Compound Inequalities & Interval Notation

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'. For example, x < 5 and x > 1 is a compound inequality.

Front

What does interval notation represent?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation (a, b) mean in interval notation?

Back

The notation (a, b) represents an open interval, meaning that the endpoints a and b are not included in the interval.

Front

What does the notation [a, b] mean in interval notation?

Back

The notation [a, b] represents a closed interval, meaning that the endpoints a and b are included in the interval.

Front

What does the notation (a, b] mean in interval notation?

Back

The notation (a, b] represents a half-open interval, meaning that the endpoint a is not included, while b is included.

Front

What does the notation [a, b) mean in interval notation?

Back

The notation [a, b) represents a half-open interval, meaning that the endpoint a is included, while b is not included.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, solve each inequality separately and then combine the results. Use 'and' for intersection and 'or' for union.

Front

What is the solution to the compound inequality x < 3 and x > 1?

Back

The solution is the interval (1, 3).

Front

What is the solution to the compound inequality x < -2 or x > 4?

Back

The solution is the union of the intervals (-∞, -2) and (4, ∞).

Front

How do you express the solution of an inequality in interval notation?

Back

To express the solution of an inequality in interval notation, identify the range of values that satisfy the inequality and use parentheses or brackets to denote inclusivity or exclusivity.