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Sagot :
To find the value of \( x \) given the points \( A, B, \) and \( C \) are collinear with \( B \) between \( A \) and \( C \) and the distances \( AB = 2x \), \( BC = x - 2 \), and \( AC = 28 \), follow these steps:
1. Set Up the Equation:
Since points \( A \), \( B \), and \( C \) are collinear and \( B \) is between \( A \) and \( C \), the total distance from \( A \) to \( C \) is the sum of the distances from \( A \) to \( B \) and from \( B \) to \( C \).
[tex]\[ AB + BC = AC \][/tex]
Substitute the given distances:
[tex]\[ 2x + (x - 2) = 28 \][/tex]
2. Combine Like Terms:
Combine the \( x \) terms on the left-hand side of the equation:
[tex]\[ 2x + x - 2 = 28 \][/tex]
[tex]\[ 3x - 2 = 28 \][/tex]
3. Solve for \( x \):
Isolate \( x \) by adding 2 to both sides of the equation:
[tex]\[ 3x - 2 + 2 = 28 + 2 \][/tex]
[tex]\[ 3x = 30 \][/tex]
Now, divide by 3:
[tex]\[ x = \frac{30}{3} \][/tex]
[tex]\[ x = 10 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{10}\)[/tex].
1. Set Up the Equation:
Since points \( A \), \( B \), and \( C \) are collinear and \( B \) is between \( A \) and \( C \), the total distance from \( A \) to \( C \) is the sum of the distances from \( A \) to \( B \) and from \( B \) to \( C \).
[tex]\[ AB + BC = AC \][/tex]
Substitute the given distances:
[tex]\[ 2x + (x - 2) = 28 \][/tex]
2. Combine Like Terms:
Combine the \( x \) terms on the left-hand side of the equation:
[tex]\[ 2x + x - 2 = 28 \][/tex]
[tex]\[ 3x - 2 = 28 \][/tex]
3. Solve for \( x \):
Isolate \( x \) by adding 2 to both sides of the equation:
[tex]\[ 3x - 2 + 2 = 28 + 2 \][/tex]
[tex]\[ 3x = 30 \][/tex]
Now, divide by 3:
[tex]\[ x = \frac{30}{3} \][/tex]
[tex]\[ x = 10 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{10}\)[/tex].
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