1. **State the problem:** Solve for $x$ in the equation $$-2(x - 3) = 3x + 41$$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses: $$-2 \times x = -2x$$ $$-2 \times (-3) = +6$$ So the equation becomes: $$-2x + 6 = 3x + 41$$ 3. **Collect like terms:** Move all terms involving $x$ to one side and constants to the other side. Add $2x$ to both sides: $$\cancel{-2x} + 6 + 2x = 3x + 41 + 2x$$ which simplifies to: $$6 = 5x + 41$$ 4. **Isolate the variable term:** Subtract $41$ from both sides: $$6 - 41 = 5x + \cancel{41} - 41$$ which simplifies to: $$-35 = 5x$$ 5. **Solve for $x$:** Divide both sides by $5$: $$\frac{-35}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ which simplifies to: $$x = -7$$ **Final answer:** $$x = -7$$