Question

if ef = 18, fg = 7x, and eg = 12x - 2, what is fg? 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 substitute the given expressions: $12x - 2=18 + 7x$.

Step2: Solve for $x$

Subtract $7x$ from both sides: $12x-7x - 2=18+7x - 7x$, which simplifies to $5x-2 = 18$. Then add 2 to both sides: $5x-2 + 2=18 + 2$, so $5x=20$. Divide both sides by 5: $x=\frac{20}{5}=4$.

Step3: Find the value of $FG$

Since $FG = 7x$, substitute $x = 4$ into the expression. So $FG=7\times4 = 28$.

Answer:

28