Question

point f is on line segment eg. given fg = 3x - 5, ef = x, and eg = 5x - 8, determine the numerical length of fg.

Explanation:

Step1: Use segment - addition postulate

Since point F is on line segment EG, we have $EF + FG=EG$. Substituting the given expressions: $x+(3x - 5)=5x - 8$.

Step2: Simplify the left - hand side of the equation

Combining like terms on the left - hand side, we get $4x-5 = 5x - 8$.

Step3: Solve for x

Subtract $4x$ from both sides: $-5=x - 8$. Then add 8 to both sides, so $x = 3$.

Step4: Find the length of FG

Substitute $x = 3$ into the expression for FG. Since $FG=3x - 5$, then $FG=3\times3 - 5$.
$FG=9 - 5$.

Answer:

$4$