Answer:
72 units
Step-by-step explanation:
Given D,E, and F are collinear points and E is between D and F, then the expression DE + EF = DF.... 1 is true
If DE is six times the length of EF, then;
DE = 6DF
DF = DE/6 .....2
Substitute equation 2 into 1;
DE + EF = DF
DE + DE/6 = DF
find the LCM
(6DE+DE)/6 = DF
cross multiply
6DE+DE = 6DF
7DE = 6DF
Given DF = 84units
7DE = 6(84)
7DE = 504
Divide both sides by 7
7DE/7 = 504/7
DE = 72
Hence the length of segment DE is 72units
