1. **State the problem:** Solve the equation $$\frac{5x - 8}{2} = \frac{5x}{6}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the least common denominator (LCD) to eliminate fractions. 3. **Find the LCD:** The denominators are 2 and 6. The LCD is 6. 4. **Multiply both sides by 6:** $$6 \times \frac{5x - 8}{2} = 6 \times \frac{5x}{6}$$ 5. **Simplify both sides:** $$3(5x - 8) = 5x$$ 6. **Distribute 3 on the left side:** $$15x - 24 = 5x$$ 7. **Subtract $5x$ from both sides:** $$15x - 5x - 24 = 0$$ $$10x - 24 = 0$$ 8. **Add 24 to both sides:** $$10x = 24$$ 9. **Divide both sides by 10:** $$x = \frac{24}{10} = \frac{12}{5} = 2.4$$ **Final answer:** $$x = \frac{12}{5}$$