User:Numiri/KinderCalculus/Dress

Often, we are given an equation, say 4x + 5y = 3, and be asked to "solve for y". In an archeology analogy, we are asked to dig through layers of dirt to discover the bare bones fossil of "y". If we look at an equation as a scale balancing 2 weights, we see how to dig through layers of dirt.



\begin{align} 4x+5y &= 3\\ -4x + 4x +5y &= 3-4x \qquad \text{(when we add something to one side of the scale, we must do the same to the other side to maintain the balance.)}\\ 5y &= 3 - 4x \qquad \text{(thus, we dig through the outer layer by reversing the verb from + to - and moving the noun 4}x\text{ to the other side.)}\\ y&=\frac{3-4x}{5} \end{align} $$

When we dig by reversing verbs and moving nouns, we say that we dress the equation by finding the "bare bones y". With invisible layers, we often confuse inner layers with outer ones. We must always dig through the outer layer first.