Question

if bc = x - 4, cd = 11, and bd = 2x - 12, what is bc?
diagram: points b, c, d on a line; bc labeled ( x - 4 ), cd labeled 11, bd labeled ( 2x - 12 )
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the number line, we know that \( BD = BC + CD \). Substituting the given expressions: \( 2x - 12=(x - 4)+11 \)

Step2: Solve for x

Simplify the right - hand side: \( 2x - 12=x + 7 \)
Subtract \( x \) from both sides: \( 2x-x-12=x - x+7 \), which gives \( x - 12 = 7 \)
Add 12 to both sides: \( x-12 + 12=7 + 12 \), so \( x=19 \)

Step3: Find BC

Since \( BC=x - 4 \), substitute \( x = 19 \) into the expression: \( BC=19 - 4=15 \)

Answer:

15