Question

if de = 6, ef = 2x, and df = 3x, what is ef? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $DF=DE + EF$, we substitute the given values: $3x=6 + 2x$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides of the equation $3x=6 + 2x$. We get $3x-2x=6+2x - 2x$, which simplifies to $x = 6$.

Step3: Find the value of $EF$

We know that $EF = 2x$. Substitute $x = 6$ into the expression for $EF$. So $EF=2\times6=12$.

Answer:

$12$