Question

d is the midpoint of $overline{ce}$. if $cd = 3x$ and $de = 8x - 7$, what is $de? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since D is the mid - point of $\overline{CE}$, then $CD = DE$. So, $3x=8x - 7$.

Step2: Solve for x

Subtract $3x$ from both sides: $0 = 8x-3x - 7$, which simplifies to $0 = 5x - 7$. Then add 7 to both sides: $5x=7$, and $x=\frac{7}{5}$.

Step3: Find DE

Substitute $x = \frac{7}{5}$ into the expression for $DE$. $DE=8x - 7=8\times\frac{7}{5}-7$. First, $8\times\frac{7}{5}=\frac{56}{5}$, and $\frac{56}{5}-7=\frac{56}{5}-\frac{35}{5}=\frac{56 - 35}{5}=\frac{21}{5}=4\frac{1}{5}$.

Answer:

$4\frac{1}{5}$