Equality: a powerful word in social, political, and humanitarian arenas. And, it’s no less powerful as far as mathematics is concerned; algebra wouldn’t have much without equality. Fortunately, algebra knows how to deal with inequality, too (far better than in those other arenas). Equality is an important tool in mathematics and science.
This chapter introduces you to algebraic inequality, which isn’t exactly the opposite of equality. You could say that algebraic inequality is a bit like equality but softer. You use inequality for comparisons. Inequality is used when determining if something is positive or negative, bigger than or smaller than, between numbers, or infinite. Inequality allows you to sandwich expressions between values on the low end and the high end.
Algebraic inequalities show relationships between a number and an expression or between two expressions. One expression is bigger or smaller than another for certain values of a given variable. For example, it could be that Janice has at least four more than twice as many cats as Eloise. There are lots of scenarios that can occur if it’s at least and not exactly as many.
Equations (statements with equal signs) are one type of relation — two things are exactly the same, it says. The inequality relation is a bit less precise. One thing can be bigger by a lot or bigger by a little, but there’s still that relationship between them — that one is bigger than the other. Many operations involving inequalities work the same as operations on equalities and equations, but you need to pay attention to some important differences that I show you in this chapter.