Question

e is the midpoint of $overline{df}$. if $de = 6x + 8$ and $df = 13x + 15$, what is $df?
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 $DF = 2DE$. So, $13x + 15=2(6x + 8)$.

Step2: Expand the right - hand side

Expand $2(6x + 8)$ to get $12x+16$. So the equation becomes $13x + 15=12x + 16$.

Step3: Solve for $x$

Subtract $12x$ from both sides: $13x-12x+15=12x - 12x+16$, which simplifies to $x+15 = 16$. Then subtract 15 from both sides: $x=16 - 15=1$.

Step4: Find the value of $DF$

Substitute $x = 1$ into the expression for $DF$. $DF=13x + 15$. So, $DF=13\times1+15=28$.

Answer:

28