Solve the inequality |5x + 2| < 0.

There is no solution to the inequality |5x + 2| < 0.

To solve this inequality, we first need to understand what absolute value means. The absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of any number is always non-negative.

In this inequality, we have |5x + 2| < 0. Since the absolute value of any number is always non-negative, it is impossible for it to be less than zero. Therefore, there is no solution to this inequality.

We can also see this algebraically. Let's assume that there is a solution to the inequality, and call it x. Then we have:

|5x + 2| < 0
5x + 2 < 0 and -(5x + 2) < 0
5x < -2 and -5x < -2
x < -2/5 and x > 2/5

However, these two inequalities cannot both be true at the same time. Therefore, there is no solution to the inequality |5x + 2| < 0.