If CD = 2x, DE = x + 1, and CE = 7, what is CD?

Answer 1

C D E

2x + x + 1 = CD that is a total of 7

Combine like terms 2x + x + 1 becomes 2x + 1x + 1 = 3x + 1

Now solve 3x + 1 = 7 by subtracting one from both sides to get 3x + 1 - 1 = 7 -1 OR 3x = 6

Now divide both sides by three to solve 3x/ 3 = 6/3 to get x = 2.

Answer 2

CD = 2x

DE = x +1 = ED

CE = 7

CD would, in most similar problems, = CE+ED

CD = x+1+7 = x+8 =2x

x= 8

CD =2x = 2(8) = 16

BUT if D is inside C and E, so that CD+ED =CE

then 2x+x+1 = 7

3x = 6

x=2

CD=2x =2(2) =4

OR if C is the inside point

then

2x+CE =ED

2x+7= x+1

x =-6

2x =-12

but unless this is a Twilight Zone or Einstian relativity problem, you probably can eliminate this solution

so go with 4 or 16 for CD

UNLESS they aren't on a straight line at all

maybe they form a right triangle? That comes out messy so maybe not.

OR they could form a triangle that's not a right triangle

You could then calculate maximum and minimum values for CD

Answer 3

Hello! This question is asking for the length of the line segment CD.

The first step is often to draw a picture. It would look like this with C and E at the endpoints and D is a point in between C and E.

C D E

--------------------------------

We know that the segment CE is 7 units long.

By the segment addition postulate, we know that CE = CD + DE.

In other words, the whole line (CE), is made up of adding the smaller pieces together.

We can substitute the values and equations that we are given into the equation:

CE = CD + DE

7 = (2x) + (x +1)

Now we can use algebra to solve for x:

7 = 3x +1

Subtract 1 from both sides:

6 = 3x

Divide both sides by 3

2 = x

Now we need to find the length of CD, so we can substitute 2 in for x in the equation for CD:

CD = 2x = 2(2) = 4

CD = 4 units