1. **State the problem:** Solve the equation $$\frac{8x}{5} - \frac{x}{4} = -3$$ for $x$. 2. **Find a common denominator:** The denominators are 5 and 4. The least common denominator (LCD) is 20. 3. **Rewrite each term with denominator 20:** $$\frac{8x}{5} = \frac{8x \times 4}{5 \times 4} = \frac{32x}{20}$$ $$\frac{x}{4} = \frac{x \times 5}{4 \times 5} = \frac{5x}{20}$$ 4. **Rewrite the equation:** $$\frac{32x}{20} - \frac{5x}{20} = -3$$ 5. **Combine the fractions:** $$\frac{32x - 5x}{20} = -3$$ $$\frac{27x}{20} = -3$$ 6. **Multiply both sides by 20 to clear the denominator:** $$\cancel{20} \times \frac{27x}{\cancel{20}} = -3 \times 20$$ $$27x = -60$$ 7. **Divide both sides by 27 to solve for $x$:** $$x = \frac{-60}{27}$$ 8. **Simplify the fraction by dividing numerator and denominator by 3:** $$x = \frac{\cancel{-60}^{\div 3}}{\cancel{27}^{\div 3}} = \frac{-20}{9}$$ **Final answer:** $$x = -\frac{20}{9}$$