Question

Point G is between F and H. FH= 102, FG=5x+9, and HG=9x-5

Answer 1

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