Question

g is the midpoint of \\(\overline{fh}\\). if \\(fg = 2x\\) and \\(gh = 3x - 2\\), what is \\(gh\\)?
f
g
h
diagram of f---g---h
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( G \) is the midpoint of \( \overline{FH} \), \( FG = GH \). So we set up the equation \( 2x = 3x - 2 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 0 = x - 2 \). Then add 2 to both sides: \( x = 2 \).

Step3: Find \( GH \)

Substitute \( x = 2 \) into \( GH = 3x - 2 \). So \( GH = 3(2) - 2 = 6 - 2 = 4 \).

Answer:

\( 4 \)