Question

1. given \\( \overline{ac} \\) with \\( ab = 2x - 4 \\), \\( bc = 4x \\) and \\( ac = 2x + 12 \\). find \\( ac \\).

(diagram: points a, b, c on a straight line with b between a and c)

Explanation:

Step1: Apply segment addition postulate

Since \( B \) is on \( \overline{AC} \), we have \( AB + BC = AC \). Substituting the given expressions: \( (2x - 4) + 4x = 2x + 12 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 6x - 4 = 2x + 12 \). Subtract \( 2x \) from both sides: \( 4x - 4 = 12 \). Add 4 to both sides: \( 4x = 16 \). Divide by 4: \( x = 4 \).

Step3: Find \( AC \)

Substitute \( x = 4 \) into \( AC = 2x + 12 \): \( AC = 2(4) + 12 = 8 + 12 = 20 \).

Answer:

\( 20 \)