Question

point g is on line segment $overline{fh}$. given $fg = 5x + 2$, $gh = 3x - 1$, and $fh = 9$, determine the numerical length of $overline{fg}$.

Explanation:

Step1: Use segment - addition postulate

Since point $G$ is on line segment $\overline{FH}$, we have $FG + GH=FH$. Substitute the given expressions: $(5x + 2)+(3x - 1)=9$.

Step2: Simplify the left - hand side

Combine like terms: $5x+3x + 2-1=9$, which simplifies to $8x+1 = 9$.

Step3: Solve for $x$

Subtract 1 from both sides: $8x=9 - 1$, so $8x=8$. Then divide both sides by 8: $x = 1$.

Step4: Find the length of $FG$

Substitute $x = 1$ into the expression for $FG$. $FG=5x + 2$, so $FG=5(1)+2=5 + 2=7$.

Answer:

7