Question

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

A) What is the value of x?
B) What is the length of FG?
C) what is HG?

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