Graph the solution set for each compound inequality, and...

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Key Concepts

Compound Inequalities

Compound inequalities involve two or more inequalities that are combined by the words 'and' or 'or'. In the context of this question, the term 'or' indicates that the solution set includes numbers that satisfy any one of the individual inequalities, rather than needing to satisfy both simultaneously.

Graphing Inequalities on the Number Line

Graphing inequalities on the number line is a visual method to represent the set of all numbers that satisfy the inequality. It involves marking critical boundary points and shading the regions that represent the solution set, using open or closed circles to indicate strict or non-strict inequalities respectively.

Interval Notation

Interval notation is a shorthand method of writing sets of numbers within a given range. It uses parentheses to denote that endpoints are not included and brackets for included endpoints, providing a clear and concise description of all elements in the solution set.

Union of Solutions

The union of solutions is used when combining separate intervals in the case of 'or' compound inequalities. It means that any number belonging to at least one of the specified intervals is part of the overall solution set. This is typically denoted by the union symbol (?) between the intervals.

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