1. **State the problem:** Simplify and solve the equation $3 (x - 3) - 5 (3 - x) + 12 = 15 - 3 (3 - x)$. 2. **Distribute the terms:** Apply the distributive property to remove parentheses. $$3x - 9 - 5 \times 3 + 5x + 12 = 15 - 3 \times 3 + 3x$$ which simplifies to $$3x - 9 - 15 + 5x + 12 = 15 - 9 + 3x$$ 3. **Combine like terms on each side:** Left side: $3x + 5x = 8x$ and $-9 - 15 + 12 = -12$ Right side: $15 - 9 = 6$ So the equation becomes $$8x - 12 = 6 + 3x$$ 4. **Isolate variable terms on one side:** Subtract $3x$ from both sides $$8x - 3x - 12 = 6 + 3x - 3x$$ Using cancellation notation: $$\cancel{8x} - \cancel{3x} - 12 = 6 + \cancel{3x} - \cancel{3x}$$ which simplifies to $$5x - 12 = 6$$ 5. **Isolate $x$:** Add 12 to both sides $$5x - 12 + 12 = 6 + 12$$ $$5x = 18$$ 6. **Solve for $x$:** Divide both sides by 5 $$\frac{5x}{\cancel{5}} = \frac{18}{\cancel{5}}$$ $$x = \frac{18}{5}$$ **Final answer:** $$x = \frac{18}{5}$$