Answer:
[tex]FG = 7[/tex]
Step-by-step explanation:
Given
[tex]EG = 5x + 7[/tex]
[tex]EF = 5x[/tex]
[tex]FG = 2x - 7[/tex]
Required
Determine the length of FG
Since, F is on segment EG, then
[tex]EG= EF + FG[/tex]
Substitute values for EG, EF and FG
[tex]5x + 7 = 5x + 2x - 7[/tex]
Collect Like Terms
[tex]5x - 5x - 2x = -7 - 7[/tex]
[tex]- 2x = -14[/tex]
Solve for x
[tex]x = -14/-2[/tex]
[tex]x = 7[/tex]
Substitute 7 for x in [tex]FG = 2x - 7[/tex]
[tex]FG = 2 * 7- 7[/tex]
[tex]FG = 14- 7[/tex]
[tex]FG = 7[/tex]
