Compound Inequalities and Interval Notation

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'. For example, 2 < x < 5 is a compound inequality.

Front

How is interval notation used to represent inequalities?

Back

Interval notation is a way to describe a set of numbers between two endpoints. For example, the inequality x ≥ 3 can be written as [3, ∞) in interval notation.

Front

What does the notation (a, b) represent?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

Front

What does the notation [a, b] represent?

Back

The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

Front

What does the notation (a, b] represent?

Back

The notation (a, b] represents a half-open interval, meaning it includes all numbers between a and b, including b but not a.

Front

What does the notation [a, b) represent?

Back

The notation [a, b) represents a half-open interval, meaning it includes all numbers between a and b, including a but not b.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, solve each inequality separately and then combine the solutions. For example, for 2 < x < 5, the solution is x > 2 and x < 5.

Front

What is the solution set for the inequality x < -3 or x > 2?

Back

The solution set is (-∞, -3) ∪ (2, ∞).

Front

How do you express the inequality -4 ≤ x < 3 in interval notation?

Back

The inequality -4 ≤ x < 3 can be expressed as [-4, 3) in interval notation.

Front

What is the solution to the inequality 3x - 5 > 1?

Back

To solve 3x - 5 > 1, add 5 to both sides to get 3x > 6, then divide by 3 to find x > 2.