There are some differences between the US basic solving process for algebra equations and inequalities and the world wide one. We teach students to solve equations by observing the principle of balancing the two sides of an equation. The common saying is likely:"Do the same thing to the right side what you did to the left side". On the contrary, the world wide solving process performs by transposing terms from one side to another, while always keeping the equation balanced. The likely saying is:"The running guy appears on the other equation's side with an opposite outfit".
This article generally explains some differences of the 2 solving processes, then it compares them through selected examples.