1. **State the problem:** Solve the inequality $3x + 5 \le 4x + 1$. 2. **Isolate variable terms:** Subtract $3x$ from both sides to get $$3x + 5 - \cancel{3x} \le 4x + 1 - \cancel{3x}$$ which simplifies to $$5 \le x + 1$$. 3. **Isolate $x$:** Subtract $1$ from both sides: $$5 - 1 \le x + 1 - 1$$ which simplifies to $$4 \le x$$. 4. **Rewrite solution:** This means $$x \ge 4$$. 5. **Interpretation:** The solution set includes all real numbers $x$ such that $x$ is greater than or equal to $4$. **Final answer:** $x \ge 4$