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?