Inequalities, Set Builder Notation, and Interval Notation

Front

What is interval notation?

Back

Interval notation is a mathematical notation used to represent a range of values on the number line, using parentheses and brackets to indicate whether endpoints are included or excluded.

Front

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

Back

The solution x ≥ -3 is represented in interval notation as [-3, ∞).

Front

What does the parenthesis ( ) signify in interval notation?

Back

Parentheses ( ) indicate that the endpoint is not included in the interval.

Front

What does the bracket [ ] signify in interval notation?

Back

Brackets [ ] indicate that the endpoint is included in the interval.

Front

How do you represent the solution z < 20 in interval notation?

Back

The solution z < 20 is represented in interval notation as (-∞, 20).

Front

Is -25 a solution to the inequality x > 15?

Back

No, -25 is not a solution to the inequality x > 15.

Front

What is the interval notation for the solution x ≥ 6?

Back

The solution x ≥ 6 is represented in interval notation as [6, ∞).

Front

What is set builder notation?

Back

Set builder notation is a mathematical notation used to describe a set by stating the properties that its members must satisfy.

Front

How would you express the set of all x such that x is greater than 5 in set builder notation?

Back

The set of all x such that x is greater than 5 can be expressed as {x | x > 5}.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (using parentheses), while closed intervals do include their endpoints (using brackets).