Question

if ef = 8x + 6, fg = 9x - 17, and eg = 18x - 19, 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: $(8x + 6)+(9x - 17)=18x-19$.

Step2: Combine like - terms on the left - hand side

$8x+9x + 6-17=18x-19$, which simplifies to $17x - 11=18x-19$.

Step3: Solve for x

Subtract $17x$ from both sides: $-11=x - 19$. Then add 19 to both sides, we get $x = 8$.

Step4: Find the value of FG

Substitute $x = 8$ into the expression for $FG$. Since $FG=9x - 17$, then $FG=9\times8-17$.
$FG = 72-17$.
$FG = 55$.

Answer:

55