E is the midpoint of DF, DE=6x+8, and EF=7x-5
Find DE, EF, and DF

If E is the midpoint Of DF, that means DE is the same length as EF. Therefore, you can make DE=EF or 6x+8=7x-5 and solve from there.

6x+8=7x-5
+5 +5

6x+13=7x
-6x -6x

13=x

Now substitute 13 for x in 6x+8 to find DE.

6(13)+8 = 86

We already know since both sides are equal that EF also equals 86, but you can still substitute 13 again in 7x-5 to get EF.

7(13)-5 = 86

Now that we have both halves of DF, we can add 86+86 to get our total length of 172.

The answer is d 18ft