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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 .

Question

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 .

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Solution

Given that CD = x, DE = 7, and CE = 2x, we can use the property of a line segment, which states that the whole is equal to the sum of its parts.

So, CE = CD + DE.

Substituting the given values, we get:

2x = x + 7.

To solve for x, subtract x from both sides of the equation:

2x - x = 7.

This simplifies to:

x = 7.

Therefore, the numerical length of CD is 7.

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