Using the following image, if DF= 120, what are x, DE, and EF.

x=19
DE=84
EF=36

reasoning:

the sum of DE and EF is 120, so to find the value of each first you find x
find x by adding DE and EF
this gives you the equation (4x+8)+(2x-2)=120
combine like terms and get 6x+6=120
subtract 6 from both sides to get 6x=114
divide both sides by 6 to get x=19

plug 19 into x in both equations to get the values of each length