Consider the inequality $\mid 3x+1\mid \le -2$. Which of the following is the correct determination and why?

All real numbers, because if the right-hand side is negative then the inequality is automatically satisfied by every real $x$

$x=-1/3$ only, because the only candidate for equality is where the inside becomes zero, and therefore might satisfy the inequality even if the right-hand side is negative

No solution, because an absolute value is always $\ge 0$ and therefore can never be $\le$ a negative number

$x\le -1/3$ or $x\ge -1/3$ because an inequality with absolute value splits into two rays, and the negative bound simply flips the direction of the rays