length of KM.

### Step 1: Set up the equation
The total length of segment \( KM \) is equal to the sum of the lengths of segments \( KL \) and \( LM \):
\[
KM = KL + LM
\]
We are given the following:
- \( KL = 10x - 19 \)
- \( LM = 1 \)
- \( KM = 5x - 8 \)

Using the equation \( KM = KL + LM \):
\[
5x - 8 = (10x - 19) + 1
\]

### Step 2: Simplify the equation
Simplify the right-hand side:
\[
5x - 8 = 10x - 19 + 1
\]
\[
5x - 8 = 10x - 18
\]

### Step 3: Solve for \( x \)
Now, subtract \( 5x \) from both sides to get:
\[
-8 = 5x - 18
\]

Add 18 to both sides:
\[
10 = 5x
\]

Divide by 5:
\[
x = 2
\]

### Step 4: Find \( KM \)
Now that we know \( x = 2 \), substitute it back into the expression for \( KM \):
\[
KM = 5x - 8 = 5(2) - 8 = 10 - 8 = 2
\]

So, \( KM = 2 \).

Would you like more details or have any questions?

### Related Questions:
1. What would the value of \( KL \) be if \( x = 2 \)?
2. How do you solve similar problems involving segment addition postulates?
3. Can the values of \( LM \) and \( KM \) change, and how would that affect \( x \)?
4. What are some real-world applications of segment addition postulates?
5. 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!

If KL = 10x − 19, LM = 1, and KM = 5x − 8, what is KM?

Solve the problem where KL = 10x − 19, LM = 1, and KM = 5x − 8. Learn how to apply the segment addition postulate and algebraic techniques to find the value of KM. Suitable for students in Grades 8-10.

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