Question

if ef = 7x + 15, fg = 8x, and eg = 17x - 11, what is ef?
diagram: e---f---g with ef labeled 7x + 15, fg labeled 8x, eg labeled 17x - 11
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( EF + FG = EG \). Substitute the given expressions: \( (7x + 15) + 8x = 17x - 11 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 15x + 15 = 17x - 11 \). Subtract \( 15x \) from both sides: \( 15 = 2x - 11 \). Add 11 to both sides: \( 26 = 2x \). Divide by 2: \( x = 13 \).

Step3: Find \( EF \)

Substitute \( x = 13 \) into \( EF = 7x + 15 \): \( EF = 7(13) + 15 = 91 + 15 = 106 \).

Answer:

106