Question

point g is on line segment $overline{fh}$. given $fg = 5x + 2$, $gh = 3x - 1$, and $fh = 9$. determine the numerical length of $overline{fg}$. a 1 b 9 c 7 d 2

Explanation:

Step1: Use segment - addition postulate

Since point $G$ is on line segment $\overline{FH}$, we have $FG + GH=FH$. Let $FH = 9$ (missing value assumed from context as it's not fully shown but needed to solve). So, $(5x + 2)+(3x - 1)=9$.

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, we get $x = 1$.

Step4: Find the length of $FG$

Substitute $x = 1$ into the expression for $FG$. $FG=5x + 2$, so $FG=5\times1+2=7$.

Answer:

C. 7