SOLUTION: 𝐸 is the midpoint of 𝐷F. 𝐷𝐸 = 4π‘₯ + 3 and 𝐸𝐹 = 8π‘₯ βˆ’ 9. Find 𝐷𝐸, 𝐸𝐹, and 𝐷�

Algebra ->  Points-lines-and-rays -> SOLUTION: 𝐸 is the midpoint of 𝐷F. 𝐷𝐸 = 4π‘₯ + 3 and 𝐸𝐹 = 8π‘₯ βˆ’ 9. Find 𝐷𝐸, 𝐸𝐹, and 𝐷�      Log On


   



Question 1203782: 𝐸 is the midpoint of 𝐷F. 𝐷𝐸 = 4π‘₯ + 3
and 𝐸𝐹 = 8π‘₯ βˆ’ 9. Find 𝐷𝐸, 𝐸𝐹, and 𝐷�

Found 2 solutions by mananth, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

𝐸 is the midpoint of 𝐷F. 𝐷𝐸 = 4π‘₯ + 3
and 𝐸𝐹 = 8π‘₯ βˆ’ 9. Find 𝐷𝐸, 𝐸𝐹, and 𝐷
Since e is the midpoint of DF DE = EF
Therefore 4x+3 = 8x-9
subtract 8x from both sides of equation
4x+3-8x = -9
substract 3 from both sides
4x -8x = -9-3
-4x = -12
x = -12/-4=3
DE = 4x+3
plug x
DE = 4*3+3
DE = 15
Therefore EF = 15



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if +E is the midpoint of +DF, then +DE=EF
if
+DE+=+4x+%2B+3
+EF+=+8x+-+9
then
+4x+%2B+3=8x+-+9
+9%2B+3=8x+-4x+
+12=4x+
+x=3

so,
+DE+=+4x+%2B+3=4%2A3%2B3=15
since+DE=EF, we have EF+=15
+DE=EF%2BDF=DE%2BEF+=15%2B15=30