1. **State the problem:** Solve the linear equation $-13 - 4x = x + 7$ for $x$. 2. **Write down the equation:** $$-13 - 4x = x + 7$$ 3. **Goal:** Isolate $x$ on one side of the equation. 4. **Add $4x$ to both sides to move all $x$ terms to the right:** $$-13 = x + 7 + 4x$$ 5. **Combine like terms on the right:** $$-13 = 5x + 7$$ 6. **Subtract 7 from both sides to isolate the term with $x$:** $$-13 - 7 = 5x$$ $$-20 = 5x$$ 7. **Divide both sides by 5 to solve for $x$:** $$x = \frac{-20}{5}$$ $$x = -4$$ **Final answer:** $$x = -4$$