Answer:
6 units
Step-by-step explanation:
The segment addition postulate states that if we are given two points on a line segment, E and G, a third point F lies on the line segment EG if and only if the distances between the points meet the requirements of the equation
EF + FG = EG (*)
In your case,
EF = 2x-2 units,
FG = 5x+1 units,
EG = 5x+7 units.
Substitute it into the equality (*)
[tex](2x-2)+(5x+1)=5x+7\\ \\2x-2+5x+1=5x+7\\ \\2x+5x-5x=7+2-1\\ \\2x=8\\ \\x=4[/tex]
Now, the length EF is equal to
[tex]EF=2\cdot 4-2=8-2=6\ units[/tex]
