Question

g is a point on segment $overline{fh}$. if $fg = x - 8$, $gh = 15$, and $fh = 2x - 12$, what is $fg$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $G$ is on segment $\overline{FH}$, we have $FG + GH=FH$. Substitute the given expressions: $(x - 8)+15 = 2x-12$.

Step2: Simplify the left - hand side

Combine like terms on the left - hand side: $x+(15 - 8)=2x - 12$, which gives $x + 7=2x-12$.

Step3: Solve for $x$

Subtract $x$ from both sides: $x - x+7=2x - x-12$, so $7=x - 12$. Then add 12 to both sides: $7 + 12=x$, and $x = 19$.

Step4: Find $FG$

Substitute $x = 19$ into the expression for $FG$. Since $FG=x - 8$, then $FG=19 - 8$.

Answer:

11