What is the new Transposing Method to solve linear equations?

The Transposing Method transposes the algebraic terms (numbers, parameters, expression...) from side to side of the equation by changing them to the opposite signs, while keeping the equation balanced. This method has many advantages over the balancing method

The balancing method creates the double writing of algebraic terms on the 2 sides of the of the equation. Example. Solve: ##x + (m - n)/2 = n + 3## ##x + (m - n)/2 - (m - n)/2 = n + 3 - (m - n)/2## ##x = n + 3 - (m - n)/2## This double writing looks simple and easy at the beginning of one step equation. However, when the equations get more complicated, this double writing takes too much time and easily leads to error/mistake. The Transposing Method smartly solves equations by much simpler operations. Example. Solve: ##(m + n - p)/(q - r) = (t + u)/(x - 7).## ##(x - 7) = ((t + u)(q - r))/(m + n - p)## ##x = 7 + ((t + u)(q - r))/(m + n - p)## There is no abundant writing of terms on both sides of the equation.