ED = x - 5 given
DG = 4x - 38 given
ED = DG definition of midpoint
x - 5 = 4x - 38 substitution
-5 = 3x - 38 subtraction property of equality (subtracted x from both sides)
33 = 3x addition property of equality (added 38 to both sides)
11 = x division property of equality (divided 3 from both sides)
ED = x - 5 → ED = 11 - 5 → ED = 6 substitution
since ED = DG, then DG = 6 transitive property
ED + DG = EG segment addition property
6 + 6 = EG substitution
12 = EG simplified like terms
Answer: 12