Question

1. pq = 3x + 3. qr = 4x + 4. rs = 5x + 15. qs = 100. solve for x. find pq, qr, and rs.

Explanation:

Step1: Set up the equation for QS

From the number line, \( QS = QR + RS \). Given \( QR = 4x + 4 \), \( RS = 5x + 15 \), and \( QS = 100 \), we have the equation:
\( (4x + 4) + (5x + 15) = 100 \)

Step2: Combine like terms

Combine the \( x \)-terms and the constant terms:
\( 4x + 5x + 4 + 15 = 100 \)
\( 9x + 19 = 100 \)

Step3: Solve for \( x \)

Subtract 19 from both sides:
\( 9x = 100 - 19 \)
\( 9x = 81 \)
Divide both sides by 9:
\( x = \frac{81}{9} = 9 \)

Step4: Find \( PQ \)

Substitute \( x = 9 \) into \( PQ = 3x + 3 \):
\( PQ = 3(9) + 3 = 27 + 3 = 30 \)

Step5: Find \( QR \)

Substitute \( x = 9 \) into \( QR = 4x + 4 \):
\( QR = 4(9) + 4 = 36 + 4 = 40 \)

Step6: Find \( RS \)

Substitute \( x = 9 \) into \( RS = 5x + 15 \):
\( RS = 5(9) + 15 = 45 + 15 = 60 \)

Answer:

\( x = 9 \), \( PQ = 30 \), \( QR = 40 \), \( RS = 60 \)