Question

if de = 2x, ef = x + 6, and df = 4x + 1, what is de? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment - addition postulate

Since $DF=DE + EF$, we substitute the given expressions: $4x + 1=2x+(x + 6)$.

Step2: Simplify the right - hand side

$4x + 1=2x+x + 6$, which simplifies to $4x + 1=3x + 6$.

Step3: Solve for x

Subtract $3x$ from both sides: $4x-3x+1=3x-3x + 6$, so $x+1 = 6$. Then subtract 1 from both sides: $x=6 - 1=5$.

Step4: Find DE

Since $DE = 2x$, substitute $x = 5$ into the expression for $DE$. So $DE=2\times5 = 10$.

Answer:

10