1. **State the problem:** Given the equation $$8x - \frac{2y}{3} = xy + y,$$ express $x$ in terms of $y$. 2. **Rewrite the equation:** Start by writing the equation clearly: $$8x - \frac{2y}{3} = xy + y$$ 3. **Group terms involving $x$ on one side:** Move all terms with $x$ to the left and others to the right: $$8x - xy = y + \frac{2y}{3}$$ 4. **Factor out $x$ on the left side:** $$x(8 - y) = y + \frac{2y}{3}$$ 5. **Simplify the right side:** $$y + \frac{2y}{3} = \frac{3y}{3} + \frac{2y}{3} = \frac{5y}{3}$$ 6. **Substitute back:** $$x(8 - y) = \frac{5y}{3}$$ 7. **Solve for $x$ by dividing both sides by $(8 - y)$:** $$x = \frac{\frac{5y}{3}}{8 - y}$$ 8. **Show cancellation explicitly:** $$x = \frac{5y}{3} \cdot \frac{1}{8 - y} = \frac{5y}{3(8 - y)}$$ **Final answer:** $$x = \frac{5y}{3(8 - y)}$$