Question

if ef = 17x, fg = 14, and eg = 20x + 8, what is ef? diagram of e---f---g with ef=17x, fg=14, eg=20x+8 simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( EG = EF + FG \). Substitute the given expressions: \( 20x + 8 = 17x + 14 \).

Step2: Solve for \( x \)

Subtract \( 17x \) from both sides: \( 20x - 17x + 8 = 14 \), which simplifies to \( 3x + 8 = 14 \). Then subtract 8 from both sides: \( 3x = 14 - 8 = 6 \). Divide both sides by 3: \( x = \frac{6}{3} = 2 \).

Step3: Find \( EF \)

Since \( EF = 17x \), substitute \( x = 2 \): \( EF = 17 \times 2 = 34 \).

Answer:

34