a)
FH = 102, FG = 5x + 9. HG = 9x - 5 Given
FG + HG = FH Segment addition postulate
5x + 9 + 9x - 5 = 102 Substitution
14x + 4 = 102 Simplify (added like terms)
14x = 98 Subtraction property of equality
x = 7 Division property of equality
b) FG = 5x + 9 = 5(7) + 9 = 35 + 9 = 44
c) HG = 9x - 5 = 9(7) - 5 = 63 - 5 = 58
Answers: a = 7, b = 44, c = 58
