Question

13 fill in the blank 2 points a, b, and c are collinear. b is between a and c. 13) $ac = 2x - 5$, $ab = 12$, and $bc = x - 6$. find $bc$. the value of x is type your answer. the length of bc is

Explanation:

Step1: Set up equation for AC

Since B is between A and C, \( AC = AB + BC \). Substitute given values: \( 2x - 5 = 12 + (x - 6) \).

Step2: Simplify and solve for x

Simplify right side: \( 12 + x - 6 = x + 6 \). Equation becomes \( 2x - 5 = x + 6 \). Subtract x: \( x - 5 = 6 \). Add 5: \( x = 11 \).

Step3: Calculate BC

\( BC = x - 6 \), substitute \( x = 11 \): \( BC = 11 - 6 = 5 \).

Answer:

The value of x is 11.
The length of BC is 5.