1. **State the problem:** Solve the equation $-10 - 7x = -3x - 2$ for $x$. 2. **Write down the equation:** $$-10 - 7x = -3x - 2$$ 3. **Goal:** Isolate $x$ on one side. 4. **Add $7x$ to both sides to move $x$ terms to the right:** $$-10 = -3x + 7x - 2$$ 5. **Simplify the right side:** $$-10 = 4x - 2$$ 6. **Add $2$ to both sides to isolate the term with $x$:** $$-10 + 2 = 4x$$ 7. **Simplify the left side:** $$-8 = 4x$$ 8. **Divide both sides by $4$ to solve for $x$:** $$x = \frac{-8}{4}$$ 9. **Simplify the fraction:** $$x = -2$$ **Final answer:** $x = -2$