Question

1. q is between p and r

pq = 5x - 10
qr = 2x + 3
pr = 42
solve for x and find pq.
x = ____
pq = ____

Explanation:

Step1: Apply segment addition postulate

Since \( Q \) is between \( P \) and \( R \), we have \( PQ + QR = PR \). Substituting the given expressions: \( (5x - 10) + (2x + 3) = 42 \).

Step2: Simplify the equation

Combine like terms: \( 5x - 10 + 2x + 3 = 42 \) becomes \( 7x - 7 = 42 \).

Step3: Solve for \( x \)

Add 7 to both sides: \( 7x = 42 + 7 = 49 \). Then divide by 7: \( x = \frac{49}{7} = 7 \).

Step4: Find \( PQ \)

Substitute \( x = 7 \) into \( PQ = 5x - 10 \): \( PQ = 5(7) - 10 = 35 - 10 = 25 \).

Answer:

\( x = 7 \), \( PQ = 25 \)