Question

on a line segment, c is between b and d. if bc = 2, cd = x − 8, and bd = 2x − 16, what is bd? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( C \) is between \( B \) and \( D \), we have \( BC + CD = BD \). Substituting the given values: \( 2+(x - 8)=2x - 16 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side: \( 2+x - 8=x - 6 \). So the equation becomes \( x - 6 = 2x-16 \).
Subtract \( x \) from both sides: \( x - 6-x=2x - 16 - x \), which gives \( - 6=x - 16 \).
Add 16 to both sides: \( -6 + 16=x-16 + 16 \), so \( x = 10 \).

Step3: Find the length of \( BD \)

Substitute \( x = 10 \) into the expression for \( BD \): \( BD=2x - 16 \).
\( BD=2\times10-16=20 - 16 = 4 \).

Answer:

\( 4 \)