Given Question
The problem can be translated to: IxI = -x.
Procedure
These lead to a system of linear equations
x = -x for x>0….Equation 1
or
x = -(-x) for x<0….Equation 2
From Equation 1 x = 0 which is not accepted since it is given x is a non-zero real number.
From the Equation 2 x = x
Which is valid for all real numbers such that x<0
Conclusion
Therefore we conclude here that x should be a negative real number to have its absolute value equals to its opposite.