Answer: The required value of x is 9.
Step-by-step explanation: Given that point E is between the points D and F.
Also, DE = x - 4, EF = 2x + 5 and DF = 4x - 8.
We are to find the value of x.
Since the point E lies between the points D and F, so we must have
[tex]DE+EF=DF\\\\\Rightarrow (x-4)+(2x+5)=4x-8\\\\\Rightarrow 3x+1=4x-8\\\\\Rightarrow 4x-3x=1+8\\\\\Rightarrow x=9.[/tex]
Thus, the required value of x is 9.
