- 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

Like a truck. In the mud.

Sometimes, when working out a math problem, we get stuck. Our tires are spinning like crazy, but we aren't moving forward a hair. Here's a neat trick: figuring out *why* we're stuck often tells us what we need to do to get *un*-stuck.

Solve the equation

We haven't seen anything like this equation before. We've seen things like it, but not exactly...we've seen other equations, but we...oh, you know what we mean. The *x *is in the denominator of the fraction instead of in the numerator. Because we don't know what to do about that, let's get the *x* out of the denominator. Quickly, before it causes any trouble. Multiply both sides of the equation by *x* to find that

1 = 10*x*

From here, we know what to do. Divide both sides by 10, and we can conclude that

Next time you get stuck on a problem, write a note in the margin saying "I don't know what to do here because...(fill in the blank)." For example, you might write "I don't know what to do here because there is an *x* in the denominator." See if knowing why you're stuck helps you find a way to get un-stuck. It may surprise you how much simply writing down the point of confusion can help you clear away the cloud. If that doesn't work, you can always try a rain dance.

Exercise 1

Solve the equation . Check your answer before looking at the solution.

Exercise 2

Solve the equation . Check your answer before looking at the solution.

Exercise 3

Solve the equation . Check your answer before looking at the solution.