# Summary: Compound and Absolute Value Inequalities

## Key Concepts

- Interval notation is a method to indicate the solution set to an inequality. Highly applicable in calculus, it is a system of parentheses and brackets that indicate what numbers are included in a set and whether the endpoints are included as well.
- Solving inequalities is similar to solving equations. The same algebraic rules apply, except for one: multiplying or dividing by a negative number reverses the inequality.
- Compound inequalities often have three parts and can be rewritten as two independent inequalities. Solutions are given by boundary values, which are indicated as a beginning boundary or an ending boundary in the solutions to the two inequalities.
- Absolute value inequalities will produce two solution sets due to the nature of absolute value. We solve by writing two equations: one equal to a positive value and one equal to a negative value.
- Absolute value inequalities can also be solved by graphing. At least we can check the algebraic solutions by graphing, as we cannot depend on a visual for a precise solution.

## Glossary

**compound inequality**a problem or a statement that includes two inequalities

**interval**an interval describes a set of numbers within which a solution falls

**interval notation**a mathematical statement that describes a solution set and uses parentheses or brackets to indicate where an interval begins and ends

**linear inequality**similar to a linear equation except that the solutions will include sets of numbers

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