By using simple algebraic manipulations and identities, a guess can be checked for accuracy.

After considerable algebraic manipulation, this may be written as:

This article deals with the propagation of uncertainty via algebraic manipulations.

It is much easier to perform algebraic manipulation on inequalities in this form.

This is done by algebraic manipulation of the formula below:

After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.

After some algebraic manipulations, the result is obtained.

The proof of (1) amounts to simple algebraic manipulation.

Thus, with these three equations, it is possible to get the following result through some algebraic manipulation:

There are many variant ways to write the equation of a line which can all be converted from one to another by algebraic manipulation.