Question

find the measure of (overline{de}).
diagram: points c, d, e on a line; segment ( overline{cd} ) labeled ( 2x + 7 ), segment ( overline{de} ) labeled ( 4(x - 3) ).
blank box units

Explanation:

Step1: Assume CD = DE (since D is the midpoint, as the segments are marked equally)

So, we set \( 2x + 7 = 4(x - 3) \)

Step2: Solve for x

Expand the right side: \( 2x + 7 = 4x - 12 \)
Subtract \( 2x \) from both sides: \( 7 = 2x - 12 \)
Add 12 to both sides: \( 19 = 2x \)
Divide by 2: \( x = \frac{19}{2} = 9.5 \)

Step3: Find DE

Substitute x into \( 4(x - 3) \)
\( 4(9.5 - 3) = 4(6.5) = 26 \)

Answer:

26