Question

in the figure, ( pr = 15x - 11 ) and ( pq = 3x + 6 ). find ( qr ) in terms of ( x ).
a) ( 18x - 5 )
b) ( 18x - 17 )
c) ( 12x - 17 )
d) ( 12x - 5 )

Explanation:

Step1: Recall segment addition postulate

For collinear points \( P \), \( Q \), \( R \) (where \( Q \) is between \( P \) and \( R \)), we have \( PR = PQ + QR \). So, we can solve for \( QR \) by rearranging the formula: \( QR = PR - PQ \).

Step2: Substitute the given expressions

We know \( PR = 15x - 11 \) and \( PQ = 3x + 6 \). Substitute these into the formula for \( QR \):
\( QR=(15x - 11)-(3x + 6) \)

Step3: Simplify the expression

First, distribute the negative sign: \( QR = 15x - 11 - 3x - 6 \). Then, combine like terms: \( (15x - 3x)+(- 11 - 6)=12x-17 \).

Answer:

C) \( 12x - 17 \)