Question

find the measure of \\(\overline{de}\\).
need help?
rectangle units
line segment with points c, d, e; cd labeled 2x + 7, de labeled 4x - 3, and d is the midpoint (implied by the tick marks)

Explanation:

Step1: Set CD = DE (since D is midpoint)

Given \( CD = 2x + 7 \) and \( DE = 4x - 3 \), so \( 2x + 7 = 4x - 3 \).

Step2: Solve for x

Subtract \( 2x \) from both sides: \( 7 = 2x - 3 \).
Add 3 to both sides: \( 10 = 2x \).
Divide by 2: \( x = 5 \).

Step3: Find DE length

Substitute \( x = 5 \) into \( DE = 4x - 3 \):
\( DE = 4(5) - 3 = 20 - 3 = 17 \).

Answer:

17