Question

pr = 36 find x
p \tq \tr
x + 1 \t2x + 11

Explanation:

Step1: Analyze the segment addition

The length of \( PR \) is the sum of \( PQ \) and \( QR \). So, \( PQ + QR = PR \).
Given \( PQ = x + 1 \), \( QR = 2x + 11 \), and \( PR = 36 \), we substitute these into the equation: \( (x + 1) + (2x + 11) = 36 \).

Step2: Simplify the left - hand side

Combine like terms: \( x+2x + 1+11=36 \), which simplifies to \( 3x+12 = 36 \).

Step3: Solve for x

Subtract 12 from both sides: \( 3x+12 - 12=36 - 12 \), so \( 3x = 24 \).
Divide both sides by 3: \( \frac{3x}{3}=\frac{24}{3} \), which gives \( x = 8 \).

Answer:

\( x = 8 \)