Solving Linear Inequalities

In this section, we learn how to solve a linear inequality in one variable. For this type of problem, we utilize two properties. The first is known as the addition property of inequality. The addition property of inequality allows us to add/subtract any value to/from both sides of an inequality, without changing the solution set. The second property we utilize is known as the multiplication property of inequality. This property is a slight variation of the multiplication property of equality. The multiplication property of inequality tells us we can multiply or divide both sides of an inequality by a positive value, and not change the solution set. If we multiply or divide by a negative value, we must change the direction of the inequality symbol. A less than becomes a greater than and vice versa. Once we have mastered these two properties, we will move into a general four-step procedure. This procedure is a slight variation of what we saw to solve linear equations in one variable. Last on our agenda, we will discuss how to check a solution for a linear inequality in one variable. This process is much more tedious than for a linear equation in one variable.