Final answer:
The length of segment EF is found to be 6 meters by setting up the equation EF + FG = EG and solving for x first before substituting it back into the expression for EF.
Step-by-step explanation:
To determine the numerical length of segment EF, we first need to recognize that EF + FG = EG because F is a point on line segment EG. Given the information EF = 2x - 2, FG = 5x + 1, and EG = 5x + 7, we can set up the following equation:
EF + FG = EG
(2x - 2) + (5x + 1) = (5x + 7)
Now, let's simplify and solve for x:
2x - 2 + 5x + 1 = 5x + 7
7x - 1 = 5x + 7
By subtracting 5x from both sides, we get:
2x - 1 = 7
2x = 8
x = 4
Having found the value of x, we can now substitute it back into the expression for EF:
EF = 2x - 2
EF = 2(4) - 2
EF = 8 - 2
EF = 6
Therefore, the length of segment EF is 6 meters.