Question

if bc = 7x, cd = 4, and bd = x + 10, what is bc? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( BD = BC + CD \). Substitute the given expressions: \( x + 10 = 7x + 4 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 10 = 6x + 4 \). Subtract 4: \( 6 = 6x \). Divide by 6: \( x = 1 \).

Step3: Find \( BC \)

Since \( BC = 7x \), substitute \( x = 1 \): \( BC = 7(1) = 7 \).

Answer:

7