Question

How can an absolute value equation have no solution?

Answer 1

For example, `|x|=-1` has no solution.

The absolute value of a number is its distance away from zero. That number will always be positive, as you cannot be negative two feet away from something. So any absolute value equation set equal to a negative number is no solution, regardless of what that number is.
`|x|!=-y`

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I hope that this was helpful.