Basically, that's all there is to it. Whenever we have a negative number on the other side of an
inequality from the absolute value, we have to be very careful with how to proceed. The nice thing is,
there’s no work to do, we just have to think about whether it’s never true (no solution), or always true
(-inf, inf).
•
If it's ||< -number, the answer is no solution, because || can never be less than a negative.
•
If it's ||= -number, the answer is again no solution, because || can not be equal to a negative.
• If it’s ||> -number, the answer is ALL REAL NUMBERS! Or (-inf,inf). This is because
no matter what you plug into the absolute value, it will become positive, which is always
bigger than a –number.
Does that make sense?