There are no solutions. [tex]|a|[/tex] gives the absolute value of the number [tex]a[/tex], defined by
[tex]|a|=\begin{cases}a&\text{for }a\ge0\\-a&\text{for }a<0\end{cases}[/tex]
That is, if [tex]a[/tex] is not negative, then [tex]|a|=a[/tex]; otherwise, if [tex]a[/tex] is a negative number - let's call it [tex]a=-b[/tex], where [tex]b[/tex] is a non-negative number - then we negate it to get [tex]|a|=|-b|=-(-b)=b=-a[/tex] so that [tex]|a|[/tex] is still non-negative.
Long story short, [tex]|x|[/tex] can never take on a negative value, so there are no solutions to [tex]|x|=-3[/tex] for [tex]x[/tex].
