FH=FG+GH due to the Segment Addition Postulate.
FH is given as 34 units. FG is 3x-1 and GH is 2x. So substitute these values into the equation.
34=(3x-1)+2x
34=3x-1+2x
34=5x-1
35=5x
x=7.
So the value of x is 7.
Now in order to find the value of FG and GH individually, we can substitute the value of x, 7, into their respective expressions.
FG=3x-1 and x=7, so
FG=3(7)-1
FG=21-1
FG=20
Now we can find GH using the similar method.
GH=2x and x=7
GH=2(7)
GH=14.
We can ensure this is correct by plugging these values back into the segment addition postulate equation.
FH=FG+GH
FH= 34, FG=20, GH=14
34=20+14
34=34
This is correct.
Succinctly, x=7, FH=20, and GH=14.