https://file.aiquickdraw.com/mathbot/file/172727253928087hm5h3y.jpg

We are given that:

- \( LN = 2x - 5 \)
- \( MN = x - 1 \)
- \( LM = 3 \)

Since point M is on the line segment \( LN \), we know that:

\[
LM + MN = LN
\]

Substitute the given values:

\[
3 + (x - 1) = 2x - 5
\]

Simplify the equation:

\[
3 + x - 1 = 2x - 5
\]
\[
x + 2 = 2x - 5
\]

Now, solve for \( x \):

\[
2 + 5 = 2x - x
\]
\[
7 = x
\]

Now that we know \( x = 7 \), substitute it back into the equation for \( LN \):

\[
LN = 2(7) - 5 = 14 - 5 = 9
\]

Thus, the numerical length of \( LN \) is **9**.

Would you like further clarification or details on this solution?

### Related Questions:
1. How would the problem change if \( MN = x + 1 \)?
2. Can the solution be verified by calculating \( MN \) after finding \( x \)?
3. What are the possible values of \( LN \) if \( LM \) is increased?
4. How can we express the length of \( MN \) in terms of \( LM \) alone?
5. What happens if point M is not exactly between L and N but outside the segment?

### Tip:
When solving for a variable in an equation, always check your solution by substituting it back into the original equation to ensure consistency.

Point M is on line segment LN. Given LN = 2x - 5, MN = x - 1, and LM = 3, determine the numerical length of LN.

Learn how to determine the length of the line segment LN given the algebraic expressions for LN, MN, and the fixed length of LM. The solution involves algebraic manipulation and the segment addition postulate. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation