https://file.aiquickdraw.com/mathbot/file/17262035038508kzbdwip.jpg

The problem states that \( R \) is the midpoint of the segment \( QS \), and you are asked to find the length of \( QS \).

Given:
- \( QR = 5x - 3 \)
- \( RS = 21 - x \)
  
Since \( R \) is the midpoint of \( QS \), the distances \( QR \) and \( RS \) must be equal. Therefore, we can set up the equation:
\[
5x - 3 = 21 - x
\]

### Solving for \( x \):
1. Add \( x \) to both sides to move the variable to one side:
\[
5x + x - 3 = 21
\]
\[
6x - 3 = 21
\]

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

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

### Finding \( QS \):
Now, substitute \( x = 4 \) back into the expressions for \( QR \) and \( RS \):

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

Thus, \( QS = QR + RS = 17 + 17 = 34 \).

So, the length of \( QS \) is 34 units.

Would you like more details or have any other questions?

### Here are 5 related questions to expand on this concept:
1. How do you find the midpoint of a line segment given two points?
2. How do you determine if a point divides a segment into a specific ratio?
3. How can you apply the distance formula in a coordinate plane for line segments?
4. What happens when the expressions for \( QR \) and \( RS \) are quadratic?
5. How do you find the coordinates of the midpoint in three-dimensional space?

### Tip:
When solving for the midpoint of a segment, always ensure that both sub-segments are equal in length.

If R is the midpoint of QS, find QS. QR = 5x - 3, RS = 21 - x.

Learn how to find the total length of a line segment QS when the midpoint is given. This problem involves solving linear equations, using algebraic techniques, and applying the midpoint theorem. Suitable for students in 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