Answer :
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]
[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]