If QR = 10, RS = 2x, and QS = 7x, what is RS?

We are given:

- \( QR = 10 \)
- \( RS = 2x \)
- \( QS = 7x \)

Since QR and RS are segments of the line QS, we can use the fact that:

\[
QR + RS = QS
\]

Substituting the given values:

\[
10 + 2x = 7x
\]

Now solve for \( x \):

\[
10 = 7x - 2x
\]

\[
10 = 5x
\]

\[
x = 2
\]

Now that we know \( x = 2 \), we can substitute it back into the expression for \( RS \):

\[
RS = 2x = 2(2) = 4
\]

Thus, \( RS = 4 \).

Would you like more details or have any questions?

Here are 5 related questions:

1. If \( QS = 14 \), what would \( QR \) and \( RS \) be?
2. How would the result change if \( QR \) was increased by 5 units?
3. What would be the value of \( QS \) if \( RS = 3x \) and \( QR = 8 \)?
4. What happens to the segments if we set \( x = 3 \)?
5. How do we apply the concept of segments in coordinate geometry?

**Tip:** When solving equations with segments, make sure to add all segment parts to equal the total length.

Learn how to solve for RS using algebraic methods. Given QR = 10, RS = 2x, and QS = 7x, this problem demonstrates how to apply the segment addition theorem to find unknown variables. Suitable for students in Grades 6-8.

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