Question

1. use the image below to answer the question.

using the segment addition postulate, find the value of x.
ab = 3x + 8
bc = 4x + 6
ac = 28
2
28
14
7

Explanation:

Step1: Apply Segment Addition Postulate

By the segment addition postulate, \( AB + BC = AC \). Substitute \( AB = 3x + 8 \), \( BC = 4x + 6 \), and \( AC = 28 \) into the equation:
\( (3x + 8) + (4x + 6) = 28 \)

Step2: Simplify and Solve for \( x \)

Combine like terms:
\( 7x + 14 = 28 \)

Subtract 14 from both sides:
\( 7x = 28 - 14 \)
\( 7x = 14 \)

Divide both sides by 7:
\( x = \frac{14}{7} = 2 \)

Answer:

2