well... the segment FG = 4x + 3, the segment GH = 7x - 12, now, the
segment FH = FG + GH, those two fellows added up, and we know that FG and GH are both equal halves because G is the midpoint.
thus, FG = GH
or
[tex]\bf 4x+3=7x-12\implies 3+12=7x-4x\implies 15=3x
\\\\\\
\cfrac{15}{3}=x\implies \boxed{5=x}\\\\
-------------------------------\\\\
thus\qquad
\begin{cases}
\overline{FG}=4x+3\\
4(5)+3\\
23\\
------\\
\overline{GH}=7x-12\\
7(5)-12\\
23
\end{cases}\impliedby equal\ halves
\\\\\\
\overline{FH}=23+23\implies \overline{FH}=46\implies 6y-2=46
\\\\\\
6y=46+2\implies y=\cfrac{48}{6}[/tex]
and fairly sure, you know how much that is.
