# Presenting a Sequence of Manipulations to an Expression

When presenting a series of operations performed on an expression, it can be clearer to state the step-by-step recipe of how to perform the manipulations, than to show only the results of each step. The clearest, of course, would be to provide a step-by-step guide that shows the result from each step. Unfortunately, space constraints often prohibit such spacious exposition.

Suppose we want to solve \((a + x)/2 = 3\) for \(x.\) In the following table, the left shows a purely symbolic approach, which leaves the reader to fill in the gaps. The right column describes what is required but does not show the result of every step.

Symbolic Manipulation | Description |
---|---|

$$\begin{aligned} &\frac{a + x}{2} = 3 \\ &a + x = 6 \\ &x = 6 - a \end{aligned}$$ | Multiply both sides by \(2,\) and subtract \(a\) from both sides. The result is \(x = 6 - a.\) |