Question

if qr = 18, rs = 6x + 9, and qs = 11x + 7, what is qs? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( QS = QR + RS \). Substitute the given expressions: \( 11x + 7 = 18 + 6x + 9 \).

Step2: Simplify and solve for \( x \)

Simplify the right side: \( 11x + 7 = 6x + 27 \). Subtract \( 6x \) from both sides: \( 5x + 7 = 27 \). Subtract 7 from both sides: \( 5x = 20 \). Divide by 5: \( x = 4 \).

Step3: Find \( QS \)

Substitute \( x = 4 \) into \( QS = 11x + 7 \): \( QS = 11(4) + 7 = 44 + 7 = 51 \).

Answer:

51