1. **State the problem:** Solve the equation $x + 7 = -2x - 2$ for $x$. 2. **Write down the equation:** $$x + 7 = -2x - 2$$ 3. **Add $2x$ to both sides to collect $x$ terms on one side:** $$x + 2x + 7 = -2x + 2x - 2$$ $$3x + 7 = -2$$ 4. **Subtract 7 from both sides to isolate the term with $x$:** $$3x + \cancel{7} - \cancel{7} = -2 - 7$$ $$3x = -9$$ 5. **Divide both sides by 3 to solve for $x$:** $$\frac{3x}{\cancel{3}} = \frac{-9}{\cancel{3}}$$ $$x = -3$$ 6. **Final answer:** $$\boxed{x = -3}$$