1. **State the problem:** Solve the inequality $$-4 \leq 3x - 1$$ for $$x$$. 2. **Add 1 to both sides** to isolate the term with $$x$$: $$-4 + 1 \leq 3x - 1 + 1$$ which simplifies to $$-3 \leq 3x$$ 3. **Divide both sides by 3** to solve for $$x$$. Since 3 is positive, the inequality direction stays the same: $$\frac{-3}{\cancel{3}} \leq \frac{3x}{\cancel{3}}$$ which simplifies to $$-1 \leq x$$ 4. **Rewrite the solution:** $$x \geq -1$$ This means $$x$$ is any number greater than or equal to $$-1$$. **Final answer:** $$x \geq -1$$