1. **State the problem:** Solve the inequality $$4 - 5 + x \neq -3$$. 2. **Simplify the left side:** Combine like terms. $$4 - 5 + x = (4 - 5) + x = -1 + x$$ So the inequality becomes: $$-1 + x \neq -3$$ 3. **Isolate the variable $x$:** Add 1 to both sides to isolate $x$. $$\cancel{-1} + x + 1 \neq -3 + 1$$ $$x \neq -2$$ 4. **Interpret the solution:** The solution means $x$ can be any real number except $-2$. **Final answer:** $$x \neq -2$$