E is the midpoint of DF, DE=2x+4 and EF= 3x -1 Find DF,DE and EF
If E is the midpoint of DF, then DF can be divided into two equal parts, DE and EF.
Since DE = EF, we can set up the following equation:
DE = EF
We are also given that DE = 2x + 4 and EF = 3x - 1.
Setting DE = EF, we have:
2x + 4 = 3x - 1
Simplifying this equation, we subtract 2x and add 1 to both sides:
4 + 1 = 3x - 2x
5 = x
Now that we have the value of x, we can substitute it back into the expressions for DE and EF to find their values:
DE = 2(5) + 4 = 10 + 4 = 14
EF = 3(5) - 1 = 15 - 1 = 14
Therefore, DF = DE + EF = 14 + 14 = 28