Solving equations

For purposes of this course, we can consider an equation with one variable solved if the variable is alone on the left-hand side and does not appear on the right-hand side.

Here's a list of techniques for solving equations:

There are always more techniques, some of which are still being discovered.

A linear equation is an equation whose sides are both linear expressions. Linear equations in one variable can always be solved using this method:

At this point, you should have the answer, with the variable equal to a constant. Failing that, you might have a constant statement (with no variable in it), which will be either true or false; then that (‘True’ or ‘False’) is your answer.

Inequalities are solved in the same way as equations, except for this important point: If you multiply or divide both sides by a negative number, then you must swap the direction of the inequality.


Go back to the course homepage.
This web page was written between 2007 and 2010 by Toby Bartels, last edited on 2010 November 28. Toby reserves no legal rights to it.

The permanent URI of this web page is http://tobybartels.name/MATH-0950/2010FA/equations/.

HTML 5