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Symbol Motion

Let's take a simple equation, 2 + x = 3, and examine the steps in solving it. It would go something like

$$2+x=3$$

$$\begin{array}{c}2+x=3\\\begin{array}[t]{ccc}-2 & & -2\end{array}\end{array}$$

$$x=3-2$$

$$x=1$$

Notice in particular the first step and the next-to-last step:

$$2+x=3$$

$$x=3-2$$

There is a pattern here. The 2 is a symbol that is, in effect, moved from the left side of the equation onto the right side. There is a logic to it, which means there are rules to be followed - for one thing, the 2 becomes a -2 as it is moved, in this case. It turns out that there are patterns like this for many algebraic manipulations you might use to solve an equation. By taking symbols, grouping them in particular ways, and moving them according to certain rules, you can solve equations. This is called symbol motion. Doing algebra in this way is not well suited to working equations on paper or a whiteboard. But it is very well suited for solving equations by visualizing them. This chapter explains the patterns of symbol motion, applied to algebra, and how to use them.