Why does ##|x| < 0## have no solution?

This is impossible due to the definition of .

An absolute value is the distance of a number from zero on the number line. For instance, three on the number line is the value of three from zero. Negative three is also three away from zero, so the absolute value of negative three is three as well. An easier way to think about absolute value is just making the value positive.

In this case, we have the absolute value of x is less than 0. Because of the definition of absolute value, the absolute value of x cannot be negative; it must be positive. Therefore, the absolute value cannot be less than 0.