- Topics At a Glance
- Solutions to Equations
- Checking Solutions to Equations
- Number of Solutions to an Equation
- Equivalent Equations
- Solving Equations with One Variable
- Adding and Subtracting Constants
- Checking Answers
- Adding and Subtracting Variables
- Multiplication and Division
**Complicated Equations**- Simplifying Equations
- Eliminating Fractions
- Keeping Both Solutions
- When You Get Stuck
- Solving Equations with Multiple Variables
- Solving Equations for Expressions
- Keeping Answers Pretty
- Factoring
- Geometry
- Single-Variable Inequalities
- Strict Inequalities
- Equivalent Inequalities
- Inequalities that Allow Equality
- Solving Inequalities
- In the Real World
- Fitting Things in Spaces
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

As Avril Lavigne would ask: Why do you have to go and make things so complicated, algebra?

Good question, Avril. The truth is that we live in a complicated world, so many of the equations we use are also complicated. We can hardly expect to be able to understand a concept as intricate as nuclear fission with equations as simple as *x* = 3*y*. If it were that easy, we wouldn't just need to worry about Iran's nuclear capabilities...we would also need to keep a wary eye on every middle schooler with an algebra textbook. The world would be a scary place.

The good news is that there are ways of taking seemingly complicated equations and breaking them down into simpler, more manageable parts. Once you've done that, you will be able to remove the fractions, or the parentheses, or whatever else it is that is sticking in your metaphorical, mathematical craw. You just need to learn the tricks.

Lucky for you, we know those tricksâ€”and we are eager and willing to share them with you. We only ask that you exercise caution when thinking about defusing a gravy grenade anywhere. You may be trying to be cool, but you look like a fool to us. (Ah, the early 2000s, when musical lyrics were indistinguishable from Shakespearean poetry.)