Question

solve the following problem.
if r is the midpoint of \\(\overline{qs}\\), find qs.

answer attempt 1 out of 2
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Explanation:

Step1: Use midpoint property

Since \( R \) is the midpoint of \( \overline{QS} \), then \( QR = RS \). So we set up the equation:
\( 5x - 3 = 21 - x \)

Step2: Solve for \( x \)

Add \( x \) to both sides:
\( 5x + x - 3 = 21 - x + x \)
\( 6x - 3 = 21 \)

Add 3 to both sides:
\( 6x - 3 + 3 = 21 + 3 \)
\( 6x = 24 \)

Divide both sides by 6:
\( x = \frac{24}{6} = 4 \)

Step3: Find \( QR \) and \( RS \)

Substitute \( x = 4 \) into \( QR = 5x - 3 \):
\( QR = 5(4) - 3 = 20 - 3 = 17 \)

Since \( QR = RS \), \( RS = 17 \)

Step4: Find \( QS \)

\( QS = QR + RS = 17 + 17 = 34 \)

Answer:

34