Answer:
x = 10 , EF = 8 , FG = 15. 
Step-by-step explanation: 
 
Given : If EF = 2x – 12, FG = 3x – 15, and EG = 23. 
 
To find : find the values of x, EF, and FG. 
 
Solution : We have given EF = 2x – 12, FG = 3x – 15, and EG = 23. 
 
Let the line E ___F___G. 
 
Here F is the mid point of EG . ( mid point divide the line EG cut the line EG in two equal parts) 
 
We can say EF = FG. 
 
EF + FG = EG -------(1) 
 
Plug tha values EF = 2x -12 and FG = 3x - 15 , EG = 23 in equation (1). 
 
2x - 12 + 3x -15 = 23 . 
 
On combine like terms 
 
2x + 3x -12 -15 = 23 . 
 
5x - 27 + 23 . 
 
on adding both side by 27. 
 
5x = 23 +27. 
 
5x = 50 . 
 
On dividing both sides by 5. 
 
x = 10. 
 
Them, EF = 2 (10) -12 
 
 20 -12 
 
 EF = 8 
 
FG = 3 (10) -15 . 
 
FG = 30 -15 . 
 
FG = 15. 
 
EG = 5 +18 = 23 . 
 
Therefore, x = 10 , EF = 8 , FG = 15.