Question

d is the midpoint of $overline{ce}$. if $de = x + 9$ and $ce = 3x + 9$, 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 $CE = 2DE$. Given $DE=x + 9$ and $CE=3x + 9$, we can set up the equation $3x + 9=2(x + 9)$.

Step2: Expand the right - hand side

Expand $2(x + 9)$ to get $2x+18$. So the equation becomes $3x + 9=2x + 18$.

Step3: Solve for x

Subtract $2x$ from both sides: $3x-2x+9=2x-2x + 18$, which simplifies to $x+9=18$. Then subtract 9 from both sides: $x=18 - 9$, so $x = 9$.

Step4: Find DE

Substitute $x = 9$ into the expression for $DE$. Since $DE=x + 9$, then $DE=9 + 9=18$.

Answer:

18