- 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

One of the nice things about solving equations is that we can check our answers without a solution key. When we solve an equation, we get a value that is supposed to be a solution to the equation. To check our answer, we see whether the value we found is the solution it is supposed to be. (If not, you can rip off its mask and expose it for the fraud that it really is. "I would have gotten away with it, too, if it wasn't for you meddling kids!")

Recall how this works: we evaluate the left-hand side of the equation at the given value, evaluate the right-hand side of the equation at the given value, and see if the numbers we have match. We sometimes call this the "plug and chug" method. *Plug* in the value you found for the variable, and *chug* out the answer by simplifying the expressions on both sides of the equality.

You can also employ the "plug and chug and hug" method, which involves warmly embracing the correct answer. This one's not for you germaphobes out there.

Solve the equation 3 = *y* - 2. Check your answer.

To solve the equation, add 2 to both sides to find that 5 = *y*. To check the answer, we look to see if 5 really is a solution to the equation 3 = *y* - 2. The left-hand side of the equation is 3. The right-hand side evaluated at *y* = 5 is 5 - 2 = 3. Since the left-hand side and right-hand side agree when evaluated at *y* = 5, *y* = 5 really is the solution to the equation. This is remarkably impressive, considering it is nearly impossible to get those two sides to agree on *anything.*