Solving Rational Inequalities | Pre-Calculus

NOTE: error in example # 1, Process is correct, however distributing the numerator of the rational function should read 7(x+4)-2(x-3) should have been 7x+28-2x+6 = 5x+32.

In this lesson we study solving rational inequalities. The basic strategy is to bring all the expressions to one side of the inequality so that we have a zero on the other side. Fully factor the rational function and identify all roots and points of discontinuity. Partition the number line with respect to these values and examine whether the rational expression is positive or negative within that interval.

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