1. **State the problem:** Solve the inequality $4x + 7 \neq 11$ for $x$. 2. **Write the inequality:** $$4x + 7 \neq 11$$ 3. **Isolate the term with $x$ by subtracting 7 from both sides:** $$4x + 7 - 7 \neq 11 - 7$$ $$4x \neq 4$$ 4. **Divide both sides by 4 to solve for $x$:** $$\frac{4x}{\cancel{4}} \neq \frac{4}{\cancel{4}}$$ $$x \neq 1$$ 5. **Interpretation:** The solution means $x$ can be any real number except 1. **Final answer:** $$x \neq 1$$