In Exercises 29-44, graph the given inequalities on the number line. (x 2) or (x ≥

step 1 First, I draw the solution of x is less than 7 and x is greater than 2. I draw an open circle at

In Exercises 29-44, graph the given inequalities on the...

Key Concepts

Number Line Graphing

Number line graphing is a visual representation of numbers and intervals on a horizontal line where points represent numbers and intervals are depicted as segments. This concept helps in visualizing solutions of inequalities by showing the region on the number line that satisfies the inequality, including open or closed endpoints as needed.

Compound Inequalities

Compound inequalities involve more than one inequality that the variable must satisfy simultaneously or alternatively. They are used to describe situations where the variable falls within a range or belongs to one of several separate ranges, often combining conditions with 'and' or 'or' operators.

Intersection (AND) in Inequalities

The intersection in inequalities, denoted by 'and', refers to the set of values that satisfy all the given conditions at once. When inequalities are joined by 'and', only the overlapping region of the individual solution sets is considered, meaning the solution must meet every condition specified.

Union (OR) in Inequalities

The union in inequalities, indicated by 'or', represents the set of values that satisfy at least one of the given conditions. This operation combines the individual solution sets such that any number in either set is a solution, potentially resulting in disjoint intervals.

Open and Closed Intervals

Open and closed intervals are ways to denote whether endpoints are included in an interval. In the context of inequalities, an open interval (represented by a parenthesis) indicates that the endpoint is not included, whereas a closed interval (represented by a bracket) signifies that the endpoint is part of the set. This distinction is crucial when graphing inequalities on a number line.

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