Question

on a line segment, d is between c and e. if cd = 12, de = x + 5, and ce = 2x, what is ce? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( D \) is between \( C \) and \( E \), we have \( CD + DE = CE \). Substituting the given values: \( 12+(x + 5)=2x \).

Step2: Simplify and solve for \( x \)

Simplify the left side: \( 12+x + 5=2x\) which becomes \( x + 17=2x \). Subtract \( x \) from both sides: \( 17 = 2x - x\), so \( x = 17 \).

Step3: Find \( CE \)

We know \( CE = 2x \). Substitute \( x = 17 \): \( CE=2\times17 = 34 \).

Answer:

\( 34 \)