1. **State the problem:** Solve the equation $-2(3x + 5) + x - 5 = -45$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses. $$-2 \times 3x = -6x$$ $$-2 \times 5 = -10$$ So the equation becomes: $$-6x - 10 + x - 5 = -45$$ 3. **Combine like terms on the left side:** Combine $-6x$ and $x$, and combine $-10$ and $-5$. $$-6x + x = -5x$$ $$-10 - 5 = -15$$ So the equation is: $$-5x - 15 = -45$$ 4. **Isolate the term with $x$:** Add 15 to both sides. $$-5x - 15 + 15 = -45 + 15$$ $$-5x = -30$$ 5. **Solve for $x$ by dividing both sides by $-5$:** $$x = \frac{-30}{-5}$$ Show cancellation: $$x = \frac{\cancel{-30}}{\cancel{-5}} = 6$$ 6. **Final answer:** $$x = 6$$