Question

if ef = 6x, fg = 8, and eg = 10x, what is ef? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $EG=EF + FG$, we have the equation $10x=6x + 8$.

Step2: Solve for $x$

Subtract $6x$ from both sides of the equation: $10x-6x=6x + 8-6x$. This simplifies to $4x=8$. Then divide both sides by 4: $x=\frac{8}{4}=2$.

Step3: Find the value of $EF$

Since $EF = 6x$ and $x = 2$, then $EF=6\times2 = 12$.

Answer:

12