Point D is on line segment start overline, C, E, end overline

CE
. Given C, D, equals, x, commaCD=x, D, E, equals, 7, commaDE=7, and C, E, equals, 2, x, commaCE=2x, determine the numerical length of start overline, C, D, end overline, .
CD
.

1 answer

To find the length of the line segment \( \overline{CD} \), we can utilize the information given in the problem. We have three segments:

\( CD = x \)
\( DE = 7 \)
\( CE = 2x \)

We know that point \( D \) is located between points \( C \) and \( E \), so we can express \( CE \) as the sum of \( CD \) and \( DE \):

\[ CE = CD + DE \]

Substituting the expressions we have for these segments:

\[ 2x = x + 7 \]

Now we can solve for \( x \):

Subtract \( x \) from both sides:

\[ 2x - x = 7 \] \[ x = 7 \]

Now that we have the value of \( x \), we can determine the length of \( \overline{CD} \):

\[ CD = x = 7 \]

Therefore, the numerical length of \( \overline{CD} \) is

\[ \boxed{7} \]