Question

a, b, and c are collinear. b is between a and c. 12) ab = 9, ac = 5x - 1, and bc = 2x + 2. find bc. the value of x is type your answer.. the length of bc is type your answer.

Explanation:

Step1: Set up equation for collinear points

Since B is between A and C, \( AC = AB + BC \). Substitute values: \( 5x - 1 = 9 + (2x + 2) \).

Step2: Simplify and solve for x

Simplify right side: \( 5x - 1 = 2x + 11 \). Subtract \( 2x \): \( 3x - 1 = 11 \). Add 1: \( 3x = 12 \). Divide by 3: \( x = 4 \).

Step3: Calculate BC

Substitute \( x = 4 \) into \( BC = 2x + 2 \): \( BC = 2(4) + 2 = 10 \).

Answer:

The value of x is 4
The length of BC is 10