Problem with solving an equation

Question

I have a problem solving the equation (167) to (168) from this page: http://nlp.stanford.edu/IR-book/html/htmledition/support-vector-machines-the-linearly-separable-case-1.html#tex2html165

I never get to that solution, how is it possible if I have y*r on one side, to become r = something *y on the other side and not divided by y?

Answer 1

$$w^T\left(x-yr\frac{w}{|w|}\right)+b = 0$$

$$w^Tx-yr\frac{w^Tw}{|w|}+b = 0$$

$$w^Tx-yr\frac{|w|^2}{|w|}+b = 0$$

$$w^Tx+b= yr |w|$$

$$r = \frac{w^Tx+b}{y|w|}$$

Since $y \in \{ -1, 1\}$, $\frac1y=y$

$$r = y\frac{w^Tx+b}{|w|}$$