Final answer:
To find FH, we set up the equation FG + GH = FH and solve for x. After calculating the value of x, we determine that FH is 90 units long.
Step-by-step explanation:
The student is working on a problem involving segment lengths on a line. Given that G is between F and H, and the given lengths of the segments are FH = 8x, FG = 4x + 7, and GH = 38, we can solve for FH. Since G is between F and H, the segments FG and GH add up to FH. The equation is FG + GH = FH, meaning 4x + 7 + 38 = 8x. Solving for x we get x = 11.25. Thus, FH, which is 8x, equals 8 * 11.25 = 90.