Question

if fg = 3x, gh = 9x - 5, and fh = 11x + 8, what is fg? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( FG + GH = FH \). Substitute the given expressions: \( 3x + (9x - 5) = 11x + 8 \).

Step2: Simplify left side

Combine like terms: \( 3x + 9x - 5 = 12x - 5 \). So the equation is \( 12x - 5 = 11x + 8 \).

Step3: Solve for x

Subtract \( 11x \) from both sides: \( 12x - 11x - 5 = 11x - 11x + 8 \), which simplifies to \( x - 5 = 8 \). Then add 5 to both sides: \( x - 5 + 5 = 8 + 5 \), so \( x = 13 \).

Step4: Find FG

Since \( FG = 3x \), substitute \( x = 13 \): \( FG = 3\times13 = 39 \).

Answer:

39