Compound Inequalities and 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 > 2 and x < 5.

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 bracket [ ] indicate in interval notation?

Back

The bracket [ ] indicates that the endpoint is included in the interval.

Front

What does the parenthesis ( ) indicate in interval notation?

Back

The parenthesis ( ) indicates that the endpoint is not included in the interval.

Front

How would you write the inequality x ≥ 3 in interval notation?

Back

In interval notation, x ≥ 3 is written as [3, ∞).

Front

How would you write the inequality x < -1 in interval notation?

Back

In interval notation, x < -1 is written as (-∞, -1).

Front

What is the solution to the compound inequality 2 < x < 5?

Back

The solution is the interval (2, 5).

Front

How do you solve the compound inequality x + 3 < 7 and x - 2 > 1?

Back

First, solve each inequality: x < 4 and x > 3. The solution is the interval (3, 4).

Front

What is the solution to the compound inequality x < -2 or x > 3?

Back

The solution is the union of the intervals (-∞, -2) and (3, ∞).

Front

How do you express the solution to the inequality 3x + 2 < -7?

Back

First, solve for x: 3x < -9, so x < -3. The solution is (-∞, -3).