$\frac{9}{8}R+31=Q$
Subtract $31$ from both sides$\frac{9}{8}R+31-31=Q-31$
Simplify$\frac{9}{8}R=Q-31$
Multiply both sides by $8$$8\cdot \frac{9}{8}R=8Q-8\cdot 31$
Simplify$9R=8Q-248$
Divide both sides by $9$$\frac{9R}{9}=\frac{8Q}{9}-\frac{248}{9}$
Simplify$R=\frac{8Q-248}{9}$