Just a question I don't understand, anything will help.
Given a triangle DEF with a segment GH parallel to EF. Find the length of FG given the following information. DG=x-4, FG=2x, DH=x-7, HE=x+3. Point H is located somewhere on line segment ED.
Here's a rough pic of the situation
x - 7 x - 4
x + 3 2x
A segment parallel to a base of a triangle splits the sides in equal proportions
DH / HE = DG / GF so we have
[ x - 7 ] / [ x + 3 ] = [ x - 4 ] / [ 2x ] cross-multiply
2x (x - 7) = (x + 3) ( x - 4) simplify
2x^2 - 14x = x^2 - x - 12 rearrange as
x^2 - 13x + 12 = 0
(x - 12) ( x - 1) = 0
Setting to 0 and solving for x produces x = 12 or x = 1
Reject the second soution since it makes (x - 7) and (x - 4) negative lengths
So x = 12 ⇒ FG = 2(12) = 24
Check that this works 5 / 15 = 8 / 24 true !!!