8.1.5 Solving Rational Equations and Inequalities (continued) Example 6 Solving Rational Inequalities Algebraically Rational inequalities can be solved algebraically. As with rational equations, the first step is to multiply the inequality by the LCD of all of the expressions in the inequality. However, two cases must be considered when solving a rational inequality. Case I: The LCD is positive. Case II: The LCD is negative. When the LCD is negative, the inequality symbol must be reversed because the inequality is being multiplied by a negative value (the negative LCD). The solution to the rational inequality is the union of the solutions of the two cases.
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