Question

question point r is on line segment \\(\overline{qs}\\). given \\(qs = 2x + 2\\), \\(qr = 3x - 5\\), and \\(rs = 5x - 5\\), determine the numerical length of \\(\overline{qr}\\). answer attempt 1 out of 2 qr = \\(\boxed{}\\) submit answer watch video show examples

Explanation:

Step1: Use segment addition postulate

Since \( R \) is on \( \overline{QS} \), we have \( QS = QR + RS \). Substitute the given expressions: \( 2x + 2=(3x - 5)+(5x - 5) \)

Step2: Simplify and solve for \( x \)

Simplify the right - hand side: \( 2x + 2 = 3x-5 + 5x-5=8x - 10 \)
Subtract \( 2x \) from both sides: \( 2=6x - 10 \)
Add 10 to both sides: \( 12 = 6x \)
Divide both sides by 6: \( x = 2 \)

Step3: Find the length of \( QR \)

Substitute \( x = 2 \) into the expression for \( QR \): \( QR=3x - 5=3\times2-5 = 6 - 5=1 \)

Answer:

\( 1 \)