Question

if bc = 6x, cd = x + 8, and bd = 15, what is bc? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the line segment, we know that \( BC + CD = BD \). Substituting the given expressions, we get \( 6x + (x + 8) = 15 \).

Step2: Simplify the equation

Combine like terms: \( 6x + x + 8 = 15 \) which simplifies to \( 7x + 8 = 15 \).

Step3: Solve for x

Subtract 8 from both sides: \( 7x = 15 - 8 = 7 \). Then divide both sides by 7: \( x = \frac{7}{7} = 1 \).

Step4: Find BC

Since \( BC = 6x \), substitute \( x = 1 \): \( BC = 6\times1 = 6 \).

Answer:

6