Question

if de = x + 1, ef = 5, and df = 4x, what is de? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

From the diagram, \( DF = DE + EF \). Substitute the given expressions: \( 4x=(x + 1)+5 \).

Step2: Solve for \( x \)

Simplify the right - hand side: \( 4x=x + 6 \). Subtract \( x \) from both sides: \( 4x-x=x + 6-x \), which gives \( 3x = 6 \). Divide both sides by 3: \( x=\frac{6}{3}=2 \).

Step3: Find the length of \( DE \)

Given \( DE=x + 1 \), substitute \( x = 2 \): \( DE=2 + 1=3 \).

Answer:

\( 3 \)