https://file.aiquickdraw.com/mathbot/file/1726082510397grg79jjb.jpg

The problem from the image reads:

**Given \( S \) is between \( T \) and \( U \), \( TS = SU \), \( TU = 5x - 4 \), and \( SU = x + 7 \). Find \( TS \).**

Let's solve this step by step.

### Step 1: Express \( TU \) in terms of \( TS \) and \( SU \)
Since \( S \) is between \( T \) and \( U \), and \( TS = SU \), we know:
\[
TU = TS + SU
\]
Given \( TS = SU \), we can substitute:
\[
TU = TS + TS = 2TS
\]
Therefore:
\[
TU = 2TS
\]

### Step 2: Use the given expressions for \( TU \) and \( SU \)
We're given:
\[
TU = 5x - 4
\]
and
\[
SU = x + 7
\]
Since \( TS = SU \), we can substitute \( TS = x + 7 \) into the equation \( TU = 2TS \):
\[
5x - 4 = 2(x + 7)
\]

### Step 3: Solve for \( x \)
Expanding the equation:
\[
5x - 4 = 2x + 14
\]
Now, subtract \( 2x \) from both sides:
\[
3x - 4 = 14
\]
Add 4 to both sides:
\[
3x = 18
\]
Finally, divide by 3:
\[
x = 6
\]

### Step 4: Find \( TS \)
Since \( TS = x + 7 \), substitute \( x = 6 \):
\[
TS = 6 + 7 = 13
\]

### Final Answer
The length of \( TS \) is **13**.

---

Would you like more details or have any questions? Here are some related questions:

1. How would you find \( TU \) after determining \( x \)?
2. What would happen if \( TS \) was not equal to \( SU \)?
3. Can this method be applied to other similar geometric problems?
4. How would you verify the solution by substituting back into the original equation?
5. What if \( S \) was not between \( T \) and \( U \), how would that change the problem?

**Tip:** When working with geometric problems involving segments, always double-check the relationships between the points and the given information before solving equations.

Given S is between T and U, TS = SU, TU = 5x - 4, and SU = x + 7. Find TS.

Learn how to find the length of TS using algebraic manipulation and the Segment Addition Postulate. This problem involves solving linear equations, specifically given TS = SU and expressions for TU and SU. 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