Question

15 if rt = 36, use the segment addition postulate to solve for x.
diagram: points r, s, t with segment rs labeled ( 6x + 1 ) and segment st labeled ( x + 7 )
a 4
b 5
c 3
d 6

Explanation:

Step1: Apply Segment Addition Postulate

By the Segment Addition Postulate, \( RT = RS + ST \). Given \( RS = 6x + 1 \), \( ST = x + 7 \), and \( RT = 36 \), we substitute these into the equation:
\( 6x + 1 + x + 7 = 36 \)

Step2: Combine Like Terms

Combine the \( x \)-terms and constant terms:
\( (6x + x) + (1 + 7) = 36 \)
\( 7x + 8 = 36 \)

Step3: Solve for \( x \)

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

Answer:

A. 4