- 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

These inequalities don't take no guff. They lay down the law. Better not cross 'em.

The symbol "<" abbreviates "is less than" while the symbol ">" abbreviates "is greater than." We personally think the latter symbol is superior, which we can express with this intentionally confusing series of symbols: "> > <." Pretty cool, right? Right?

When using the symbols "<" and ">," the larger quantity is on the big, open side of the symbol, while the smaller quantity gets the little tiny point of the symbol. If it helps, picture the lines of the symbol extending outward so the value on the open side dwarfs the one on the pointy side.

Don't forget that this symbol can be flip-flopped so it's not pointing in the same direction every time. Always check for the big open side. This little guy is hungry; he's always trying to get his chompers on the biggest meal.

- "Three is less than
*x*" can be written in symbols as 3 <*x*. - We can abbreviate "
*x*is less than -1" by*x*< -1. - "Four is greater than
*y*" can be written "4 >*y*". - The statement in symbols "
*x*> 100" means "*x*is greater than 100."

A **solution** of an inequality is any number that **satisfies** the inequality, or makes the inequality true. It is all about satisfaction. The inequality will be bummed if it can't get no satisfaction. Um, solution.

Remember that as we go further right on the number line that the numbers become larger, and as we go further left, the numbers become smaller. They may get even smaller yet if they take a sip from that bottle with the label "Drink Me."

*x*= 4 is a solution to the inequality 3 <*x*, since 4 is to the right of 3 on the number line.*x*= - 2 satisfies the inequality*x*< - 1, so*x*= - 2 is a solution to this inequality.*y*= 4 is not a solution to the inequality 4 >*y*, because 4 is not greater than itself.*x*= 5 is not a solution to the inequality*x*> 100. Don't even bother trying to pay for that $100 digital camera with a $5 bill. Trust us.

Exercise 1

Write the statement as an inequality using < or > as appropriate: *y* is greater than 25.

Exercise 2

Write the statement as an inequality using < or > as appropriate: -17 is less than *x*.

Exercise 3

Write the statement as an inequality using < or > as appropriate: *x* is less than 45.

Exercise 4

Is 3 a solution to the inequality *x* < -19?

Exercise 5

Is -19 a solution to the inequality *x* < -19?

Exercise 6

Is 0 a solution to the inequality *x* < -19?

Exercise 7

Is -18 a solution to the inequality *x* < -19?

Exercise 8

Is -21 a solution to the inequality *x* < -19?

Exercise 9

Is -100 a solution to the inequality *x* < -19?