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The problem presents the line segment \( AD \) with a total length of 27 units. It is divided into three smaller segments: 

- \( AB = 2x \)
- \( BC = 3 \)
- \( CD = x \)

To solve for \( x \), we can use the **Segment Addition Postulate**, which states that the sum of the lengths of the smaller segments equals the total length of the segment.

According to this postulate:

\[
AB + BC + CD = AD
\]

Substitute the given values:

\[
2x + 3 + x = 27
\]

Now, combine like terms:

\[
3x + 3 = 27
\]

Subtract 3 from both sides:

\[
3x = 24
\]

Now, divide both sides by 3:

\[
x = 8
\]

Thus, the value of \( x \) is \( 8 \).

### The postulate that helps in solving this problem is **the Segment Addition Postulate**.

Would you like any further details or clarifications?

Here are some related questions you could explore:

1. What is the Segment Addition Postulate?
2. How do we verify the solution once \( x \) is found?
3. How would the problem change if \( AD \) was given a different value?
4.

AD = 27. Find x. Given that AB = 2x, BC = 3, and CD = x.

Learn how to solve for x in a line segment where AD = 27, AB = 2x, BC = 3, and CD = x. This problem uses the Segment Addition Postulate and involves basic algebraic steps to find x. Suitable for students in Grades 6-8.

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