IDNLearn.com offers a reliable platform for finding accurate and timely answers. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.
Sagot :
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]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.