Question

e is the midpoint of $overline{df}$. if $de = x + 7$ and $ef = 4x - 7$, 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 DF, then $DE = EF$. So we have the equation $x + 7=4x - 7$.

Step2: Solve for x

Subtract x from both sides: $7 = 4x-x - 7$, which simplifies to $7 = 3x - 7$. Then add 7 to both sides: $7 + 7=3x$, so $14 = 3x$. Divide both sides by 3, we get $x=\frac{14}{3}$.

Step3: Find the value of DE

Substitute $x = \frac{14}{3}$ into the expression for DE. $DE=x + 7=\frac{14}{3}+7=\frac{14}{3}+\frac{21}{3}=\frac{14 + 21}{3}=\frac{35}{3}=11\frac{2}{3}$.

Answer:

$11\frac{2}{3}$