>>12220445>how is this wrong?The problem with solving equations is, we are only able to directly solve a very small subset of Simple Equations.
To get around this, we apply certain transformations to the equations we can't solve, to produce equations which we can solve.
Definition: we call two equations equivalent if they have the same set of solutions. No matter how different they look like.
Now, depending on the type of transformations there are two common methods of solving equations:
Equivalent equation methods - in this method we apply the type of transformations to the equations which for certain will produce an equivalent equation. Those transformations are eg. adding a number to both sides of an equation, multiplication by a number different than zero, division by a number different than a zero, or more in general: applying same injective function to both sides of an equation, or extracting the arguments of the same injective function from both sides of an equation.
But anything goes really - if you can prove some equation has the same set of roots as yours, no matter how alien it looks, you can go with it.
This way we try to get to an equivalent Simple Equation which can finally solve.
