Question

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

Explanation:

Step1: Use mid - point property

Since F is the mid - point of $\overline{EG}$, then $EF = FG$. So we set up the equation $x + 8=5x$.

Step2: Solve the equation for x

Subtract x from both sides: $8 = 5x−x$. Simplify the right - hand side to get $8 = 4x$. Then divide both sides by 4: $x=\frac{8}{4}=2$.

Step3: Find the value of EF

Substitute $x = 2$ into the expression for EF. Since $EF=x + 8$, then $EF=2 + 8=10$.

Answer:

10