Question

points a, b, and c are collinear. point b is between a and

1. find x if ab = x + 14, ac = 23, and bc = x + 13. x =
2. find x if ab = 2x - 1, bc = 11, and ac = 5x - 2. x =

points a, b, and c are collinear. point b is between a and

1. ac = 3 + 4x, bc = 5x - 1, and ab = 2. find ac. ac =
2. find ab if bc = 2x + 28, ac = 10, and ab = 2x + 22. ab =

Explanation:

Problem 13:

Step1: Use segment addition postulate

Since \( B \) is between \( A \) and \( C \), \( AB + BC = AC \). Substitute the given expressions: \( (x + 14) + (x + 13) = 23 \)

Step2: Simplify and solve for \( x \)

Combine like terms: \( 2x + 27 = 23 \). Subtract 27 from both sides: \( 2x = 23 - 27 = -4 \). Divide by 2: \( x = \frac{-4}{2} = -2 \)

Step1: Apply segment addition postulate

\( AB + BC = AC \), so \( (2x - 1) + 11 = 5x - 2 \)

Step2: Solve for \( x \)

Simplify left side: \( 2x + 10 = 5x - 2 \). Subtract \( 2x \): \( 10 = 3x - 2 \). Add 2: \( 12 = 3x \). Divide by 3: \( x = 4 \)

Step1: Use segment addition postulate

\( AB + BC = AC \), so \( 2 + (5x - 1) = 3 + 4x \)

Step2: Solve for \( x \)

Simplify left side: \( 5x + 1 = 3 + 4x \). Subtract \( 4x \): \( x + 1 = 3 \). Subtract 1: \( x = 2 \)

Step3: Find \( AC \)

Substitute \( x = 2 \) into \( AC = 3 + 4x \): \( AC = 3 + 4(2) = 3 + 8 = 11 \)

Answer:

\( x = -2 \)

Problem 15: