Question

on a line segment, f is between e and g. if ef = 12, fg = x + 14, and eg = 3x - 12, what is fg? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $F$ is between $E$ and $G$, we have $EF + FG=EG$. Substitute the given expressions: $12+(x + 14)=3x-12$.

Step2: Simplify the left - hand side of the equation

Combine like terms on the left - hand side: $12+x + 14=x+26$. So the equation becomes $x + 26=3x-12$.

Step3: Isolate the variable terms

Subtract $x$ from both sides: $x+26-x=3x - 12-x$, which simplifies to $26 = 2x-12$.

Step4: Solve for $x$

Add 12 to both sides: $26 + 12=2x-12 + 12$, getting $38 = 2x$. Then divide both sides by 2: $\frac{38}{2}=\frac{2x}{2}$, so $x = 19$.

Step5: Find the length of $FG$

Since $FG=x + 14$, substitute $x = 19$ into the expression for $FG$. Then $FG=19 + 14=33$.

Answer:

33