Question

objective 2: i can write and solve equations involving lines and line segments

1. solve for x. then find ab.

b is between points a and c.
ab = 3x - 4
bc = 6x + 2
ac = 5x + 22

Explanation:

Step1: Use segment addition postulate

Since \( B \) is between \( A \) and \( C \), we have \( AB + BC = AC \). Substituting the given expressions: \( (3x - 4) + (6x + 2) = 5x + 22 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 3x - 4 + 6x + 2 = 5x + 22 \) becomes \( 9x - 2 = 5x + 22 \). Subtract \( 5x \) from both sides: \( 4x - 2 = 22 \). Add 2 to both sides: \( 4x = 24 \). Divide by 4: \( x = 6 \).

Step3: Find \( AB \)

Substitute \( x = 6 \) into \( AB = 3x - 4 \): \( AB = 3(6) - 4 = 18 - 4 = 14 \).

Answer:

\( x = 6 \), \( AB = 14 \)