Understanding Intervals and Inequalities

This video tutorial explains how to graph intervals given by inequalities and express them using interval notation. It covers examples of simple inequalities like 'X > 2' and 'X ≤ 2', as well as compound inequalities such as '-3 ≤ X < 4' and 'X ≤ -3 or X > 4'. The tutorial emphasizes the importance of using open and closed points on graphs and the correct use of parentheses and brackets in interval notation.

What does an open point on a number line indicate?

• The interval is finite.

• The interval is infinite.

• The number is not included in the interval.

• The number is included in the interval.

In interval notation, what symbol is used to indicate that a number is not included?

• Angle bracket

• Rounded parenthesis

• Curly brace

• Square bracket

What is the interval notation for 'X is greater than +2'?

• [2, ∞)

• (2, ∞)

• (2, ∞]

• [2, ∞]

How is 'X is less than or equal to +2' represented on a number line?

• Open point at +2 with an arrow to the left

• Open point at +2 with an arrow to the right

• Closed point at +2 with an arrow to the right

• Closed point at +2 with an arrow to the left

What is the interval notation for 'X is less than or equal to +2'?

• (2, ∞)

• (-∞, 2]

• [2, ∞)

• (-∞, 2)

In the compound inequality '-3 ≤ X < 4', which numbers are included?

• -3 and 4

• -3 only

• 4 only

• Neither -3 nor 4

How is the compound inequality '-3 ≤ X < 4' represented in interval notation?

• [-3, 4]

• (-3, 4)

• [-3, 4)

• (-3, 4]

What does the 'U' symbol represent in interval notation?

• Complement

• Difference

• Union

• Intersection

In the inequality 'X ≤ -3 or X > 4', which interval includes -3?

• (-∞, -3)

• (-∞, -3]

• [4, ∞)

• (4, ∞)

What is the interval notation for 'X > 4'?

• [4, ∞]

• (4, ∞]

• (4, ∞)

• [4, ∞)