Question

find df
d •——• e ——• f
de: ( x + 7 ), ef: ( 7 ), df: ( 4x + 2 )
( df = \boxed{?} ) (with 14 visible on the right)

Explanation:

Step1: Set up the equation

From the segment addition postulate, \( DF = DE + EF \). So, \( 4x + 2=(x + 7)+7 \).

Step2: Solve for \( x \)

Simplify the right side: \( 4x + 2=x + 14 \).
Subtract \( x \) from both sides: \( 3x + 2 = 14 \).
Subtract 2 from both sides: \( 3x=12 \).
Divide by 3: \( x = 4 \).

Step3: Find \( DF \)

Substitute \( x = 4 \) into \( DF = 4x + 2 \).
\( DF=4(4)+2=16 + 2=18 \).

Answer:

18