Understanding Compound Inequalities

The video tutorial explains compound inequalities, which are two or more inequalities connected by 'AND' or 'OR'. It provides examples of both types, demonstrating how to graph them and interpret their solutions. The 'AND' example requires both conditions to be true, while the 'OR' example requires only one. The tutorial also covers interval notation and the use of the union symbol 'U'.

What is a compound inequality?

• An equation with two variables

• A single inequality with no variables

• An equation with one variable

• Two or more inequalities combined with 'and' or 'or'

In a compound inequality connected by 'and', what must be true for a solution to be valid?

• It must satisfy a different inequality

• It must satisfy at least one inequality

• It must satisfy both inequalities

• It must satisfy neither inequality

How is the solution of an 'and' compound inequality represented on a number line?

• With two separate arrows

• With a single arrow covering the overlap

• With no arrows

• With arrows pointing in opposite directions

What does the interval notation (-5, 7] represent?

• All numbers less than -5 and up to and including 7

• All numbers greater than -5 and less than 7

• All numbers less than -5 and greater than 7

• All numbers greater than -5 and up to and including 7

In a compound inequality connected by 'or', what must be true for a solution to be valid?

• It must satisfy at least one inequality

• It must satisfy both inequalities

• It must satisfy neither inequality

• It must satisfy a different inequality

How is the solution of an 'or' compound inequality represented on a number line?

• With two separate arrows

• With arrows pointing in opposite directions

• With a single arrow covering the overlap

• With no arrows

What does the interval notation (-∞, -3] U (7, ∞) represent?

• All numbers greater than -3 and less than 7

• All numbers less than -3 and greater than 7

• All numbers greater than or equal to -3 or less than 7

• All numbers less than or equal to -3 or greater than 7

What symbol is sometimes used in textbooks to represent 'or' in compound inequalities?

• The symbol '&'

• The symbol 'U'

• The symbol '∩'

• The symbol '∪'

Which of the following is true for a compound inequality using 'or'?

• The solution must satisfy neither inequality

• The solution must satisfy both inequalities

• The solution must satisfy at least one inequality

• The solution must satisfy a different inequality

What does a closed point on a number line indicate?

• The number is not included in the interval

• The number is included in the interval

• The interval is finite

• The interval is infinite