1. **State the problem:** Solve the equation $$\frac{5 - 2x}{6} = 3x - 4$$ for $x$. 2. **Multiply both sides by 6** to eliminate the denominator: $$6 \times \frac{5 - 2x}{6} = 6 \times (3x - 4)$$ which simplifies to $$5 - 2x = 18x - 24$$ 3. **Bring all terms involving $x$ to one side and constants to the other:** Add $2x$ to both sides: $$5 = 18x - 24 + 2x$$ $$5 = 20x - 24$$ Add $24$ to both sides: $$5 + 24 = 20x$$ $$29 = 20x$$ 4. **Solve for $x$ by dividing both sides by 20:** $$x = \frac{29}{20}$$ 5. **Final answer:** $$x = \frac{29}{20}$$ or $1.45$ approximately. This means the solution to the equation is $x = \frac{29}{20}$.