Question

if ef = 2x, fg = x + 5, and eg = 8, 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 have the equation $2x+(x + 5)=8$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $2x+x+5 = 8$, which simplifies to $3x+5 = 8$.

Step3: Isolate the variable term

Subtract 5 from both sides of the equation: $3x+5 - 5=8 - 5$, resulting in $3x=3$.

Step4: Solve for $x$

Divide both sides of the equation $3x = 3$ by 3: $\frac{3x}{3}=\frac{3}{3}$, so $x = 1$.

Step5: Find the length of $FG$

Substitute $x = 1$ into the expression for $FG$. Since $FG=x + 5$, then $FG=1 + 5=6$.

Answer:

6