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Line segment AB intersects line segment ED in the middle at the point C
If DC=6+x and CE=2x+1, what is the lenth of ED?
A. 5
B. 11
C. 22
D. 10
Answer: C
Line segment AB intersects line segment ED in the middle at the point C
If DC=6+x and CE=2x+1, find the value of x
A. 10
B. 5
C. 22
D. 11
Answer: a.
To find the length of line segment ED, we need to subtract the lengths of line segment DC and line segment CE from the total length of line segment DE.
Given that DC = 6 + x and CE = 2x + 1, we can set up an equation using the fact that line segment AB intersects line segment ED at the midpoint C:
DC + CE = DE
Substituting the given values:
(6 + x) + (2x + 1) = DE
Combining like terms:
3x + 7 = DE
To find the value of x, we can set up another equation using the fact that line segment AB intersects line segment ED at the midpoint C:
DC = CE
Substituting the given values:
6 + x = 2x + 1
Simplifying the equation:
x = 5
Now we can substitute the value of x back into the equation for DE:
DE = 3x + 7 = 15 + 7 = 22
Therefore, the length of line segment ED is 22.
For the second question, given that DC = 6 + x and CE = 2x + 1, we need to find the value of x that makes DC equal to CE.
Setting up the equation:
6 + x = 2x + 1
Simplifying the equation:
x = 5
Therefore, the value of x is 5.