Question

if bc = x + 10, cd = 7x - 2, and bd = 16, what is cd?
diagram: line segment b to d with point c between them; bc labeled ( x + 10 ), cd labeled ( 7x - 2 ), bd labeled 16
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the segment addition postulate, \( BC + CD = BD \). Substituting the given expressions, we get \((x + 10) + (7x - 2) = 16\).

Step2: Simplify the left side

Combine like terms: \(x + 7x + 10 - 2 = 16\), which simplifies to \(8x + 8 = 16\).

Step3: Solve for x

Subtract 8 from both sides: \(8x = 16 - 8 = 8\). Then divide both sides by 8: \(x = \frac{8}{8} = 1\).

Step4: Find CD

Substitute \(x = 1\) into the expression for \(CD\): \(CD = 7x - 2 = 7(1) - 2 = 7 - 2 = 5\).

Answer:

5