Question

f is the midpoint of $overline{eg}$. if $fg = 6x - 2$ and $eg = 7x + 8$, what is $fg? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $F$ is mid - point of $EG$, $EG = 2FG$. So, $7x + 8=2(6x - 2)$.

Step2: Solve the equation

$7x + 8 = 12x-4$, $8 + 4=12x - 7x$, $12 = 5x$, $x=\frac{12}{5}$.

Step3: Find $FG$

$FG = 6x - 2=6\times\frac{12}{5}-2=\frac{72}{5}-\frac{10}{5}=\frac{62}{5}=12\frac{2}{5}$.

Answer:

$12\frac{2}{5}$