1. **State the problem:** Solve for $x$ in the equation $$\frac{3x - 3}{5} = \frac{2x - 2}{4}$$ using cross multiplication. 2. **Formula and rule:** Cross multiplication means multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal: $$ (3x - 3) \times 4 = (2x - 2) \times 5 $$ 3. **Apply cross multiplication:** $$ 4(3x - 3) = 5(2x - 2) $$ 4. **Distribute:** $$ 12x - 12 = 10x - 10 $$ 5. **Bring like terms together:** $$ 12x - 10x = -10 + 12 $$ 6. **Simplify:** $$ 2x = 2 $$ 7. **Divide both sides by 2:** $$ x = \frac{\cancel{2}x}{\cancel{2}} = \frac{2}{2} $$ 8. **Final answer:** $$ x = 1 $$