If KL = 2x, LM = x + 3, andKM = 12, what is LM?

Given the problem where \( KL = 2x \), \( LM = x + 3 \), and \( KM = 12 \), we are to find the value of \( LM \).

The points \( K \), \( L \), and \( M \) lie on a straight line, so:

\[
KL + LM = KM
\]

Substituting the given values:

\[
2x + (x + 3) = 12
\]

Simplifying the equation:

\[
3x + 3 = 12
\]

Subtract 3 from both sides:

\[
3x = 9
\]

Now, divide both sides by 3:

\[
x = 3
\]

Finally, substitute \( x = 3 \) into the expression for \( LM \):

\[
LM = x + 3 = 3 + 3 = 6
\]

So, \( LM = 6 \).

Would you like more details or have any questions? 

Here are some related questions for further practice:

1. If \( KL = 3x - 2 \) and \( KM = 20 \), what is \( LM \)?
2. If \( KL = 5x \) and \( LM = x + 5 \), find \( KM \) when \( x = 2 \).
3. If \( KL = 4x + 1 \) and \( LM = x - 2 \), find \( KM \) in terms of \( x \).
4. What would \( LM \) be if \( KM \) were 18 instead of 12?
5. If \( KL = x \), \( LM = x + 4 \), and \( KM = 20 \), solve for \( x \).

**Tip:** When solving equations involving segments on a line, always ensure the sum of the segments equals the total length, which helps in setting up your equation correctly.

Learn how to solve a line segment problem involving KL = 2x, LM = x + 3, and KM = 12. Understand the concept of linear equations and their application in determining segment lengths on a straight line. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation