https://file.aiquickdraw.com/mathbot/file/17265919233942hjqo66b.jpg

The problem presented in the image asks to find the length of segment \( QS \), where point \( R \) lies between \( Q \) and \( S \). The algebraic expressions for the segments are as follows:

- \( QR = 2x + 31 \)
- \( RS = 3x + 26 \)
- \( QS = 9x + 21 \)

We know from segment addition that:

\[
QR + RS = QS
\]

Substitute the given expressions into this equation:

\[
(2x + 31) + (3x + 26) = 9x + 21
\]

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

\[
5x + 57 = 9x + 21
\]

Subtract \( 5x \) from both sides:

\[
57 = 4x + 21
\]

Subtract 21 from both sides:

\[
36 = 4x
\]

Divide by 4:

\[
x = 9
\]

Now substitute \( x = 9 \) back into the expression for \( QS \):

\[
QS = 9(9) + 21 = 81 + 21 = 102
\]

Thus, the length of \( QS \) is 102 units.

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. What would happen if the expression for \( QS \) were changed?
2. How can we verify if \( R \) is the midpoint of \( QS \)?
3. How do segment addition problems apply to real-world situations?
4. How would the equation change if the positions of \( Q \), \( R \), and \( S \) were swapped?
5. Can you find the lengths of segments \( QR \) and \( RS \) with \( x = 9 \)?

**Tip:** Always substitute the value of \( x \) back into all given expressions to verify the accuracy of your solution.

Find the length of QS where QR = 2x + 31, RS = 3x + 26, and QS = 9x + 21.

This problem asks you to find the length of QS where QR = 2x + 31, RS = 3x + 26, and QS = 9x + 21. Learn how to apply the Segment Addition Postulate and solve for x using algebraic methods. This solution is ideal 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