To determine the value of \( x \), given the points \( A \), \( B \), and \( C \) are collinear and that \( B \) lies between \( A \) and \( C \), we start with the given measurements:
[tex]\[
AB = 3x
\][/tex]
[tex]\[
BC = 2x - 7
\][/tex]
[tex]\[
AC = 2x + 35
\][/tex]
Since point \( B \) is between \( A \) and \( C \), the sum of the segments \( AB \) and \( BC \) should equal the total segment \( AC \). Therefore, we can set up the following equation:
[tex]\[
AB + BC = AC
\][/tex]
Substituting the given expressions for \( AB \), \( BC \), and \( AC \):
[tex]\[
3x + (2x - 7) = 2x + 35
\][/tex]
Now, we combine like terms on the left side of the equation:
[tex]\[
3x + 2x - 7 = 2x + 35
\][/tex]
This simplifies to:
[tex]\[
5x - 7 = 2x + 35
\][/tex]
Next, to isolate \( x \), we subtract \( 2x \) from both sides of the equation:
[tex]\[
5x - 2x - 7 = 35
\][/tex]
This further simplifies to:
[tex]\[
3x - 7 = 35
\][/tex]
Next, we add 7 to both sides of the equation to isolate the term with \( x \):
[tex]\[
3x = 42
\][/tex]
Finally, we divide both sides by 3 to solve for \( x \):
[tex]\[
x = \frac{42}{3} = 14
\][/tex]
Therefore, the value of \( x \) is
[tex]\[
\boxed{14}
\][/tex]
So, the correct answer is:
[tex]\[
\text{D. 14}
\][/tex]
