https://file.aiquickdraw.com/mathbot/file/1726196175575b3m975tl.jpg

We are given that \( M \) is the midpoint of segment \( ST \), and we have the expressions for the segments:

- \( SM = 5x - 4 \)
- \( MT = 3x + 6 \)

Since \( M \) is the midpoint of \( ST \), the lengths of \( SM \) and \( MT \) are equal. Therefore, we can set the two expressions equal to each other:

\[
5x - 4 = 3x + 6
\]

Now, let's solve for \( x \):

\[
5x - 3x = 6 + 4
\]

\[
2x = 10
\]

\[
x = 5
\]

Now that we have the value of \( x \), we can substitute it back into the expression for \( SM \) to find its value:

\[
SM = 5x - 4 = 5(5) - 4 = 25 - 4 = 21
\]

Thus, the value of \( x \) is \( 5 \) and the length of \( SM \) is \( 21 \).

Would you like any further details or explanations?

Here are 5 related questions to explore further:

1. What is the length of the entire segment \( ST \) using the given values?
2. How do you find the midpoint of a line segment in the coordinate plane?
3. Can this problem be solved graphically, and if so, how?
4. What is the geometric significance of the midpoint in a line segment?
5. How do you solve a system of equations in a case where multiple segments are involved?

**Tip:** When dealing with midpoint problems, setting the two segment expressions equal is key to finding unknown values.

Suppose M is the midpoint of ST. If SM = 5x - 4 and MT = 3x + 6, find the value of x and SM.

Learn how to solve for x and the segment SM using the midpoint theorem in the algebraic expression SM = 5x - 4 and MT = 3x + 6. This solution is suitable for students in Grades 7-9 and involves setting the two segments equal since M is the midpoint.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation