SOLUTION: Please help me solve these equations: Line segment: AB=2x, BC=4x-3, CD=3x, DE=2x+3 Given: The length of BD exceeds the length of CE by 10. What is the length of CD? Which i

Algebra ->  Length-and-distance -> SOLUTION: Please help me solve these equations: Line segment: AB=2x, BC=4x-3, CD=3x, DE=2x+3 Given: The length of BD exceeds the length of CE by 10. What is the length of CD? Which i      Log On


   

Question 159875: Please help me solve these equations:
Line segment: AB=2x, BC=4x-3, CD=3x, DE=2x+3
Given: The length of BD exceeds the length of CE by 10.
What is the length of CD?
Which is longer, AC or CE?
What is the total length of AE?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The length of BD exceeds the length of CE by 10.
1.BD=CE%2B10
I'm assuming the following
BD=BC%2BCD
CE=CD%2BDE
Then substituting,
BD=%284x-3%29%2B%283x%29=7x-3
CE=%283x%29%2B%282x%2B3%29=5x%2B3
Then, going back to eq. 1,
1.BD=CE%2B10
7x-3=%285x%2B3%29%2B10
7x-3=5x%2B13
2x=16
x=8
.
.
.
AB=2x=16
BC=4x-3=4%288%29-3=29
CD=3x=24
DE=2x%2B3=2%288%29%2B3=19
.
.
.
Now to the questions,
What is the length of CD?
24
Which is longer, AC or CE?
AC=16%2B29=45
CE=24%2B19=43
AC is longer
What is the total length of AE?
AE=16%2B29%2B24%2B19=88
or
AE=2x%2B4x-3%2B3x%2B2x%2B3=11x=88