https://file.aiquickdraw.com/mathbot/file/1726545516364mlis86mb.jpg

To solve the problem from the image:

### Given:
- \( R \) is the midpoint of segment \( QS \).
- The distance between \( Q \) and \( R \) is \( 5x - 3 \).
- The distance between \( R \) and \( S \) is \( 21 - x \).

Since \( R \) is the midpoint of \( QS \), the distance from \( Q \) to \( R \) should be equal to the distance from \( R \) to \( S \).

Thus, we set the two expressions equal to each other:
\[
5x - 3 = 21 - x
\]

### Solving the equation:

1. Add \( x \) to both sides:
   \[
   5x + x - 3 = 21
   \]
   \[
   6x - 3 = 21
   \]

2. Add 3 to both sides:
   \[
   6x = 24
   \]

3. Divide both sides by 6:
   \[
   x = 4
   \]

Now, substitute \( x = 4 \) into either expression to find the length of \( QR \) (which is also the same as \( RS \)):

- \( QR = 5x - 3 = 5(4) - 3 = 20 - 3 = 17 \)
- \( RS = 21 - x = 21 - 4 = 17 \)

Thus, the total length of \( QS \) is:
\[
QS = QR + RS = 17 + 17 = 34
\]

### Final Answer:
The length of \( QS \) is \( 34 \).

---

Would you like more details or clarifications? 

Here are some related questions:
1. What does it mean for a point to be the midpoint of a segment?
2. How do you solve linear equations with variables on both sides?
3. Can a midpoint formula be applied in 2D or 3D space?
4. What happens if the midpoint isn’t exactly halfway between two points?
5. How would you verify your solution in a different way?

**Tip:** When solving linear equations, always isolate the variable step by step to avoid errors.

Learn how to solve for the length of QS when R is the midpoint. This step-by-step solution covers how to set up and solve linear equations using the midpoint theorem. Ideal 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