Question

e is the midpoint of $overline{df}$. if $de = 6x$ and $ef=x + 5$, what is $de$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since E is the mid - point of $\overline{DF}$, then $DE = EF$. So, we set up the equation $6x=x + 5$.

Step2: Solve the equation for x

Subtract x from both sides: $6x−x=x + 5−x$. This gives $5x=5$. Then divide both sides by 5: $x = 1$.

Step3: Find the value of DE

Substitute $x = 1$ into the expression for $DE$. Since $DE = 6x$, then $DE=6\times1=6$.

Answer:

6