In this lesson, students learn how to solve rational inequalities and understand how the signs of a rational expression change across its key points. Theyโll connect what they already know about graphing rational functions, like intercepts and vertical asymptotes, to solving inequalities algebraically.
Instead of multiplying both sides or cross-multiplying, students learn the correct reasoning: keep the rational expression in factored form to see how each factor affects the sign of the whole fraction. Theyโll practice identifying zeros of the numerator and denominator, reasoning about where the expression is positive or negative, and writing solutions in interval notation with clear understanding of brackets and parentheses.
Built-in checks for understanding and a mixed-format exit ticket help students apply the full process with confidence.
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