Question

f is a point on segment \\( \overline{eg} \\). if \\( ef = 5x \\), \\( fg = x + 10 \\), and \\( eg = 9x - 8 \\), what is \\( fg \\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( F \) is on \( \overline{EG} \), we have \( EF + FG = EG \). Substituting the given expressions: \( 5x + (x + 10) = 9x - 8 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 6x + 10 = 9x - 8 \). Subtract \( 6x \) from both sides: \( 10 = 3x - 8 \). Add 8 to both sides: \( 18 = 3x \). Divide by 3: \( x = 6 \).

Step3: Find \( FG \)

Substitute \( x = 6 \) into \( FG = x + 10 \): \( FG = 6 + 10 = 16 \).

Answer:

\( 16 \)