Question

f is the midpoint of (overline{eg}). if (ef = 9x) and (eg = 14x + 9), 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 $EF = FG$ and $EG=EF + FG = 2EF$.
We know that $EF = 9x$ and $EG=14x + 9$, and also $EG = 2EF$. So $14x+9 = 2\times9x$.

Step2: Solve the equation for $x$

Expand the right - hand side: $14x+9 = 18x$.
Subtract $14x$ from both sides: $9=18x - 14x$.
Simplify the right - hand side: $9 = 4x$.
Solve for $x$: $x=\frac{9}{4}$.

Step3: Find the value of $EG$

Substitute $x = \frac{9}{4}$ into the expression for $EG$.
$EG=14x + 9=14\times\frac{9}{4}+9$.
$EG=\frac{14\times9}{4}+9=\frac{126}{4}+9$.
Make a common denominator: $EG=\frac{126}{4}+\frac{9\times4}{4}=\frac{126 + 36}{4}=\frac{162}{4}=\frac{81}{2}=40\frac{1}{2}$.

Answer:

$40\frac{1}{2}$