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 \(x = 6 - a.\)