1. **State the problem:** Solve for $x$ in the equation $$-3(2x - 6) = -5 - (x - 8)$$. 2. **Apply the distributive property:** Multiply $-3$ by each term inside the parentheses on the left side. $$-3 \times 2x = -6x$$ $$-3 \times (-6) = +18$$ So the equation becomes: $$-6x + 18 = -5 - (x - 8)$$ 3. **Simplify the right side:** Distribute the negative sign across the parentheses. $$-5 - x + 8$$ Combine like terms: $$-5 + 8 = 3$$ So the right side is: $$3 - x$$ 4. **Rewrite the equation:** $$-6x + 18 = 3 - x$$ 5. **Get all $x$ terms on one side and constants on the other:** Add $6x$ to both sides. $$-6x + 6x + 18 = 3 - x + 6x$$ Intermediate step showing cancellation: $$\cancel{-6x} + \cancel{6x} + 18 = 3 - x + 6x$$ Simplify: $$18 = 3 + 5x$$ 6. **Subtract 3 from both sides:** $$18 - 3 = 3 - 3 + 5x$$ Intermediate step: $$15 = \cancel{3} - \cancel{3} + 5x$$ Simplify: $$15 = 5x$$ 7. **Divide both sides by 5 to solve for $x$:** $$\frac{15}{5} = \frac{5x}{5}$$ Intermediate step showing cancellation: $$\frac{15}{\cancel{5}} = x$$ Simplify: $$3 = x$$ **Final answer:** $$x = 3$$