Question

find de
d • ———x+4———• e ———2x-11———• f
|←———14———→|

Explanation:

Step1: Set up the equation

From the line segment, we know that \( DE + EF = DF \). So, \( (x + 4) + (2x - 11) = 14 \).

Step2: Simplify the left side

Combine like terms: \( x + 2x + 4 - 11 = 14 \), which simplifies to \( 3x - 7 = 14 \).

Step3: Solve for x

Add 7 to both sides: \( 3x = 14 + 7 = 21 \). Then divide by 3: \( x = \frac{21}{3} = 7 \).

Step4: Find DE

Substitute \( x = 7 \) into \( DE = x + 4 \): \( DE = 7 + 4 = 11 \).

Answer:

11