Inequalities are statements that express quantities that are not equal. In this chapter, we expand on and modify the methods used for solving one-variable equations, which are statements where quantities are equal, and apply them to solve one-variable inequalities.
To solve an inequality means to find the value or, as often is the case, the values of the variable that make the inequality true. When there is more than one such value the solutions are referred to as a solution set. A solution set of an inequality may include infinitely many values.
The chapter begins with writing one-variable inequalities and representing them on number lines. Then, by using the Properties of Inequality and inverse operations, one-step and multi-step inequalities are solved similarly to solving one-variable equations are solved. Modifications to the previously known methods are presented and explained.
The methods for solving one-variable inequalities can also be used to solve compound inequalities. A compound inequality is an inequality that consists of two or more inequalities. When solving compound inequalities it is useful to analyze their solutions sets through intersections and unions.
Inequalities can be used to model various situations in daily life. In the chapter it is shown how one-variable inequalities are created to solve situations in context.