Question

g is the midpoint of $overline{fh}$. if $fg = x + 5$ and $gh = 3x - 8$, what is $gh?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since G is the mid - point of $\overline{FH}$, then $FG = GH$. So we set up the equation $x + 5=3x - 8$.

Step2: Solve for x

Subtract x from both sides: $5 = 3x - x-8$, which simplifies to $5 = 2x - 8$. Then add 8 to both sides: $5 + 8=2x$, so $13 = 2x$. Divide both sides by 2, we get $x=\frac{13}{2}$.

Step3: Find the value of GH

Substitute $x = \frac{13}{2}$ into the expression for GH. $GH=3x - 8=3\times\frac{13}{2}-8=\frac{39}{2}-8=\frac{39}{2}-\frac{16}{2}=\frac{39 - 16}{2}=\frac{23}{2}=11\frac{1}{2}$.

Answer:

$11\frac{1}{2}$