Question

point f is on line segment $overline{eg}$. given $fg = 3x - 5$, $ef = x$, and $eg = 5x - 8$, determine the numerical length of $overline{fg}$.

Explanation:

Step1: Use segment - addition postulate

Since point F is on line segment $\overline{EG}$, we know that $EF + FG=EG$. Substitute the given expressions: $x+(3x - 5)=5x - 8$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+3x-5 = 4x-5$. So the equation becomes $4x - 5=5x - 8$.

Step3: Solve for x

Subtract $4x$ from both sides: $4x-5-4x=5x - 8-4x$, which simplifies to $-5=x - 8$. Then add 8 to both sides: $-5 + 8=x-8 + 8$, so $x = 3$.

Step4: Find the length of FG

Substitute $x = 3$ into the expression for $FG$. Since $FG=3x - 5$, then $FG=3\times3-5$.
Calculate $3\times3-5=9 - 5=4$.

Answer:

4