A inequality is an algebraic expression involving less than (), less than or equal to (), greater than (), or greater than or equal to ()..
Inequalities are often used to describe intervals. Here are some examples.
|Conditions||Set Notation||Interval Notation|
|is greater than|
|is less than or equal to|
|is less than and greater than|
|is less than and greater than or equal to|
|is less than or is greater than|
The last three examples are called compound inequalities. Compound inequalities are associated with the words "and" or "or".
To graph an inequality, we shade the interval(s) along a number line. Use parentheses ( ) to exclude endpoints, and use brackets [ ] include endpoints.
To solve an inequality means to find ALL replacements for the variable that make the inequality true. Your answers will typically (but not always) be intervals.
To solve a linear inequality, we apply the same process as we used for solving linear equations, with one exception: When solving a linear inequality, whenever you multiply across by a negative number, you must reverse the inequality symbol.