Question

find the measure of \\( \overline { d e } \\).

Explanation:

Step1: Set up the equation

Since \(CD = DE\), we have \(2x + 7=4(x - 3)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b - c)=ab - ac\), \(4(x - 3)=4x-12\). So the equation becomes \(2x + 7 = 4x-12\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(7=4x - 12-2x\), which simplifies to \(7 = 2x-12\).
Add \(12\) to both sides: \(7 + 12=2x\), so \(19 = 2x\). Then \(x=\frac{19}{2}=9.5\).

Step4: Find the length of \(DE\)

Substitute \(x = 9.5\) into the expression for \(DE\) (\(4(x - 3)\)).
\(DE=4(9.5 - 3)=4\times6.5 = 26\).

Answer:

\(26\)