Question

Consider the following subset of the real number line. how can this set be expressed using inequalities? a.) 0 ≤ x < 3 b.) 0 < x ≤ 3 c.) 0 < x < 3 d.) 0 ≤ x ≤ 3

Answer 1

A subset of the real number line is expressed using inequalities that indicate whether the endpoints are included or excluded, with symbols such as ≤ for inclusive and < for exclusive endpoints.

Step-by-step explanation:

When expressing a subset of the real number line using inequalities, it is important to consider whether the endpoints are included or excluded. An inclusive endpoint is denoted by the symbol ≤, meaning "less than or equal to," while an exclusive endpoint is denoted by <, meaning "less than."

For example, if we have a horizontal line ranging from 0 to 3 and we want to include 0 but not 3, we would use the inequality 0 ≤ x < 3. If both endpoints are included, the inequality would be 0 ≤ x ≤ 3. Conversely, if both endpoints are excluded, it would be 0 < x < 3. And if 0 is excluded but 3 is included, it would be 0 < x ≤ 3.