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Learn how to solve rational inequalities when the inequality involves a rational expression on one side and a constant on the other side using the interval testing method. Master the systematic approach of finding critical points, creating sign charts, and testing intervals to determine where the rational expression satisfies the given inequality condition. Explore step-by-step techniques for identifying undefined points in the rational function, establishing test intervals on the number line, and evaluating the sign of the expression in each interval. Develop proficiency in interpreting the results to write the solution set in interval notation, understanding when to include or exclude boundary points based on the inequality symbol and domain restrictions. Practice applying this method to various types of rational inequalities involving linear and quadratic expressions in both numerator and denominator, building essential skills for precalculus and advanced algebra coursework.
