Interval Notation and Inequalities

Front

What is interval notation?

Back

Interval notation is a mathematical notation used to represent a range of values, typically for solutions to inequalities. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

How do you represent 'x ≥ -3' in interval notation?

Back

The interval notation for 'x ≥ -3' is [-3, ∞).

Front

What does a parenthesis '(' or ')' indicate in interval notation?

Back

A parenthesis indicates that the endpoint is not included in the interval.

Front

What does a bracket '[' or ']' indicate in interval notation?

Back

A bracket indicates that the endpoint is included in the interval.

Front

How would you write 'x < 8' in interval notation?

Back

The interval notation for 'x < 8' is (-∞, 8).

Front

What is the significance of a closed circle on a number line?

Back

A closed circle indicates that the value at that point is included in the solution set, typically used for 'less than or equal to' (≤) or 'greater than or equal to' (≥).

Front

What is the significance of an open circle on a number line?

Back

An open circle indicates that the value at that point is not included in the solution set, typically used for 'less than' (<) or 'greater than' (>).

Front

How do you represent 'x ≤ 5' in interval notation?

Back

The interval notation for 'x ≤ 5' is (-∞, 5].

Front

How do you represent 'x > 2' in interval notation?

Back

The interval notation for 'x > 2' is (2, ∞).

Front

What is the difference between 'x < 4' and 'x ≤ 4' in interval notation?

Back

'x < 4' is represented as (-∞, 4) while 'x ≤ 4' is represented as (-∞, 4].