Here's a list of techniques useful for solving equations by turning them into equivalent equations:

- Simplify either side (or both);
- Add or subtract the same expression to both sides (and then simplify them);
- Multiply or divide both sides by the same nonzero constant (and then simplify them);
- Swap the sides.

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

- Simplify both sides (if necessary).
- If there is a variable term on the right-hand side, then subtract this term from both sides (and simplify them).
- If there is a constant term on the left-hand side, then subtract this term from both sides (and simplify them).
- If there is now a coefficient on the variable on the left-hand side, then divide both sides by that coefficient (and simplify them).

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 switch the direction of the inequality.

Go back to the course homepage.

This web page was written between 2007 and 2014 by Toby Bartels, last edited on 2014 May 19. Toby reserves no legal rights to it.

The permanent URI of this web page
is
`http://tobybartels.name/MATH-0950/2013FA/equations/`

.