Explain why absolute value equations have more than one solution. create an absolute value equation with no solution and explain why it does not have one

Absolute value equations have more than one solution because when the answer is in abs. value, it is positive, so there could be a negative answer and it would still be positive. For example |-5|=5 and |5|=5 as well. 
4+|2x|=-1 would have no solution because you cannot have the equation equal a negative since the 2x is in absolute value.