Compound Inequalities and Interval Notation

Mr. Appel explains compound inequalities, focusing on 'and' and 'or' conditions. He illustrates how to interpret these inequalities on a number line and discusses scenarios where there is no solution or where all real numbers are solutions. The video also covers how inequalities pointing in the same direction affect the solution set.

What is the result when solving a compound inequality where one part is 'X < 3' and the other is 'X > 6'?

• X is between 3 and 6

• No solution

• X is less than 6

• X is greater than 3

In a compound inequality with 'and', what are we looking for?

• Numbers that satisfy at least one condition

• Numbers that are equal to 3 or 6

• Numbers that satisfy both conditions

• Numbers that satisfy neither condition

What happens when both inequalities in a compound inequality point in the same direction?

• The solution is the overlap of both inequalities

• There is no solution

• The solution is the less restrictive inequality

• The solution is the more restrictive inequality

If 'X > 3' and 'X > 6', what is the solution?

• X > 3

• X > 6

• X < 3

• X < 6

How is the solution to 'X > 6' expressed in interval notation?

• (6, ∞]

• [6, ∞)

• (-∞, 6)

• (6, ∞)

What does the word 'and' imply in compound inequalities?

• Neither condition must be true

• At least one condition must be true

• Only one condition must be true

• Both conditions must be true

In an 'or' situation, what is required for a number to satisfy the compound inequality?

• Both conditions must be true

• At least one condition must be true

• Neither condition must be true

• Only the first condition must be true

What is the solution to the compound inequality 'X > 3 or X < 6'?

• No solution

• All real numbers

• X is between 3 and 6

• X is exactly 3 or 6

How is the solution to 'X > 3 or X < 6' expressed in interval notation?

• (3, 6)

• (-∞, ∞)

• [3, 6]

• (-∞, 3) ∪ (6, ∞)

What does the word 'or' imply in compound inequalities?

• Both conditions must be true

• At least one condition must be true

• Neither condition must be true

• Only the first condition must be true