Final answer:
The numerical length of line segment EF can be found by solving the equation (2x + 4) + 8 = 4x - 10 for x, which gives us x = 11. Plugging x back into EF's expression yields EF = 26 units.
Step-by-step explanation:
The student is trying to find the numerical length of line segment EF when given the lengths of segments FG and EG, and that point F is on line segment EG. Since FG and EF are parts of the whole segment EG, the lengths of FG and EF added together equal the total length of EG. We are given the following: FG = 8, EF = 2x + 4, and EG = 4x - 10. By setting up the equation (2x + 4) + 8 = 4x - 10, we can solve for x and then use the value of x to find the length of line segment EF.
Step 1: Write the equation based on the segments
EF + FG = EG which translates to (2x + 4) + 8 = 4x - 10.
Step 2: Combine like terms
2x + 12 = 4x - 10
Step 3: Solve for x
Subtract 2x from both sides: 12 = 2x - 10
Add 10 to both sides: 22 = 2x
Divide by 2: x = 11
Step 4: Calculate the length of EF
EF = 2x + 4, so EF = 2(11) + 4 = 22 + 4 = 26.
The numerical length of line segment EF is 26 units.