Graphing Compound Inequalities and Interval Notation

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 on a number line and express them using interval notation. The 'and' example requires both conditions to be satisfied, while the 'or' example requires only one. The tutorial also explains the use of union symbols in place of 'or'.

What are compound inequalities?

• Inequalities that have no solution

• Inequalities that are always true

• Inequalities that involve only one variable

• Inequalities that are connected with 'AND' or 'OR'

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

• It must be less than both values

• It must be greater than both values

• It must satisfy both inequalities

• It must satisfy at least one of the inequalities

How do you graph the inequality x > -5 on a number line?

• Open point on -5 with an arrow to the right

• Closed point on -5 with an arrow to the left

• Open point on -5 with an arrow to the left

• Closed point on -5 with an arrow to the right

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

• All numbers greater than -5 and less than 7

• All numbers less than -5 and greater than 7

• All numbers between -5 and 7, excluding -5 and including 7

• All numbers between -5 and 7, including -5 and excluding 7

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

• It must be less than both values

• It must satisfy at least one of the inequalities

• It must satisfy both inequalities

• It must be greater than both values

How do you graph the inequality x ≤ -3 on a number line?

• Open point on -3 with an arrow to the left

• Open point on -3 with an arrow to the right

• Closed point on -3 with an arrow to the right

• Closed point on -3 with an arrow to the left

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

• All numbers greater than or equal to -3

• All numbers between -3 and infinity

• All numbers less than or equal to -3

• All numbers greater than -3

What symbol is sometimes used in textbooks instead of 'OR'?

• ∪

• ∩

• ⊇

• ⊆

What does the interval notation [7, ∞) represent?

• All numbers less than or equal to 7

• All numbers between 7 and infinity

• All numbers greater than or equal to 7

• All numbers less than 7

In the context of compound inequalities, what does the term 'union' mean?

• The difference between two sets

• The combination of two sets

• The intersection of two sets

• The complement of a set