Q is between P and R. PQ = 2w º 3, QR =4+ w, and PR = 34.
Find the value of w. Then find the lengths of PQÆand QRÆ. 

We are given the following conditions:

- \( P \), \( Q \), and \( R \) are points on a line with \( Q \) between \( P \) and \( R \).
- \( PQ = 2w - 3 \)
- \( QR = 4 + w \)
- \( PR = 34 \)

Since \( Q \) is between \( P \) and \( R \), we know that:

\[
PR = PQ + QR
\]

Substitute the given expressions for \( PQ \) and \( QR \):

\[
34 = (2w - 3) + (4 + w)
\]

Now, solve for \( w \):

\[
34 = 2w - 3 + 4 + w
\]
\[
34 = 3w + 1
\]
\[
34 - 1 = 3w
\]
\[
33 = 3w
\]
\[
w = 11
\]

### Finding the lengths of \( PQ \) and \( QR \):

1. \( PQ = 2w - 3 = 2(11) - 3 = 22 - 3 = 19 \)
2. \( QR = 4 + w = 4 + 11 = 15 \)

Thus, the value of \( w \) is \( 11 \), and the lengths are:

- \( PQ = 19 \)
- \( QR = 15 \)

Would you like further details or clarification?

Here are 5 related questions:

1. How do you solve linear equations with one variable?
2. How does the concept of points on a line help in geometry?
3. What are some real-life applications of solving for unknowns in linear expressions?
4. How would this problem change if \( QR \) was given as \( 4 - w \) instead of \( 4 + w \)?
5. What happens if \( Q \) is not between \( P \) and \( R \)?

**Tip:** Always verify your solution by substituting the found values back into the original equation to check for consistency.

Q is between P and R. PQ = 2w - 3, QR = 4 + w, and PR = 34. Find the value of w. Then find the lengths of PQ and QR.

Learn how to solve for the variable w in the problem where Q is between P and R, with segment lengths PQ = 2w - 3 and QR = 4 + w, and PR = 34. This problem demonstrates algebraic manipulation and the Segment Addition Postulate, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation