Question

1. if rt = 36, find the value of x.

6x + 1 \t x + 7.
r \t s \t t
6x+1=x+7

Explanation:

Step1: Analyze the segment sum

From the diagram, \( RT = RS + ST \). Given \( RS = 6x + 1 \), \( ST = x + 7 \), and \( RT = 36 \), so \( (6x + 1)+(x + 7)=36 \).

Step2: Simplify the equation

Combine like terms: \( 6x + x + 1 + 7 = 36 \), which becomes \( 7x + 8 = 36 \).

Step3: Solve for \( x \)

Subtract 8 from both sides: \( 7x = 36 - 8 = 28 \). Then divide by 7: \( x=\frac{28}{7}=4 \).

Answer:

\( x = 4 \)