*KL* = *x* + 3

,

*LM* = 2*x*

, and

*KM* = 6

, what is *LM*?

We are given the following equations:

1. \( KL = x + 3 \)
2. \( LM = 2x \)
3. \( KM = 6 \)

The segment \( KL + LM = KM \), since \( KM \) is the total length made up of \( KL \) and \( LM \).

So, we can write:

\[
KL + LM = KM
\]

Substitute the given values:

\[
(x + 3) + 2x = 6
\]

Simplify and solve for \( x \):

\[
3x + 3 = 6
\]

Subtract 3 from both sides:

\[
3x = 3
\]

Divide both sides by 3:

\[
x = 1
\]

Now, substitute \( x = 1 \) into the equation for \( LM \):

\[
LM = 2x = 2(1) = 2
\]

Thus, \( LM = 2 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we solve for \( KL \) after finding \( x \)?
2. What if \( KM \) had a different value? How would that affect \( LM \)?
3. How do we know that \( KL + LM = KM \) is a valid equation?
4. Can we graph the values of \( x \), \( KL \), and \( LM \)?
5. What if \( LM \) was a function of \( x^2 \)? How would the equation change?

**Tip:** When solving equations, always verify if the sum of parts equals the total length or value.

KL = x + 3, LM = 2x, and KM = 6, what is LM?

Discover how to solve for LM given KL = x + 3, LM = 2x, and KM = 6. This solution walks through key algebraic steps, using linear equations and the Segment Addition Postulate. Perfect for students in Grades 6-8.

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