- 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

Two equations are said to be equivalent if they have exactly the same solutions.

- The equations
*x*= 1 and 2*x*= 2 are equivalent, since the only solution to either equation is 1. - The equations 2
*x*= 0 and 3*x*= 0 are equivalent, since the only solution to either equation is 0. - The equations
*x*= 1 and*x*= 2 are not equivalent, since their solutions, 1 and 2, respectively, differ.