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Given that AD = 2, DB = 5, AE = 4, find the length of EC. If AD = x + 2, AE = 6, EC = 8, and DB = 4, solve for the value of x.

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Final answer:

To find the value of x, we use the relationship between the segments of a line, setting the equation (x + 2) + 4 = 6 + 8, which simplifies to x = 8, indicating that AD = 10 and the length of EC is 8.

Step-by-step explanation:

To solve for the value of x when given that AD = x + 2, AE = 6, EC = 8, and DB = 4, we first recognize that AD and DB are parts of the same line segment, and the same is true for AE and EC. Since AD and DB form a line segment together, we can say AD + DB = AE + EC, because AE + EC also forms a full line segment.

By substituting the given values into the equation, we get $(x + 2) + 4 = 6 + 8$. Simplifying the equation, we arrive at $x + 6 = 14$. Solving for x, we subtract 6 from both sides and find that $x = 8$.

The value of x is 8, and this means that the length of AD is 10 since AD is represented by x + 2. The length of EC remains 8 in this context, and is not affected by the value of x.

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