Problem scale dependence with equilibrate function

I am interested in using equilibrate and noticed a note written here Rescaling to Solve a Linear System. Could someone explain to me what the following statement means with an example?

"equilibrate is most useful when the scales of the b and x vectors in the original system x = A\b are irrelevant. However, if the scales of b and x are relevant, then using equilibrate to rescale A only for the linear system solve is not recommended."