Inequalities

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1Denoting Inequalities

Properties

Solving Inequalities

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Definition An inequality is a statement that two

quantities or expressions are not equal

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Denoting Inequalities Notation

Endpoints are the extreme limits of the inequality

Closed Interval Denoted by [ ] Includes the endpoint(s) Associated with ≥ and ≤

Open Interval Denoted by ( ) Includes all values up to , but not including the

endpoint(s) Associated with > and <

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Examples of Notation

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Properties of Inequalities

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Solving Inequalities Solve as you would an equation…

With three new rules Reverse the signs (i.e. < to >, etc.) when:

Dividing by a negative number Multiplying by a negative number Swapping positions of the variable and final

answer Variable needs to be on the left in the event

of a single inequality symbol Variable needs to be in the middle in the

event of two inequality symbols (continued inequality)

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An Example of Solving an Inequality

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Another Example of Solving an Inequality

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Yet Another Example of Solving an Inequality

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Practice Problems Page 119

Problems 3-46 Do not sketch graphs