Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Inequalities
Rational inequalities involve expressions where a rational function is compared to a constant using inequality symbols (e.g., ≥, ≤, >, <). To solve these inequalities, one typically finds the critical points where the rational expression is equal to zero or undefined, and then tests intervals around these points to determine where the inequality holds true.
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Rationalizing Denominators
Interval Notation
Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed intervals) or excluded (open intervals). For example, the interval (2, 5] includes all numbers greater than 2 and up to 5, including 5 but not 2.
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Critical Points
Critical points are values of the variable that make the rational expression either zero or undefined. These points are essential in solving rational inequalities as they divide the number line into intervals. By testing these intervals, one can determine where the inequality is satisfied, leading to the final solution set.
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