Question

review: find the indicated length.

a---14---b---3x - 4---c
ac = 4x + 4 units
(diagram shows segment ac with point b between a and c, ab = 14, bc = 3x - 4, ac = 4x + 4; find ac.)

Explanation:

Step1: Analyze segment addition

From the diagram, \( AB + BC = AC \), and \( AC = 4x + 4 \), \( AB = 14 \), \( BC = 3x - 4 \). So \( 14 + (3x - 4)=4x + 4 \).

Step2: Solve for \( x \)

Simplify left side: \( 14 + 3x - 4 = 3x + 10 \). Equation: \( 3x + 10 = 4x + 4 \). Subtract \( 3x \) and 4: \( 10 - 4 = 4x - 3x \), so \( x = 6 \).

Step3: Calculate \( AC \)

Substitute \( x = 6 \) into \( AC = 4x + 4 \): \( 4(6)+4 = 24 + 4 = 28 \).

Answer:

28