Question

f is the midpoint of $overline{eg}$. if $ef = 5x + 9$ and $fg = 8x + 4$, what is $ef? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set EF equal to FG

$5x + 9=8x + 4$

Step2: Solve for x

$9 - 4=8x - 5x$, $3x = 5$, $x=\frac{5}{3}$

Step3: Find EF

$EF = 5\times\frac{5}{3}+9=\frac{25}{3}+9=\frac{25 + 27}{3}=\frac{52}{3}=17\frac{1}{3}$

Answer:

$17\frac{1}{3}$