Question

f is a point on segment eg. if ef = 3x, fg = x + 9, and eg = 5(2x - 7), what is fg? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation (Segment Addition)

Since \( F \) is on \( EG \), we have \( EF + FG = EG \). Substituting the given expressions: \( 3x + (x + 9) = 12x - 7 \).

Step2: Simplify the left side

Combine like terms: \( 3x + x + 9 = 4x + 9 \). So the equation is \( 4x + 9 = 12x - 7 \).

Step3: Solve for \( x \)

Subtract \( 4x \) from both sides: \( 9 = 8x - 7 \). Then add 7 to both sides: \( 16 = 8x \). Divide by 8: \( x = 2 \).

Step4: Find \( FG \)

Substitute \( x = 2 \) into \( FG = x + 9 \): \( FG = 2 + 9 = 11 \).

Answer:

11