1. **Problem:** Solve the inequality $4x < -x$. 2. **Formula and rules:** To solve inequalities, we isolate $x$ on one side. When dividing or multiplying by a negative number, the inequality sign reverses. 3. **Step-by-step solution:** 1. Start with the inequality: $$4x < -x$$ 2. Add $x$ to both sides to collect $x$ terms on one side: $$4x + x < -x + x$$ $$5x < 0$$ 3. Divide both sides by 5 (positive number, so inequality sign stays the same): $$\cancel{5}x < \cancel{5}0$$ $$x < 0$$ 4. **Answer:** The solution is $x < 0$, which corresponds to option А).