Question

c is the midpoint of $overline{bd}$. if $bc = x + 9$ and $cd = 5x - 2$, what is $bc$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

Since C is the mid - point of BD, then $BC = CD$. So we set up the equation $x + 9=5x - 2$.

Step2: Solve for x

Subtract x from both sides: $9 = 5x-x - 2$, which simplifies to $9 = 4x-2$. Then add 2 to both sides: $9 + 2=4x$, so $11 = 4x$. Divide both sides by 4 to get $x=\frac{11}{4}$.

Step3: Find BC

Substitute $x = \frac{11}{4}$ into the expression for BC. $BC=x + 9=\frac{11}{4}+9$. Rewrite 9 as $\frac{36}{4}$, then $BC=\frac{11 + 36}{4}=\frac{47}{4}=11\frac{3}{4}$.

Answer:

$11\frac{3}{4}$