Solve the inequality |11x + 3| <= 0.

The inequality |11x + 3| <= 0 has no solutions.

To solve this inequality, we first note that the absolute value of any real number is always non-negative. That is, |a| >= 0 for all a in R. Therefore, |11x + 3| >= 0 for all x in R.

Now, suppose there exists some x in R such that |11x + 3| <= 0. Then, by the definition of absolute value, we must have 11x + 3 = 0. Solving for x, we get x = -3/11.

However, this value of x does not satisfy the original inequality, since |11(-3/11) + 3| = |-3 + 3| = 0 > 0. Therefore, there are no solutions to the inequality |11x + 3| <= 0.

In summary, the inequality |11x + 3| <= 0 has no solutions, since the absolute value of any real number is always non-negative.