There is probably no reason for me to need this, but I was just curious if you could theoretically form an algebraic equation as a replacement for the absolute value function. It may already exist, but I searched for a little while and couldn't find one, including the other question on here where the only solution enters imaginary numbers. I feel like I was getting close with
f(x) = x*(blah)
where blah would just be 1 either with or without the negative based on what f(x) is.
Sorry if this seems like an insignificant question!