1. **State the problem:** Solve the inequality $x + 3 \neq -1$. 2. **Formula and rules:** To isolate $x$, subtract 3 from both sides of the inequality. 3. **Intermediate work:** $$x + 3 \neq -1$$ Subtract 3 from both sides: $$x + 3 - \cancel{3} \neq -1 - \cancel{3}$$ $$x \neq -4$$ 4. **Explanation:** We moved the constant term 3 to the right side by subtracting it from both sides, which isolates $x$. The inequality sign remains the same because we are subtracting a number, not multiplying or dividing by a negative. 5. **Final answer:** $$x \neq -4$$