1. Stating the problem: Solve the equation $$2X - \frac{2}{3} = 5X + 3$$. 2. Write down the equation: $$2X - \frac{2}{3} = 5X + 3$$ 3. Move all terms involving $X$ to one side and constants to the other side: $$2X - 5X = 3 + \frac{2}{3}$$ 4. Simplify both sides: $$-3X = 3 + \frac{2}{3}$$ 5. Convert 3 to a fraction with denominator 3: $$3 = \frac{9}{3}$$ 6. Add the fractions on the right side: $$-3X = \frac{9}{3} + \frac{2}{3} = \frac{11}{3}$$ 7. Divide both sides by $-3$ to solve for $X$: $$X = \frac{\frac{11}{3}}{-3} = \frac{11}{3} \times \frac{-1}{3} = -\frac{11}{9}$$ Final answer: $$X = -\frac{11}{9}$$