Basic Technical Mathematics, 11th Edition

17.1 Properties of Inequalities

• Solution of an Inequality • Conditional Inequality • Absolute Inequality • Properties of Inequalities

In Chapter 1, we first introduced the signs of inequality. To this point, only a basic understanding of their meanings has been necessary to show certain intervals associated with a variable. In this section, we review the meanings and develop certain basic properties of inequalities. We also show the meaning of the solution of an inequality and how it is shown on the number line.

The expression $a\hspace{0.17em}<\hspace{0.17em}b$ is read as “a is less than b,” and the expression $a\hspace{0.17em}>\hspace{0.17em}b$ is read as “a is greater than b.” These signs define what is known as the sense (indicated by the direction of the sign) of the inequality. Two inequalities ...