Question

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

Explanation:

Step1: Set up the equation

Since D is the mid - point of $\overline{CE}$, then $CD = DE$. So we have the equation $x + 3=5x - 4$.

Step2: Solve for x

Subtract x from both sides: $3 = 5x-x - 4$, which simplifies to $3 = 4x - 4$. Then add 4 to both sides: $3 + 4=4x$, so $7 = 4x$. Divide both sides by 4 to get $x=\frac{7}{4}$.

Step3: Find CD

Substitute $x = \frac{7}{4}$ into the expression for CD. $CD=x + 3=\frac{7}{4}+3$. Rewrite 3 as $\frac{12}{4}$, then $CD=\frac{7}{4}+\frac{12}{4}=\frac{7 + 12}{4}=\frac{19}{4}=4\frac{3}{4}$.

Answer:

$4\frac{3}{4}$