# prediction for a linear sum

I am learning about SVMs in particular linear SVMs through many questions here. However, one problem i faced is that there seems to be no indepth explanation on how does linear SVM works in terms of predicting new data.

I understand that the main purpose of SVM is to find linear separating hyperplane $$w^Tx+b$$ and a linear SVM is actually a set of super long equation. Let's consider a 2 class problem : A and B. Suppose $$(w^*,b^*)$$ are the minimizing hyperplane parameters for a fixed choice of $$\lambda$$.

Then how we classify a new, unlabeled test point $$x_{test}$$? Simple way that I thought would be reasonable is to have $$(w^*)^Tx+b^*>0$$ to class A and $$(w^*)^Tx+b^*<0$$ to class B. But how do we assign if it's 0 and what if there is an outlier in other class for example? IS this a good way of labeling test data?