Question

E is the midpoint of DF, DE = 2x + 4 and EF = 3x - 1 how do I find the value of x, DE, EF and DF

Answer 1

We know that

E is midpoint of DF, that means DE is equal to EF, so we can form the following equation

`DE=EF`

Replacing the given equations, we have

`\begin{gathered} 2x+4=3x-1 \\ 4+1=3x-2x \\ x=5 \end{gathered}`

Now, we replace this value in each equation to find each part of the segment.

`\begin{gathered} DE=2x+4=2(5)+4=10+4=14 \\ EF=3x-1=3(5)-1=15-1=14 \end{gathered}`

Therefore, each part of the segment is 14 units, and DF is 28.