Question

eb=2x, bd=24, ed=6x-4. x= ed=

Explanation:

Step1: Analyze the segment addition

From the diagram, \( ED = EB + BD \). Substitute the given expressions: \( 6x - 4 = 2x + 24 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 6x - 2x - 4 = 24 \) → \( 4x - 4 = 24 \). Add 4 to both sides: \( 4x = 24 + 4 \) → \( 4x = 28 \). Divide by 4: \( x = \frac{28}{4} = 7 \).

Step3: Calculate \( ED \)

Substitute \( x = 7 \) into \( ED = 6x - 4 \): \( ED = 6(7) - 4 = 42 - 4 = 38 \).

Answer:

\( x = 7 \)
\( ED = 38 \)