SAMPLE College Algebra

66 Chapter 2: Inequalities and Quadratics Tip The < symbol means "less than". It means that the quantity on the left is less than the quantity on the right. The symbol > has an open side and a closed, pointy side. The open side of the symbol tells which side is greater. The closed, pointy side tells which side is lower. With this understanding the following statements would be true. weight of a car > weight of a bicycle temperature of an ice cube < temperature of the sun Tip The ≥ symbol means "greater than or equal to". It means that the quantity on the left is greater than or equal to the quantity on the right. Tip The ≤ symbol means "less than or equal to". It means that the quantity on the left is less than or equal to the quantity on the right. cell phone price ≥ $500 delivery time ≤ 24 hours What cell phone brands and models have a price that is greater than or equal to $500? Are there cases where the delivery time for a product or service is less than or equal to 24 hours? If one is able to understand these questions one is able to understand the full meaning of the inequalities just above. Inequalities can also be illustrated with a number line. Definition 2.1 — Number Line. A number line extends infinitely in both positive and negative directions, with increasing numbers to the right and decreasing to the left, but usually, we only focus on a small part of it. − 4 − 3 − 2 − 1 0 1 2 3 4 x Still, a number line will almost always display a window or sample. − 2 − 1 0 1 2 3 4 5 6 x The number line, above, shows numbers between about -2 and 6. In the definition, just above, both number lines, are labeled with the variable x which is common. However, it could also be labeled with the variable y or z , or any other label.

2 < x

− 4 − 3 − 2 − 1 0 1 2 3 x

The orange line begins at -2, and it increases in the positive direction. Notice, just above, that a hollow or open orange dot occurs at -2. This means that the value -2 is not included. Only values of x that are greater than -2, are included. This, is described by inequality 2