Inequalities & Interval Notation

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In this lesson, we will learn how to show the relationship between two numbers using inequalities. We begin with the strict inequalities: "<" less than and ">" greater than. For these inequalities, we are stating a strict relationship between two numbers, without the possibility of equality. For a less than, the number on the left is less than the number on the right: 5 < 9. The reverse is true for a greater than. With a greater than, the number on the left is greater than the number on the right: 6 > 2. Additionally, we will have non-strict inequalities: "≤" less than or equal to and "≥" greater than or equal to. For these inequalities, we allow for the possibility of equality. Next, we will learn about our number line. Numbers increase as we move to the right and decrease as we move to the left. A number that is to the right of another is, therefore, a larger number. We can use facts about the number line to determine the proper inequality relationship between two or more numbers. Lastly, we will learn about interval notation. Interval notation is a special type of notation that allows us to display a range of numbers where the endpoints may or may not be included. We will also show how to write an inequality in interval notation and graph the interval on the number line.
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