Given the lengths of the segments [tex]\( FG = 2 \)[/tex] units, [tex]\( FI = 7 \)[/tex] units, and [tex]\( HI = 1 \)[/tex] unit, we need to find the length of [tex]\( GH \)[/tex].
We can use the information to solve for [tex]\( GH \)[/tex]. According to the triangle inequality theorem, the length of [tex]\( FI \)[/tex] can be represented as a sum of the lengths of the smaller segments on the line, such as [tex]\( FG \)[/tex], [tex]\( GH \)[/tex], and [tex]\( HI \)[/tex]. Thus, we have:
[tex]\[ FI = FG + GH + HI \][/tex]
Plugging in the given lengths:
[tex]\[ 7 = 2 + GH + 1 \][/tex]
We can now solve for [tex]\( GH \)[/tex] by isolating it on one side of the equation. First, combine the known lengths on one side:
[tex]\[ 7 = 3 + GH \][/tex]
Next, subtract 3 from both sides of the equation to solve for [tex]\( GH \)[/tex]:
[tex]\[ 7 - 3 = GH \][/tex]
[tex]\[ GH = 4 \][/tex]
Therefore, the length of [tex]\( GH \)[/tex] is [tex]\( 4 \)[/tex] units.
So, the correct answer is [tex]\( \boxed{4} \)[/tex] units.
