Given :
R is the midpoint of QS
QR = 6x - 9
RS = 2x - 1
We need to find QS
So, as R is the midpoint
[tex]\begin{gathered} QR=RS \\ 6x-9=2x-1 \end{gathered}[/tex]Solve the equation to find x :
[tex]\begin{gathered} 6x-9=2x-1 \\ 6x-2x=-1+9 \\ 4x=8 \\ \\ x=\frac{8}{4}=2 \end{gathered}[/tex]Substitute with x to find QR and QS
[tex]\begin{gathered} QR=6\cdot2-9=12-9=3 \\ RS=2\cdot2-1=4-1=3 \\ \\ QS=QR+RS=3+3=6 \end{gathered}[/tex]