Solve each compound inequality. Use graphs to show the...

Solve each compound inequality. Use graphs to show the solution set to each of the two given inequalities, as well as a third graph that shows the solution set of the compound inequality. Express the solution set in interval notation.
$$x \geq 2 \text { or } x<-1$$

Key Concepts

Interval Notation

Interval notation is a concise way to represent a set of numbers along a continuum. It uses brackets to denote whether endpoints are included ([ or ]) or excluded (( or )). This notation is widely used to specify the solution sets of inequalities, especially when depicting unions or intersections of intervals.

Graphing Inequalities on a Number Line

Graphical representation on a number line provides a visual means to illustrate the solution set of inequalities. It involves marking critical points and shading regions corresponding to the solutions. For compound inequalities, overlapping or union of these regions is depicted clearly, helping verify the accuracy of the interval notation derived from the algebraic solution.

Logical Operators (OR)

The ‘or’ operator in compound inequalities means that the solution set includes values that satisfy at least one of the individual inequalities. This often results in the union of two solution sets. Recognizing when to combine intervals or conditions under an ‘or’ statement is essential for correct problem solving.

Compound Inequalities

Compound inequalities involve two or more inequalities connected by logical operators such as ‘and’ or ‘or’. They require determining the set of all values that satisfy at least one (in the case of ‘or’) or all (in the case of ‘and’) of the inequalities. Understanding how to work with these operators is crucial in solving problems where multiple conditions are present at once.

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