Question

If D is the midpoint of EG, find the length of EG

Answer 1

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