Question

if ef = 2x, fg = x - 2, and eg = 2x + 16, what is ef?
diagram: e---f---g with ef labeled 2x, fg labeled x - 2, eg labeled 2x + 16
simplify your answer and write it as a proper fraction, mixed number, or integer.
submit button

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( EG = EF + FG \). Substitute the given expressions: \( 2x + 16 = 2x + (x - 2) \).

Step2: Simplify and solve for \( x \)

Simplify the right - hand side: \( 2x + 16 = 3x - 2 \).
Subtract \( 2x \) from both sides: \( 16=x - 2 \).
Add 2 to both sides: \( x=16 + 2=18 \).

Step3: Find the length of \( EF \)

Since \( EF = 2x \) and \( x = 18 \), then \( EF=2\times18 = 36 \).

Answer:

36