Question

if cd = 6x, de = 5, and ce = x + 10, what is cd?
c d e
6x 5
x + 10
simplify your answer and write it as a proper fraction, mixed number, or integer.
submit

Explanation:

Step1: Use segment addition postulate

From the diagram, \( CD + DE = CE \). Substitute the given expressions: \( 6x + 5 = x + 10 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 6x - x + 5 = 10 \), which simplifies to \( 5x + 5 = 10 \). Then subtract 5 from both sides: \( 5x = 10 - 5 = 5 \). Divide both sides by 5: \( x = \frac{5}{5} = 1 \).

Step3: Find \( CD \)

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

Answer:

6