1. **Stating the problem:** The inequality given is $1 + 3x \neq 1 + 3x$. 2. **Analyzing the inequality:** Both sides of the inequality are the same expression: $1 + 3x$. 3. **Conclusion:** Since both sides are identical for all values of $x$, the inequality $1 + 3x \neq 1 + 3x$ cannot be true for any real number $x$. Therefore, the inequality has no solution.