Solve the inequality |4x + 1| >= 0.

The inequality |4x + 1| >= 0 is true for all real values of x.

To solve this inequality, we first need to understand what the absolute value function represents. The absolute value of a number is its distance from zero on the number line. Therefore, |4x + 1| represents the distance between 4x + 1 and zero on the number line.

Since distance is always non-negative, we know that |4x + 1| is always greater than or equal to zero. Therefore, the inequality |4x + 1| >= 0 is true for all real values of x.

In other words, there are no restrictions on the values of x that satisfy this inequality. Any real number can be plugged in for x and the inequality will still be true.

This may seem like a trivial solution, but it is important to understand that not all inequalities have restrictions on their solutions. In this case, the inequality is always true, regardless of the value of x.