Question

if g is the midpoint of \\( \overline{fh} \\), find fg.
\\( 11x - 7 \\) \\( 3x + 9 \\)
\\( f \\) \\( g \\) \\( h \\)
put the number only.

Explanation:

Step1: Set FG = GH (midpoint property)

Since G is the midpoint of \( \overline{FH} \), \( FG = GH \). So, \( 11x - 7 = 3x + 9 \).

Step2: Solve for x

Subtract \( 3x \) from both sides: \( 11x - 3x - 7 = 9 \) → \( 8x - 7 = 9 \).
Add 7 to both sides: \( 8x = 9 + 7 \) → \( 8x = 16 \).
Divide by 8: \( x = \frac{16}{8} = 2 \).

Step3: Find FG

Substitute \( x = 2 \) into \( FG = 11x - 7 \):
\( FG = 11(2) - 7 = 22 - 7 = 15 \).

Answer:

15