Question

if cd = 9x, de = 8, and ce = 14x + 3, what is ce? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( CE = CD + DE \). Substitute the given expressions: \( 14x + 3 = 9x + 8 \).

Step2: Solve for \( x \)

Subtract \( 9x \) from both sides: \( 14x - 9x + 3 = 8 \), which simplifies to \( 5x + 3 = 8 \). Then subtract 3 from both sides: \( 5x = 8 - 3 = 5 \). Divide both sides by 5: \( x = \frac{5}{5} = 1 \).

Step3: Find \( CE \)

Substitute \( x = 1 \) into \( CE = 14x + 3 \): \( CE = 14(1) + 3 = 14 + 3 = 17 \).

Answer:

\( 17 \)