Question

if ef = x + 5, fg = 17x - 3, and eg = 20, 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: $20=(x + 5)+(17x-3)$.

Step2: Simplify the right - hand side

Combine like terms: $20=x + 5+17x-3=18x + 2$.

Step3: Solve for x

Subtract 2 from both sides: $20-2=18x$, so $18 = 18x$. Then divide both sides by 18, we get $x = 1$.

Step4: Find the value of FG

Substitute $x = 1$ into the expression for $FG$. Since $FG=17x-3$, then $FG=17\times1-3$.
$FG=17 - 3=14$.

Answer:

14