RATIONAL FUNCTIONS Solving Rational Inequalities (Page 1 of 3)

Solving a rational inequality is nearly the same as solving an equation. In fact, we solve the equation first using the x-intercept method, then analyze the graph to determine the solution set of the inequality.

To solve the inequality (x+6)/(x+1) >= 2, first get a zero on the right: (x+6)/(x+1)-2 >= 0. Then replace the inequality symbol with an equal sign: (x+6)/(x+1)-2 = 0. This equation was solved in the previous example using CALC zero and the solution was determined to be x = 4. The graph of the function represented by the left side of the equation, f(x) = (x+6)/(x+1)-2, is shown along with the zero.

GRAPH key. Calculator screen image.
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