Question

9 fill in the blank 1 point
if r is the midpoint of \\(\overline{qs}\\), find \\(qs\\).
\\(\boldsymbol{q}\\) --- \\(5x - 3\\) --- \\(\boldsymbol{r}\\) --- \\(21 - x\\) --- \\(\boldsymbol{s}\\)
\\(qs = \\) type your answer...

Explanation:

Step1: Set segments equal (midpoint)

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

Step2: Solve for \( x \)

Add \( x \) to both sides: \( 5x + x - 3 = 21 \), which simplifies to \( 6x - 3 = 21 \). Then add 3 to both sides: \( 6x = 21 + 3 = 24 \). Divide by 6: \( x = \frac{24}{6} = 4 \).

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

Substitute \( x = 4 \) into \( QR = 5x - 3 \): \( 5(4) - 3 = 20 - 3 = 17 \). Substitute into \( RS = 21 - x \): \( 21 - 4 = 17 \).

Step4: Calculate \( QS \)

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

Answer:

34