In this Section:
In this section, we continue to learn the basics of a linear inequality in one variable. This includes revisiting many of the basic properties of inequalities that we discussed in prealgebra. We will learn how to solve a linear inequality in one variable using two key properties. The first property is known as the addition property of inequality. This property allows us to add/subtract any value to/from both sides of an inequality without changing the solution. The second property is known as the multiplication property of inequality. This property allows us to multiply/divide any positive value by both sides of an inequality without changing the solution. If we multiply/divide both sides by a negative, we must flip the direction of the inequality symbol. Additionally, we will cover how to solve a three-part inequality. Lastly, we will cover a new method to express our answer known as interval notation. This allows us to notate a solution that encompasses a range of values. We will also show how to display this type of solution using a number line.