Question

the information to find the missing value.14. $pq = 2x + 1$ and $qr = 5x - 44$; find $pq$.

Explanation:

Step1: Set up the equation

Assume \(PQ = QR\) (since no other information about the relationship between \(PQ\) and \(QR\) is given, this is a common assumption in such problems where they are equal). So, \(2x + 1=5x - 44\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(1 = 3x-44\).
Add \(44\) to both sides: \(45 = 3x\).
Divide both sides by \(3\): \(x = 15\).

Step3: Find \(PQ\)

Substitute \(x = 15\) into \(PQ=2x + 1\). So, \(PQ=2\times15 + 1=30 + 1\).

Answer:

\(31\)