Question

e is the midpoint of $overline{df}$. if $de = 3x - 4$ and $ef = x + 5$, what is $de$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

Since E is the mid - point of $\overline{DF}$, then $DE = EF$. So we set up the equation $3x−4=x + 5$.

Step2: Solve for x

Subtract x from both sides: $3x−x−4=x−x + 5$, which simplifies to $2x−4 = 5$. Then add 4 to both sides: $2x−4 + 4=5 + 4$, getting $2x=9$. Divide both sides by 2: $x=\frac{9}{2}$.

Step3: Find the value of DE

Substitute $x = \frac{9}{2}$ into the expression for DE. $DE=3x−4=3\times\frac{9}{2}-4=\frac{27}{2}-4=\frac{27}{2}-\frac{8}{2}=\frac{27 - 8}{2}=\frac{19}{2}=9\frac{1}{2}$.

Answer:

$9\frac{1}{2}$