Question

E is the midpoint of DF, DE = 2x + 4, and EF = 3x + 1. Find DE, EF, and DF.

Answer 1

When there is a midpoint in a line segment, the two segments that are then produced have to be equal. So that means that because E is a midpoint of DF, DE=EF.
Set up the equation.
DE=EF
2x+4=3x+1
Then solve for x.
x=3
Then plug it back in the equation to find DE and EF.
DE=2x+4=2(3)+4=10
Because DE=EF then EF is also 10.
DF is made from the addition of DE and EF so DF is twice EF.
DF= 20

DE= 10, EF= 10, DF= 20

Hope this helps.