You have the segment EG and point F in it.
Point F separates the segment in two smaller ones EF and FG.
You can say that
EG= EF + FG
You have to replace the name of the segments with their values to get the equation:
[tex]6x+14=19+(x+13)[/tex]
Now that you have a one unknown equation you can clear X
[tex]\begin{gathered} 6x=19+x+13-14 \\ 6x-x=\text{ 18} \\ 5x=18 \\ x=\frac{18}{5}=\text{ 3.6} \end{gathered}[/tex]
The value of x is 3.6
