Basic Technical Mathematics, 11th Edition

17.3 Solving Nonlinear Inequalities

• Critical Values • Solving Polynomial and Rational Inequalities • Solving Inequalities Graphically

In this section, we develop methods of solving inequalities with polynomials, rational expressions (expressions involving fractions), and nonalgebraic expressions. To develop the basic method for solving these types of inequalities, we now take another look at a linear inequality.

In Fig. 17.18, we see that all values of the linear function $f(x)\hspace{0.17em}=\hspace{0.17em}ax\hspace{0.17em}+\hspace{0.17em}b(a\hspace{0.17em}\ne \hspace{0.17em}0)$ are positive on one side of the point at which $f(x)\hspace{0.17em}=\hspace{0.17em}0\hspace{0.17em},\hspace{0.17em}$ and all values of f(x) are negative on the opposite side of the same point. The means that we can solve a linear inequality by expressing it with zero on the right and then finding the sign