Question

f is the midpoint of $overline{eg}$. if $ef = x - 4$ and $eg = 3x - 13$, what is $eg?
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 $EG = 2EF$. So we have the equation $3x−13 = 2(x - 4)$.

Step2: Expand the right - hand side

Expand $2(x - 4)$ to get $2x-8$. The equation becomes $3x−13=2x - 8$.

Step3: Solve for $x$

Subtract $2x$ from both sides: $3x-2x−13=2x-2x - 8$, which simplifies to $x−13=-8$. Then add 13 to both sides: $x=-8 + 13$, so $x = 5$.

Step4: Find the value of $EG$

Substitute $x = 5$ into the expression for $EG$. $EG=3x−13=3\times5−13=15 - 13=2$.

Answer:

$2$