Question

f is the midpoint of $overline{eg}$. if $ef = 2x$ and $fg = x + 7$, 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 the mid - point of $\overline{EG}$, we have $EF = FG$. So, $2x=x + 7$.

Step2: Solve for $x$

Subtract $x$ from both sides of the equation $2x=x + 7$. We get $2x-x=x + 7-x$, which simplifies to $x = 7$.

Step3: Find the value of $FG$

Substitute $x = 7$ into the expression for $FG$. Since $FG=x + 7$, then $FG=7 + 7=14$.

Answer:

14